Multistate multivariate statistical process control

For high-dimensional, autocorrelated, nonlinear, and nonstationary data, adaptive-dynamic principal component analysis (AD-PCA) has been shown to do as well or better than nonlinear dimension reduction methods in flagging outliers. In some engineered systems, designed features can create a known multistate scheme among multiple autocorrelated, nonlinear, and nonstationary processes, and incorporating this additional known information into AD-PCA can further improve it. In simulations with one of three types of faults introduced, we compare accounting for the states versus ignoring them. We find that multistate AD-PCA reduces the proportion of false alarms and reduces the average time to fault detection. Conversely, we also investigate the impact of assuming multiple states when only one exists, and find that as long as the number of observations is sufficient, this misspecification is not detrimental. We then apply multistate AD-PCA to real-world data collected from a decentralized wastewater treatment system during in control and out of control conditions. Multistate AD-PCA flags a strong system fault earlier and more consistently than its single-state competitor. Furthermore, accounting for the physical switching system does not increase the number of false alarms when the process is in control and may ultimately assist with fault attribution.