A novel white component analysis for dynamic process monitoring

Abstract

Dynamic principal component analysis has long been a popular multivariate statistical process monitoring method. However, the resulting residuals are typically subject to serial correlations, thereby compromising the detection capability in face of dynamic data. In this paper, a novel white component analysis (WCA) model is proposed to enforce latent variables to have noise-like properties, thereby well catering to the independent assumption that is critical in monitoring statistic design. A new whiteness index for finite-length time series is put forward, which acts as the objective of each component. To solve the optimization problem, a tailored algorithm based on alternating direction method of multipliers is developed. Using “white” components, a new W-statistic is coined to effectively detect violation of dynamic relations by inspecting the presence of unmodeled dynamics. By incorporating classical variance-based statistics, we arrive at a new dynamic process monitoring scheme that offers deep insights into abnormal situations. Comprehensive case studies corroborate the validity of the WCA-based process monitoring approach, and in particular, the sensitivity of W-statistic to dynamics anomalies.