Multivariate Statistical Process Monitoring Based on Statistics Pattern Analysis

TLDR

The SPA framework was recently introduced to address challenges in batch process monitoring, such as unsynchronized trajectories and multimodal distributions, by monitoring statistics of process variables rather than the variables themselves, contrasting with PCA which monitors the variables' variance–covariance. This study develops a window‑based SPA method to monitor continuous processes, aiming to overcome nonlinear dynamics and other challenges. The method applies a sliding‑window SPA that analyzes statistics such as mean, variance, autocorrelation, and cross‑correlation, and its fault‑detection properties are demonstrated on a simple nonlinear example and two case studies, with performance compared to PCA and DPCA. Results show that the window‑based SPA method outperforms benchmark PCA and DPCA approaches.

Abstract

In this work, a new multivariate method to monitor continuous processes is developed based on the statistics pattern analysis (SPA) framework. The SPA framework was proposed recently to address some challenges associated with batch process monitoring, such as unsynchronized batch trajectories and multimodal distribution. The major difference between the principal component analysis (PCA) based and SPA-based fault detection methods is that PCA monitors process variables while SPA monitors the statistics of process variables. In other words, PCA examines the variance−covariance of the process variables to perform fault detection while SPA examines the variance−covariance of the process variable statistics (e.g., mean, variance, autocorrelation, cross-correlation, etc.) to perform fault detection. In this paper, a window-based SPA method is proposed to address the challenges associated with continuous processes such as nonlinear process dynamics. First, the details of the window-based SPA method are presented; then the basic properties of the SPA method for fault detection are discussed and illustrated using a simple nonlinear example. Finally, the potential of the window-based SPA method in monitoring continuous processes is explored using two case studies (a 2 × 2 linear dynamic process and the challenging Tennessee Eastman process). The performance of the window-based SPA method is compared with the benchmark PCA and DPCA methods. The monitoring results clearly demonstrate the superiority of the proposed method.