PSINDy: Probabilistic sparse identification of nonlinear dynamics for temporal process modeling and fault detection

Abstract

BackgroundMultivariate statistical process monitoring (MSPM) methods have been widely studied and applied for dynamic process monitoring. However, limitations exist in the extant literature, as numerous extant MSPM approaches fail to concurrently account for the governing dynamics and inherent non-linearity of systems. MethodsTo handle the above-mentioned issue, a novel probabilistic dynamic process monitoring algorithm named probabilistic sparse identification of nonlinear dynamics (PSINDy) is proposed. In this algorithm, the Expectation–Maximization (EM) method is employed to estimate the parameters. In the E-step, the particle filtering technique is adopted to calculate corresponding latent expectations whose posterior distributions are not Gaussian. Furthermore, Hotelling's T2 and two novel monitoring statistics, termed Mahalanobis-based predictive error (MPE) and dynamic predictive error (DPE), are designed and utilized for fault detection. Significant FindingsThe effectiveness of the proposed method is validated through the Tennessee Eastman (TE) chemical process and the three-phase flow facility (TPFF).