Kantorovich Distance Based Fault Detection Scheme for Non-Linear Processes

Fault detection is necessary for safe operation in modern process plants. The kernel principal component analysis (KPCA) technique has been widely utilized for monitoring non-linear processes because it enhances dimension reduction and fault detection in non-linear space. In this paper, an improved non-linear fault detection strategy based on Kantorovich distance (KD) and kernel principal component analysis is proposed. The KD statistic is based on the optimal mass transport theory where the distance between two distributions is computed with respect to a cost function. The addressed fault detection problem models the data using the KPCA framework and utilizes the ability of the KD statistical indicator to detect faults. The detection stage involves comparing the residuals of training fault-free data and testing faulty data using the KD statistic. Additionally, the reference threshold for the KD statistic is computed using the kernel density estimation (KDE) approach as compared to the previously utilized three-sigma rule approach. The detection performance is illustrated with the help of three benchmark case studies: a continuous stirred tank reactor (CSTR) process, Tennessee Eastman (TE) process and an experimental distillation column process. The performance analysis suggests the superiority of the KPCA-KD fault detection scheme in monitoring various sensor faults. Moreover, comparison with traditional statistical indicators of PCA and KPCA schemes shows that the proposed scheme enhances fault detection and achieves an improved detection rate in monitoring different categories of faults.