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Repository: waico/SKAB
Branch: master
Commit: b2c0d46c2971
Files: 75
Total size: 4.9 MB
Directory structure:
gitextract_hxo2wk1q/
├── .gitignore
├── .pre-commit-config.yaml
├── LICENSE
├── README.md
├── core/
│ ├── Conv_AE.py
│ ├── Isolation_Forest.py
│ ├── LSTM_AE.py
│ ├── LSTM_VAE.py
│ ├── MSCRED.py
│ ├── MSET.py
│ ├── Vanilla_AE.py
│ ├── Vanilla_LSTM.py
│ ├── __init.py__
│ ├── metrics.py
│ ├── t2.py
│ └── utils.py
├── data/
│ ├── README.md
│ ├── anomaly-free/
│ │ └── anomaly-free.csv
│ ├── other/
│ │ ├── 1.csv
│ │ ├── 10.csv
│ │ ├── 11.csv
│ │ ├── 12.csv
│ │ ├── 13.csv
│ │ ├── 14.csv
│ │ ├── 2.csv
│ │ ├── 3.csv
│ │ ├── 4.csv
│ │ ├── 5.csv
│ │ ├── 6.csv
│ │ ├── 7.csv
│ │ ├── 8.csv
│ │ └── 9.csv
│ ├── valve1/
│ │ ├── 0.csv
│ │ ├── 1.csv
│ │ ├── 10.csv
│ │ ├── 11.csv
│ │ ├── 12.csv
│ │ ├── 13.csv
│ │ ├── 14.csv
│ │ ├── 15.csv
│ │ ├── 2.csv
│ │ ├── 3.csv
│ │ ├── 4.csv
│ │ ├── 5.csv
│ │ ├── 6.csv
│ │ ├── 7.csv
│ │ ├── 8.csv
│ │ └── 9.csv
│ └── valve2/
│ ├── 0.csv
│ ├── 1.csv
│ ├── 2.csv
│ └── 3.csv
├── docs/
│ └── contributing.md
├── notebooks/
│ ├── ArimaFD.ipynb
│ ├── Conv_AE.ipynb
│ ├── LSTM_AE.ipynb
│ ├── MSET.ipynb
│ ├── README.md
│ ├── Vanilla_AE.ipynb
│ ├── Vanilla_LSTM.ipynb
│ ├── isolation_forest.ipynb
│ ├── mscred.ipynb
│ ├── t2_SKAB.ipynb
│ └── t2_with_q_SKAB.ipynb
├── pyproject.toml
└── results/
├── results-Arima_anomaly_detection.pkl
├── results-Conv_AE.pkl
├── results-Isolation_Forest.pkl
├── results-LSTM_AE.pkl
├── results-MSCRED.pkl
├── results-MSET.pkl
├── results-T2-q.pkl
├── results-T2.pkl
├── results-Vanilla_AE.pkl
└── results-Vanilla_LSTM.pkl
================================================
FILE CONTENTS
================================================
================================================
FILE: .gitignore
================================================
.DS_Store
*.pickle
# Byte-compiled / optimized / DLL files
__pycache__/
algorithms/__pycache__/
notebooks/__pycache__/
*.py[cod]
*$py.class
# Distribution / packaging
.Python
build/
develop-eggs/
dist/
downloads/
eggs/
.eggs/
lib/
lib64/
parts/
sdist/
var/
wheels/
pip-wheel-metadata/
share/python-wheels/
*.egg-info/
.installed.cfg
*.egg
MANIFEST
# PyInstaller
# Usually these files are written by a python script from a template
# before PyInstaller builds the exe, so as to inject date/other infos into it.
*.manifest
*.spec
# Installer logs
pip-log.txt
pip-delete-this-directory.txt
# Unit test / coverage reports
htmlcov/
.tox/
.nox/
.coverage
.coverage.*
.cache
nosetests.xml
coverage.xml
*.cover
*.py,cover
.hypothesis/
.pytest_cache/
# Jupyter Notebook
.ipynb_checkpoints
notebooks/.ipynb_checkpoints
algorithms/.ipynb_checkpoints
# IPython
profile_default/
ipython_config.py
# pyenv
.python-version
# PEP 582; used by e.g. github.com/David-OConnor/pyflow
__pypackages__/
# Environments
.env
.venv
env/
venv/
ENV/
env.bak/
venv.bak/
================================================
FILE: .pre-commit-config.yaml
================================================
# https://pre-commit.com
exclude: 'examples|reports'
repos:
- repo: https://github.com/pre-commit/pre-commit-hooks
rev: v4.5.0
hooks:
- id: debug-statements #Check for debugger imports and breakpoint() in python files
- id: check-ast #Simply check whether files parse as valid python
- id: fix-byte-order-marker #removes UTF-8 byte order marker
- id: check-json
- id: detect-private-key # detect-private-key is not in repo
- id: check-yaml
- id: check-added-large-files
- id: check-shebang-scripts-are-executable
- id: check-case-conflict #Check for files with names that would conflict on a case-insensitive filesystem like MacOS HFS+ or Windows FAT
- id: end-of-file-fixer #Makes sure files end in a newline and only a newline
- id: trailing-whitespace
- id: mixed-line-ending
- repo: https://github.com/astral-sh/ruff-pre-commit
rev: v0.3.4
hooks:
- id: ruff
args: [--fix, --exit-non-zero-on-fix, --line-length=79]
types_or: [python, pyi, jupyter]
- id: ruff-format
args: [--line-length=79]
types_or: [python, pyi, jupyter]
- repo: https://github.com/pycqa/isort
rev: 5.13.2
hooks:
- id: isort #isort is a pre-commit hook that runs to check for issues in imports and docstrings
args: [
"--profile", "black", "--filter-files",
"-l", "79"
]
- repo: https://github.com/asottile/blacken-docs
rev: 1.16.0
hooks:
- id: blacken-docs #blacken-docs is a pre-commit hook that runs to check for issues in the docs
additional_dependencies: [black]
- repo: https://github.com/asottile/pyupgrade
rev: v3.15.2
hooks:
- id: pyupgrade #pyupgrade is a pre-commit hook that runs to check for issues in the code
args: [--py36-plus]
- repo: local
hooks:
- id: mypy # mypy is a pre-commit hook that runs as a linter to check for type errors
name: mypy
entry: mypy --implicit-optional
language: system
types: [python]
args: [
"--ignore-missing-imports",
"--explicit-package-bases",
"--check-untyped-defs"
]
stages:
- "pre-push"
- "pre-merge-commit"
- repo: local
hooks:
- id: pytest-check
name: pytest-check
language: python
types: [python]
entry: pytest
pass_filenames: false
always_run: true
args: [
--doctest-modules,
-o, addopts=""
]
- repo: https://github.com/roy-ht/pre-commit-jupyter
rev: v1.2.1
hooks:
- id: jupyter-notebook-cleanup
args:
- --remove-kernel-metadata
- --pin-patterns
- "[pin];[donotremove]"
================================================
FILE: LICENSE
================================================
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================================================
FILE: README.md
================================================
# 
🛠🛠🛠**The testbed is under repair right now. Unfortunately, we can't tell exactly when it will be ready and we be able to continue data collection. Information about it will be in the repository. Sorry for the delay.**
❗️❗️❗️The current version of SKAB (v0.9) contains 34 datasets with collective anomalies. But the update to v1.0 will contain 300+ additional files with point and collective anomalies. It will make SKAB one of the largest changepoint-containing benchmarks, especially in the technical field.
## About SKAB [](https://github.com/waico/SKAB/graphs/commit-activity) [](https://doi.org/10.34740/KAGGLE/DSV/1693952) [](https://www.gnu.org/licenses/gpl-3.0.html)
We propose the [Skoltech](https://www.skoltech.ru/en) Anomaly Benchmark (SKAB) designed for evaluating the anomaly detection core. SKAB allows working with two main problems (there are two markups for anomalies):
1. Outlier detection (anomalies considered and marked up as single-point anomalies)
2. Changepoint detection (anomalies considered and marked up as collective anomalies)
SKAB consists of the following artifacts:
1. [Datasets](#datasets)
2. [Proposed Leaderboard](#proposed-leaderboard) for outlier detection and changepoint detection problems
3. Python modules for algorithms’ evaluation (now evaluation modules are being imported from [TSAD](https://github.com/waico/tsad) framework, while the details regarding the evaluation process are presented [here](https://github.com/waico/tsad/blob/main/examples/Evaluating.ipynb))
4. Python [core](core/) with algorithms’ implementation
5. Python [notebooks](#notebooks) with anomaly detection pipeline implementation for various algorithms
All the details about SKAB are presented in the following artifacts:
- Position paper (*currently submitted for publication*)
- Talk about the project: [English](https://youtu.be/hjzuKeNYUho) version and [Russian](https://www.youtube.com/watch?v=VLmmYGc4v2c) version
- Slides about the project: [English](https://drive.google.com/open?id=1dHUevwPp6ftQCEKnRgB4KMp9oLBMSiDM) version and [Russian](https://drive.google.com/file/d/1gThPCNbEaIxhENLm-WTFGO_9PU1Wdwjq/view?usp=share_link) version
## Datasets
The SKAB v0.9 corpus contains 35 individual data files in .csv format (datasets). The [data](data/) folder contains datasets from the benchmark. The structure of the data folder is presented in the [structure](./data/README.md) file. Each dataset represents a single experiment and contains a single anomaly. The datasets represent a multivariate time series collected from the sensors installed on the testbed. Columns in each data file are following:
- `datetime` - Represents dates and times of the moment when the value is written to the database (YYYY-MM-DD hh:mm:ss)
- `Accelerometer1RMS` - Shows a vibration acceleration (Amount of g units)
- `Accelerometer2RMS` - Shows a vibration acceleration (Amount of g units)
- `Current` - Shows the amperage on the electric motor (Ampere)
- `Pressure` - Represents the pressure in the loop after the water pump (Bar)
- `Temperature` - Shows the temperature of the engine body (The degree Celsius)
- `Thermocouple` - Represents the temperature of the fluid in the circulation loop (The degree Celsius)
- `Voltage` - Shows the voltage on the electric motor (Volt)
- `RateRMS` - Represents the circulation flow rate of the fluid inside the loop (Liter per minute)
- `anomaly` - Shows if the point is anomalous (0 or 1)
- `changepoint` - Shows if the point is a changepoint for collective anomalies (0 or 1)
Exploratory Data Analysis (EDA) for SKAB is presented [here (tbd)]. Russian version of EDA is available on [kaggle](https://www.kaggle.com/newintown/eda-example).
ℹ️We have also made a *SKAB teaser* that is a small dataset collected separately but from the same testbed. SKAB teaser is made just for learning/teaching purposes and contains only 4 collective anomalies. All the information is available on [kaggle](https://www.kaggle.com/datasets/yuriykatser/skoltech-anomaly-benchmark-skab-teaser).
## Proposed Leaderboard
This leaderboard shows performance of algorithms on test set, unlike leaderboard for SKAB v0.9 which evaluates both training and testing data all together. Moreover, the evaluated window of change points is to the right side of actual change point occurence which is in accordance with fact, that it should be impossible to capture event before it occurs. Lastly, the window size for the NAB detection algorithm is set to 60 seconds to reflect the dynamics of the transition as presented in the slides to enable detection of the start of the transition phase which is also marked as change-point.
You can present and evaluate your algorithm using SKAB on [kaggle](https://www.kaggle.com/yuriykatser/skoltech-anomaly-benchmark-skab). Leaderboards are also available at paperswithcode.com: [CPD problem](https://paperswithcode.com/sota/change-point-detection-on-skab).
Information about the metrics for anomaly detection and intuition behind the metrics selection can be found in [this](https://medium.com/@katser/a-review-of-anomaly-detection-metrics-with-a-lot-of-related-information-736d88774712) medium article.
### Outlier detection problem
*Sorted by F1; for F1 bigger is better; both for FAR (False Alarm Rate) and MAR (Missing Alarm Rate) less is better*
*Evaluated as binary classification problem.*
| Algorithm | F1 | FAR, % | MAR, %
|---|---|---|---
|Perfect detector | 1 | 0 | 0
|Conv-AE |0.78 | 13.55 | 28.02
|MSET |0.78 | 39.73 | 14.13
|T-squared+Q (PCA-based) | 0.76 | 26.62 | 24.92
|LSTM-AE |0.74 | 29.96 | 25.92
|T-squared | 0.66 | 19.21 | 42.6
|LSTM-VAE | 0.56 | 9.13 | 55.03
|Vanilla LSTM | 0.54 | 12.54 | 59.53
|MSCRED | 0.36 | 49.94 | 69.88
|Vanilla AE | 0.39 | 2.59 | 75.15
|Isolation forest | 0.29 | 2.56 | 82.89
|Null detector | 0 | 0 | 100
### Changepoint detection problem
*Sorted by NAB (standard); for NAB (standard), NAB (LowFP), NAB (LowFN) bigger is better, for Number of Missed CPs, Number of FPs lower is better*
*The current leaderboard is obtained with the window size for the NAB detection algorithm equal to 60 sec and to the right side of true change point.*
| Algorithm | NAB (standard) | NAB (LowFP) | NAB (LowFN) | Number of Missed CPs | Number of FPs
|---|---|---|---|---|---
|Perfect detector | 100 | 100 | 100 | 0 | 0
|MSCRED | 32.42 | 16.53 | 40.28 | 55 | 342
|Isolation forest | 26.16 | 19.5 | 30.82 | 76 | 135
|T-squared+Q (PCA-based) | 25.35 | 14.51 | 31.33 | 72 | 232
|Conv-AE | 23.61 | 21.54 | 27.55 | 82 | 23
|LSTM-AE | 23.51 | 20.11 | 25.91 | 88 | 69
|T-squared | 19.54 | 10.2 | 24.31 | 70 | 106
|MSET | 13.84 | 10.22 | 17.37 | 96 | 66
|Vanilla AE | 11.41 | 6.53 | 13.91 | 103 | 106
|Vanilla LSTM | 11.31 | -3.8 | 17.25 | 90 | 342
|ArimaFD | -0.09 | -0.17 | -0.06 | 127 | 2
|Null detector | 0 | 0 | 0 | - | -
## Notebooks
The [notebooks](notebooks/) folder contains jupyter notebooks with the code for the proposed leaderboard results reproducing. We have calculated the results for following commonly known anomaly detection algorithms:
- Isolation forest - *Outlier detection algorithm based on Random forest concept*
- Vanilla LSTM - *NN with LSTM layer*
- Vanilla AE - *Feed-Forward Autoencoder*
- LSTM-AE - *LSTM Autoencoder*
- LSTM-VAE - *LSTM Variational Autoencoder*
- Conv-AE - *Convolutional Autoencoder*
- MSCRED - *Multi-Scale Convolutional Recurrent Encoder-Decoder*
- MSET - *Multivariate State Estimation Technique*
Additionally on the leaderboard were shown the externally calculated results of the following algorithms:
- [ArimaFD](https://github.com/waico/arimafd) - *ARIMA-based fault detection algorithm*
- [T-squared](http://github.com/YKatser/ControlCharts/tree/main/examples) - *Hotelling's T-squared statistics*
- [T-squared+Q (PCA-based)](http://github.com/YKatser/ControlCharts/tree/main/examples) - *Hotelling's T-squared statistics + Q statistics based on PCA*
- [ruptures](https://github.com/deepcharles/ruptures) - *Changepoint detection (CPD) algorithms from ruptures package*
- [CPDE](https://github.com/YKatser/CPDE) - *Ruptures-based changepoint detection ensemble (CPDE) algorithms*
Details regarding the algorithms, including short description, references to scientific papers and code of the initial implementation is available in [this readme](https://github.com/waico/SKAB/tree/master/notebooks#anomaly-detection-algorithms).
## Installation
1. install Python 3.10+ (tested on 3.10.13)
1. install [poetry](https://python-poetry.org/docs/) package manager
- `brew install poetry`
> Poetry installs dependencies and locks versions for deterministic installs. Poetry uses [Python's built-in `venv` module](https://docs.python.org/3/library/venv.html) to create virtual environments. It also uses PEP [517](https://peps.python.org/pep-0517) & [518](https://peps.python.org/pep-0518) specifications to build packages without requiring `setup.py` or `requirements.txt` files.
1. LightGBM base install
- `brew install lightgbm`
1. install SKAB dependencies, see [pyproject.toml](pyproject.toml) for details
- `poetry install`
1. confirm installation
- `poetry show --tree` - shows all dependencies installed
- `poetry env info` - displays information about the current environment (Python version, path, etc)
- `poetry list` - lists all cli commands
## Citation
Please cite our project in your publications if it helps your research.
```bibtex
@misc{skab,
author = {Katser, Iurii D. and Kozitsin, Vyacheslav O.},
title = {Skoltech Anomaly Benchmark (SKAB)},
year = {2020},
publisher = {Kaggle},
howpublished = {\url{https://www.kaggle.com/dsv/1693952}},
DOI = {10.34740/KAGGLE/DSV/1693952}
}
```
## Notable mentions
SKAB is acknowledged by some ML resources.
- [Anomaly Detection Learning Resources](https://github.com/yzhao062/anomaly-detection-resources#34-datasets)
- [awesome-TS-anomaly-detection](https://github.com/rob-med/awesome-TS-anomaly-detection#benchmark-datasets)
- [List of datasets for machine-learning research](https://en.wikipedia.org/wiki/List_of_datasets_for_machine-learning_research#Anomaly_data)
- [paperswithcode.com](https://paperswithcode.com/dataset/skab)
- [Google datasets](https://datasetsearch.research.google.com/search?query=skoltech%20anomaly%20benchmark&docid=IIIE4VWbqUKszygyAAAAAA%3D%3D)
- [Industrial ML Datasets](https://github.com/nicolasj92/industrial-ml-datasets)
- etc.
================================================
FILE: core/Conv_AE.py
================================================
from tensorflow.keras.callbacks import EarlyStopping
from tensorflow.keras.layers import Conv1D, Conv1DTranspose, Dropout, Input
from tensorflow.keras.models import Sequential
from tensorflow.keras.optimizers import Adam
class Conv_AE:
"""
A reconstruction convolutional autoencoder model to detect anomalies in timeseries data using reconstruction error as an anomaly score.
Parameters
----------
No parameters are required for initializing the class.
Attributes
----------
model : Sequential
The trained convolutional autoencoder model.
Examples
--------
>>> from Conv_AE import Conv_AE
>>> CAutoencoder = Conv_AE()
>>> CAutoencoder.fit(train_data)
>>> prediction = CAutoencoder.predict(test_data)
"""
def __init__(self):
self._Random(0)
def _Random(self, seed_value):
import os
os.environ["PYTHONHASHSEED"] = str(seed_value)
import random
random.seed(seed_value)
import numpy as np
np.random.seed(seed_value)
import tensorflow as tf
tf.random.set_seed(seed_value)
def _build_model(self):
model = Sequential(
[
Input(shape=(self.shape[1], self.shape[2])),
Conv1D(
filters=32,
kernel_size=7,
padding="same",
strides=2,
activation="relu",
),
Dropout(rate=0.2),
Conv1D(
filters=16,
kernel_size=7,
padding="same",
strides=2,
activation="relu",
),
Conv1DTranspose(
filters=16,
kernel_size=7,
padding="same",
strides=2,
activation="relu",
),
Dropout(rate=0.2),
Conv1DTranspose(
filters=32,
kernel_size=7,
padding="same",
strides=2,
activation="relu",
),
Conv1DTranspose(filters=1, kernel_size=7, padding="same"),
]
)
model.compile(optimizer=Adam(learning_rate=0.001), loss="mse")
return model
def fit(self, data):
"""
Train the convolutional autoencoder model on the provided data.
Parameters
----------
data : numpy.ndarray
Input data for training the autoencoder model.
"""
self.shape = data.shape
self.model = self._build_model()
self.model.fit(
data,
data,
epochs=100,
batch_size=32,
validation_split=0.1,
verbose=0,
callbacks=[
EarlyStopping(
monitor="val_loss", patience=5, mode="min", verbose=0
)
],
)
def predict(self, data):
"""
Generate predictions using the trained convolutional autoencoder model.
Parameters
----------
data : numpy.ndarray
Input data for generating predictions.
Returns
-------
numpy.ndarray
Predicted output data.
"""
return self.model.predict(data)
================================================
FILE: core/Isolation_Forest.py
================================================
from sklearn.ensemble import IsolationForest
class Isolation_Forest:
"""
Isolation Forest or iForest builds an ensemble of iTrees for a given data set, then anomalies are those instances which have short average path lengths on the iTrees.
Parameters
----------
params : list
A list containing three parameters: random_state, n_jobs, and contamination.
Attributes
----------
random_state : int
The random seed used for reproducibility.
n_jobs : int
The number of CPU cores to use for parallelism.
contamination : float
The expected proportion of anomalies in the dataset.
Examples
--------
>>> from Isolation_Forest import Isolation_Forest
>>> PARAMS = [random_state, n_jobs, contamination]
>>> model = Isolation_Forest(PARAMS)
>>> model.fit(X_train)
>>> predictions = model.predict(test_data)
"""
def __init__(self, params):
self.params = params
self.random_state = self.params[0]
self.n_jobs = self.params[1]
self.contamination = self.params[2]
def _Random(self, seed_value):
import os
os.environ["PYTHONHASHSEED"] = str(seed_value)
import random
random.seed(seed_value)
import numpy as np
np.random.seed(seed_value)
import tensorflow as tf
tf.random.set_seed(seed_value)
def _build_model(self):
self._Random(0)
model = IsolationForest(
random_state=self.random_state,
n_jobs=self.n_jobs,
contamination=self.contamination,
)
return model
def fit(self, X):
"""
Train the Isolation Forest model on the provided data.
Parameters
----------
X : numpy.ndarray
Input data for training the model.
"""
self.model = self._build_model()
self.model.fit(X)
def predict(self, data):
"""
Generate predictions using the trained Isolation Forest model.
Parameters
----------
data : numpy.ndarray
Input data for generating predictions.
Returns
-------
numpy.ndarray
Predicted output data.
"""
return self.model.predict(data)
================================================
FILE: core/LSTM_AE.py
================================================
from tensorflow.keras import Model
from tensorflow.keras.callbacks import EarlyStopping
from tensorflow.keras.layers import (
LSTM,
Dense,
Input,
RepeatVector,
TimeDistributed,
)
class LSTM_AE:
"""
A reconstruction sequence-to-sequence (LSTM-based) autoencoder model to detect anomalies in timeseries data using reconstruction error as an anomaly score.
Parameters
----------
params : list
A list of hyperparameters for the model, containing the following elements:
- EPOCHS : int
The number of training epochs.
- BATCH_SIZE : int
The batch size for training.
- VAL_SPLIT : float
The validation split ratio during training.
Attributes
----------
params : list
The hyperparameters for the model.
Examples
--------
>>> from LSTM_AE import LSTM_AE
>>> PARAMS = [EPOCHS, BATCH_SIZE, VAL_SPLIT]
>>> model = LSTM_AE(PARAMS)
>>> model.fit(train_data)
>>> predictions = model.predict(test_data)
"""
def __init__(self, params):
self.params = params
def _Random(self, seed_value):
import os
os.environ["PYTHONHASHSEED"] = str(seed_value)
import random
random.seed(seed_value)
import numpy as np
np.random.seed(seed_value)
import tensorflow as tf
tf.random.set_seed(seed_value)
def _build_model(self):
self._Random(0)
inputs = Input(shape=(self.shape[1], self.shape[2]))
encoded = LSTM(100, activation="relu")(inputs)
decoded = RepeatVector(self.shape[1])(encoded)
decoded = LSTM(100, activation="relu", return_sequences=True)(decoded)
decoded = TimeDistributed(Dense(self.shape[2]))(decoded)
model = Model(inputs, decoded)
_ = Model(inputs, encoded)
model.compile(optimizer="adam", loss="mae", metrics=["mse"])
return model
def fit(self, X):
"""
Train the sequence-to-sequence (LSTM-based) autoencoder model on the provided data.
Parameters
----------
X : numpy.ndarray
Input data for training the model.
"""
self.shape = X.shape
self.model = self._build_model()
early_stopping = EarlyStopping(patience=5, verbose=0)
self.model.fit(
X,
X,
validation_split=self.params[2],
epochs=self.params[0],
batch_size=self.params[1],
verbose=0,
shuffle=False,
callbacks=[early_stopping],
)
def predict(self, data):
"""
Generate predictions using the trained sequence-to-sequence (LSTM-based) autoencoder model.
Parameters
----------
data : numpy.ndarray
Input data for generating predictions.
Returns
-------
numpy.ndarray
Predicted output data.
"""
return self.model.predict(data)
================================================
FILE: core/LSTM_VAE.py
================================================
from tensorflow.keras import backend as K
from tensorflow.keras import losses
from tensorflow.keras.callbacks import EarlyStopping
from tensorflow.keras.layers import LSTM, Dense, Input, Layer, RepeatVector
from tensorflow.keras.models import Model
class KLDivergenceLayer(Layer):
def __init__(self, **kwargs):
super().__init__(**kwargs)
def call(self, inputs):
z_mean, z_log_sigma = inputs
kl_loss = -0.5 * K.mean(
1 + z_log_sigma - K.square(z_mean) - K.exp(z_log_sigma), axis=-1
)
self.add_loss(kl_loss)
return kl_loss # Return KL loss value
class Sampling(Layer):
def __init__(self, latent_dim, epsilon_std=1.0, **kwargs):
super().__init__(**kwargs)
self.latent_dim = latent_dim
self.epsilon_std = epsilon_std
def call(self, inputs):
z_mean, z_log_sigma = inputs
batch = K.shape(z_mean)[0]
dim = K.shape(z_mean)[1]
epsilon = K.random_normal(
shape=(batch, dim), mean=0.0, stddev=self.epsilon_std
)
return z_mean + z_log_sigma * epsilon
def compute_output_shape(self, input_shape):
return input_shape[0] # Same shape as z_mean and z_log_sigma
class LSTM_VAE:
"""
A reconstruction LSTM variational autoencoder model to detect anomalies in timeseries data using reconstruction error as an anomaly score.
Parameters
----------
TenserFlow_backend : bool, optional
Flag to specify whether to use TensorFlow backend (default is False).
Attributes
----------
None
Examples
-------
>>> from LSTM_VAE import LSTM_VAE
>>> model = LSTM_VAE()
>>> model.fit(train_data)
>>> predictions = model.predict(test_data)
"""
def __init__(self, params):
self.params = params
def _build_model(self, input_dim, timesteps, intermediate_dim, latent_dim):
self._Random(0)
x = Input(
shape=(
timesteps,
input_dim,
)
)
h = LSTM(intermediate_dim)(x)
self.z_mean = Dense(latent_dim)(h)
self.z_log_sigma = Dense(latent_dim)(h)
z = Sampling(latent_dim)([self.z_mean, self.z_log_sigma])
h_decoded = RepeatVector(timesteps)(z)
decoder_h = LSTM(intermediate_dim, return_sequences=True)(h_decoded)
decoder_mean = LSTM(input_dim, return_sequences=True)(decoder_h)
vae = Model(x, decoder_mean)
_ = Model(x, self.z_mean)
decoder_input = Input(shape=(latent_dim,))
_h_decoded = RepeatVector(timesteps)(decoder_input)
_h_decoded = LSTM(intermediate_dim, return_sequences=True)(_h_decoded)
_x_decoded_mean = LSTM(input_dim, return_sequences=True)(_h_decoded)
_ = Model(decoder_input, _x_decoded_mean)
vae.compile(optimizer="rmsprop", loss=self.vae_loss)
return vae
def _Random(self, seed_value):
import os
os.environ["PYTHONHASHSEED"] = str(seed_value)
import random
random.seed(seed_value)
import numpy as np
np.random.seed(seed_value)
import tensorflow as tf
tf.random.set_seed(seed_value)
def vae_loss(self, x, x_decoded_mean):
"""
Calculate the VAE loss.
Parameters
----------
x : tensorflow.Tensor
Input data.
x_decoded_mean : tensorflow.Tensor
Decoded output data.
Returns
-------
loss : tensorflow.Tensor
VAE loss value.
"""
mse = losses.MeanSquaredError()
xent_loss = mse(x, x_decoded_mean)
kl_loss = KLDivergenceLayer()([self.z_mean, self.z_log_sigma])
loss = xent_loss + kl_loss
return loss
def fit(self, X):
"""
Train the LSTM variational autoencoder model on the provided data.
Parameters
----------
data : numpy.ndarray
Input data for training.
epochs : int, optional
Number of training epochs (default is 20).
validation_split : float, optional
Fraction of the training data to be used as validation data (default is 0.1).
BATCH_SIZE : int, optional
Batch size for training (default is 1).
early_stopping : bool, optional
Whether to use early stopping during training (default is True).
"""
self.shape = X.shape
self.input_dim = self.shape[-1]
self.timesteps = self.shape[1]
self.latent_dim = 100
self.epsilon_std = 1.0
self.intermediate_dim = 32
self.model = self._build_model(
self.input_dim,
timesteps=self.timesteps,
intermediate_dim=self.intermediate_dim,
latent_dim=self.latent_dim,
)
early_stopping = EarlyStopping(patience=5, verbose=0)
self.model.fit(
X,
X,
validation_split=self.params[2],
epochs=self.params[0],
batch_size=self.params[1],
verbose=0,
shuffle=False,
callbacks=[early_stopping],
)
def predict(self, data):
"""
Generate predictions using the trained LSTM variational autoencoder model.
Parameters
----------
data : numpy.ndarray
Input data for making predictions.
Returns
-------
predictions : numpy.ndarray
The reconstructed output predictions.
"""
return self.model.predict(data)
================================================
FILE: core/MSCRED.py
================================================
import math
import tensorflow as tf
from tensorflow.keras import Model
from tensorflow.keras.callbacks import ReduceLROnPlateau
from tensorflow.keras.layers import (
Conv2D,
Conv2DTranspose,
ConvLSTM2D,
Input,
Layer,
TimeDistributed,
)
from tensorflow.keras.optimizers import Adam
class MSCRED:
"""
MSCRED - Multi-Scale Convolutional Recurrent Encoder-Decoder first constructs multi-scale (resolution) signature matrices to characterize multiple levels of the system statuses across different time steps. In particular, different levels of the system statuses are used to indicate the severity of different abnormal incidents. Subsequently, given the signature matrices, a convolutional encoder is employed to encode the inter-sensor (time series) correlations patterns and an attention based Convolutional Long-Short Term Memory (ConvLSTM) network is developed to capture the temporal patterns. Finally, with the feature maps which encode the inter-sensor correlations and temporal information, a convolutional decoder is used to reconstruct the signature matrices and the residual signature matrices are further utilized to detect and diagnose anomalies. The intuition is that MSCRED may not reconstruct the signature matrices well if it never observes similar system statuses before.
Parameters
----------
params : list
A list containing configuration parameters for the MSCRED model.
Attributes
----------
model : Model
The trained MSCRED model.
Examples
--------
>>> from MSCRED import MSCRED
>>> PARAMS = [sensor_n, scale_n, step_max]
>>> model = MSCRED(PARAMS)
>>> model.fit(X_train, Y_train, X_test, Y_test)
>>> prediction = model.predict(test_data)
"""
def __init__(self, params):
self.params = params
def _build_model(self):
self._Random(0)
class MyPadLayer(Layer):
def __init__(self, paddings, **kwargs):
super().__init__(**kwargs)
self.paddings = paddings
def call(self, inputs):
return tf.pad(inputs, self.paddings)
class MyAttentionLayer(Layer):
def __init__(self, attention_fun, **kwargs):
super().__init__(**kwargs)
self.attention = attention_fun
def call(self, inputs, **kwargs):
# Your attention mechanism implementation here
return self.attention(inputs, **kwargs)
class MyConcatLayer(Layer):
def __init__(self, axis, **kwargs):
super().__init__(**kwargs)
self.axis = axis
def call(self, inputs):
return tf.concat(inputs, axis=self.axis)
input_size = (
self.params[2],
self.params[0],
self.params[0],
self.params[1],
)
inputs = Input(input_size)
if self.params[0] % 8 != 0:
self.sensor_n_pad = (self.params[0] // 8) * 8 + 8
else:
self.sensor_n_pad = self.params[0]
paddings = tf.constant(
[
[0, 0],
[0, 0],
[0, self.sensor_n_pad - self.params[0]],
[0, self.sensor_n_pad - self.params[0]],
[0, 0],
]
)
inputs_pad = MyPadLayer(paddings)(inputs)
conv1 = TimeDistributed(
Conv2D(
filters=32,
kernel_size=3,
strides=1,
kernel_initializer="glorot_uniform",
padding="same",
activation="selu",
name="conv1",
)
)(inputs_pad)
conv2 = TimeDistributed(
Conv2D(
filters=64,
kernel_size=3,
strides=2,
kernel_initializer="glorot_uniform",
padding="same",
activation="selu",
name="conv2",
)
)(conv1)
conv3 = TimeDistributed(
Conv2D(
filters=128,
kernel_size=2,
strides=2,
kernel_initializer="glorot_uniform",
padding="same",
activation="selu",
name="conv3",
)
)(conv2)
conv4 = TimeDistributed(
Conv2D(
filters=256,
kernel_size=2,
strides=2,
kernel_initializer="glorot_uniform",
padding="same",
activation="selu",
name="conv4",
)
)(conv3)
convLSTM1 = ConvLSTM2D(
filters=32,
kernel_size=2,
padding="same",
return_sequences=True,
name="convLSTM1",
)(conv1)
convLSTM1_out = MyAttentionLayer(self.attention)(
convLSTM1, **{"koef": 1}
)
convLSTM2 = ConvLSTM2D(
filters=64,
kernel_size=2,
padding="same",
return_sequences=True,
name="convLSTM2",
)(conv2)
convLSTM2_out = MyAttentionLayer(self.attention)(
convLSTM2, **{"koef": 2}
)
convLSTM3 = ConvLSTM2D(
filters=128,
kernel_size=2,
padding="same",
return_sequences=True,
name="convLSTM3",
)(conv3)
convLSTM3_out = MyAttentionLayer(self.attention)(
convLSTM3, **{"koef": 4}
)
convLSTM4 = ConvLSTM2D(
filters=256,
kernel_size=2,
padding="same",
return_sequences=True,
name="convLSTM4",
)(conv4)
convLSTM4_out = MyAttentionLayer(self.attention)(
convLSTM4, **{"koef": 8}
)
deconv4 = Conv2DTranspose(
filters=128,
kernel_size=2,
strides=2,
kernel_initializer="glorot_uniform",
padding="same",
activation="selu",
name="deconv4",
)(convLSTM4_out)
deconv4_out = MyConcatLayer(axis=3)([deconv4, convLSTM3_out])
deconv3 = Conv2DTranspose(
filters=64,
kernel_size=2,
strides=2,
kernel_initializer="glorot_uniform",
padding="same",
activation="selu",
name="deconv3",
)(deconv4_out)
deconv3_out = MyConcatLayer(axis=3)([deconv3, convLSTM2_out])
deconv2 = Conv2DTranspose(
filters=32,
kernel_size=3,
strides=2,
kernel_initializer="glorot_uniform",
padding="same",
activation="selu",
name="deconv2",
)(deconv3_out)
deconv2_out = MyConcatLayer(axis=3)([deconv2, convLSTM1_out])
deconv1 = Conv2DTranspose(
filters=self.params[1],
kernel_size=3,
strides=1,
kernel_initializer="glorot_uniform",
padding="same",
activation="selu",
name="deconv1",
)(deconv2_out)
model = Model(
inputs=inputs,
outputs=deconv1[:, : self.params[0], : self.params[0], :],
)
return model
def attention(self, outputs, koef):
"""
Attention mechanism to weigh the importance of each step in the sequence.
Parameters
----------
outputs : tf.Tensor
The output tensor from ConvLSTM layers.
koef : int
A coefficient to scale the attention mechanism.
Returns
-------
tf.Tensor
Weighted output tensor.
"""
attention_w = []
for k in range(self.params[2]):
attention_w.append(
tf.reduce_sum(
tf.multiply(outputs[:, k], outputs[:, -1]), axis=(1, 2, 3)
)
/ self.params[2]
)
attention_w = tf.reshape(
tf.nn.softmax(tf.stack(attention_w, axis=1)),
[-1, 1, self.params[2]],
)
outputs = tf.reshape(
outputs,
[-1, self.params[2], tf.reduce_prod(outputs.shape.as_list()[2:])],
)
outputs = tf.matmul(attention_w, outputs)
outputs = tf.reshape(
outputs,
[
-1,
math.ceil(self.sensor_n_pad / koef),
math.ceil(self.sensor_n_pad / koef),
32 * koef,
],
)
return outputs
def _Random(self, seed_value):
import os
os.environ["PYTHONHASHSEED"] = str(seed_value)
import random
random.seed(seed_value)
import numpy as np
np.random.seed(seed_value)
import tensorflow as tf
tf.random.set_seed(seed_value)
def _loss_fn(self, y_true, y_pred):
return tf.reduce_mean(tf.square(y_true - y_pred))
def fit(self, X_train, Y_train, batch_size=200, epochs=25):
"""
Train the MSCRED model on the provided data.
Parameters
----------
X_train : numpy.ndarray
The training input data.
Y_train : numpy.ndarray
The training target data.
X_test : numpy.ndarray
The testing input data.
Y_test : numpy.ndarray
The testing target data.
batch_size : int, optional
The batch size for training, by default 200.
epochs : int, optional
The number of training epochs, by default 25.
"""
self.model = self._build_model()
self.model.compile(
optimizer=Adam(learning_rate=1e-3),
loss=self._loss_fn,
)
reduce_lr = ReduceLROnPlateau(
monitor="loss", factor=0.8, patience=6, min_lr=0.000001, verbose=1
)
self.model.fit(
X_train,
Y_train,
batch_size=batch_size,
epochs=epochs,
# validation_data=(X_test, Y_test),
callbacks=reduce_lr,
)
def predict(self, data):
"""
Generate predictions using the trained MSCRED model.
Parameters
----------
data : numpy.ndarray
Input data for generating predictions.
Returns
-------
numpy.ndarray
Predicted output data.
"""
return self.model.predict(data)
================================================
FILE: core/MSET.py
================================================
import numpy as np
import pandas as pd
from scipy import linalg as spla
from sklearn.preprocessing import StandardScaler
class MSET:
"""
MSET - multivariate state estimation technique is a non-parametric and statistical modeling method, which calculates the estimated values based on the weighted average of historical data. In terms of procedure, MSET is similar to some nonparametric regression methods, such as, auto-associative kernel regression.
Parameters
----------
None
Attributes
----------
None
Examples
--------
>>> from MSET import MSET
>>> model = MSET()
>>> model.fit(data)
>>> prediction = model.predict(test_data)
"""
def __init__(self):
self._Random(0)
def _build_model(self):
self.SS = StandardScaler()
def _Random(self, seed_value):
import os
os.environ["PYTHONHASHSEED"] = str(seed_value)
import random
random.seed(seed_value)
import numpy as np
np.random.seed(seed_value)
import tensorflow as tf
tf.random.set_seed(seed_value)
def calc_W(self, X_obs):
"""
Calculate the weight matrix W.
Parameters
----------
X_obs : numpy.ndarray
Observations for which to calculate the weight matrix.
Returns
-------
numpy.ndarray
Weight matrix W.
"""
DxX_obs = self.otimes(self.D, X_obs)
# try:
W = spla.lu_solve(self.LU_factors, DxX_obs)
# except:
# W = np.linalg.solve(self.DxD, DxX_obs)
return W
def otimes(self, X, Y):
"""
Compute the outer product of two matrices X and Y.
Parameters
----------
X : numpy.ndarray
First matrix.
Y : numpy.ndarray
Second matrix.
Returns
-------
numpy.ndarray
Outer product of X and Y.
"""
m1, n = np.shape(X)
m2, p = np.shape(Y)
if m1 != m2:
raise Exception("dimensionality mismatch between X and Y.")
Z = np.zeros((n, p))
if n != p:
for i in range(n):
for j in range(p):
Z[i, j] = self.kernel(X[:, i], Y[:, j])
else:
for i in range(n):
for j in range(i, p):
Z[i, j] = self.kernel(X[:, i], Y[:, j])
Z[j, i] = Z[i, j]
return Z
def kernel(self, x, y):
"""
Compute the kernel function value.
Parameters
----------
x : numpy.ndarray
First vector.
y : numpy.ndarray
Second vector.
Returns
-------
float
Kernel function s(x,y) = 1 - ||x-y||/(||x|| + ||y||) value.
"""
if all(x == y):
return 1.0
else:
return 1.0 - np.linalg.norm(x - y) / (
np.linalg.norm(x) + np.linalg.norm(y)
)
def fit(self, df, train_start=None, train_stop=None):
"""
Train the MSET model on the provided data.
Parameters
----------
df : pandas.DataFrame
Input data for training the model.
train_start : int, optional
Index to start training, by default None.
train_stop : int, optional
Index to stop training, by default None.
Returns
-------
None
"""
self.model = self._build_model()
self.D = df[train_start:train_stop].values.T.copy()
self.D = self.SS.fit_transform(self.D.T).T
self.DxD = self.otimes(self.D, self.D)
self.LU_factors = spla.lu_factor(self.DxD)
def predict(self, data):
"""
Generate predictions using the trained MSET model.
Parameters
----------
data : pandas.DataFrame
Input data for generating predictions.
Returns
-------
pandas.DataFrame
Predicted output data.
"""
X_obs = data.values.T.copy()
X_obs = self.SS.transform(X_obs.T).T
pred = np.zeros(X_obs.T.shape)
for i in range(X_obs.shape[1]):
pred[[i], :] = (
self.D @ self.calc_W(X_obs[:, i].reshape([-1, 1]))
).T
return pd.DataFrame(
self.SS.inverse_transform(pred),
index=data.index,
columns=data.columns,
)
================================================
FILE: core/Vanilla_AE.py
================================================
from tensorflow.keras.callbacks import EarlyStopping
from tensorflow.keras.layers import (
Activation,
BatchNormalization,
Dense,
Input,
)
from tensorflow.keras.models import Model
from tensorflow.keras.optimizers import Adam
class Vanilla_AE:
"""
Feed-forward neural network with autoencoder architecture for anomaly detection using reconstruction error as an anomaly score.
Parameters
----------
params : list
List containing the following hyperparameters in order:
- Number of neurons in the first encoder layer
- Number of neurons in the bottleneck layer (latent representation)
- Number of neurons in the first decoder layer
- Learning rate for the optimizer
- Batch size for training
Attributes
----------
model : tensorflow.keras.models.Model
The autoencoder model.
Examples
-------
>>> from Vanilla_AE import AutoEncoder
>>> autoencoder = AutoEncoder(param=[5, 4, 2, 0.005, 32])
>>> autoencoder.fit(train_data)
>>> predictions = autoencoder.predict(test_data)
"""
def __init__(self, params):
self.param = params
def _build_model(self):
self._Random(0)
input_dots = Input(shape=(self.shape,))
x = Dense(self.param[0])(input_dots)
x = BatchNormalization()(x)
x = Activation("relu")(x)
x = Dense(self.param[1])(x)
x = BatchNormalization()(x)
x = Activation("relu")(x)
bottleneck = Dense(self.param[2], activation="linear")(x)
x = Dense(self.param[1])(bottleneck)
x = BatchNormalization()(x)
x = Activation("relu")(x)
x = Dense(self.param[0])(x)
x = BatchNormalization()(x)
x = Activation("relu")(x)
out = Dense(self.shape, activation="linear")(x)
model = Model(input_dots, out)
model.compile(
optimizer=Adam(self.param[3]), loss="mae", metrics=["mse"]
)
self.model = model
return model
def _Random(self, seed_value):
import os
os.environ["PYTHONHASHSEED"] = str(seed_value)
import random
random.seed(seed_value)
import numpy as np
np.random.seed(seed_value)
import tensorflow as tf
tf.random.set_seed(seed_value)
def fit(
self,
data,
early_stopping=True,
validation_split=0.2,
epochs=40,
verbose=0,
shuffle=True,
):
"""
Train the autoencoder model on the provided data.
Parameters
----------
data : numpy.ndarray
Input data for training.
early_stopping : bool, optional
Whether to use early stopping during training.
validation_split : float, optional
Fraction of the training data to be used as validation data.
epochs : int, optional
Number of training epochs.
verbose : int, optional
Verbosity mode (0 = silent, 1 = progress bar, 2 = current epoch and losses, 3 = each training iteration).
shuffle : bool, optional
Whether to shuffle the training data before each epoch.
"""
self.shape = data.shape[1]
self.model = self._build_model()
callbacks = []
if early_stopping:
callbacks.append(EarlyStopping(patience=3, verbose=0))
self.model.fit(
data,
data,
validation_split=validation_split,
epochs=epochs,
batch_size=self.param[4],
verbose=verbose,
shuffle=shuffle,
callbacks=callbacks,
)
def predict(self, data):
"""
Generate predictions using the trained autoencoder model.
Parameters
----------
data : numpy.ndarray
Input data for making predictions.
Returns
-------
numpy.ndarray
The reconstructed output predictions.
"""
return self.model.predict(data)
================================================
FILE: core/Vanilla_LSTM.py
================================================
from tensorflow.keras.callbacks import EarlyStopping, ReduceLROnPlateau
from tensorflow.keras.layers import LSTM, Dense
from tensorflow.keras.models import Sequential
class Vanilla_LSTM:
"""
LSTM-based neural network for anomaly detection using reconstruction error as an anomaly score.
Parameters
----------
params : list
A list containing various parameters for configuring the LSTM model.
Attributes
----------
model : Sequential
The trained LSTM model.
Examples
--------
>>> from Vanilla_LSTM import Vanilla_LSTM
>>> PARAMS = [N_STEPS, EPOCHS, BATCH_SIZE, VAL_SPLIT]
>>> lstm_model = Vanilla_LSTM(PARAMS)
>>> lstm_model.fit(train_data, train_labels)
>>> predictions = lstm_model.predict(test_data)
"""
def __init__(self, params):
self.params = params
def _Random(self, seed_value):
import os
os.environ["PYTHONHASHSEED"] = str(seed_value)
import random
random.seed(seed_value)
import numpy as np
np.random.seed(seed_value)
import tensorflow as tf
tf.random.set_seed(seed_value)
def _build_model(self):
self._Random(0)
model = Sequential()
model.add(
LSTM(
100,
activation="relu",
return_sequences=True,
input_shape=(self.params[0], self.n_features),
)
)
model.add(LSTM(100, activation="relu"))
model.add(Dense(self.n_features))
model.compile(optimizer="adam", loss="mae", metrics=["mse"])
return model
def fit(self, X, y):
"""
Train the LSTM model on the provided data.
Parameters
----------
X : numpy.ndarray
Input data for training the model.
y : numpy.ndarray
Target data for training the model.
"""
self.n_features = X.shape[2]
self.model = self._build_model()
early_stopping = EarlyStopping(patience=10, verbose=0)
reduce_lr = ReduceLROnPlateau(
factor=0.1, patience=5, min_lr=0.0001, verbose=0
)
self.model.fit(
X,
y,
validation_split=self.params[3],
epochs=self.params[1],
batch_size=self.params[2],
verbose=0,
shuffle=False,
callbacks=[early_stopping, reduce_lr],
)
def predict(self, data):
"""
Generate predictions using the trained LSTM model.
Parameters
----------
data : numpy.ndarray
Input data for generating predictions.
Returns
-------
numpy.ndarray
Predicted output data.
"""
return self.model.predict(data)
================================================
FILE: core/__init.py__
================================================
================================================
FILE: core/metrics.py
================================================
"""
This module is part of library (tsad)[https://github.com/waico/tsad]
"""
import matplotlib.gridspec as gridspec
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
def filter_detecting_boundaries(detecting_boundaries):
"""
[[t1,t2],[],[t1,t2]] -> [[t1,t2],[t1,t2]]
[[],[]] -> []
"""
_detecting_boundaries = []
for couple in detecting_boundaries.copy():
if len(couple) != 0:
_detecting_boundaries.append(couple)
detecting_boundaries = _detecting_boundaries
return detecting_boundaries
def single_detecting_boundaries(
true_series,
true_list_ts,
prediction,
portion,
window_width,
anomaly_window_destination,
intersection_mode,
):
"""
Extract detecting_boundaries from series or list of timestamps
"""
if (true_series is not None) and (true_list_ts is not None):
raise Exception("Choose the ONE type")
elif true_series is not None:
true_timestamps = true_series[true_series == 1].index
elif true_list_ts is not None:
if len(true_list_ts) == 0:
return [[]]
else:
true_timestamps = true_list_ts
else:
raise Exception("Choose the type")
#
detecting_boundaries = []
td = (
pd.Timedelta(window_width)
if window_width is not None
else pd.Timedelta(
(prediction.index[-1] - prediction.index[0])
/ (len(true_timestamps) + 1)
* portion
)
)
for val in true_timestamps:
if anomaly_window_destination == "lefter":
detecting_boundaries.append([val - td, val])
elif anomaly_window_destination == "righter":
detecting_boundaries.append([val, val + td])
elif anomaly_window_destination == "center":
detecting_boundaries.append([val - td / 2, val + td / 2])
else:
raise RuntimeError("choose anomaly_window_destination")
# block for resolving intersection problem:
# important to watch right boundary to be never included to avoid windows intersection
if len(detecting_boundaries) == 0:
return detecting_boundaries
new_detecting_boundaries = detecting_boundaries.copy()
intersection_count = 0
for i in range(len(new_detecting_boundaries) - 1):
if (
new_detecting_boundaries[i][1]
>= new_detecting_boundaries[i + 1][0]
):
# transform print to list of intersections
# print(f'Intersection of scoring windows {new_detecting_boundaries[i][1], new_detecting_boundaries[i+1][0]}')
intersection_count += 1
if intersection_mode == "cut left window":
new_detecting_boundaries[i][1] = new_detecting_boundaries[
i + 1
][0]
elif intersection_mode == "cut right window":
new_detecting_boundaries[i + 1][0] = new_detecting_boundaries[
i
][1]
elif intersection_mode == "cut both":
_a = new_detecting_boundaries[i][1]
new_detecting_boundaries[i][1] = new_detecting_boundaries[
i + 1
][0]
new_detecting_boundaries[i + 1][0] = _a
else:
raise Exception("choose the intersection_mode")
# print(f'There are {intersection_count} intersections of scoring windows')
detecting_boundaries = new_detecting_boundaries.copy()
return detecting_boundaries
def check_errors(my_list):
"""
Check format of input true data
Parameters
----------
my_list - uniform format of true (See evaluate.evaluate)
Returns
----------
mx : depth of list, or variant of processing
"""
assert isinstance(my_list, list)
mx = 1
# ravel = []
level_list = {}
def check_error(my_list):
return not (
(all(isinstance(my_el, list) for my_el in my_list))
or (all(isinstance(my_el, pd.Series) for my_el in my_list))
or (all(isinstance(my_el, pd.Timestamp) for my_el in my_list))
)
def recurse(my_list, level=1):
nonlocal mx
nonlocal level_list
if check_error(my_list):
raise Exception(
f"Non uniform data format in level {level}: {my_list}"
)
if level not in level_list.keys():
level_list[level] = [] # for checking format
for my_el in my_list:
level_list[level].append(my_el)
if isinstance(my_el, list):
mx = max([mx, level + 1])
recurse(my_el, level + 1)
recurse(my_list)
for level in level_list:
if check_error(level_list[level]):
raise Exception(
f"Non uniform data format in level {level}: {my_list}"
)
if 3 in level_list:
for el in level_list[2]:
if not ((len(el) == 2) or (len(el) == 0)):
raise Exception(
f"Non uniform data format in level {2}: {my_list}"
)
return mx
def extract_cp_confusion_matrix(
detecting_boundaries, prediction, point=0, binary=False
):
"""
prediction: pd.Series
point=None for binary case
Returns
----------
dict: TPs: dict of numer window of [t1,t_cp,t2]
FPs: list of timestamps
FNs: list of numer window
"""
_detecting_boundaries = []
for couple in detecting_boundaries.copy():
if len(couple) != 0:
_detecting_boundaries.append(couple)
detecting_boundaries = _detecting_boundaries
times_pred = prediction[prediction.dropna() == 1].sort_index().index
my_dict = {}
my_dict["TPs"] = {}
my_dict["FPs"] = []
my_dict["FNs"] = []
if len(detecting_boundaries) != 0:
my_dict["FPs"].append(
times_pred[times_pred < detecting_boundaries[0][0]]
) # left
for i in range(len(detecting_boundaries)):
times_pred_window = times_pred[
(times_pred >= detecting_boundaries[i][0])
& (times_pred <= detecting_boundaries[i][1])
]
times_prediction_in_window = prediction[
detecting_boundaries[i][0] : detecting_boundaries[i][1]
].index
if len(times_pred_window) == 0:
if not binary:
my_dict["FNs"].append(i)
else:
my_dict["FNs"].append(times_prediction_in_window)
else:
my_dict["TPs"][i] = [
detecting_boundaries[i][0],
times_pred_window[point]
if not binary
else times_pred_window, # attention
detecting_boundaries[i][1],
]
if binary:
my_dict["FNs"].append(
times_prediction_in_window[
~times_prediction_in_window.isin(times_pred_window)
]
)
if len(detecting_boundaries) > i + 1:
my_dict["FPs"].append(
times_pred[
(times_pred > detecting_boundaries[i][1])
& (times_pred < detecting_boundaries[i + 1][0])
]
)
my_dict["FPs"].append(
times_pred[times_pred > detecting_boundaries[i][1]]
) # right
else:
my_dict["FPs"].append(times_pred)
if len(my_dict["FPs"]) > 1:
my_dict["FPs"] = np.concatenate(my_dict["FPs"])
elif len(my_dict["FPs"]) == 1:
my_dict["FPs"] = my_dict["FPs"][0]
if len(my_dict["FPs"]) == 0: # not elif on purpose
my_dict["FPs"] = []
if binary:
if len(my_dict["FNs"]) > 1:
my_dict["FNs"] = np.concatenate(my_dict["FNs"])
elif len(my_dict["FNs"]) == 1:
my_dict["FNs"] = my_dict["FNs"][0]
if len(my_dict["FNs"]) == 0: # not elif on purpose
my_dict["FNs"] = []
return my_dict
def confusion_matrix(true, prediction):
true_ = true == 1
prediction_ = prediction == 1
TP = (true_ & prediction_).sum()
TN = (~true_ & ~prediction_).sum()
FP = (~true_ & prediction_).sum()
FN = (true_ & ~prediction_).sum()
return TP, TN, FP, FN
def single_average_delay(
detecting_boundaries,
prediction,
anomaly_window_destination,
clear_anomalies_mode,
):
"""
anomaly_window_destination: 'lefter', 'righter', 'center'. Default='right'
"""
detecting_boundaries = filter_detecting_boundaries(detecting_boundaries)
point = 0 if clear_anomalies_mode else -1
dict_cp_confusion = extract_cp_confusion_matrix(
detecting_boundaries, prediction, point=point
)
missing = 0
detectHistory = []
all_true_anom = 0
FP = 0
FP += len(dict_cp_confusion["FPs"])
missing += len(dict_cp_confusion["FNs"])
all_true_anom += len(dict_cp_confusion["TPs"]) + len(
dict_cp_confusion["FNs"]
)
if anomaly_window_destination == "lefter":
def average_time(output_cp_cm_tp):
return output_cp_cm_tp[2] - output_cp_cm_tp[1]
elif anomaly_window_destination == "righter":
def average_time(output_cp_cm_tp):
return output_cp_cm_tp[1] - output_cp_cm_tp[0]
elif anomaly_window_destination == "center":
def average_time(output_cp_cm_tp):
return output_cp_cm_tp[1] - (
output_cp_cm_tp[0]
+ (output_cp_cm_tp[2] - output_cp_cm_tp[0]) / 2
)
else:
raise Exception("Choose anomaly_window_destination")
for fp_case_window in dict_cp_confusion["TPs"]:
detectHistory.append(
average_time(dict_cp_confusion["TPs"][fp_case_window])
)
return missing, detectHistory, FP, all_true_anom
def my_scale(
fp_case_window=None,
A_tp=1,
A_fp=0,
koef=1,
detalization=1000,
clear_anomalies_mode=True,
plot_figure=False,
):
"""
ts - segment on which the window is applied
"""
x = np.linspace(-np.pi / 2, np.pi / 2, detalization)
x = x if clear_anomalies_mode else x[::-1]
y = (
(A_tp - A_fp)
/ 2
* -1
* np.tanh(koef * x)
/ (np.tanh(np.pi * koef / 2))
+ (A_tp - A_fp) / 2
+ A_fp
)
if not plot_figure and fp_case_window is not None:
event = int(
(fp_case_window[1] - fp_case_window[0])
/ (fp_case_window[-1] - fp_case_window[0])
* detalization
)
if event >= len(x):
event = len(x) - 1
score = y[event]
return score
else:
return y
def single_evaluate_nab(
detecting_boundaries,
prediction,
table_of_coef=None,
clear_anomalies_mode=True,
scale_func="improved",
scale_koef=1,
):
"""
detecting_boundaries: list of list of two float values
The list of lists of left and right boundary indices
for scoring results of labeling if empty. Can be [[]], or [[],[t1,t2],[]]
table_of_coef: pandas array (3x4) of float values
Table of coefficients for NAB score function
indices: 'Standard','LowFP','LowFN'
columns:'A_tp','A_fp','A_tn','A_fn'
scale_func {default}, improved
недостатки scale_func default -
1 - зависит от относительного шага, а это значит, что если
слишком много точек в scoring window то перепад будет слишком
жестким в середение.
2- то самая левая точка не равно Atp, а права не равна Afp
(особенно если пррименять расплывающую множитель)
clear_anomalies_mode тогда слева от границы Atp срправа Afp,
иначе fault mode, когда слева от границы Afp срправа Atp
"""
if scale_func == "improved":
scale_func = my_scale
else:
raise Exception("choose the scale_func")
# filter
detecting_boundaries = filter_detecting_boundaries(detecting_boundaries)
if table_of_coef is None:
table_of_coef = pd.DataFrame(
[
[1.0, -0.11, 1.0, -1.0],
[1.0, -0.22, 1.0, -1.0],
[1.0, -0.11, 1.0, -2.0],
]
)
table_of_coef.index = pd.Index(["Standard", "LowFP", "LowFN"])
table_of_coef.index.name = "Metric"
table_of_coef.columns = ["A_tp", "A_fp", "A_tn", "A_fn"]
# GO
point = 0 if clear_anomalies_mode else -1
dict_cp_confusion = extract_cp_confusion_matrix(
detecting_boundaries, prediction, point=point
)
Scores, Scores_perfect, Scores_null = [], [], []
for profile in ["Standard", "LowFP", "LowFN"]:
A_tp = table_of_coef["A_tp"][profile]
A_fp = table_of_coef["A_fp"][profile]
A_fn = table_of_coef["A_fn"][profile]
score = 0
score += A_fp * len(dict_cp_confusion["FPs"])
score += A_fn * len(dict_cp_confusion["FNs"])
for fp_case_window in dict_cp_confusion["TPs"]:
set_times = dict_cp_confusion["TPs"][fp_case_window]
score += scale_func(set_times, A_tp, A_fp, koef=scale_koef)
Scores.append(score)
Scores_perfect.append(len(detecting_boundaries) * A_tp)
Scores_null.append(len(detecting_boundaries) * A_fn)
return np.array(
[np.array(Scores), np.array(Scores_null), np.array(Scores_perfect)]
)
def chp_score(
true,
prediction,
metric="nab",
window_width=None,
portion=0.1,
anomaly_window_destination="lefter",
clear_anomalies_mode=True,
intersection_mode="cut right window",
table_of_coef=None,
scale_func="improved",
scale_koef=1,
plot_figure=False,
verbose=True,
):
"""
Parameters
----------
true: variants:
or: if one dataset : pd.Series with binary int labels (1 is
anomaly, 0 is not anomaly);
or: if one dataset : list of pd.Timestamp of true labels, or []
if haven't labels ;
or: if one dataset : list of list of t1,t2: left and right
detection, boundaries of pd.Timestamp or [[]] if haven't labels
or: if many datasets: list (len of number of datasets) of pd.Series
with binary int labels;
or: if many datasets: list of list of pd.Timestamp of true labels, or
true = [ts,[]] if haven't labels for specific dataset;
or: if many datasets: list of list of list of t1,t2: left and right
detection boundaries of pd.Timestamp;
If we haven't true labels for specific dataset then we must insert
empty list of labels: true = [[[]],[[t1,t2],[t1,t2]]].
__True labels of anomalies or changepoints.
It is important to have appropriate labels (CP or
anomaly) for corresponding metric (See later "metric")
prediction: variants:
or: if one dataset : pd.Series with binary int labels
(1 is anomaly, 0 is not anomaly);
or: if many datasets: list (len of number of datasets)
of pd.Series with binary int labels.
__Predicted labels of anomalies or changepoints.
It is important to have appropriate labels (CP or
anomaly) for corresponding metric (See later "metric")
metric: {'nab', 'binary', 'average_time', 'confusion_matrix'}.
Default='nab'
Affects to output (see later: Returns)
Changepoint problem: {'nab', 'average_time'}.
Standard AD problem: {'binary', 'confusion_matrix'}.
'nab' is Numenta Anomaly Benchmark metric
'average_time' is both average delay or time to failure
depend on situation.
'binary': FAR, MAR, F1.
'confusion_matrix' standard confusion_matrix for any point.
window_width: 'str' for pd.Timedelta
Width of detection window. Default=None.
portion : float, default=0.1
The portion is needed if window_width = None.
The width of the detection window in this case is equal
to a portion of the width of the length of prediction divided
by the number of real CPs in this dataset. Default=0.1.
anomaly_window_destination: {'lefter', 'righter', 'center'}. Default='right'
The parameter of the location of the detection window relative to the anomaly.
'lefter' : the detection window will be on the left side of the anomaly
'righter' : the detection window will be on the right side of the anomaly
'center' : the scoring window will be positioned relative to the center of anom.
clear_anomalies_mode : boolean, default=True.
True : then the `left value of a Scoring function is Atp and the
`right is Afp. Only the `first value inside the detection window is taken.
False: then the `right value of a Scoring function is Atp and the
`left is Afp. Only the `last value inside the detection window is taken.
intersection_mode: {'cut left window', 'cut right window', 'both'}.
Default='cut right window'
The parameter will be used if the detection windows overlap for
true changepoints, which is generally undesirable and requires a
different approach than simply cropping the scoring window using
this parameter.
'cut left window' : will cut the overlapping part of the left window
'cut right window': will cut the intersecting part of the right window
'both' : will crop the intersecting portion of both the left
and right windows
verbose: boolean, default=True.
If True, then output useful information
plot_figure : boolean, default=False.
If True, then drawing the score fuctions, detection windows and predictions
It is used for example, for calibration the scale_koef.
table_of_coef (metric='nab'): pd.DataFrame of specific form. See bellow.
Application profiles of NAB metric.If Default is None:
table_of_coef = pd.DataFrame([[1.0,-0.11,1.0,-1.0],
[1.0,-0.22,1.0,-1.0],
[1.0,-0.11,1.0,-2.0]])
table_of_coef.index = ['Standard','LowFP','LowFN']
table_of_coef.index.name = "Metric"
table_of_coef.columns = ['A_tp','A_fp','A_tn','A_fn']
scale_func (metric='nab'): "default" of "improved". Default="improved".
Scoring function in NAB metric.
'default' : standard NAB scoring function
'improved' : Our function for resolving disadvantages
of standard NAB scoring function
scale_koef : float > 0. Default=1.0.
Smoothing factor. The smaller it is,
the smoother the scoring function is.
Returns
----------
metrics : value of metrics, depend on metric
'nab': tuple
- Standard profile, float
- Low FP profile, float
- Low FN profile
'average_time': tuple
- Average time (average delay, or time to failure)
- Missing changepoints, int
- FPs, int
- Number of true changepoints, int
'binary': tuple
- F1 metric, float
- False alarm rate, %, float
- Missing Alarm Rate, %, float
'binary': tuple
- TPs, int
- TNs, int
- FPs, int
- FNS, int
"""
assert isinstance(true, pd.Series) or isinstance(true, list)
# checking prediction
if isinstance(prediction, pd.Series):
true = [true]
prediction = [prediction]
elif isinstance(prediction, list):
if not all(isinstance(my_el, pd.Series) for my_el in prediction):
raise Exception("Incorrect format for prediction")
else:
raise Exception("Incorrect format for prediction")
# checking dataset length: Number of dataset unequal
assert len(true) == len(prediction)
# final check
input_variant = check_errors(true)
def check_sort(my_list, input_variant):
for dataset in my_list:
if input_variant == 2:
assert all(np.sort(dataset) == np.array(dataset))
elif input_variant == 3:
assert all(
np.sort(np.concatenate(dataset)) == np.concatenate(dataset)
)
elif input_variant == 1:
assert all(
dataset.index.values == dataset.sort_index().index.values
)
check_sort(true, input_variant)
check_sort(prediction, 1)
# part 2. To detected boundaries
if (
((metric == "nab") or (metric == "average_time"))
and (window_width is None)
and (input_variant != 3)
):
print(
f"Since you didn't choose window_width and portion, portion will be default ({portion})"
)
if input_variant == 1:
detecting_boundaries = [
single_detecting_boundaries(
true_series=true[i],
true_list_ts=None,
prediction=prediction[i],
window_width=window_width,
portion=portion,
anomaly_window_destination=anomaly_window_destination,
intersection_mode=intersection_mode,
)
for i in range(len(true))
]
elif input_variant == 2:
detecting_boundaries = [
single_detecting_boundaries(
true_series=None,
true_list_ts=true[i],
prediction=prediction[i],
window_width=window_width,
portion=portion,
anomaly_window_destination=anomaly_window_destination,
intersection_mode=intersection_mode,
)
for i in range(len(true))
]
elif input_variant == 3:
detecting_boundaries = true.copy()
# Next anti fool system [[[t1,t2]],[]] -> [[[t1,t2]],[[]]]
for i in range(len(detecting_boundaries)):
if len(detecting_boundaries[i]) == 0:
detecting_boundaries[i] = [[]]
else:
raise Exception("Unknown format for true data")
# part 3. To compute metric
if plot_figure:
num_datasets = len(true)
if ((metric == "binary") or (metric == "confusion_matrix")) and (
input_variant == 1
):
f = plt.figure(figsize=(16, 5 * num_datasets))
grid = gridspec.GridSpec(num_datasets, 1)
for i in range(num_datasets):
globals()["ax" + str(i)] = f.add_subplot(grid[i])
prediction[i].plot(
ax=globals()["ax" + str(i)], label="pred", marker="o"
)
true[i].plot( # type: ignore
ax=globals()["ax" + str(i)], label="true", marker="o"
)
globals()["ax" + str(i)].legend()
plt.show()
else:
f = plt.figure(figsize=(16, 5 * num_datasets))
grid = gridspec.GridSpec(num_datasets, 1)
detalization = 100
for i in range(num_datasets):
globals()["ax" + str(i)] = f.add_subplot(grid[i])
print_legend_boundary = True
def plot_cp(couple, anomaly_window_destination, ax, label):
if anomaly_window_destination == "lefter":
ax.axvline(couple[1], c="r", label=label)
elif anomaly_window_destination == "righter":
ax.axvline(couple[0], c="r", label=label)
elif anomaly_window_destination == "center":
ax.axvline(
couple[0] + ((couple[1] - couple[0]) / 2),
c="r",
label=label,
)
for couple in detecting_boundaries[i]:
if len(couple) > 0:
globals()["ax" + str(i)].axvspan(
couple[0],
couple[1],
alpha=0.5,
color="green",
label="detection \nboundary"
if print_legend_boundary
else None,
)
nab = pd.Series(
my_scale(
plot_figure=True, detalization=detalization
),
index=pd.date_range(
couple[0], couple[1], periods=detalization
),
)
nab.plot(
ax=globals()["ax" + str(i)],
linewidth=0.4,
color="brown",
label="nab scoring func"
if print_legend_boundary
else None,
)
plot_cp(
couple,
anomaly_window_destination,
globals()["ax" + str(i)],
label="Changepoint"
if print_legend_boundary
else None,
)
print_legend_boundary = False
else:
pass
prediction[i].plot(
ax=globals()["ax" + str(i)], label="pred", marker="o"
)
globals()["ax" + str(i)].legend()
plt.show()
if metric == "nab":
matrix = np.zeros((3, 3))
for i in range(len(prediction)):
matrix_ = single_evaluate_nab(
detecting_boundaries[i],
prediction[i],
table_of_coef=table_of_coef,
clear_anomalies_mode=clear_anomalies_mode,
scale_func=scale_func,
scale_koef=scale_koef,
# plot_figure=plot_figure,
)
matrix = matrix + matrix_
results = {}
desc = ["Standard", "LowFP", "LowFN"]
for t, profile_name in enumerate(desc):
results[profile_name] = round(
100
* (matrix[0, t] - matrix[1, t])
/ (matrix[2, t] - matrix[1, t]),
2,
)
if verbose:
print(profile_name, " - ", results[profile_name])
return results
elif metric == "average_time":
missing, detectHistory, FP, all_true_anom = 0, [], 0, 0
for i in range(len(prediction)):
missing_, detectHistory_, FP_, all_true_anom_ = (
single_average_delay(
detecting_boundaries[i],
prediction[i],
anomaly_window_destination=anomaly_window_destination,
clear_anomalies_mode=clear_anomalies_mode,
)
)
missing, detectHistory, FP, all_true_anom = (
missing + missing_,
detectHistory + detectHistory_,
FP + FP_,
all_true_anom + all_true_anom_,
)
add = np.mean(detectHistory)
if verbose:
print("Amount of true anomalies", all_true_anom)
print(f"A number of missed CPs = {missing}")
print(f"A number of FPs = {int(FP)}")
print("Average time", add)
return add, missing, int(FP), all_true_anom
elif (metric == "binary") or (metric == "confusion_matrix"):
if all(isinstance(my_el, pd.Series) for my_el in true):
TP, TN, FP, FN = 0, 0, 0, 0
for i in range(len(prediction)):
TP_, TN_, FP_, FN_ = confusion_matrix(true[i], prediction[i])
TP, TN, FP, FN = TP + TP_, TN + TN_, FP + FP_, FN + FN_
else:
print(
"For this metric it is better if you use pd.Series format for true \nwith common index of true and prediction"
)
TP, TN, FP, FN = 0, 0, 0, 0
for i in range(len(prediction)):
dict_cp_confusion = extract_cp_confusion_matrix(
detecting_boundaries[i], prediction[i], binary=True
)
TP += np.sum(
[
len(dict_cp_confusion["TPs"][window][1])
for window in dict_cp_confusion["TPs"]
]
)
FP += len(dict_cp_confusion["FPs"])
FN += len(dict_cp_confusion["FNs"])
TN += len(prediction[i]) - TP - FP - FN
if metric == "binary":
f1 = round(TP / (TP + (FN + FP) / 2), 2)
far = round(FP / (FP + TN) * 100, 2)
mar = round(FN / (FN + TP) * 100, 2)
if verbose:
print(f"False Alarm Rate {far} %")
print(f"Missing Alarm Rate {mar} %")
print(f"F1 metric {f1}")
return f1, far, mar
elif metric == "confusion_matrix":
if verbose:
print("TP", TP)
print("TN", TN)
print("FP", FP)
print("FN", FN)
return TP, TN, FP, FN
else:
raise Exception("Choose the performance metric")
================================================
FILE: core/t2.py
================================================
# Author: Iurii Katser
import os
from math import sqrt
import numpy as np
import scipy.stats as SS
from matplotlib import pyplot as plt
from numpy import linalg as LA
from pandas import DataFrame
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
class T2:
"""Calculation of the Hotelling's 1-dimensional T-squared
statistic or T-squared statistic+Q-statistic based on PCA for
anomaly detection in multivariate data.
Based on the following papers:
[1] - Q-statistic and T2-statistic PCA-based measures for damage
assessment in structures / LE Mujica, J. Rodellar, A. Ferna ́ndez,
A. Gu ̈emes // Structural Health Monitoring: An International
Journal. — 2010. — nov. — Vol. 10, no. 5. — Pp. 539–553.
[2] - Zhao Chunhui, Gao Furong. Online fault prognosis with
relative deviation analysis and vector autoregressive modeling //
Chemical Engineering Science. — 2015. — dec. — Vol. 138. — Pp.
531–543.
[3] - Li Wei, Peng Minjun, Wang Qingzhong. False alarm reducing in
PCA method for sensor fault detection in a nuclear power plant //
Annals of Nuclear Energy. — 2018. — aug. — Vol. 118. — Pp. 131–139.
Parameters
----------
scaling : boolean, default = False
If True StandartScaler is used in the pipeline.
If False no scaling procedures are used.
using_pca : boolean, default = True
If True T2+Q based on PCA is used as anomaly detection method.
If False T2 without PCA is used as anomaly detection method.
explained_variance : object, default = 0.85
Proportion of the explained variance for principal components
selection. Relevant only if using_pca=True.
p_value : object, default = 0.999
P value for upper control limits selection. Shows the proportion
of the number of points in train set perceived as normal.
Examples
--------
T2+Q based on PCA:
from ControlCharts import T2
import pandas as pd
import numpy as np
df = pd.DataFrame(np.random.randn(100, 4), columns=list('ABCD'))
t2 = T2()
t2.fit(df.iloc[:20])
t2.predict(df)
T2 without PCA:
from ControlCharts import T2
import pandas as pd
import numpy as np
df = pd.DataFrame(np.random.randn(100, 4), columns=list('ABCD'))
t2 = T2(using_pca=False)
t2.fit(df.iloc[:20])
t2.predict(df)
More examples at:
https://github.com/YKatser/control-charts/tree/main/examples
"""
def __init__(
self,
scaling=False,
using_pca=True,
explained_variance=0.85,
p_value=0.999,
):
self.scaling = scaling
self.using_pca = using_pca
self.explained_variance = explained_variance
self.p_value = p_value
# T2 and Q statistics calculations
def _t2_calculation(self, x):
t2 = []
for i in range(len(x)):
t2.append(x[i] @ self.inv_cov @ x[i].T)
return t2
def _q_calculation(self, x):
q = []
for i in range(len(x)):
q.append(x[i] @ self.transform_rc @ x[i].T)
return q
# CALCULATING UPPER CONTROL LIMITS
def _t2_ucl(self, x):
if self.using_pca:
m = self.n_components
else:
m = x.shape[1]
n = len(x)
linspace = np.linspace(0, 15, 10000)
c_alpha = linspace[SS.f.cdf(linspace, m, n - m) < self.p_value][-1]
# koef = m * (n-1) / (n-m)
koef = m * (n - 1) * (n + 1) / (n * (n - m))
self.t2_ucl = koef * c_alpha
def _q_ucl(self, x):
w, v = LA.eig(np.cov(x.T))
sum_ = 0
for i in range(self.n_components, len(w)):
sum_ += w[i]
tetta = []
for i in [1, 2, 3]:
tetta.append(sum_**i)
h0 = 1 - 2 * tetta[0] * tetta[2] / (3 * tetta[1] ** 2)
linspace = np.linspace(0, 15, 10000)
c_alpha = linspace[SS.norm.cdf(linspace) < self.p_value][-1]
self.q_ucl = tetta[0] * (
1
+ (c_alpha * h0 * sqrt(2 * tetta[1]) / tetta[0])
+ tetta[1] * h0 * (h0 - 1) / tetta[0] ** 2
) ** (1 / h0)
# applying pca
def _pca_applying(self, x):
self.pca = PCA(n_components=self.explained_variance).fit(x)
self.n_components = self.pca.n_components_
self._EV = self.pca.components_.T
return self.pca.transform(x)
# PLOTTING AND SAVING RESULTS
def plot_t2(self, t2=None, t2_ucl=None, save_fig=False, fig_name="T2"):
"""Plotting results of T2-statistic calculation with matplotlib
Parameters
----------
t2 : pandas.DataFrame(), default = None
Results of T2-statistic calculation.
t2_ucl : float or int, default = None
Upper control limit for T2.
save_fig : boolean, default = False
If True there will be saved T2 chart as .png to the
current folder.
fig_name : str, default = 'T2'
Name of the saved figure.
Returns
-------
self : object.
"""
if t2 is None:
t2 = self.t2
if t2_ucl is None:
t2_ucl = self.t2_ucl
plt.figure(figsize=(12, 4))
plt.plot(t2, label="$T^2$-statistic")
# for i in self.final_list:
# plt.axvspan(i[0], i[1], facecolor='green', alpha=0.2, zorder=0,
# label='Train set')
plt.grid(True)
plt.axhline(t2_ucl, zorder=10, color="r", label="UCL")
plt.ylim(0, 3 * max(t2.min().values, t2_ucl))
plt.xlim(t2.index.values[0], t2.index.values[-1])
plt.title("$T^2$-statistic chart")
plt.xlabel("Time")
plt.ylabel("$T^2$-statistic value")
plt.legend(["$T^2$-statistic", "UCL", "Train set"])
plt.tight_layout()
if save_fig:
self._save(name=fig_name)
def plot_q(self, q=None, q_ucl=None, save_fig=False, fig_name="Q"):
"""Plotting results of Q-statistic calculation with matplotlib
Parameters
----------
q : pandas.DataFrame(), default = None
Results of Q-statistic calculation.
q_ucl : float or int, default = None
Upper control limit for Q.
save_fig : boolean, default = False
If True there will be saved Q chart as .png to the
current folder.
fig_name : str, default = 'Q'
Name of the saved figure.
Returns
-------
self : object.
"""
if q is None:
q = self.q
if q_ucl is None:
q_ucl = self.q_ucl
plt.figure(figsize=(12, 4))
plt.plot(q, label="$Q$-statistic")
# for i in self.final_list:
# plt.axvspan(i[0], i[1], facecolor='green', alpha=0.2, zorder=0,
# label='Train set')
plt.grid(True)
plt.axhline(q_ucl, zorder=10, color="r", label="UCL")
plt.ylim(0, 3 * max(q.min().values, q_ucl))
plt.xlim(q.index.values[0], q.index.values[-1])
plt.title("$Q$-statistic chart")
plt.xlabel("Time")
plt.ylabel("$Q$-statistic value")
plt.legend(["$Q$-statistic", "UCL", "Train set"])
plt.tight_layout()
if save_fig:
self._save(name=fig_name)
@staticmethod
def _save(name="", fmt="png"):
pwd = os.getcwd()
iPath = pwd + "/pictures/"
if not os.path.exists(iPath):
os.mkdir(iPath)
os.chdir(iPath)
plt.savefig(f"{name}.{fmt}", fmt="png", dpi=150, bbox_inches="tight")
os.chdir(pwd)
def fit(self, x):
"""Computation of the inversed covariance matrix, matrix of
transformation to the residual space (in case of
using_pca=True) and standart scaler fitting (in case of using
scaling=True).
Parameters
----------
x : pandas.DataFrame()
Training set.
Returns
-------
self : object.
"""
x = x.copy()
# removing constant columns
initial_cols_number = len(x.columns)
x = x.loc[:, (x != x.iloc[0]).any()]
self._feature_names_in = x.columns
if initial_cols_number > len(x.columns):
print("Constant columns removed")
if self.scaling:
# fitting PCA and calculation of scaler, EV
self.scaler = StandardScaler()
self.scaler.fit(x)
x_ = self.scaler.transform(x)
else:
x_ = x.values
if self.using_pca:
x_pc = self._pca_applying(x_)
else:
self.n_components = x.shape[1]
if self.n_components == x.shape[1]:
# preparing inv_cov for T2
self.inv_cov = LA.inv(np.cov(x_.T))
# calculating T2_ucl
self._t2_ucl(x_)
if self.using_pca:
print("""Number of principal components is equal to dataset \
shape. Q-statistics is unavailable.""")
else:
# preparing inv_cov for T2 (principal space)
self.inv_cov = LA.inv(np.cov(x_pc.T))
# preparing transform matrix for Q (to residual space)
self.transform_rc = np.eye(len(self._EV)) - np.dot(
self._EV, self._EV.T
)
# calculating t2_ucl and q_ucl
self._t2_ucl(x_)
self._q_ucl(x_)
# calculating train indices
# indices = x.index.tolist()
# diff = x.index.to_series().diff()
# list_of_ind = diff[diff > diff.mean() + 3 * diff.std()].index.tolist()
def predict(
self,
x,
plot_fig=True,
save_fig=False,
fig_name=["T2", "Q"],
window_size=1,
):
"""Computation of T2-statistic or T2-statistic+Q-statistic for
the test dataset.
Parameters
----------
x : pandas.DataFrame()
Testing dataset.
plot_fig : boolean, default = True
If True there will be plotted T2-statistics or
T2-statistics+Q-statistics chart.
save_fig : boolean, default = False
If True there will be saved T2 and Q charts as .png to the
current folder.
fig_name : list of one or two str, default = ['T2','Q']
Names of the saved figures.
window_size : int, default = 1
Size of the window for median filter as a postprocessing.
Returns
-------
self : object
Plotting and saving T2 or T2+Q charts. To get DataFrames
with T2 or Q values call self.t2 or self.q.
"""
x = x.copy()
x = x.loc[:, self._feature_names_in]
if self.scaling:
x_ = self.scaler.transform(x)
else:
x_ = x.values
if self.n_components != x.shape[1]:
# calculating T2
self.t2 = (
DataFrame(
self._t2_calculation(self.pca.transform(x_)),
index=x.index,
columns=["T2"],
)
.rolling(window_size)
.median()
)
# calculating Q
self.q = (
DataFrame(
self._q_calculation(x_), index=x.index, columns=["Q"]
)
.rolling(window_size)
.median()
)
# plotting
if plot_fig:
self.plot_t2(
t2=self.t2,
t2_ucl=self.t2_ucl,
save_fig=save_fig,
fig_name=fig_name[0],
)
self.plot_q(
q=self.q,
q_ucl=self.q_ucl,
save_fig=save_fig,
fig_name=fig_name[1],
)
else:
# calculating T2
self.t2 = (
DataFrame(
self._t2_calculation(x_), index=x.index, columns=["T2"]
)
.rolling(window_size)
.median()
)
# plotting
if plot_fig:
self.plot_t2(self.t2)
if save_fig:
self._save(name=fig_name[0])
================================================
FILE: core/utils.py
================================================
import os
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from .metrics import chp_score
def load_skab():
path_to_data = "../data/"
# benchmark files checking
all_files = []
for root, dirs, files in os.walk(path_to_data):
for file in files:
if file.endswith(".csv"):
all_files.append(os.path.join(root, file))
# datasets with anomalies loading
list_of_df = [
pd.read_csv(file, sep=";", index_col="datetime", parse_dates=True)
for file in all_files
if "anomaly-free" not in file
]
# anomaly-free df loading
anomaly_free_df = pd.read_csv(
[file for file in all_files if "anomaly-free" in file][0],
sep=";",
index_col="datetime",
parse_dates=True,
)
return list_of_df, anomaly_free_df
def preprocess_skab(list_of_df):
Xy_traintest_list: list[list] = []
for df in list_of_df:
Xy_traintest_list.append(
train_test_split(
df.drop(["anomaly", "changepoint"], axis=1),
df[["anomaly", "changepoint"]],
train_size=400,
shuffle=False,
random_state=0,
)
)
return Xy_traintest_list
def load_preprocess_skab():
list_of_df, _ = load_skab()
Xy_traintest_list = preprocess_skab(list_of_df)
return Xy_traintest_list
# Generated training sequences for use in the model.
def create_sequences(values, time_steps):
output = []
for i in range(len(values) - time_steps + 1):
output.append(values[i : (i + time_steps)])
return np.stack(output)
def plot_results(*true_pred_pairs: tuple[pd.Series, pd.Series]):
n = len(true_pred_pairs)
fig, axs = plt.subplots(n, 1, figsize=(12, 3 * n), sharex=True)
if not isinstance(axs, (list | np.ndarray)):
axs = [axs]
for ax, (true, pred) in zip(axs, true_pred_pairs):
ax.plot(true, label="True", marker="o", markersize=5)
ax.plot(pred, label="Predicted", marker="x", markersize=5)
ax.set_title(f"{true.name} detection")
ax.legend()
fig.show()
def print_results(
y_true,
y_pred,
score_kwargs: list[dict],
):
for kwargs in score_kwargs:
print(kwargs)
chp_score(y_true, y_pred, **kwargs)
print()
================================================
FILE: data/README.md
================================================
```
└── data # Data files and processing Jupyter Notebook
├── Load data.ipynb # Jupyter Notebook to load all data
├── anomaly-free
│ └── anomaly-free.csv # Data obtained from the experiments with normal mode
├── valve2 # Data obtained from the experiments with closing the valve at the outlet of the flow from the pump.
│ ├── 1.csv
│ ├── 2.csv
│ ├── 3.csv
│ └── 4.csv
├── valve1 # Data obtained from the experiments with closing the valve at the flow inlet to the pump.
│ ├── 1.csv
│ ├── 2.csv
│ ├── 3.csv
│ ├── 4.csv
│ ├── 5.csv
│ ├── 6.csv
│ ├── 7.csv
│ ├── 8.csv
│ ├── 9.csv
│ ├── 10.csv
│ ├── 11.csv
│ ├── 12.csv
│ ├── 12.csv
│ ├── 13.csv
│ ├── 14.csv
│ ├── 15.csv
│ └── 16.csv
└── other # Data obtained from the other experiments
├── 1.csv # Simulation of fluid leaks and fluid additions
├── 2.csv # Simulation of fluid leaks and fluid additions
├── 3.csv # Simulation of fluid leaks and fluid additions
├── 4.csv # Simulation of fluid leaks and fluid additions
├── 5.csv # Sharply behavior of rotor imbalance
├── 6.csv # Linear behavior of rotor imbalance
├── 7.csv # Step behavior of rotor imbalance
├── 8.csv # Dirac delta function behavior of rotor imbalance
├── 9.csv # Exponential behavior of rotor imbalance
├── 10.csv # The slow increase in the amount of water in the circuit
├── 11.csv # The sudden increase in the amount of water in the circuit
├── 12.csv # Draining water from the tank until cavitation
├── 13.csv # Two-phase flow supply to the pump inlet (cavitation)
└── 14.csv # Water supply of increased temperature
```
================================================
FILE: data/anomaly-free/anomaly-free.csv
================================================
datetime;Accelerometer1RMS;Accelerometer2RMS;Current;Pressure;Temperature;Thermocouple;Voltage;Volume Flow RateRMS
2020-02-08 13:30:47;0.202394;0.275154;2.16975;0.382638;90.6454;26.8508;238.852;122.664
2020-02-08 13:30:48;0.203153;0.277857;2.07999;-0.273216;90.7978;26.8639;227.943;122.338
2020-02-08 13:30:50;0.202054;0.27579;2.52577;0.382638;90.773;26.8603;223.486;121.338
2020-02-08 13:30:51;0.203595;0.278101;2.49742;0.054711;90.8424;26.8616;244.904;121.664
2020-02-08 13:30:52;0.201889;0.276363;2.29194;0.710565;90.6664;26.8603;239.196;122.0
2020-02-08 13:30:53;0.203646;0.277887;2.57094;0.054711;90.7608;26.8723;240.549;121.338
2020-02-08 13:30:54;0.201434;0.278046;3.10397;0.054711;90.7526;26.8573;251.862;121.664
2020-02-08 13:30:55;0.201625;0.276807;2.40694;0.054711;90.9229;26.8573;228.402;122.0
2020-02-08 13:30:56;0.202689;0.276321;2.56711;-0.601143;90.9333;26.8676;226.631;122.0
2020-02-08 13:30:57;0.200964;0.27653;2.4602;0.054711;90.7807;26.8673;218.205;122.0
2020-02-08 13:30:58;0.20078;0.275502;3.0298;0.054711;90.8002;26.8661;235.331;122.0
2020-02-08 13:30:59;0.199534;0.275357;2.65212;0.054711;90.6518;26.8704;233.248;121.338
2020-02-08 13:31:00;0.200691;0.276844;2.88061;0.054711;90.5834;26.8694;245.606;121.0
2020-02-08 13:31:01;0.200582;0.274749;2.91862;0.054711;90.6741;26.8677;223.261;121.664
2020-02-08 13:31:02;0.201456;0.278072;2.90396;0.054711;90.682;26.8682;206.892;122.0
2020-02-08 13:31:03;0.201179;0.274142;2.86733;0.054711;90.5654;26.8716;236.717;122.0
2020-02-08 13:31:04;0.201656;0.278369;3.05417;0.054711;91.241;26.8708;218.205;122.0
2020-02-08 13:31:05;0.201256;0.275102;1.44434;0.054711;90.6573;26.8708;220.715;122.0
2020-02-08 13:31:06;0.201859;0.277502;2.82781;0.054711;91.147;26.8708;234.287;122.0
2020-02-08 13:31:07;0.201533;0.27457;2.80555;0.382638;91.3925;26.8745;224.112;122.0
2020-02-08 13:31:09;0.202535;0.277921;2.65724;0.054711;90.6303;26.8746;228.314;122.0
2020-02-08 13:31:10;0.20218;0.274233;2.50867;0.054711;91.0215;26.8738;229.464;122.0
2020-02-08 13:31:11;0.202958;0.278955;1.7947;-0.273216;91.0884;26.8722;226.338;121.338
2020-02-08 13:31:12;0.202142;0.273675;2.11039;0.054711;91.3434;26.8774;229.44;122.33
2020-02-08 13:31:13;0.202968;0.278913;2.53479;0.382638;91.1781;26.8773;221.335;121.677
2020-02-08 13:31:14;0.203006;0.278176;1.78388;0.054711;91.3868;26.8755;220.416;122.0
2020-02-08 13:31:15;0.20165;0.274977;1.93663;0.054711;91.4091;26.8755;233.562;122.0
2020-02-08 13:31:16;0.203455;0.27775;2.12854;0.054711;91.2651;26.8796;249.643;122.0
2020-02-08 13:31:17;0.201956;0.276255;2.49631;0.054711;91.3436;26.8721;236.765;121.338
2020-02-08 13:31:18;0.203732;0.276862;1.77498;0.382638;91.3471;26.8698;230.408;121.664
2020-02-08 13:31:19;0.202208;0.276628;2.18757;0.054711;91.4359;26.8696;235.981;122.0
2020-02-08 13:31:20;0.203388;0.276921;2.59247;0.054711;91.5322;26.8738;226.787;122.0
2020-02-08 13:31:21;0.201756;0.276941;2.1304;0.382638;91.4333;26.8799;228.136;122.664
2020-02-08 13:31:22;0.203337;0.275863;1.10258;0.710565;91.3338;26.8774;207.957;122.338
2020-02-08 13:31:23;0.202889;0.279188;2.5835;0.054711;91.4644;26.8805;220.186;122.0
2020-02-08 13:31:24;0.202892;0.276247;2.59213;0.054711;91.4116;26.8805;247.061;122.664
2020-02-08 13:31:25;0.202663;0.278133;2.34228;0.054711;91.5159;26.8789;221.83;122.338
2020-02-08 13:31:26;0.202927;0.276576;2.82599;0.054711;91.5381;26.8714;247.629;122.0
2020-02-08 13:31:27;0.202803;0.277764;2.63721;0.054711;91.5433;26.8805;227.858;122.0
2020-02-08 13:31:29;0.202641;0.277407;2.89982;0.054711;91.4687;26.8863;231.031;122.0
2020-02-08 13:31:30;0.202956;0.276692;2.53872;0.054711;91.4909;26.8931;220.812;122.0
2020-02-08 13:31:31;0.202348;0.277728;2.73273;0.382638;91.5249;26.8815;228.067;122.664
2020-02-08 13:31:32;0.203967;0.276637;1.16224;0.382638;91.5556;26.8815;216.861;122.337
2020-02-08 13:31:33;0.201349;0.277308;2.74667;0.382638;91.477;26.8871;233.377;121.337
2020-02-08 13:31:34;0.200571;0.278024;3.16155;0.054711;91.5395;26.8813;244.014;122.0
2020-02-08 13:31:35;0.204545;0.276255;2.94976;0.054711;91.1725;26.8864;238.787;121.337
2020-02-08 13:31:36;0.199853;0.277263;3.1974;-0.273216;91.0416;26.8858;231.295;121.0
2020-02-08 13:31:37;0.204443;0.276939;2.75143;0.054711;91.7249;26.8928;228.721;121.664
2020-02-08 13:31:38;0.199748;0.276356;2.795;0.382638;91.461;26.8852;224.052;122.0
2020-02-08 13:31:39;0.204396;0.277859;2.65971;0.054711;91.4668;26.8995;227.27;121.337
2020-02-08 13:31:40;0.200139;0.276344;2.8309;0.054711;91.6582;26.8916;215.82;121.664
2020-02-08 13:31:41;0.204098;0.278483;1.96856;0.054711;91.6027;26.8924;228.589;120.677
2020-02-08 13:31:42;0.200508;0.276701;1.87314;0.054711;90.9221;26.8924;233.631;121.331
2020-02-08 13:31:43;0.203735;0.278418;1.86916;0.054711;91.63;26.9016;233.071;121.337
2020-02-08 13:31:45;0.201375;0.27667;2.9345;0.382638;90.8612;26.8961;227.096;121.664
2020-02-08 13:31:46;0.203003;0.278076;2.71685;0.054711;90.9518;26.8968;229.92;121.337
2020-02-08 13:31:47;0.202282;0.276403;2.32621;0.382638;91.0317;26.8998;229.632;121.0
2020-02-08 13:31:48;0.202934;0.278753;2.35647;0.054711;91.4841;26.8989;234.154;121.664
2020-02-08 13:31:49;0.203112;0.279921;2.54302;-0.273216;91.2924;26.8983;237.438;121.0
2020-02-08 13:31:50;0.20362;0.275284;1.17905;-0.273216;90.973;26.8965;212.71;121.664
2020-02-08 13:31:51;0.20319;0.279851;2.12139;0.054711;90.9835;26.8941;231.748;121.337
2020-02-08 13:31:52;0.203808;0.275474;2.36979;0.054711;90.8981;26.8963;223.551;121.0
2020-02-08 13:31:53;0.203234;0.278726;1.90811;0.054711;90.9675;26.8963;229.721;121.664
2020-02-08 13:31:54;0.203846;0.27673;1.94538;0.382638;91.1058;26.8994;227.809;122.0
2020-02-08 13:31:55;0.204063;0.278713;2.17024;0.054711;90.9522;26.8975;236.404;121.337
2020-02-08 13:31:56;0.20354;0.277728;1.88012;0.382638;90.9248;26.9014;228.693;121.0
2020-02-08 13:31:57;0.203702;0.27873;1.91311;0.054711;90.9024;26.8967;228.367;121.664
2020-02-08 13:31:58;0.204211;0.278117;2.8069;-0.273216;90.7676;26.8967;233.06;121.337
2020-02-08 13:32:00;0.203301;0.2784;1.4851;0.054711;91.0784;26.8963;217.373;121.664
2020-02-08 13:32:01;0.204402;0.278045;1.86499;0.054711;90.8502;26.8919;231.72;121.337
2020-02-08 13:32:02;0.203152;0.277707;1.73478;0.054711;91.0369;26.8934;229.611;121.664
2020-02-08 13:32:03;0.204291;0.277063;1.33767;0.382638;91.0965;26.8991;216.347;122.0
2020-02-08 13:32:04;0.204424;0.276919;2.64369;0.382638;90.9954;26.8946;227.199;121.337
2020-02-08 13:32:05;0.202478;0.278476;2.07008;0.054711;90.9443;26.8946;229.411;121.664
2020-02-08 13:32:06;0.203725;0.27606;1.62458;0.054711;90.9069;26.9006;217.402;122.0
2020-02-08 13:32:07;0.202044;0.277724;1.87632;0.382638;90.9202;26.9047;219.911;122.0
2020-02-08 13:32:08;0.20321;0.277652;1.99206;0.710565;90.916;26.904;228.684;121.337
2020-02-08 13:32:09;0.202153;0.276054;1.85799;0.054711;90.9754;26.895;240.172;121.0
2020-02-08 13:32:10;0.202588;0.277846;2.21462;0.054711;90.7667;26.9007;239.669;121.664
2020-02-08 13:32:11;0.202353;0.276322;1.97256;0.054711;91.0284;26.91;227.234;121.337
2020-02-08 13:32:12;0.202051;0.278101;2.08963;0.054711;90.8792;26.9014;231.617;121.0
2020-02-08 13:32:13;0.203094;0.276276;2.39032;0.054711;91.0317;26.9014;240.337;121.664
2020-02-08 13:32:15;0.202811;0.278587;2.3898;0.054711;90.7115;26.9014;215.654;122.0
2020-02-08 13:32:16;0.202916;0.276655;2.4305;0.054711;90.6442;26.9005;237.831;121.337
2020-02-08 13:32:17;0.20286;0.278295;2.49241;0.054711;90.849;26.9031;232.057;121.664
2020-02-08 13:32:18;0.203068;0.276377;2.5644;0.054711;90.7042;26.8983;234.251;122.0
2020-02-08 13:32:19;0.203171;0.276512;2.92341;0.054711;90.6392;26.9145;225.182;121.337
2020-02-08 13:32:20;0.203772;0.276416;2.86705;0.054711;90.7799;26.9075;221.042;121.0
2020-02-08 13:32:21;0.20336;0.278105;3.12412;0.054711;90.9032;26.9053;246.417;121.664
2020-02-08 13:32:22;0.203826;0.277362;2.85834;0.054711;91.2132;26.9074;203.03;122.0
2020-02-08 13:32:23;0.203979;0.277666;2.93701;0.382638;90.8696;26.9046;230.016;121.337
2020-02-08 13:32:24;0.202792;0.277856;2.23631;0.054711;91.2039;26.9048;234.756;121.664
2020-02-08 13:32:25;0.204168;0.277909;2.72595;0.054711;90.8385;26.9048;228.556;121.337
2020-02-08 13:32:26;0.201595;0.277465;2.68889;0.054711;90.9612;26.9074;220.586;121.664
2020-02-08 13:32:27;0.204007;0.277062;2.86649;0.054711;91.1996;26.9024;236.988;121.337
2020-02-08 13:32:28;0.200801;0.2763;2.46936;-0.273216;90.9077;26.9071;218.249;120.337
2020-02-08 13:32:29;0.203107;0.275955;2.07838;0.054711;91.51;26.9142;224.596;121.331
2020-02-08 13:32:30;0.201619;0.277278;2.92597;0.054711;90.889;26.9124;231.115;121.337
2020-02-08 13:32:31;0.202849;0.276444;2.99375;0.382638;91.4119;26.9048;229.115;121.664
2020-02-08 13:32:32;0.202353;0.277043;2.3909;-0.601143;91.235;26.918;217.926;121.337
2020-02-08 13:32:34;0.201693;0.275748;2.47058;0.054711;91.0214;26.9081;202.837;121.0
2020-02-08 13:32:35;0.202764;0.276798;2.55831;0.054711;91.0664;26.9081;242.95;121.664
2020-02-08 13:32:36;0.201253;0.275378;2.75913;0.054711;90.933;26.9068;228.949;121.337
2020-02-08 13:32:37;0.203189;0.277535;2.77939;0.054711;91.2998;26.9158;231.476;121.0
2020-02-08 13:32:38;0.201027;0.274771;2.0381;0.054711;91.2532;26.9178;218.377;121.0
2020-02-08 13:32:39;0.201977;0.275242;2.70161;0.054711;91.3651;26.9136;232.799;121.664
2020-02-08 13:32:40;0.202986;0.27668;2.15896;0.054711;91.3932;26.8976;239.288;121.337
2020-02-08 13:32:41;0.202767;0.276654;1.73863;0.054711;91.2958;26.9129;220.224;121.664
2020-02-08 13:32:42;0.20329;0.276987;2.70441;0.382638;91.235;26.9134;241.115;122.0
2020-02-08 13:32:43;0.203113;0.274985;1.59595;0.382638;90.9557;26.9134;211.16;122.0
2020-02-08 13:32:44;0.203699;0.278468;2.05692;0.054711;91.223;26.9002;250.147;122.0
2020-02-08 13:32:45;0.203469;0.275114;1.47197;0.382638;91.1348;26.9135;205.508;121.337
2020-02-08 13:32:46;0.204086;0.277362;1.82531;0.054711;91.4152;26.9196;225.896;121.664
2020-02-08 13:32:47;0.202768;0.276771;2.30097;0.382638;91.417;26.9052;220.772;121.337
2020-02-08 13:32:48;0.203637;0.276762;1.9125;-0.273216;91.3152;26.9108;215.896;121.0
2020-02-08 13:32:50;0.202528;0.277444;1.82034;0.054711;91.3158;26.9038;229.138;121.664
2020-02-08 13:32:51;0.203804;0.276834;1.59955;-0.601143;91.3117;26.9172;214.144;121.337
2020-02-08 13:32:52;0.202196;0.277231;1.94797;0.054711;91.4821;26.9143;230.532;121.664
2020-02-08 13:32:53;0.203277;0.27671;1.94793;0.382638;91.1985;26.9109;225.553;122.0
2020-02-08 13:32:54;0.202651;0.27632;3.0301;-0.273216;91.236;26.9201;239.733;121.664
2020-02-08 13:32:55;0.202462;0.276181;2.24507;-0.273216;91.5756;26.9201;224.908;122.0
2020-02-08 13:32:56;0.202572;0.276993;2.74998;0.382638;91.495;26.9187;230.613;121.337
2020-02-08 13:32:57;0.203223;0.277245;0.975812;0.054711;91.2401;26.923;211.851;121.664
2020-02-08 13:32:58;0.20185;0.27589;3.03718;0.710565;91.4555;26.9209;251.759;121.337
2020-02-08 13:32:59;0.203796;0.276685;2.61361;0.382638;91.3885;26.9132;227.389;121.664
2020-02-08 13:33:00;0.20162;0.275948;2.34423;0.054711;91.5052;26.9129;229.01;121.337
2020-02-08 13:33:01;0.204699;0.276481;2.78643;0.054711;91.4046;26.9233;251.906;121.664
2020-02-08 13:33:02;0.200687;0.276803;2.4931;0.054711;91.5538;26.9246;227.731;121.337
2020-02-08 13:33:03;0.204852;0.277114;2.70083;0.382638;91.3783;26.9113;212.41;121.664
2020-02-08 13:33:05;0.201054;0.275377;2.53768;0.054711;91.3008;26.9191;228.164;122.0
2020-02-08 13:33:06;0.20433;0.277359;2.70616;0.382638;91.4629;26.9191;235.402;122.0
2020-02-08 13:33:07;0.201603;0.275831;1.02491;0.382638;91.4129;26.9191;213.16;122.0
2020-02-08 13:33:08;0.203785;0.277813;2.70855;0.382638;90.9494;26.9053;218.326;122.0
2020-02-08 13:33:09;0.202575;0.275532;2.02131;0.054711;90.9277;26.9183;227.704;122.0
2020-02-08 13:33:10;0.203373;0.274949;2.72938;0.054711;91.4436;26.9244;228.804;122.0
2020-02-08 13:33:11;0.204009;0.277793;3.14693;0.054711;91.3074;26.9217;248.606;121.337
2020-02-08 13:33:12;0.203666;0.276235;2.72675;0.054711;91.0905;26.9166;226.503;121.664
2020-02-08 13:33:13;0.204681;0.27766;2.57339;0.054711;91.4028;26.9142;223.513;122.0
2020-02-08 13:33:14;0.203003;0.276362;2.57636;0.382638;91.3484;26.9158;231.235;120.677
2020-02-08 13:33:15;0.204448;0.277701;2.74848;0.382638;91.3631;26.9226;229.531;120.664
2020-02-08 13:33:16;0.203337;0.277437;2.60732;0.382638;90.9595;26.9226;224.354;121.664
2020-02-08 13:33:17;0.204417;0.277876;2.41819;0.054711;91.2295;26.9202;213.19;121.337
2020-02-08 13:33:18;0.203533;0.27748;2.51937;0.054711;91.5354;26.9176;242.975;121.0
2020-02-08 13:33:19;0.203107;0.2769;1.68277;0.054711;91.112;26.9264;216.167;121.664
2020-02-08 13:33:20;0.204217;0.277738;2.42472;0.382638;90.7997;26.9181;219.105;121.337
2020-02-08 13:33:21;0.20155;0.276536;2.5966;0.054711;90.9195;26.9383;227.897;121.664
2020-02-08 13:33:23;0.204814;0.276737;2.47715;0.382638;90.7841;26.9216;206.982;121.337
2020-02-08 13:33:24;0.201517;0.275294;2.38098;0.382638;90.7968;26.9239;229.704;121.664
2020-02-08 13:33:25;0.204017;0.277301;2.88817;0.382638;90.8545;26.9239;245.266;122.0
2020-02-08 13:33:26;0.2026;0.275337;2.45524;0.054711;90.7343;26.9234;222.12;122.0
2020-02-08 13:33:27;0.20433;0.278463;1.34165;0.054711;90.825;26.9267;207.65;121.337
2020-02-08 13:33:28;0.204735;0.278139;2.48144;0.054711;90.9473;26.9181;231.407;122.0
2020-02-08 13:33:29;0.202977;0.277093;2.54047;0.382638;90.8785;26.9263;220.376;122.0
2020-02-08 13:33:30;0.20423;0.276626;2.76375;0.054711;90.7021;26.9359;233.333;121.337
2020-02-08 13:33:31;0.203281;0.278361;2.91244;-0.273216;90.8235;26.932;229.178;121.664
2020-02-08 13:33:32;0.203467;0.276499;3.09434;-0.273216;90.7756;26.932;240.744;122.0
2020-02-08 13:33:33;0.203784;0.278246;2.17882;0.054711;90.7825;26.9326;229.389;122.0
2020-02-08 13:33:34;0.202384;0.27612;1.23783;0.054711;90.7176;26.9219;216.347;122.0
2020-02-08 13:33:35;0.204118;0.277036;2.41699;0.382638;90.8297;26.9339;235.139;121.337
2020-02-08 13:33:36;0.200716;0.275843;2.4387;0.054711;90.7148;26.9242;236.332;121.664
2020-02-08 13:33:37;0.204146;0.276359;2.77221;0.054711;90.8417;26.9391;233.567;122.664
2020-02-08 13:33:38;0.199797;0.275582;2.75048;0.054711;90.6822;26.9314;232.613;121.677
2020-02-08 13:33:39;0.202899;0.275383;2.7201;0.382638;90.9424;26.9269;229.316;121.0
2020-02-08 13:33:41;0.198511;0.274159;2.7082;0.382638;90.7954;26.9419;226.013;121.0
2020-02-08 13:33:42;0.200571;0.274026;2.69329;0.382638;90.7835;26.9419;243.64;121.0
2020-02-08 13:33:43;0.199045;0.274118;2.45263;0.054711;90.7251;26.938;220.62;120.337
2020-02-08 13:33:44;0.200977;0.275121;2.52017;0.054711;90.6549;26.9302;247.897;121.337
2020-02-08 13:33:45;0.199807;0.273874;2.77465;0.054711;90.7865;26.9392;232.29;120.337
2020-02-08 13:33:46;0.201309;0.27558;1.18893;0.054711;90.8713;26.9416;208.189;120.664
2020-02-08 13:33:47;0.200041;0.274928;2.9757;0.054711;90.6648;26.9357;224.7;121.0
2020-02-08 13:33:48;0.201613;0.276304;2.83633;0.054711;90.6467;26.9462;232.544;120.337
2020-02-08 13:33:49;0.200692;0.274522;2.83105;0.054711;90.7317;26.9382;213.536;121.331
2020-02-08 13:33:51;0.201588;0.276642;2.83374;0.054711;90.535;26.9426;230.883;121.337
2020-02-08 13:33:52;0.201954;0.277098;1.62647;0.054711;90.4192;26.9307;206.534;121.0
2020-02-08 13:33:53;0.201415;0.274077;2.68805;0.382638;90.7752;26.9322;237.494;121.664
2020-02-08 13:33:54;0.202192;0.277539;1.88575;0.382638;90.6629;26.9322;228.521;121.337
2020-02-08 13:33:55;0.201814;0.274659;2.73347;0.054711;91.0272;26.9443;234.087;121.0
2020-02-08 13:33:56;0.202547;0.27707;2.67449;0.054711;91.2636;26.9317;230.773;121.0
2020-02-08 13:33:57;0.201862;0.275988;2.77285;0.382638;90.5111;26.935;236.458;122.331
2020-02-08 13:33:58;0.203021;0.276823;2.47028;0.054711;91.0708;26.9453;240.164;121.677
2020-02-08 13:33:59;0.202458;0.277598;2.62643;0.054711;90.9589;26.9387;229.204;121.664
2020-02-08 13:34:00;0.20279;0.276393;2.75302;-0.273216;91.0808;26.9327;228.894;120.677
2020-02-08 13:34:01;0.202438;0.276377;2.59704;0.054711;91.2047;26.9483;211.482;120.664
2020-02-08 13:34:03;0.202849;0.277164;2.66102;-0.273216;90.7393;26.9441;229.059;121.664
2020-02-08 13:34:04;0.203254;0.276436;2.74603;-0.273216;90.8297;26.9441;221.02;120.677
2020-02-08 13:34:05;0.202509;0.277382;2.58532;-0.273216;91.1285;26.9447;232.872;120.664
2020-02-08 13:34:06;0.203375;0.276458;2.74018;-0.273216;90.5435;26.9422;226.103;121.664
2020-02-08 13:34:07;0.202375;0.277224;2.65584;0.054711;91.2073;26.9477;232.042;121.337
2020-02-08 13:34:08;0.202155;0.278106;1.14694;-0.273216;91.0811;26.9452;204.283;121.665
2020-02-08 13:34:09;0.204069;0.275766;2.58492;0.382638;90.9841;26.9458;234.379;121.337
2020-02-08 13:34:10;0.201901;0.278608;2.73339;0.054711;91.1814;26.9519;227.395;121.665
2020-02-08 13:34:11;0.203959;0.275759;2.76712;0.054711;90.8703;26.9579;230.532;122.665
2020-02-08 13:34:12;0.201409;0.278272;0.986383;0.054711;91.3138;26.9579;203.097;121.676
2020-02-08 13:34:13;0.203854;0.276499;2.5956;0.054711;91.2562;26.945;228.207;121.665
2020-02-08 13:34:14;0.202035;0.276685;2.41079;0.054711;91.1014;26.9416;223.12;120.676
2020-02-08 13:34:15;0.203155;0.277777;2.64452;0.054711;90.9895;26.9473;205.02;121.331
2020-02-08 13:34:16;0.201801;0.274275;2.78516;0.054711;91.0227;26.9467;231.178;121.337
2020-02-08 13:34:17;0.202239;0.277525;2.66061;0.382638;90.9675;26.948;226.601;121.0
2020-02-08 13:34:18;0.202526;0.274197;2.18032;-0.273216;91.1696;26.9492;228.238;121.665
2020-02-08 13:34:19;0.202525;0.277917;2.54384;0.710565;91.2072;26.9511;251.746;121.337
2020-02-08 13:34:20;0.202827;0.274607;2.47483;0.054711;91.0281;26.949;250.279;121.0
2020-02-08 13:34:22;0.202582;0.277948;2.2957;0.054711;90.9595;26.949;243.802;121.665
2020-02-08 13:34:23;0.203428;0.274814;2.09584;-0.273216;91.0278;26.9557;230.04;121.337
2020-02-08 13:34:24;0.202869;0.276594;1.22368;0.382638;91.1831;26.9609;213.853;121.665
2020-02-08 13:34:25;0.203464;0.278015;1.35354;0.382638;91.1032;26.9527;204.108;121.337
2020-02-08 13:34:26;0.202971;0.275172;2.63029;0.054711;91.1648;26.961;242.402;121.0
2020-02-08 13:34:27;0.203116;0.278624;2.66061;0.382638;90.9478;26.9566;228.258;122.331
2020-02-08 13:34:28;0.20355;0.276765;2.70275;0.054711;91.1971;26.9597;230.711;121.337
2020-02-08 13:34:29;0.203275;0.277679;1.86374;0.054711;91.2905;26.9574;229.903;121.0
2020-02-08 13:34:30;0.203581;0.276064;2.54958;0.054711;91.1255;26.9518;229.005;121.0
2020-02-08 13:34:31;0.202622;0.278388;2.68935;0.054711;91.2422;26.9518;228.894;121.0
2020-02-08 13:34:32;0.204158;0.275185;1.92331;0.054711;91.2579;26.9551;233.56;121.665
2020-02-08 13:34:33;0.202049;0.277531;1.83949;0.054711;91.1212;26.9617;205.303;121.337
2020-02-08 13:34:34;0.203569;0.275569;3.10917;0.054711;91.0987;26.963;251.949;121.665
2020-02-08 13:34:35;0.202685;0.275809;1.93394;0.054711;91.2415;26.9681;202.633;121.337
2020-02-08 13:34:36;0.201946;0.27582;2.64445;-0.273216;91.5047;26.9584;229.006;121.0
2020-02-08 13:34:37;0.203241;0.276305;2.53943;0.054711;91.2801;26.9717;240.476;121.665
2020-02-08 13:34:38;0.201573;0.27434;2.91235;0.054711;91.2416;26.9549;236.019;122.0
2020-02-08 13:34:39;0.203296;0.275601;2.80549;0.054711;91.1034;26.9549;225.387;122.0
2020-02-08 13:34:40;0.20295;0.274963;2.6262;0.054711;91.41;26.9577;238.35;121.337
2020-02-08 13:34:42;0.203213;0.276318;2.16377;-0.273216;91.3624;26.962;228.554;121.665
2020-02-08 13:34:43;0.203777;0.274798;2.23419;0.710565;91.3748;26.9616;227.654;121.337
2020-02-08 13:34:44;0.203861;0.276775;2.57599;-0.273216;91.3638;26.9633;234.055;121.665
2020-02-08 13:34:45;0.204149;0.276264;2.6566;-0.273216;91.3615;26.9671;235.416;122.337
2020-02-08 13:34:46;0.203306;0.277616;2.21937;0.382638;91.1764;26.9606;228.192;121.337
2020-02-08 13:34:47;0.203685;0.27601;1.77899;0.382638;91.4331;26.968;215.601;121.665
2020-02-08 13:34:48;0.201551;0.278525;2.70353;0.382638;91.1876;26.968;251.143;121.337
2020-02-08 13:34:49;0.202313;0.276835;2.50437;0.054711;91.1846;26.9776;219.712;121.0
2020-02-08 13:34:50;0.201637;0.278495;2.65524;0.382638;91.3298;26.9694;231.596;121.0
2020-02-08 13:34:51;0.200879;0.277679;2.73227;0.382638;91.0574;26.9661;247.118;121.0
2020-02-08 13:34:52;0.201669;0.277434;2.45355;0.382638;91.063;26.9724;229.94;121.665
2020-02-08 13:34:53;0.200159;0.276807;2.49332;0.054711;91.3639;26.9672;228.564;122.0
2020-02-08 13:34:54;0.202237;0.278271;2.63814;0.054711;90.5807;26.9696;225.49;121.337
2020-02-08 13:34:55;0.201571;0.276594;2.32989;0.054711;91.3617;26.9758;229.084;120.337
2020-02-08 13:34:56;0.202077;0.277799;2.42559;0.054711;90.7587;26.9682;224.226;122.0
2020-02-08 13:34:58;0.202148;0.275031;1.32336;0.054711;90.649;26.9702;205.463;121.676
2020-02-08 13:34:59;0.202698;0.277583;2.65718;0.054711;91.3754;26.9811;236.178;121.665
2020-02-08 13:35:00;0.20165;0.277286;2.6073;0.382638;90.708;26.9721;234.486;121.337
2020-02-08 13:35:01;0.203165;0.277614;3.05365;0.382638;90.7064;26.9721;239.665;121.665
2020-02-08 13:35:02;0.202523;0.278088;2.73203;0.054711;90.7726;26.977;207.67;121.665
2020-02-08 13:35:03;0.201514;0.278186;2.43754;0.382638;90.7151;26.9708;218.596;122.0
2020-02-08 13:35:04;0.200609;0.277224;1.77087;0.054711;90.6573;26.9784;222.154;122.0
2020-02-08 13:35:05;0.202514;0.277473;2.29745;0.382638;91.021;26.9784;215.971;122.0
2020-02-08 13:35:06;0.200315;0.275593;1.83187;0.054711;90.9134;26.9744;228.932;121.337
2020-02-08 13:35:07;0.202089;0.278123;1.71051;0.382638;90.6323;26.9752;224.562;121.0
2020-02-08 13:35:08;0.20145;0.274232;1.88618;0.054711;90.5895;26.9749;221.889;121.665
2020-02-08 13:35:09;0.202644;0.27785;1.91152;0.054711;90.7203;26.9749;235.03;122.0
2020-02-08 13:35:10;0.202027;0.276101;2.76704;0.054711;90.6171;26.9862;229.357;121.337
2020-02-08 13:35:11;0.202848;0.276724;1.49746;0.054711;90.7404;26.9691;216.002;121.665
2020-02-08 13:35:13;0.201342;0.27795;1.86932;0.382638;90.7012;26.9736;230.791;122.0
2020-02-08 13:35:14;0.202241;0.276797;2.16649;0.382638;90.6739;26.979;250.729;122.0
2020-02-08 13:35:15;0.201596;0.278927;2.57836;0.710565;90.6128;26.9776;238.972;122.0
2020-02-08 13:35:16;0.20195;0.277028;1.21926;0.054711;90.7417;26.9828;206.662;122.665
2020-02-08 13:35:17;0.199708;0.276591;2.06152;0.382638;90.7064;26.9809;229.5;121.665
2020-02-08 13:35:18;0.202893;0.278021;2.10074;0.054711;90.773;26.9896;226.687;122.0
2020-02-08 13:35:19;0.200036;0.275982;3.13967;0.054711;90.6133;26.9896;248.143;122.665
2020-02-08 13:35:20;0.20263;0.278183;3.07187;0.382638;90.7584;26.9842;231.703;122.337
2020-02-08 13:35:21;0.201711;0.274833;1.04568;0.054711;90.664;26.983;205.276;122.0
2020-02-08 13:35:22;0.203178;0.278084;2.36753;-0.273216;90.6281;26.9841;214.759;122.0
2020-02-08 13:35:23;0.202033;0.276414;0.961102;0.382638;90.6148;26.985;224.861;122.665
2020-02-08 13:35:24;0.203123;0.27722;2.60708;0.054711;90.6961;26.9913;230.961;121.676
2020-02-08 13:35:25;0.201552;0.278706;2.7544;0.382638;90.4965;26.9909;243.478;121.665
2020-02-08 13:35:26;0.202503;0.277579;2.92836;0.382638;90.5724;26.9909;236.708;122.665
2020-02-08 13:35:27;0.202281;0.278853;0.967872;0.054711;90.758;26.9798;203.527;122.337
2020-02-08 13:35:29;0.20089;0.277749;3.22884;-0.273216;90.7601;26.989;239.181;122.0
2020-02-08 13:35:30;0.203053;0.276871;2.64773;0.054711;90.654;26.9901;224.495;123.331
2020-02-08 13:35:31;0.199159;0.276022;2.76408;0.382638;90.6438;27.0028;249.05;122.676
2020-02-08 13:35:32;0.203255;0.27812;2.70976;0.382638;90.7184;26.9982;223.515;122.0
2020-02-08 13:35:33;0.202668;0.279154;2.72531;-0.273216;90.6659;26.9987;247.08;122.0
2020-02-08 13:35:34;0.201486;0.273616;2.5832;0.054711;90.6485;26.9951;249.549;122.665
2020-02-08 13:35:35;0.203158;0.278257;2.79508;0.054711;90.4651;26.9939;226.139;121.676
2020-02-08 13:35:36;0.201462;0.277078;2.25365;-0.273216;90.4851;27.0076;226.644;121.665
2020-02-08 13:35:37;0.203008;0.278344;2.71956;-0.273216;90.6855;27.0076;226.088;122.0
2020-02-08 13:35:38;0.201646;0.278345;2.17699;0.382638;90.7029;27.0017;204.784;122.0
2020-02-08 13:35:39;0.202319;0.277479;2.06648;0.382638;90.5653;27.0006;220.686;122.0
2020-02-08 13:35:40;0.202452;0.277454;2.09151;0.054711;90.9364;26.9994;232.291;122.0
2020-02-08 13:35:41;0.200213;0.276714;2.10007;-0.273216;91.0127;27.0046;222.302;122.0
2020-02-08 13:35:42;0.203148;0.277335;2.48836;0.382638;90.5537;26.9971;227.197;122.665
2020-02-08 13:35:43;0.200234;0.276263;1.91287;-0.273216;90.995;27.0042;237.478;122.337
2020-02-08 13:35:44;0.202182;0.277877;2.59904;0.382638;90.6534;27.0046;229.389;122.0
2020-02-08 13:35:46;0.201258;0.274705;2.46085;0.382638;90.4671;27.0046;224.921;122.0
2020-02-08 13:35:47;0.202767;0.279035;2.68806;0.054711;90.4694;27.0053;228.692;122.0
2020-02-08 13:35:48;0.202931;0.277124;2.90579;0.054711;90.5033;27.0017;232.123;122.331
2020-02-08 13:35:49;0.201289;0.277257;2.41349;0.382638;91.0629;27.0095;224.488;121.676
2020-02-08 13:35:50;0.202156;0.276722;2.51612;0.054711;90.9831;27.0104;231.068;121.665
2020-02-08 13:35:51;0.201375;0.277576;2.72207;0.054711;90.8585;27.0011;228.27;122.0
2020-02-08 13:35:52;0.201955;0.277152;2.72891;-0.273216;91.0215;27.0147;239.606;122.0
2020-02-08 13:35:53;0.202356;0.277019;2.78519;0.054711;90.9836;27.0036;224.644;122.665
2020-02-08 13:35:54;0.200719;0.276803;0.905453;0.054711;91.0322;27.0036;215.423;122.337
2020-02-08 13:35:55;0.203281;0.276931;2.55378;-0.273216;91.1285;27.0016;237.227;121.337
2020-02-08 13:35:56;0.199142;0.276308;2.81828;0.054711;90.8445;27.0055;234.256;122.331
2020-02-08 13:35:57;0.203488;0.277434;2.59655;0.054711;91.1065;27.0117;226.844;122.337
2020-02-08 13:35:59;0.200565;0.275327;2.59967;0.054711;91.1652;26.997;224.255;122.0
2020-02-08 13:36:00;0.202133;0.278345;2.61961;0.054711;91.0475;27.0173;229.078;122.665
2020-02-08 13:36:01;0.201827;0.274495;2.54495;-0.273216;91.1989;27.0073;226.609;122.337
2020-02-08 13:36:02;0.202027;0.279222;2.38806;0.054711;91.063;27.0114;222.114;122.665
2020-02-08 13:36:03;0.202812;0.277506;2.07171;0.054711;91.0265;26.9962;228.834;122.665
2020-02-08 13:36:04;0.202512;0.277939;2.66108;0.710565;91.1159;27.0174;230.106;123.0
2020-02-08 13:36:05;0.202354;0.277718;1.52559;0.710565;91.0444;27.0174;215.475;122.337
2020-02-08 13:36:06;0.20312;0.277323;3.07246;0.054711;91.1152;27.0037;247.068;121.337
2020-02-08 13:36:07;0.200698;0.278178;2.55793;-0.273216;91.0908;26.9953;226.744;121.665
2020-02-08 13:36:08;0.204063;0.276483;1.78852;0.054711;91.1711;27.0059;224.898;122.0
2020-02-08 13:36:09;0.199008;0.276504;3.05621;0.054711;91.2224;27.0087;251.572;122.0
2020-02-08 13:36:10;0.203269;0.277332;2.69664;0.710565;91.4404;27.005;229.07;122.0
2020-02-08 13:36:11;0.200623;0.274909;1.97383;0.054711;91.2978;27.0182;223.457;122.0
2020-02-08 13:36:12;0.201467;0.278096;2.55521;0.054711;91.1457;27.0052;233.284;122.665
2020-02-08 13:36:14;0.201431;0.274168;2.01735;0.382638;91.1379;26.9946;237.522;122.337
2020-02-08 13:36:15;0.201138;0.278163;1.96607;0.382638;90.9653;27.0123;232.464;122.665
2020-02-08 13:36:16;0.201716;0.273717;2.59886;0.382638;91.2397;27.0081;224.707;122.337
2020-02-08 13:36:17;0.202073;0.277137;2.05334;0.382638;91.1769;27.0081;229.776;122.0
2020-02-08 13:36:18;0.20221;0.277148;1.84556;-0.273216;91.4262;27.0036;214.006;121.676
2020-02-08 13:36:19;0.202327;0.276685;2.68911;0.054711;91.1557;27.0115;230.265;121.665
2020-02-08 13:36:20;0.201615;0.277523;2.62515;0.054711;90.929;27.0139;228.002;122.0
2020-02-08 13:36:21;0.203005;0.276789;1.77811;0.054711;90.7004;27.0059;202.118;122.665
2020-02-08 13:36:22;0.200909;0.277487;2.7065;0.054711;91.1296;27.0155;235.019;122.337
2020-02-08 13:36:23;0.203371;0.276167;2.47457;0.382638;91.2627;27.0111;209.127;122.0
2020-02-08 13:36:24;0.20025;0.275797;1.77588;-0.273216;90.7155;27.013;227.581;122.0
2020-02-08 13:36:25;0.202064;0.276902;2.38448;0.054711;90.7029;27.0074;225.496;122.0
2020-02-08 13:36:26;0.20095;0.273354;2.64027;0.054711;91.2834;27.0074;230.18;122.0
2020-02-08 13:36:27;0.201544;0.277146;2.39064;0.054711;90.9706;27.0071;230.636;122.0
2020-02-08 13:36:28;0.201936;0.274009;2.40691;0.054711;91.1958;27.0071;215.055;122.0
2020-02-08 13:36:29;0.202123;0.275723;1.77154;0.054711;91.0656;27.01;225.399;122.0
2020-02-08 13:36:30;0.201884;0.277235;2.45519;0.054711;90.5721;27.0252;240.136;121.337
2020-02-08 13:36:31;0.202791;0.276009;2.65916;0.382638;90.7406;27.0149;230.565;121.665
2020-02-08 13:36:33;0.202346;0.277135;2.68071;0.054711;90.6688;27.0182;226.793;122.665
2020-02-08 13:36:34;0.202676;0.277578;2.5323;0.054711;90.7465;27.0182;218.69;122.337
2020-02-08 13:36:35;0.202791;0.276409;2.58565;0.382638;90.6057;27.0104;227.845;122.0
2020-02-08 13:36:36;0.201468;0.278884;2.60169;-0.273216;90.3984;27.0087;226.676;122.0
2020-02-08 13:36:37;0.203025;0.276169;2.81803;-0.273216;90.8233;27.0185;242.936;122.0
2020-02-08 13:36:38;0.202191;0.276756;3.06207;0.054711;90.8698;27.0224;247.361;121.665
2020-02-08 13:36:39;0.201953;0.275565;2.69702;0.054711;90.4905;27.0201;227.91;122.0
2020-02-08 13:36:40;0.201468;0.276387;2.89443;0.054711;90.6794;27.0136;210.028;122.0
2020-02-08 13:36:41;0.202236;0.276922;2.03975;-0.273216;90.6057;27.0254;226.115;122.0
2020-02-08 13:36:42;0.202654;0.275215;0.993349;-0.273216;90.497;27.0254;207.925;122.0
2020-02-08 13:36:43;0.203103;0.278692;2.67897;0.054711;90.5473;27.0128;220.781;122.0
2020-02-08 13:36:44;0.20355;0.277149;1.89993;-0.273216;90.5241;27.0241;218.411;122.0
2020-02-08 13:36:45;0.202854;0.276175;2.25605;0.382638;90.5705;27.0231;250.183;122.0
2020-02-08 13:36:46;0.202157;0.278735;1.87427;0.382638;90.5771;27.0207;224.41;122.0
2020-02-08 13:36:47;0.202846;0.27551;2.1382;-0.273216;90.6003;27.0098;221.982;122.0
2020-02-08 13:36:48;0.201177;0.27838;2.65915;0.054711;90.6049;27.0233;223.668;122.665
2020-02-08 13:36:49;0.20283;0.27583;2.66312;0.054711;90.6148;27.0233;229.294;122.337
2020-02-08 13:36:50;0.201751;0.276329;1.90408;0.382638;90.6558;27.0247;224.993;122.0
2020-02-08 13:36:51;0.2006;0.275403;1.8504;0.054711;90.7646;27.0249;224.137;122.0
2020-02-08 13:36:52;0.202586;0.275919;2.35273;0.382638;90.4618;27.0253;218.635;122.0
2020-02-08 13:36:54;0.200461;0.274861;1.92477;0.710565;90.4921;27.0229;233.99;122.665
2020-02-08 13:36:55;0.202322;0.275594;1.53741;0.054711;90.4735;27.0145;221.601;121.676
2020-02-08 13:36:56;0.201838;0.275423;2.59316;0.054711;90.5199;27.0229;215.338;122.332
2020-02-08 13:36:57;0.202986;0.276744;2.69149;0.054711;90.4156;27.0247;228.637;122.337
2020-02-08 13:36:58;0.202508;0.274508;2.70766;0.382638;90.5173;27.012;224.97;122.0
2020-02-08 13:36:59;0.201712;0.276336;1.59926;0.054711;90.4987;27.0259;206.661;122.665
2020-02-08 13:37:00;0.203027;0.27567;1.96555;0.054711;90.5901;27.0259;227.475;122.337
2020-02-08 13:37:01;0.201688;0.277775;1.87228;0.054711;90.5808;27.0332;233.512;122.0
2020-02-08 13:37:02;0.202833;0.276428;2.52727;0.054711;90.5274;27.025;233.742;122.0
2020-02-08 13:37:03;0.201622;0.27748;3.13464;0.382638;90.4136;27.0159;249.996;122.0
2020-02-08 13:37:04;0.201518;0.276884;2.10984;0.054711;90.7077;27.0198;251.325;122.0
2020-02-08 13:37:05;0.201836;0.276333;2.76074;0.382638;90.6689;27.0218;235.219;122.665
2020-02-08 13:37:06;0.200276;0.275889;2.53783;0.054711;90.3682;27.0218;222.366;122.337
2020-02-08 13:37:07;0.202752;0.276354;1.48909;0.054711;90.6165;27.0187;226.921;122.665
2020-02-08 13:37:08;0.200057;0.274922;2.63364;0.710565;90.2362;27.0325;232.424;122.337
2020-02-08 13:37:09;0.202711;0.277118;2.6816;0.054711;90.3917;27.0257;229.934;122.0
2020-02-08 13:37:10;0.20085;0.274452;2.88725;0.054711;90.4782;27.0257;232.454;122.0
2020-02-08 13:37:11;0.203095;0.277174;1.53416;0.054711;90.4351;27.034;222.39;122.0
2020-02-08 13:37:13;0.201844;0.273879;1.93817;0.054711;90.5211;27.0364;222.951;122.665
2020-02-08 13:37:14;0.202991;0.276879;1.80614;0.054711;90.3939;27.0341;231.053;121.676
2020-02-08 13:37:15;0.201648;0.275268;2.67954;0.382638;90.4813;27.027;233.558;121.665
2020-02-08 13:37:16;0.202977;0.276535;2.68627;0.382638;90.3782;27.0348;229.017;123.332
2020-02-08 13:37:17;0.202353;0.275589;2.53196;0.710565;90.2076;27.0241;212.933;122.665
2020-02-08 13:37:18;0.201002;0.276713;3.09026;0.382638;90.963;27.0324;235.355;122.337
2020-02-08 13:37:19;0.202052;0.275201;2.44107;0.054711;90.433;27.0314;222.028;122.0
2020-02-08 13:37:20;0.2013;0.277543;2.70244;0.054711;90.8865;27.0314;230.449;122.0
2020-02-08 13:37:21;0.201596;0.274984;2.62122;0.054711;90.411;27.0281;202.056;122.0
2020-02-08 13:37:22;0.202158;0.277453;2.42606;-0.273216;91.0499;27.0271;222.505;122.0
2020-02-08 13:37:23;0.200399;0.275421;2.54759;0.382638;90.6501;27.034;222.813;122.665
2020-02-08 13:37:24;0.203455;0.27619;2.61802;0.054711;90.2069;27.0484;226.438;123.0
2020-02-08 13:37:25;0.198826;0.274907;2.58146;0.054711;91.0039;27.0366;225.258;123.0
2020-02-08 13:37:26;0.203302;0.276169;2.3241;0.710565;91.072;27.0434;227.229;122.337
2020-02-08 13:37:27;0.19991;0.274757;2.21608;0.054711;90.881;27.0472;230.571;122.0
2020-02-08 13:37:28;0.202434;0.276645;2.49173;-0.273216;90.9531;27.0352;203.372;122.0
2020-02-08 13:37:30;0.20097;0.273409;2.31964;0.054711;90.9319;27.0428;228.792;122.0
2020-02-08 13:37:31;0.202673;0.277559;2.33459;0.054711;90.94;27.0428;208.678;122.0
2020-02-08 13:37:32;0.202001;0.27373;2.39435;0.054711;90.9567;27.0474;230.068;122.0
2020-02-08 13:37:33;0.202768;0.27579;2.59942;0.382638;90.9468;27.0446;224.399;122.0
2020-02-08 13:37:34;0.202737;0.275665;2.77679;0.054711;90.8465;27.0534;234.898;122.665
2020-02-08 13:37:35;0.201784;0.276975;2.30777;0.382638;91.0344;27.0487;236.203;122.337
2020-02-08 13:37:36;0.20258;0.275679;2.43929;0.382638;90.8196;27.0486;240.024;122.0
2020-02-08 13:37:37;0.20219;0.276322;2.95274;0.054711;91.0195;27.0496;218.067;122.0
2020-02-08 13:37:38;0.201142;0.2751;2.46666;0.054711;90.9978;27.0493;248.931;122.0
2020-02-08 13:37:39;0.203129;0.277365;2.49941;0.054711;90.9721;27.0442;245.735;122.0
2020-02-08 13:37:40;0.199418;0.274822;2.42783;0.054711;90.9897;27.0442;227.542;122.665
2020-02-08 13:37:41;0.203471;0.277348;2.231;0.382638;90.8852;27.0511;235.23;122.337
2020-02-08 13:37:42;0.200056;0.273862;2.69801;0.382638;91.003;27.0565;229.727;122.0
2020-02-08 13:37:43;0.202538;0.278317;2.41927;0.710565;90.8658;27.0595;235.664;122.0
2020-02-08 13:37:45;0.201567;0.273687;2.24861;-0.273216;91.1023;27.0449;236.436;122.665
2020-02-08 13:37:46;0.202586;0.277645;2.87409;0.382638;90.9749;27.0465;242.387;122.337
2020-02-08 13:37:47;0.20215;0.274485;2.14499;0.710565;91.0493;27.0512;239.549;122.0
2020-02-08 13:37:48;0.202795;0.276821;1.16881;0.054711;91.0624;27.0471;206.906;122.337
2020-02-08 13:37:49;0.203055;0.275609;2.95621;0.054711;90.9209;27.056;237.554;122.665
2020-02-08 13:37:50;0.202411;0.277612;3.04679;0.054711;91.0089;27.056;247.109;122.337
2020-02-08 13:37:51;0.202552;0.275611;1.9796;-0.601143;91.0427;27.0493;229.049;122.0
2020-02-08 13:37:52;0.202676;0.277457;2.94662;0.382638;91.3671;27.0583;227.377;122.665
2020-02-08 13:37:53;0.200812;0.274836;2.04101;0.054711;90.9733;27.0563;228.806;122.337
2020-02-08 13:37:54;0.203772;0.276981;1.27616;0.054711;91.1451;27.0538;206.42;122.665
2020-02-08 13:37:55;0.19937;0.274145;1.8146;0.054711;91.0433;27.0591;215.861;123.0
2020-02-08 13:37:56;0.203218;0.277566;3.18701;0.054711;91.2754;27.0604;249.45;122.337
2020-02-08 13:37:58;0.200715;0.275036;1.94608;0.054711;91.2459;27.0579;228.748;123.332
2020-02-08 13:37:59;0.202001;0.274145;2.67567;0.382638;90.6107;27.0675;236.007;122.665
2020-02-08 13:38:00;0.202604;0.27687;2.84146;0.054711;90.9872;27.0663;203.873;123.0
2020-02-08 13:38:01;0.202486;0.276277;2.62072;0.382638;90.7505;27.0553;229.604;123.0
2020-02-08 13:38:02;0.202715;0.276615;1.78449;0.054711;90.9118;27.062;228.192;122.337
2020-02-08 13:38:04;0.202017;0.276393;2.89271;0.054711;90.5081;27.0579;246.339;122.665
2020-02-08 13:38:05;0.202423;0.27689;2.7194;0.054711;91.1479;27.0666;229.11;123.0
2020-02-08 13:38:06;0.202638;0.276341;2.57869;0.054711;91.1578;27.0666;228.817;123.0
2020-02-08 13:38:07;0.203579;0.275536;3.03403;0.054711;90.7745;27.0615;246.214;122.665
2020-02-08 13:38:08;0.199398;0.275644;2.63961;0.382638;90.6942;27.0733;232.866;123.0
2020-02-08 13:38:09;0.203449;0.275853;0.96454;0.054711;90.5328;27.0718;205.148;122.337
2020-02-08 13:38:10;0.20045;0.274283;2.81414;0.054711;90.5208;27.0658;210.669;122.665
2020-02-08 13:38:11;0.202233;0.277327;2.84113;0.054711;90.4685;27.0692;250.917;123.0
2020-02-08 13:38:12;0.202146;0.274062;0.991237;0.054711;90.8178;27.0662;211.799;122.337
2020-02-08 13:38:13;0.201598;0.277569;3.16284;0.382638;90.5379;27.0715;247.828;122.665
2020-02-08 13:38:14;0.202405;0.273178;2.88088;-0.273216;90.4236;27.0701;248.667;123.0
2020-02-08 13:38:15;0.202166;0.277024;2.54069;0.382638;90.4683;27.0729;232.077;123.0
2020-02-08 13:38:16;0.201961;0.274891;2.98405;0.382638;90.5498;27.069;251.444;122.337
2020-02-08 13:38:17;0.202543;0.276999;2.75457;0.382638;90.4448;27.0689;235.576;122.0
2020-02-08 13:38:19;0.201963;0.275672;2.7623;0.054711;90.4067;27.0689;226.502;122.0
2020-02-08 13:38:20;0.20188;0.276534;2.83534;0.382638;90.3937;27.0754;245.164;122.665
2020-02-08 13:38:21;0.202795;0.2763;2.6622;0.054711;90.5781;27.0681;234.025;123.0
2020-02-08 13:38:22;0.203728;0.276628;2.73306;-0.601143;90.6103;27.0697;243.103;122.665
2020-02-08 13:38:23;0.200273;0.276284;2.44448;0.382638;90.5844;27.0754;221.773;123.0
2020-02-08 13:38:24;0.203324;0.27549;2.76851;0.054711;90.4411;27.0772;247.046;123.0
2020-02-08 13:38:25;0.200606;0.275295;2.59386;0.054711;90.527;27.0741;233.266;123.0
2020-02-08 13:38:26;0.201902;0.275525;2.72132;0.054711;90.5104;27.0741;243.491;122.337
2020-02-08 13:38:27;0.201828;0.274875;0.946556;0.054711;90.4992;27.0774;207.315;122.665
2020-02-08 13:38:28;0.201363;0.275989;2.48358;0.382638;90.6388;27.0738;236.713;122.337
2020-02-08 13:38:29;0.20242;0.272486;2.69518;0.054711;90.5655;27.0736;230.397;122.665
2020-02-08 13:38:30;0.201909;0.276513;2.63951;0.382638;90.5053;27.0741;228.491;123.0
2020-02-08 13:38:31;0.202077;0.273318;2.63589;0.054711;90.579;27.0855;226.016;122.337
2020-02-08 13:38:32;0.202528;0.275744;2.55783;0.054711;90.5859;27.088;216.495;122.665
2020-02-08 13:38:33;0.202111;0.275106;2.83255;0.382638;90.5043;27.075;236.843;123.0
2020-02-08 13:38:34;0.202555;0.276108;2.3437;0.382638;90.4444;27.075;241.422;123.0
2020-02-08 13:38:35;0.202313;0.275367;2.27597;0.054711;90.6063;27.0789;218.7;122.337
2020-02-08 13:38:36;0.202437;0.277088;1.98981;0.382638;90.4298;27.0879;225.227;122.0
2020-02-08 13:38:38;0.202921;0.274632;3.11379;0.054711;90.3622;27.0875;234.634;123.332
2020-02-08 13:38:39;0.201562;0.278002;2.39491;0.710565;90.5237;27.0847;228.64;123.337
2020-02-08 13:38:40;0.202869;0.274263;2.91285;0.054711;90.5352;27.0905;235.789;123.0
2020-02-08 13:38:41;0.200426;0.275964;1.93564;0.382638;90.6196;27.0926;233.075;122.337
2020-02-08 13:38:42;0.201313;0.273617;1.56789;0.054711;90.4525;27.0848;208.761;123.0
2020-02-08 13:38:43;0.201768;0.276651;2.55746;0.054711;90.6044;27.0868;231.005;122.337
2020-02-08 13:38:44;0.202175;0.273467;2.06896;-0.273216;90.4875;27.0751;224.771;122.0
2020-02-08 13:38:45;0.20228;0.276378;2.80993;-0.273216;90.1525;27.0751;237.902;122.665
2020-02-08 13:38:46;0.202486;0.276312;1.88989;0.054711;90.4906;27.0861;228.336;123.0
2020-02-08 13:38:47;0.202745;0.273928;2.31642;0.054711;90.5171;27.0845;234.769;122.337
2020-02-08 13:38:48;0.202948;0.277312;2.64546;0.054711;90.5602;27.0964;222.654;122.0
2020-02-08 13:38:49;0.202699;0.27473;3.13008;0.054711;90.344;27.0824;241.821;122.665
2020-02-08 13:38:50;0.203168;0.276121;2.85871;0.054711;90.7444;27.0924;246.134;123.0
2020-02-08 13:38:51;0.20199;0.276606;2.76896;0.054711;90.2806;27.0877;252.073;122.337
2020-02-08 13:38:53;0.203577;0.275569;2.73528;0.382638;90.4986;27.0798;231.369;122.665
2020-02-08 13:38:54;0.200887;0.276205;2.46422;0.054711;90.9647;27.0823;225.97;123.0
2020-02-08 13:38:55;0.203141;0.275598;0.880291;0.054711;90.9216;27.0823;215.911;123.0
2020-02-08 13:38:56;0.201746;0.274989;2.42252;-0.273216;90.4621;27.0943;217.514;122.337
2020-02-08 13:38:57;0.201269;0.275422;0.983064;0.382638;90.7605;27.0943;216.28;122.665
2020-02-08 13:38:58;0.203072;0.27468;1.33892;0.382638;90.8327;27.0968;203.952;122.0
2020-02-08 13:38:59;0.202742;0.275642;2.65506;0.382638;90.934;27.0896;207.182;122.665
2020-02-08 13:39:00;0.202401;0.273812;2.77449;0.710565;90.8657;27.095;209.536;122.337
2020-02-08 13:39:01;0.202939;0.276638;2.62753;0.382638;90.9422;27.0929;227.056;122.665
2020-02-08 13:39:02;0.202762;0.274595;2.56456;0.054711;90.9381;27.0904;238.989;122.337
2020-02-08 13:39:03;0.203422;0.276426;2.78046;0.054711;90.5767;27.1041;225.621;122.665
2020-02-08 13:39:04;0.202045;0.276805;3.09703;0.054711;90.3512;27.0921;240.012;123.0
2020-02-08 13:39:05;0.203486;0.275046;3.0221;0.054711;90.9189;27.0921;238.566;123.0
2020-02-08 13:39:06;0.201914;0.277338;1.7326;0.710565;90.9925;27.0921;224.282;123.0
2020-02-08 13:39:07;0.20314;0.275213;2.72182;0.382638;90.9247;27.0925;231.434;122.337
2020-02-08 13:39:08;0.201995;0.276448;2.58488;0.054711;90.9437;27.0976;222.71;122.665
2020-02-08 13:39:09;0.20122;0.27485;2.61605;0.054711;90.2973;27.0985;223.622;122.337
2020-02-08 13:39:10;0.202038;0.274736;2.63633;0.382638;90.8864;27.0833;235.611;122.665
2020-02-08 13:39:12;0.200313;0.274564;2.62659;0.054711;90.8026;27.0951;205.173;122.337
2020-02-08 13:39:13;0.202478;0.275377;2.67372;0.054711;90.8139;27.0908;230.905;122.665
2020-02-08 13:39:14;0.199805;0.274844;3.01598;0.054711;90.9305;27.0908;240.469;123.0
2020-02-08 13:39:15;0.202739;0.276392;2.19095;0.054711;90.9901;27.0907;246.971;123.0
2020-02-08 13:39:16;0.202356;0.274703;1.9027;-0.273216;90.8505;27.0975;228.467;122.665
2020-02-08 13:39:17;0.200277;0.275468;1.34075;0.382638;90.8791;27.0978;206.191;122.337
2020-02-08 13:39:18;0.202172;0.27504;1.96142;0.382638;91.0049;27.0905;229.246;122.665
2020-02-08 13:39:19;0.200958;0.274307;1.72863;0.382638;90.9579;27.094;216.767;123.0
2020-02-08 13:39:20;0.202177;0.276168;2.76657;0.054711;90.9108;27.0976;235.636;122.337
2020-02-08 13:39:21;0.200927;0.272189;2.13752;0.054711;91.0481;27.0943;227.602;122.0
2020-02-08 13:39:22;0.202586;0.277514;3.04073;0.054711;90.9815;27.0908;245.271;122.665
2020-02-08 13:39:23;0.201598;0.2731;3.14481;0.054711;90.8551;27.0908;248.543;122.337
2020-02-08 13:39:24;0.202702;0.276558;2.83677;0.054711;90.9784;27.0982;235.131;122.0
2020-02-08 13:39:25;0.201711;0.274325;1.78177;0.710565;90.922;27.0981;216.662;122.0
2020-02-08 13:39:27;0.203309;0.275964;2.31951;0.054711;90.9446;27.0987;251.427;122.665
2020-02-08 13:39:28;0.201458;0.275636;2.8845;-0.273216;90.9622;27.0972;205.311;123.0
2020-02-08 13:39:29;0.203352;0.276134;1.90017;0.054711;90.9695;27.0958;224.719;123.0
2020-02-08 13:39:30;0.201519;0.27603;2.03852;0.054711;91.1518;27.101;247.453;123.0
2020-02-08 13:39:31;0.201699;0.2759;1.97623;0.054711;91.3049;27.1049;224.064;122.337
2020-02-08 13:39:32;0.201785;0.275429;3.00148;0.054711;91.0502;27.1049;217.16;122.665
2020-02-08 13:39:33;0.20307;0.275453;2.74608;0.382638;91.0489;27.1009;232.893;123.0
2020-02-08 13:39:34;0.200087;0.274754;2.65891;0.382638;90.9899;27.0963;221.224;123.0
2020-02-08 13:39:35;0.203307;0.275728;1.96711;0.054711;90.9874;27.0923;223.819;123.0
2020-02-08 13:39:36;0.200549;0.274682;3.14352;0.054711;91.0723;27.1002;250.371;123.0
2020-02-08 13:39:37;0.203068;0.27573;2.54733;0.054711;90.7127;27.0979;232.601;123.0
2020-02-08 13:39:38;0.201606;0.274294;3.1573;0.054711;90.8669;27.106;250.934;123.0
2020-02-08 13:39:39;0.203489;0.276897;2.99171;0.054711;91.2232;27.099;213.239;123.0
2020-02-08 13:39:40;0.202242;0.2743;2.99062;0.382638;90.9362;27.1031;234.615;123.0
2020-02-08 13:39:41;0.203727;0.276507;2.95613;-0.273216;90.9779;27.1084;216.721;123.0
2020-02-08 13:39:43;0.201908;0.274931;2.71496;-0.273216;91.1465;27.1084;212.274;123.0
2020-02-08 13:39:44;0.203921;0.277198;3.04715;0.054711;91.1603;27.1068;241.764;123.0
2020-02-08 13:39:45;0.202317;0.276081;3.07371;0.710565;91.192;27.1076;239.328;122.337
2020-02-08 13:39:46;0.203252;0.276846;2.62787;0.054711;90.3841;27.1118;229.363;122.665
2020-02-08 13:39:47;0.200978;0.27549;2.97847;0.054711;91.2872;27.1138;239.413;123.0
2020-02-08 13:39:48;0.203665;0.275257;2.87096;0.054711;91.1356;27.1193;238.144;123.665
2020-02-08 13:39:49;0.199794;0.274058;2.68212;0.054711;90.4282;27.111;225.796;122.675
2020-02-08 13:39:50;0.20346;0.276146;2.63203;0.382638;90.398;27.1053;228.657;123.332
2020-02-08 13:39:51;0.201169;0.273826;2.19752;0.382638;90.9943;27.1053;249.326;123.337
2020-02-08 13:39:52;0.20257;0.275972;2.75458;0.054711;90.387;27.1084;232.517;123.0
2020-02-08 13:39:53;0.201501;0.27193;2.35856;0.382638;91.2382;27.1125;213.779;122.337
2020-02-08 13:39:54;0.2031;0.277025;2.65609;0.054711;90.5574;27.1242;214.303;122.665
2020-02-08 13:39:55;0.201672;0.273574;2.77899;0.382638;90.3839;27.1226;217.429;123.0
2020-02-08 13:39:56;0.203418;0.27679;3.04179;-0.273216;90.4109;27.1196;227.488;123.665
2020-02-08 13:39:57;0.201667;0.275656;3.05059;0.054711;90.4185;27.1234;238.039;123.337
2020-02-08 13:39:59;0.203412;0.275863;2.62778;0.382638;90.3721;27.1189;230.156;123.665
2020-02-08 13:40:00;0.20253;0.276893;2.66863;0.382638;90.5402;27.1176;226.971;123.337
2020-02-08 13:40:01;0.20218;0.275141;2.37007;0.382638;90.4361;27.1309;234.645;123.0
2020-02-08 13:40:02;0.203196;0.276038;2.28154;0.382638;90.5148;27.1309;228.08;122.337
2020-02-08 13:40:03;0.204135;0.275148;2.49164;-0.273216;90.475;27.1215;218.13;123.0
2020-02-08 13:40:04;0.199751;0.273781;2.19108;0.710565;90.9562;27.1246;237.317;123.0
2020-02-08 13:40:05;0.203029;0.275762;2.12776;-0.273216;90.4919;27.1257;230.367;122.337
2020-02-08 13:40:06;0.201533;0.273567;3.0354;0.382638;90.6057;27.1184;241.423;122.665
2020-02-08 13:40:07;0.202944;0.276622;2.20606;0.054711;90.4979;27.1154;229.898;123.0
2020-02-08 13:40:08;0.203007;0.273554;2.43656;0.382638;90.5448;27.1248;215.853;122.337
2020-02-08 13:40:09;0.203257;0.275796;1.95617;0.054711;90.4696;27.1142;234.556;122.0
2020-02-08 13:40:10;0.202452;0.276188;1.71846;-0.273216;90.469;27.1119;214.979;122.0
2020-02-08 13:40:11;0.203137;0.276297;2.56562;0.382638;90.281;27.1261;223.592;122.0
2020-02-08 13:40:12;0.202433;0.276137;2.43119;0.382638;90.5378;27.1261;227.33;122.665
2020-02-08 13:40:13;0.202656;0.276314;1.90364;0.382638;90.3255;27.1236;228.819;122.337
2020-02-08 13:40:15;0.203355;0.275586;2.25163;0.054711;90.4087;27.1283;228.989;122.0
2020-02-08 13:40:16;0.200457;0.275926;2.51346;0.054711;90.5516;27.1231;215.501;122.0
2020-02-08 13:40:17;0.204148;0.273738;2.24107;0.382638;90.5155;27.1307;241.88;122.0
2020-02-08 13:40:18;0.19976;0.275141;2.25188;0.382638;90.4614;27.1219;229.005;122.0
2020-02-08 13:40:19;0.203542;0.274754;2.64902;0.054711;90.1751;27.1286;241.699;122.0
2020-02-08 13:40:20;0.203084;0.276931;2.38313;0.054711;90.5053;27.1232;219.693;121.337
2020-02-08 13:40:21;0.202952;0.272008;2.51799;0.054711;90.5474;27.1289;237.409;122.332
2020-02-08 13:40:22;0.203186;0.277081;2.93583;0.054711;90.5946;27.1289;213.135;121.675
2020-02-08 13:40:23;0.202409;0.274703;3.00668;0.054711;90.5675;27.1344;235.072;122.332
2020-02-08 13:40:24;0.202876;0.275956;2.12001;0.054711;90.5842;27.1243;222.178;123.0
2020-02-08 13:40:25;0.202564;0.275618;2.72585;0.054711;90.3188;27.1237;213.805;122.337
2020-02-08 13:40:26;0.201882;0.275263;1.92436;0.054711;90.5014;27.1358;229.16;122.0
2020-02-08 13:40:27;0.202876;0.274772;2.72626;0.382638;90.5533;27.131;235.636;122.0
2020-02-08 13:40:28;0.201115;0.2757;1.75323;0.054711;90.5299;27.1262;223.104;122.665
2020-02-08 13:40:29;0.203349;0.274245;2.80654;0.054711;90.6103;27.1262;250.466;123.0
2020-02-08 13:40:30;0.200157;0.275363;2.73539;0.054711;90.2552;27.1225;232.032;123.0
2020-02-08 13:40:31;0.203592;0.274729;2.71168;0.710565;90.8761;27.1287;226.503;122.337
2020-02-08 13:40:32;0.200596;0.275291;2.24085;0.382638;90.6862;27.1249;214.378;122.665
2020-02-08 13:40:34;0.203151;0.274941;2.64417;0.382638;90.5583;27.1298;226.856;122.337
2020-02-08 13:40:35;0.201706;0.273778;2.7;0.054711;90.4567;27.1294;233.016;122.665
2020-02-08 13:40:36;0.202398;0.276735;2.64861;0.054711;90.4516;27.1336;228.528;123.0
2020-02-08 13:40:37;0.202347;0.272765;3.03909;0.054711;90.9855;27.1336;241.313;123.0
2020-02-08 13:40:38;0.203029;0.277089;1.35877;0.054711;90.3794;27.1394;209.907;123.0
2020-02-08 13:40:39;0.202655;0.275546;1.17219;0.054711;90.767;27.1171;210.766;122.665
2020-02-08 13:40:40;0.202981;0.276457;1.13913;-0.273216;90.9213;27.134;204.222;123.0
2020-02-08 13:40:41;0.202374;0.274998;2.6515;-0.273216;90.8881;27.1414;225.835;122.337
2020-02-08 13:40:42;0.203569;0.27584;2.51888;0.054711;90.928;27.1361;231.525;122.665
2020-02-08 13:40:43;0.202032;0.275765;2.99603;0.054711;90.9237;27.1361;247.412;123.0
2020-02-08 13:40:44;0.203901;0.274852;2.77995;0.382638;90.9573;27.1368;228.283;123.0
2020-02-08 13:40:45;0.201784;0.276062;2.3289;0.054711;90.892;27.1323;224.939;123.0
2020-02-08 13:40:47;0.203691;0.274068;2.74849;0.054711;90.8696;27.1328;240.95;123.0
2020-02-08 13:40:48;0.201456;0.274923;2.54204;0.054711;90.777;27.1417;219.033;123.0
2020-02-08 13:40:49;0.202426;0.274989;1.216;0.382638;90.9322;27.1345;218.393;122.337
2020-02-08 13:40:50;0.202257;0.273433;2.112;0.054711;90.7602;27.1379;228.581;122.665
2020-02-08 13:40:51;0.202921;0.274125;1.97635;0.054711;90.9891;27.1379;231.051;123.665
2020-02-08 13:40:52;0.203307;0.276127;1.91154;0.382638;90.9053;27.136;224.392;123.337
2020-02-08 13:40:53;0.203188;0.275898;1.97626;0.054711;90.8553;27.1471;224.738;123.0
2020-02-08 13:40:54;0.203788;0.27533;1.82665;-0.273216;90.7719;27.141;229.554;122.337
2020-02-08 13:40:55;0.203588;0.276011;1.93605;0.054711;91.0308;27.1386;241.483;122.665
2020-02-08 13:40:56;0.203723;0.27719;2.70075;-0.273216;90.9614;27.1434;233.299;123.665
2020-02-08 13:40:57;0.203983;0.27519;2.11595;0.382638;90.9944;27.1511;227.746;123.337
2020-02-08 13:40:58;0.201883;0.276319;2.12068;-0.273216;90.9829;27.1376;215.301;123.665
2020-02-08 13:40:59;0.204183;0.275769;2.19344;0.054711;91.1468;27.1437;226.853;123.337
2020-02-08 13:41:00;0.201464;0.274709;2.96068;0.054711;91.1753;27.1406;248.765;123.0
2020-02-08 13:41:02;0.202351;0.276158;2.5715;0.054711;91.3137;27.1423;226.023;123.0
2020-02-08 13:41:03;0.203384;0.275145;2.75769;0.382638;91.1061;27.1443;235.534;124.332
2020-02-08 13:41:04;0.201685;0.274981;2.61754;0.382638;91.1204;27.1443;225.983;123.675
2020-02-08 13:41:05;0.20323;0.275953;2.80574;0.382638;91.1997;27.1443;216.385;123.0
2020-02-08 13:41:06;0.203356;0.277093;2.876;-0.273216;90.9547;27.1449;242.89;122.337
2020-02-08 13:41:07;0.203997;0.275549;1.24731;0.054711;91.0889;27.1449;211.988;122.665
2020-02-08 13:41:08;0.203471;0.275011;1.83481;0.054711;91.075;27.1394;204.839;123.0
2020-02-08 13:41:09;0.202675;0.277354;2.54591;-0.273216;90.9665;27.1502;238.943;123.0
2020-02-08 13:41:10;0.203323;0.274949;2.5986;0.382638;91.0616;27.1412;232.363;123.0
2020-02-08 13:41:11;0.201038;0.27574;1.95459;0.054711;91.1937;27.1364;230.463;122.337
2020-02-08 13:41:12;0.203274;0.274744;2.63049;-0.273216;91.2843;27.1457;239.49;122.665
2020-02-08 13:41:13;0.200474;0.274551;2.41867;0.054711;90.3779;27.1399;230.396;123.0
2020-02-08 13:41:14;0.202554;0.275565;2.61052;0.054711;91.0176;27.1347;226.229;123.0
2020-02-08 13:41:16;0.201178;0.275496;2.58904;0.054711;90.5556;27.1347;228.238;123.0
2020-02-08 13:41:17;0.20185;0.274593;2.60874;0.382638;90.2761;27.1431;232.803;122.337
2020-02-08 13:41:18;0.20217;0.275806;2.76779;0.382638;90.7037;27.1423;231.56;123.332
2020-02-08 13:41:19;0.200676;0.273372;3.08063;0.054711;90.6387;27.1469;230.206;123.337
2020-02-08 13:41:20;0.199784;0.271681;2.69349;0.054711;90.3989;27.1446;229.647;122.337
2020-02-08 13:41:21;0.199828;0.274462;2.7277;-0.601143;90.602;27.1396;235.034;122.0
2020-02-08 13:41:22;0.200733;0.272505;2.67746;0.054711;90.9767;27.1347;232.206;122.0
2020-02-08 13:41:23;0.199335;0.274388;2.52875;0.054711;91.1308;27.1485;241.763;122.665
2020-02-08 13:41:24;0.200536;0.272669;2.70149;0.054711;91.0118;27.1485;227.458;122.337
2020-02-08 13:41:25;0.202762;0.274084;2.65399;0.710565;90.4237;27.139;249.243;122.0
2020-02-08 13:41:26;0.204191;0.273;2.56508;-0.273216;90.4466;27.1513;245.469;122.665
2020-02-08 13:41:27;0.201147;0.273523;1.97578;0.054711;90.3355;27.1484;227.688;122.337
2020-02-08 13:41:28;0.20256;0.274528;2.22638;0.054711;90.5522;27.1374;238.278;122.665
2020-02-08 13:41:29;0.200964;0.272605;2.28286;0.382638;90.4138;27.1512;227.784;123.0
2020-02-08 13:41:31;0.202982;0.273626;1.89964;-0.273216;90.4125;27.1425;228.787;123.0
2020-02-08 13:41:32;0.201585;0.272698;2.72539;0.054711;90.6816;27.143;239.522;123.0
2020-02-08 13:41:33;0.203087;0.273726;1.29453;0.054711;90.4198;27.1448;205.9;122.337
2020-02-08 13:41:34;0.201629;0.273802;1.87591;0.054711;90.2583;27.1482;230.187;122.665
2020-02-08 13:41:35;0.202921;0.273075;2.37709;-0.273216;90.6385;27.1436;237.217;123.0
2020-02-08 13:41:36;0.203019;0.272472;2.69003;-0.273216;90.4576;27.1436;230.443;122.665
2020-02-08 13:41:37;0.202512;0.274403;0.957623;-0.601143;90.4859;27.1467;203.44;123.0
2020-02-08 13:41:38;0.203244;0.272792;2.67808;0.054711;90.5022;27.1466;234.353;122.337
2020-02-08 13:41:39;0.202608;0.27344;2.88633;0.382638;90.3242;27.146;234.358;122.665
2020-02-08 13:41:40;0.203443;0.273203;2.48726;0.054711;90.4496;27.1455;233.91;123.0
2020-02-08 13:41:41;0.202407;0.273602;1.19855;0.382638;90.3592;27.1411;214.936;123.0
2020-02-08 13:41:42;0.203587;0.273216;2.65337;0.054711;90.4707;27.1442;236.325;122.337
2020-02-08 13:41:43;0.202392;0.273649;1.3322;0.382638;90.3909;27.1434;214.13;122.665
2020-02-08 13:41:44;0.203765;0.273074;1.90103;0.710565;90.2936;27.146;213.926;123.0
2020-02-08 13:41:45;0.202214;0.273767;1.88612;0.710565;90.4426;27.146;229.977;123.0
2020-02-08 13:41:46;0.203727;0.273449;2.13919;0.054711;90.4686;27.1384;245.052;123.665
2020-02-08 13:41:47;0.202796;0.272944;1.99742;0.054711;90.3387;27.1586;223.308;122.675
2020-02-08 13:41:48;0.20314;0.273241;2.06741;0.054711;90.4719;27.1497;240.904;122.665
2020-02-08 13:41:50;0.204213;0.273748;1.84116;0.382638;90.3998;27.1509;223.815;123.665
2020-02-08 13:41:51;0.201739;0.272418;1.70826;0.382638;90.4752;27.1522;202.153;123.337
2020-02-08 13:41:52;0.205113;0.274188;2.06713;0.382638;90.2791;27.1467;236.656;123.0
2020-02-08 13:41:53;0.20117;0.272242;1.94595;0.054711;90.4836;27.1514;228.383;123.0
2020-02-08 13:41:54;0.20508;0.274887;2.90946;0.054711;90.227;27.1514;246.301;123.665
2020-02-08 13:41:55;0.2043;0.274941;2.05807;0.054711;90.3551;27.1482;222.457;123.337
2020-02-08 13:41:56;0.203425;0.272582;2.99087;0.054711;90.4625;27.1428;234.963;123.0
2020-02-08 13:41:57;0.203714;0.274614;3.11379;0.382638;90.3527;27.1451;244.276;123.0
2020-02-08 13:41:58;0.203516;0.272049;2.99287;0.382638;90.253;27.1424;242.5;123.0
2020-02-08 13:41:59;0.204371;0.274669;2.56845;0.382638;90.4525;27.1442;231.954;123.0
2020-02-08 13:42:00;0.203363;0.272629;2.51828;0.054711;90.8657;27.1526;239.026;123.665
2020-02-08 13:42:01;0.204059;0.274463;1.68059;0.710565;90.9441;27.151;229.848;122.675
2020-02-08 13:42:02;0.203212;0.273622;2.64611;0.710565;90.8157;27.151;226.18;122.665
2020-02-08 13:42:03;0.204637;0.273936;2.68067;0.382638;90.6994;27.1527;236.139;123.665
2020-02-08 13:42:04;0.203344;0.27409;2.78166;-0.273216;90.8381;27.159;230.323;123.337
2020-02-08 13:42:05;0.20428;0.274084;2.56691;0.054711;90.6543;27.1499;222.716;123.0
2020-02-08 13:42:07;0.203301;0.27408;3.08598;0.710565;90.9528;27.1548;240.111;123.0
2020-02-08 13:42:08;0.20413;0.274773;2.84138;0.054711;90.7318;27.1495;235.06;123.665
2020-02-08 13:42:09;0.204486;0.274032;2.63215;0.054711;90.8727;27.1483;222.77;122.675
2020-02-08 13:42:10;0.20247;0.273942;2.28412;0.054711;90.7238;27.1528;225.968;123.332
2020-02-08 13:42:11;0.201658;0.272481;2.52956;-0.273216;90.6595;27.1583;228.112;123.665
2020-02-08 13:42:12;0.205051;0.274771;2.63828;-0.273216;90.8975;27.1583;228.013;123.337
2020-02-08 13:42:13;0.202719;0.271337;2.46314;0.054711;90.8543;27.1458;228.868;123.0
2020-02-08 13:42:14;0.20477;0.275635;2.89141;0.054711;90.8139;27.1553;221.088;123.0
2020-02-08 13:42:15;0.204345;0.270157;2.46667;0.054711;90.7509;27.1568;229.134;122.336
2020-02-08 13:42:16;0.205294;0.27445;2.59059;-0.273216;90.9033;27.166;220.837;122.665
2020-02-08 13:42:17;0.204227;0.273587;2.50845;0.054711;90.9122;27.1542;225.531;123.0
2020-02-08 13:42:18;0.20537;0.273874;2.83015;0.382638;90.7564;27.1541;220.442;123.665
2020-02-08 13:42:19;0.20436;0.275855;2.41581;0.054711;90.938;27.1574;214.11;124.0
2020-02-08 13:42:20;0.204643;0.274015;2.72906;0.054711;91.0675;27.1598;225.471;123.336
2020-02-08 13:42:22;0.205335;0.274789;2.31497;0.710565;90.8919;27.1535;225.012;123.0
2020-02-08 13:42:23;0.202785;0.273905;2.81755;0.054711;91.0162;27.161;234.615;123.0
2020-02-08 13:42:24;0.206128;0.274189;2.67573;0.054711;90.7565;27.161;233.232;123.665
2020-02-08 13:42:25;0.200987;0.272636;2.67902;0.054711;90.8204;27.1555;229.607;124.0
2020-02-08 13:42:26;0.205879;0.274657;2.00884;0.054711;90.7043;27.16;221.956;123.336
2020-02-08 13:42:27;0.204838;0.275593;2.5396;0.382638;90.9273;27.1561;222.521;123.665
2020-02-08 13:42:28;0.204195;0.27133;2.8325;0.054711;91.2167;27.1541;232.874;123.336
2020-02-08 13:42:29;0.20431;0.275751;2.89829;0.710565;91.1367;27.1576;220.456;123.0
2020-02-08 13:42:30;0.20494;0.27198;2.78008;0.054711;91.0205;27.15;227.335;123.665
2020-02-08 13:42:31;0.204933;0.274163;2.85745;0.054711;90.9182;27.1561;215.108;123.336
2020-02-08 13:42:32;0.204289;0.273997;2.48449;0.054711;90.9984;27.1561;216.892;123.0
2020-02-08 13:42:33;0.20461;0.274147;2.6672;0.054711;90.9409;27.1651;228.416;123.0
2020-02-08 13:42:34;0.204628;0.273752;2.9614;0.054711;91.0276;27.1585;230.716;123.0
2020-02-08 13:42:35;0.203804;0.275271;2.50231;0.382638;90.8072;27.1537;224.912;123.0
2020-02-08 13:42:36;0.205558;0.273498;2.96203;-0.273216;90.9021;27.1603;218.304;123.665
2020-02-08 13:42:37;0.201586;0.274456;1.78016;0.054711;90.7118;27.1669;225.638;123.336
2020-02-08 13:42:38;0.206266;0.274405;2.7367;-0.273216;90.4988;27.1589;220.936;123.0
2020-02-08 13:42:39;0.202175;0.273019;2.7751;0.054711;91.0192;27.1621;230.479;123.0
2020-02-08 13:42:40;0.204063;0.275245;2.01894;0.054711;91.0984;27.1621;219.576;123.0
2020-02-08 13:42:42;0.204181;0.272233;2.53174;0.382638;90.3531;27.1677;230.153;123.665
2020-02-08 13:42:43;0.203622;0.275529;1.80997;0.054711;90.9503;27.1655;228.383;123.336
2020-02-08 13:42:44;0.204731;0.272306;2.64749;0.054711;91.1429;27.1685;231.042;123.0
2020-02-08 13:42:45;0.204713;0.274495;1.60959;0.054711;90.2781;27.1671;216.85;123.0
2020-02-08 13:42:46;0.204127;0.274671;1.77372;0.054711;90.4587;27.1614;219.305;123.336
2020-02-08 13:42:47;0.205007;0.274919;2.77869;0.054711;90.4538;27.1652;233.168;123.665
2020-02-08 13:42:48;0.203086;0.275166;2.58331;-0.273216;90.3408;27.1666;219.433;123.336
2020-02-08 13:42:49;0.205729;0.274353;2.54652;0.054711;90.3133;27.1651;241.855;123.0
2020-02-08 13:42:50;0.20261;0.274062;2.68808;0.054711;90.3965;27.1651;230.625;123.665
2020-02-08 13:42:51;0.204611;0.273949;2.74453;0.054711;90.5794;27.1746;227.738;123.336
2020-02-08 13:42:52;0.20325;0.272123;1.70203;0.382638;90.4482;27.1703;239.789;123.665
2020-02-08 13:42:53;0.203069;0.274665;2.76293;0.054711;90.3749;27.1793;225.705;123.336
2020-02-08 13:42:54;0.203857;0.271279;2.51293;0.054711;90.4561;27.1743;228.561;123.665
2020-02-08 13:42:55;0.203129;0.2742;2.54958;0.382638;90.5104;27.1754;224.197;123.336
2020-02-08 13:42:56;0.204531;0.271348;2.63771;0.382638;90.4858;27.174;215.553;123.0
2020-02-08 13:42:58;0.20367;0.2732;2.28544;-0.273216;90.4448;27.1728;231.233;123.665
2020-02-08 13:42:59;0.204111;0.274441;2.35506;0.054711;90.3673;27.1675;230.719;123.336
2020-02-08 13:43:00;0.204001;0.272832;2.67011;0.054711;90.2519;27.1738;234.247;123.0
2020-02-08 13:43:01;0.204214;0.273866;2.36767;0.054711;90.508;27.1738;230.215;123.665
2020-02-08 13:43:02;0.204145;0.272364;2.47199;0.054711;90.344;27.1743;225.703;122.665
2020-02-08 13:43:03;0.203565;0.275755;2.33527;0.710565;90.363;27.1785;222.303;123.0
2020-02-08 13:43:04;0.204662;0.272859;2.62124;0.054711;90.4573;27.1738;228.14;123.0
2020-02-08 13:43:05;0.202508;0.274021;1.02393;0.054711;90.266;27.1738;204.037;123.0
2020-02-08 13:43:06;0.203714;0.273453;3.11572;0.054711;90.1881;27.1703;250.969;123.665
2020-02-08 13:43:07;0.203558;0.272662;1.57977;0.054711;90.3025;27.1761;215.896;123.336
2020-02-08 13:43:08;0.202865;0.273356;2.87682;0.054711;90.3287;27.1848;235.137;123.665
2020-02-08 13:43:09;0.203931;0.273277;2.90931;0.054711;90.3074;27.1848;208.53;123.336
2020-02-08 13:43:10;0.203829;0.27328;2.81816;0.054711;90.4977;27.1828;247.222;123.665
2020-02-08 13:43:11;0.203947;0.274165;2.07185;0.054711;90.3601;27.1801;231.51;123.336
2020-02-08 13:43:13;0.20477;0.272029;1.16103;0.054711;90.3312;27.1892;211.615;123.0
2020-02-08 13:43:14;0.204055;0.273907;3.00623;0.054711;90.3198;27.1852;240.976;123.0
2020-02-08 13:43:15;0.204514;0.275254;1.93066;0.054711;90.1305;27.1815;227.782;123.665
2020-02-08 13:43:16;0.204377;0.272858;2.61577;0.054711;90.1608;27.1774;233.381;123.336
2020-02-08 13:43:17;0.203505;0.273533;1.24761;0.054711;90.1214;27.1767;207.343;123.0
2020-02-08 13:43:18;0.202551;0.27533;3.01934;0.054711;90.3216;27.1767;240.476;123.665
2020-02-08 13:43:19;0.204084;0.273645;1.90191;-0.273216;90.618;27.1834;227.868;123.336
2020-02-08 13:43:20;0.203629;0.275125;1.9601;0.054711;90.5901;27.1851;235.393;122.336
2020-02-08 13:43:21;0.202827;0.273119;2.66195;-0.273216;90.1449;27.1909;228.685;123.333
2020-02-08 13:43:22;0.203883;0.273984;2.70432;0.054711;90.7328;27.1853;224.869;122.675
2020-02-08 13:43:23;0.203119;0.273345;2.82811;0.382638;90.8532;27.1741;207.733;122.665
2020-02-08 13:43:24;0.203927;0.274094;2.90189;0.054711;90.1525;27.1783;247.272;123.665
2020-02-08 13:43:25;0.204186;0.272637;0.952645;0.054711;90.8787;27.1816;206.601;123.336
2020-02-08 13:43:26;0.204208;0.274401;2.53165;0.054711;90.7882;27.1816;229.818;123.0
2020-02-08 13:43:27;0.204192;0.27293;2.48551;0.054711;90.7688;27.1789;220.987;123.665
2020-02-08 13:43:28;0.20449;0.273019;2.54628;0.382638;90.8455;27.1809;230.431;123.336
2020-02-08 13:43:30;0.203295;0.274573;2.65648;-0.273216;90.7385;27.1781;222.524;123.0
2020-02-08 13:43:31;0.204388;0.273997;2.66482;0.054711;90.8018;27.1828;228.434;123.665
2020-02-08 13:43:32;0.203058;0.274674;2.54862;0.054711;90.7693;27.1824;214.61;123.336
2020-02-08 13:43:33;0.203489;0.273821;2.91772;0.054711;90.8759;27.1811;251.422;123.0
2020-02-08 13:43:34;0.202288;0.274074;1.10202;0.382638;90.8767;27.1843;217.223;123.665
2020-02-08 13:43:35;0.202625;0.273959;2.6763;0.382638;90.807;27.1843;218.813;123.336
2020-02-08 13:43:36;0.202278;0.272734;2.41211;0.054711;90.7791;27.1862;228.763;123.0
2020-02-08 13:43:37;0.203216;0.273509;1.38143;0.054711;90.7785;27.1925;220.015;123.0
2020-02-08 13:43:38;0.201711;0.272471;2.62633;0.054711;90.9283;27.1954;242.562;123.665
2020-02-08 13:43:39;0.20339;0.273586;2.50727;0.382638;90.767;27.1814;234.682;123.336
2020-02-08 13:43:40;0.202207;0.272196;0.933544;-0.273216;90.8298;27.1893;207.794;123.0
2020-02-08 13:43:41;0.203481;0.274489;2.47146;-0.273216;90.9472;27.1945;219.34;123.665
2020-02-08 13:43:42;0.202182;0.271611;2.46996;0.054711;90.8498;27.1898;229.552;123.336
2020-02-08 13:43:43;0.201479;0.272913;2.61538;0.054711;90.7291;27.1898;238.179;123.0
2020-02-08 13:43:44;0.200798;0.27128;2.51958;0.054711;90.7153;27.1883;235.507;123.0
2020-02-08 13:43:45;0.20308;0.274051;2.748;0.054711;90.559;27.1895;205.519;123.0
2020-02-08 13:43:46;0.201232;0.271969;2.56635;0.382638;90.7465;27.1935;224.208;123.0
2020-02-08 13:43:48;0.203369;0.274151;2.59237;0.054711;91.0149;27.1964;228.806;123.665
2020-02-08 13:43:49;0.20147;0.272443;2.75821;0.054711;90.8198;27.1857;211.273;123.336
2020-02-08 13:43:50;0.203128;0.274535;2.48406;0.054711;90.9554;27.2033;226.201;123.0
2020-02-08 13:43:51;0.202987;0.274011;0.928332;0.382638;90.8084;27.2021;208.842;123.0
2020-02-08 13:43:52;0.202604;0.271989;2.07062;0.382638;90.9933;27.2057;220.592;123.0
2020-02-08 13:43:53;0.203564;0.27465;2.63387;0.382638;91.1219;27.2057;226.699;123.0
2020-02-08 13:43:54;0.202471;0.27161;2.85154;0.382638;91.0529;27.2121;220.652;123.0
2020-02-08 13:43:55;0.203554;0.274649;2.66752;0.382638;90.6515;27.2087;228.823;123.0
2020-02-08 13:43:56;0.20341;0.271416;2.67986;0.382638;91.1442;27.2057;234.235;123.665
2020-02-08 13:43:57;0.203956;0.274426;2.66076;0.382638;90.4586;27.2058;220.364;123.336
2020-02-08 13:43:58;0.203087;0.272937;3.0844;0.382638;90.5911;27.2118;250.708;123.665
2020-02-08 13:43:59;0.204607;0.273931;2.76333;0.054711;90.6276;27.2014;202.999;123.336
2020-02-08 13:44:00;0.202849;0.274086;2.65345;0.382638;90.8445;27.2181;222.528;123.0
2020-02-08 13:44:02;0.204367;0.27392;2.28419;-0.273216;90.4352;27.2145;215.313;123.665
2020-02-08 13:44:03;0.202932;0.274561;2.52758;-0.273216;90.8796;27.2095;224.428;123.336
2020-02-08 13:44:04;0.204073;0.273964;2.43204;-0.273216;90.4899;27.2095;229.714;123.665
2020-02-08 13:44:05;0.20352;0.274186;2.19068;0.054711;90.5142;27.2156;228.726;123.336
2020-02-08 13:44:06;0.204434;0.274671;2.45135;0.382638;90.2074;27.2178;226.048;123.0
2020-02-08 13:44:07;0.201587;0.272458;3.00648;0.054711;90
gitextract_hxo2wk1q/
├── .gitignore
├── .pre-commit-config.yaml
├── LICENSE
├── README.md
├── core/
│ ├── Conv_AE.py
│ ├── Isolation_Forest.py
│ ├── LSTM_AE.py
│ ├── LSTM_VAE.py
│ ├── MSCRED.py
│ ├── MSET.py
│ ├── Vanilla_AE.py
│ ├── Vanilla_LSTM.py
│ ├── __init.py__
│ ├── metrics.py
│ ├── t2.py
│ └── utils.py
├── data/
│ ├── README.md
│ ├── anomaly-free/
│ │ └── anomaly-free.csv
│ ├── other/
│ │ ├── 1.csv
│ │ ├── 10.csv
│ │ ├── 11.csv
│ │ ├── 12.csv
│ │ ├── 13.csv
│ │ ├── 14.csv
│ │ ├── 2.csv
│ │ ├── 3.csv
│ │ ├── 4.csv
│ │ ├── 5.csv
│ │ ├── 6.csv
│ │ ├── 7.csv
│ │ ├── 8.csv
│ │ └── 9.csv
│ ├── valve1/
│ │ ├── 0.csv
│ │ ├── 1.csv
│ │ ├── 10.csv
│ │ ├── 11.csv
│ │ ├── 12.csv
│ │ ├── 13.csv
│ │ ├── 14.csv
│ │ ├── 15.csv
│ │ ├── 2.csv
│ │ ├── 3.csv
│ │ ├── 4.csv
│ │ ├── 5.csv
│ │ ├── 6.csv
│ │ ├── 7.csv
│ │ ├── 8.csv
│ │ └── 9.csv
│ └── valve2/
│ ├── 0.csv
│ ├── 1.csv
│ ├── 2.csv
│ └── 3.csv
├── docs/
│ └── contributing.md
├── notebooks/
│ ├── ArimaFD.ipynb
│ ├── Conv_AE.ipynb
│ ├── LSTM_AE.ipynb
│ ├── MSET.ipynb
│ ├── README.md
│ ├── Vanilla_AE.ipynb
│ ├── Vanilla_LSTM.ipynb
│ ├── isolation_forest.ipynb
│ ├── mscred.ipynb
│ ├── t2_SKAB.ipynb
│ └── t2_with_q_SKAB.ipynb
├── pyproject.toml
└── results/
├── results-Arima_anomaly_detection.pkl
├── results-Conv_AE.pkl
├── results-Isolation_Forest.pkl
├── results-LSTM_AE.pkl
├── results-MSCRED.pkl
├── results-MSET.pkl
├── results-T2-q.pkl
├── results-T2.pkl
├── results-Vanilla_AE.pkl
└── results-Vanilla_LSTM.pkl
SYMBOL INDEX (88 symbols across 11 files)
FILE: core/Conv_AE.py
class Conv_AE (line 7) | class Conv_AE:
method __init__ (line 28) | def __init__(self):
method _Random (line 31) | def _Random(self, seed_value):
method _build_model (line 48) | def _build_model(self):
method fit (line 89) | def fit(self, data):
method predict (line 116) | def predict(self, data):
FILE: core/Isolation_Forest.py
class Isolation_Forest (line 4) | class Isolation_Forest:
method __init__ (line 31) | def __init__(self, params):
method _Random (line 37) | def _Random(self, seed_value):
method _build_model (line 54) | def _build_model(self):
method fit (line 64) | def fit(self, X):
method predict (line 78) | def predict(self, data):
FILE: core/LSTM_AE.py
class LSTM_AE (line 12) | class LSTM_AE:
method __init__ (line 41) | def __init__(self, params):
method _Random (line 44) | def _Random(self, seed_value):
method _build_model (line 61) | def _build_model(self):
method fit (line 78) | def fit(self, X):
method predict (line 104) | def predict(self, data):
FILE: core/LSTM_VAE.py
class KLDivergenceLayer (line 8) | class KLDivergenceLayer(Layer):
method __init__ (line 9) | def __init__(self, **kwargs):
method call (line 12) | def call(self, inputs):
class Sampling (line 21) | class Sampling(Layer):
method __init__ (line 22) | def __init__(self, latent_dim, epsilon_std=1.0, **kwargs):
method call (line 27) | def call(self, inputs):
method compute_output_shape (line 36) | def compute_output_shape(self, input_shape):
class LSTM_VAE (line 40) | class LSTM_VAE:
method __init__ (line 61) | def __init__(self, params):
method _build_model (line 64) | def _build_model(self, input_dim, timesteps, intermediate_dim, latent_...
method _Random (line 101) | def _Random(self, seed_value):
method vae_loss (line 118) | def vae_loss(self, x, x_decoded_mean):
method fit (line 140) | def fit(self, X):
method predict (line 185) | def predict(self, data):
FILE: core/MSCRED.py
class MSCRED (line 17) | class MSCRED:
method __init__ (line 40) | def __init__(self, params):
method _build_model (line 43) | def _build_model(self):
method attention (line 238) | def attention(self, outputs, koef):
method _Random (line 283) | def _Random(self, seed_value):
method _loss_fn (line 300) | def _loss_fn(self, y_true, y_pred):
method fit (line 303) | def fit(self, X_train, Y_train, batch_size=200, epochs=25):
method predict (line 341) | def predict(self, data):
FILE: core/MSET.py
class MSET (line 7) | class MSET:
method __init__ (line 27) | def __init__(self):
method _build_model (line 30) | def _build_model(self):
method _Random (line 33) | def _Random(self, seed_value):
method calc_W (line 50) | def calc_W(self, X_obs):
method otimes (line 73) | def otimes(self, X, Y):
method kernel (line 110) | def kernel(self, x, y):
method fit (line 134) | def fit(self, df, train_start=None, train_stop=None):
method predict (line 160) | def predict(self, data):
FILE: core/Vanilla_AE.py
class Vanilla_AE (line 12) | class Vanilla_AE:
method __init__ (line 39) | def __init__(self, params):
method _build_model (line 42) | def _build_model(self):
method _Random (line 74) | def _Random(self, seed_value):
method fit (line 91) | def fit(
method predict (line 135) | def predict(self, data):
FILE: core/Vanilla_LSTM.py
class Vanilla_LSTM (line 6) | class Vanilla_LSTM:
method __init__ (line 29) | def __init__(self, params):
method _Random (line 32) | def _Random(self, seed_value):
method _build_model (line 49) | def _build_model(self):
method fit (line 66) | def fit(self, X, y):
method predict (line 97) | def predict(self, data):
FILE: core/metrics.py
function filter_detecting_boundaries (line 11) | def filter_detecting_boundaries(detecting_boundaries):
function single_detecting_boundaries (line 24) | def single_detecting_boundaries(
function check_errors (line 105) | def check_errors(my_list):
function extract_cp_confusion_matrix (line 163) | def extract_cp_confusion_matrix(
function confusion_matrix (line 251) | def confusion_matrix(true, prediction):
function single_average_delay (line 261) | def single_average_delay(
function my_scale (line 312) | def my_scale(
function single_evaluate_nab (line 349) | def single_evaluate_nab(
function chp_score (line 426) | def chp_score(
FILE: core/t2.py
class T2 (line 15) | class T2:
method __init__ (line 77) | def __init__(
method _t2_calculation (line 90) | def _t2_calculation(self, x):
method _q_calculation (line 96) | def _q_calculation(self, x):
method _t2_ucl (line 103) | def _t2_ucl(self, x):
method _q_ucl (line 117) | def _q_ucl(self, x):
method _pca_applying (line 137) | def _pca_applying(self, x):
method plot_t2 (line 144) | def plot_t2(self, t2=None, t2_ucl=None, save_fig=False, fig_name="T2"):
method plot_q (line 188) | def plot_q(self, q=None, q_ucl=None, save_fig=False, fig_name="Q"):
method _save (line 233) | def _save(name="", fmt="png"):
method fit (line 242) | def fit(self, x):
method predict (line 307) | def predict(
FILE: core/utils.py
function load_skab (line 11) | def load_skab():
function preprocess_skab (line 38) | def preprocess_skab(list_of_df):
function load_preprocess_skab (line 53) | def load_preprocess_skab():
function create_sequences (line 60) | def create_sequences(values, time_steps):
function plot_results (line 67) | def plot_results(*true_pred_pairs: tuple[pd.Series, pd.Series]):
function print_results (line 80) | def print_results(
Condensed preview — 75 files, each showing path, character count, and a content snippet. Download the .json file or copy for the full structured content (5,241K chars).
[
{
"path": ".gitignore",
"chars": 1053,
"preview": ".DS_Store\n*.pickle\n\n# Byte-compiled / optimized / DLL files\n__pycache__/\nalgorithms/__pycache__/\nnotebooks/__pycache__/\n"
},
{
"path": ".pre-commit-config.yaml",
"chars": 2805,
"preview": "# https://pre-commit.com\nexclude: 'examples|reports'\nrepos:\n - repo: https://github.com/pre-commit/pre-commit-hooks\n "
},
{
"path": "LICENSE",
"chars": 35149,
"preview": " GNU GENERAL PUBLIC LICENSE\n Version 3, 29 June 2007\n\n Copyright (C) 2007 Free "
},
{
"path": "README.md",
"chars": 10683,
"preview": "# \n\n🛠🛠🛠**The testbed is under repair right now. Unfortunately, we can't tell exactly when"
},
{
"path": "core/Conv_AE.py",
"chars": 3453,
"preview": "from tensorflow.keras.callbacks import EarlyStopping\nfrom tensorflow.keras.layers import Conv1D, Conv1DTranspose, Dropou"
},
{
"path": "core/Isolation_Forest.py",
"chars": 2302,
"preview": "from sklearn.ensemble import IsolationForest\n\n\nclass Isolation_Forest:\n \"\"\"\n Isolation Forest or iForest builds an"
},
{
"path": "core/LSTM_AE.py",
"chars": 3021,
"preview": "from tensorflow.keras import Model\nfrom tensorflow.keras.callbacks import EarlyStopping\nfrom tensorflow.keras.layers imp"
},
{
"path": "core/LSTM_VAE.py",
"chars": 5604,
"preview": "from tensorflow.keras import backend as K\nfrom tensorflow.keras import losses\nfrom tensorflow.keras.callbacks import Ear"
},
{
"path": "core/MSCRED.py",
"chars": 10560,
"preview": "import math\n\nimport tensorflow as tf\nfrom tensorflow.keras import Model\nfrom tensorflow.keras.callbacks import ReduceLRO"
},
{
"path": "core/MSET.py",
"chars": 4525,
"preview": "import numpy as np\nimport pandas as pd\nfrom scipy import linalg as spla\nfrom sklearn.preprocessing import StandardScaler"
},
{
"path": "core/Vanilla_AE.py",
"chars": 4096,
"preview": "from tensorflow.keras.callbacks import EarlyStopping\nfrom tensorflow.keras.layers import (\n Activation,\n BatchNorm"
},
{
"path": "core/Vanilla_LSTM.py",
"chars": 2826,
"preview": "from tensorflow.keras.callbacks import EarlyStopping, ReduceLROnPlateau\nfrom tensorflow.keras.layers import LSTM, Dense\n"
},
{
"path": "core/__init.py__",
"chars": 0,
"preview": ""
},
{
"path": "core/metrics.py",
"chars": 29598,
"preview": "\"\"\"\nThis module is part of library (tsad)[https://github.com/waico/tsad]\n\"\"\"\n\nimport matplotlib.gridspec as gridspec\nimp"
},
{
"path": "core/t2.py",
"chars": 12391,
"preview": "# Author: Iurii Katser\n\nimport os\nfrom math import sqrt\n\nimport numpy as np\nimport scipy.stats as SS\nfrom matplotlib imp"
},
{
"path": "core/utils.py",
"chars": 2399,
"preview": "import os\n\nimport matplotlib.pyplot as plt\nimport numpy as np\nimport pandas as pd\nfrom sklearn.model_selection import tr"
},
{
"path": "data/README.md",
"chars": 2166,
"preview": "```\n └── data # Data files and processing Jupyter Notebook\n ├── Load data.ipynb # J"
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// ... and 10 more files (download for full content)
About this extraction
This page contains the full source code of the waico/SKAB GitHub repository, extracted and formatted as plain text for AI agents and large language models (LLMs). The extraction includes 75 files (4.9 MB), approximately 1.3M tokens, and a symbol index with 88 extracted functions, classes, methods, constants, and types. Use this with OpenClaw, Claude, ChatGPT, Cursor, Windsurf, or any other AI tool that accepts text input. You can copy the full output to your clipboard or download it as a .txt file.
Extracted by GitExtract — free GitHub repo to text converter for AI. Built by Nikandr Surkov.