Prognostics and Health Management (PHM) Algorithms

In this repository, we introduce nonparametric method for examining machine healthiness. Including methodology to identify maintainence effectiveness with the features and PHM algorithms for uni- and multi-virate data.

• The main.py module is the sample for user to set the parameter for each algorithm.
• The unit test code is writen in each module, and can be precess immediately. Each module is introduced below...

statisticalTest

In practice, the main challenge for PHM in the firest step is to identify the correlation between data and maintianence. Under the assumption that the maintianence will make machine more stable, we vidualize data and use statistical test for two slice of univirate data to check the overall correlation between each.
Where the statistical tests are:

Test	Usage of Both Data
t test	the mean of distribution
f test	the variance of distribution
skewness	the skewness of distribution
kurtosis	the kurtosis of distribution
KS test	check the distribution of both data is identical or not, the distribution is different if pvalue < 0.01
correlation	the correlation of two data
dtw distance	the dynamic time wrapping distance of two data, the smaller value the closer distance

• The visualization of two data:

• The DTW plot:

chamber2chamber

• chamber to chamber: comparing the standard deviation of all machines to find the unstable ones. You could take out extreme data points in advance to prevent false alarm.

Method	Usage
z score	detect outliers

x_bar_S

$\overline X$ and S control chart is an univirate method for single machine to detect anomalies. By watching the trends of the samples, we can identify manufacturing anomaly and measurement anomaly.

Submethod	Usage
sliding window	detect anomaly with trend factor

• $\overline X$ and S control chart example:

ewma

The EWMA control chart help us detect time-dependent data with sliding window and weights. The EWMA chart is sensitive to small shifts in the process mean, but does not match the ability of Shewhart-style charts (namely the $\overline X$ and $R$, and $\overline X$ and $S$ charts) to detect larger shifts. It is univirate version in this implementation, while EWMA control chart can be used in multivirate feature once the determinant of slided data is calculated.

• EWMA control chart example:

hotelling_t2

The Hotelling's T-squared control chart aims to identify the feature distance between multivirate data, under the assumption that the data is independently collected. Data point is regards to be anomaly once its t-squared value is too large, i.e., jump over UCL. However, Hotelling's T-squared control chart can be too sensitive if we break the assumptions of Hotelling's T-squared (see).

• Hotelling's T-squared control chart example: