Fault Detection Based on Least Squares with Limited Samples

Abstract

In this paper, a data-driven method using least squares is proposed for finite training samples, with a focus on parameter identification and the corresponding performance evaluation. In the procedures of parameter identification, “probably approximately correct” (PAC) is used for determining the confidence of the obtained the modeling error that affects Fault Detection (FD) performance. The main contributions of this paper are: 1) The modeling error expressed by infinite norm norm can be reduced by increasing the size of training data; 2) the sub-Gaussian noise is taken into account; 3) the difference between system outputs and their predictions is used as the residual signal, based on which test statistics are defined to obtain FD results. Finally, the effectiveness of the proposed method is demonstrated through rigorous mathematical derivation and case studies.