Application of principal component pursuit to process fault detection and diagnosis

Abstract

Data-driven process monitoring has been extensively discussed in both academia and industry because of its applicability and effectiveness. One of the most applied techniques is the principal component analysis (PCA). Recently a new technique called principal component pursuit (PCP) is introduced. Compared to PCA, PCP is more robust to outliers. In this paper, the application of the PCP technique to process monitoring is thoroughly discussed from training data preprocessing to residual signal post-filtering. A new scaling preprocessing step is proposed to improve quality of data matrices in the sense of low coherence. A residual generator and a post-filter suitable for PCP generated process models are also provided. The post-filtered residual represents the fault signal, which makes the fault detection, isolation and reconstruction procedures simple and straightforward. A numerical example is provided to describe and illustrate the PCP-based process modeling and monitoring procedures.

Robust Principal Component Pursuit for Fault Detection in a Blast Furnace Process

“…The normalization formula of testing matrix Z is given as follows: where d ij is the ij th element of normalized testing matrix D. z ij is the ij th element of the original testing matrix Z. a̅ j and s j are the mean and standard deviation, respectively, of the j th variable calculated in step 2.…”

“…In 2011, the PCP method was used for process monitoring for the first time by Isom et al; they illustrated that PCP is robust to outliers and that it can detect and isolate faults simultaneously by observing the obtained sparse matrix. A new standardized method and a residual generator suitable for PCP generated process models were developed by Cheng et al Pan et al proposed a new mean-correlation statistic suitable for online process monitoring based on the PCP method . A coordinate descent algorithm based on PCP and its convergence proof that directly utilized a Lyapunov approach were also presented by Cheng et al A process monitoring model and an online monitoring statistic with stable PCP were developed by Yan et al Pan et al introduced a novel IPCP method derived from low rank representation (LRR) and PCP methods, and an online process monitoring statistic was also developed …”