Fault detection in process control plants using principal component analysis

Abstract

The aim of this thesis is to use a statistical method (principal component analysis) to detect a fault in a system. PCA is a dimensionality reduction technique that is used here. First the PCA algorithm was implemented on a simple two dimensional random data to reduce its dimensionality. Then the algorithm was implemented on a three dimensional data from a linear first order process and introduce some white noise later on and compare the results with that under normal operating conditions, thus determining the presence of a fault. Then data from a real time plant is considered for testing. This is done by considering a Simulink model of the Tennessee Eastman challenge problem from downs and vogel‘s, which has around 42 output variables. The crucial step in a dimensionality reduction technique is determining the number of principal components. When we have data in two dimensions or three dimensions it is easy to figure out the number of principal components by simply looking at the eigenvalues of the covariance matrix. However when there is a huge data it becomes difficult to find the number of principal components by inspection. Here, the number of principal components is found by using parallel analysis. The simulation results are carried out with a one fault at a time and the results are compared with the plots under normal operating conditions. The delay times of some of the faults is tabulated (The delay time to detect the fault largely depend on the number of principle components, so with a different approach to find the principal components the delay times may vary from what we got here). Finally, a case study of one of the faults (IDV1) is done.