Hi Fernando,

Thank you for answer.

First, consider that I have a X(15 variables, 100 observation for normal, 100 observation for fault 1 and 100 observation for fault 2) for example. Fault DETECTION is  discrimination between Normal and Faulty. Therefore, loading matrix are determined only based on Normal dataset by PCA. Then, any other observation project to this space (just by inner product). the distance of new observation to Normal space is determined by T-squared. if the distance is high, the system is under fault. But, the kind of fault can not be distinguished.

Second, for fault DIAGNOSIS, PCA should try to determine the type of fault. it should be considered that the fault is just a label to dataset, not a measurement (variable).

Third, I suppose that you advise me to add a label for each observation and consider it as a variable. in this way the input of PCA should be a matrix  X(18 variables, 100 observation), then find loading matrix based on PCA.

But I cannot understand  for a new observation, How I can find the state of system (Normal/fault 1/fault2) based on your explanation.

I suppose that one should add three different labels to new observation, and then check  which state the is nearest to projection . 

Please keep contact.

Hi

for fault detection, please find the attached article.

for fault diagnosis, please find the attached file. Figure 7 represents the contribution chart.

however, fault is a measurable variable in this paper!! But for my case study the concept is that the fault is not measurable.  Therefore, as you said it is a classification problem.

Thank you :)