Improved Relative-transformation Principal Component Analysis Based on Mahalanobis Distance and Its Application for Fault Detection

Principal component analysis (PCA) has been widely used in process industries, which could maintain the maximum fault detection rate. Although many issues have been addressed in PCA, some essential problems remain unresolved. This study improves PCA for fault detection performance in the following ways. Firstly, a relative transformation scheme based on Mahalanobis distance (MD) is introduced to eliminate the effect of dimension of data instead of dimensionless standardization, and improve the accuracy and real-time performance of fault detection. The theoretical derivation proves that relative transformation based on MD can directly eliminate the effect of dimension and give reasonable explanation of PCA in the relative space, the analysis and simulation results show its superiority and effectiveness. Secondly, an improved squared prediction error (SPE) statistic is given to improve the fault detection performance of standardized PCA, which can make the standardized PCA-based fault detection method more suitable for the actual industrial process. Finally, two improved methods are combined to detect the fault more effectively. The proposed methods are applied to detect single fault and multi-fault of looper system in hot continuous rolling process, simulation results demonstrate the effectiveness of these improvements for fault detection performance in terms of sensitiveness, accuracy and real-time performance of fault detection.