Fault detection and diagnosis in multivariate systems using multiple correlation regression

Abstract

Correlations among variables are inherent features of a multivariate system. Making a good use of variable correlations is important to fault detection and diagnosis (FDD). In this paper, a novel FDD method is proposed using multiple correlation regression (MCR). MCR builds a regression model using the multiple correlation of a variable with other variables. MCR is the best linear regression that produces residuals with the minimal variance. Based on the MCR residuals of variables, a T2 statistic is defined for fault detection. This T2 statistic consists of a set of independent components, with each component corresponding to the MCR residual of a variable. To reduce the amplification and masking effects caused by fault-free components, three improvements to the residual-based T2 statistic are proposed, called the intersecting T2 (IT), weighted T2 (WT) and enhanced T2 (ET) statistics. In particular, the WT and ET statistics and their control limits vary with samples to adapt to dynamic changes of the system. An online fault detection strategy is proposed by combining the WT and ET statistics. The WT statistic is firstly used to detect the occurrence of faults. After faults were detected, the ET statistic is used to replace the WT statistic in order to enhance the capability of detecting subsequent faulty samples. A contribution-based fault diagnosis method is also developed. Faulty variables are identified by comparing variable contributions to the key faulty component of the residual-based T2 statistic. The implementation and advantages of the proposed FDD method are illustrated with a simulation example and an industrial case study.