/lorentz-atractor-blind-fault-detection-dataset

a small synthetic benchmark for blind anomaly detectors

MIT LicenseMIT

Lorentz-attractor-blind-fault-detection-dataset

A small synthetic benchmark for blind anomaly detectors for industrial time series

DOI

Description of the dataset

This is a synthetic dataset that might be used to challenge **Blind anomaly detector for time series **

The dynamical system for which the dataset is created is the famous Lorentz attractor which is governed by the following set of Ordinary Differential Equations:

$$ \begin{align} \dot x_1&=\sigma(x_2-x_1) \\ \dot x_2&=x_1({\color{red} \rho}-x_3)-x_2 \\ \dot x_3&=x_1x_2-{\color{blue} \beta} x_3 \end{align} $$

where $\sigma$, $\rho$ and $\beta$ are the parameters that might be affected by unpredictable changes one would like to detect thanks to the anomaly detector using the two measurement sensors defined by $s_1=x_1$ and $s_2=x_3$. The raw version of the time series is given in the figure below:

Note that green regions corresponds to nominal parameters (normalized values = 1) while the red regions correspond to changes in the values of the parameters to be detected by the anomalies detector.

The dataset consists of four csv pandas dataframes:

  • df_train.csv: The Dataframe of features for training
  • df_train_labels.csv : The Dataframe of labels for training
  • df_test.csv: The Dataframe of features for test
  • df_test_labels.csv : The Dataframe of labels for test

In order to read the dataframe, use the following pandas command

import pandas as pd
df_train = pd.read_csv('df_train.csv', index_col=0)

The following images show the columns in the df_train and df_test_label dataframes

  • df_train

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  • df_test_label

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Important information on test data

Please note that the training data lies in the first block of the df_testdataset. If you want to draw statistic, it is important to know that the first 6-th part of the test data is simply the training data. It is therefore expected that you get nice results on this part of the test data.

Benchmark Description

Use the training dataset df_trainin order to fit your anomalies detector. Use the test dataset df_testto predict the presence or not of anomalies in dataset. Compare your prediction to the column labelof the dataframe df_test_labels. Note that 0represent normal data while 1represent anomalous data. The prediction can be performed over a moving window spanning the time series or using point-wise prediction. The nominal benchmark involves only the columns x1and x3of the dataframe, but you might feel free to use less or more columns. The other columns in the df_test_labels are provided as extra columns that explains the origin of the anomalies.

If interested in having more rich set of anomalies values, please contact me.