the PLS allows both to classify the types of faults and to reduce the dimensionality of the problem by trying to maximize the covariance between X and Y, useful in supervised learning. The algorithm chosen to solve the problem is NIPALS which allows to obtain a solution iteratively and in a very short time, not requiring the decomposition of X and Y. Methodological references belong to the book [Braatz] Fault Detection and Diagnosis in Industrial Systems, chapter 6. The algorithm was tested on2 case studies:
the first concerns a well-known classification problem in literature, ie the iris dataset, trying to classify the types of flowers knowing some characteristics. of this we will only do training and low order reduction, to visually see the PLS concepts.
The second case study is specific to fault detection. The data was generated by the NSF I/UCR Center for Intelligent Maintenance Systems (IMS – www.imscenter.net). Four bearings were installed on a shaft. The rotation speed was kept constant at 2000 RPM by an AC motor coupled to the shaft via rub belts. A radial load of 6000 lbs is applied onto the shaft and bearing by a spring mechanism. All bearings are force lubricated. The idea is not to look at the observations as individual snapshots, but to take them as statistical information about the process with a time interval T, at this point it would be a batch sampling of data. The aim is to recognise 3 type of faults: inner race fault, outer race fault and rolling eements faults, the results allow us to say that by reducing the dimensionality of X we are able to reduce the overfitting phenomenon on the test data, also in this case we plot the case from 1 to 3 dimensions of the problem.
