A Sequential Bayesian Partitioning Approach for Online Steady-State Detection of Multivariate Systems

Abstract

The steady-state detection is critically important in many engineering fields, such as fault detection and diagnosis and process monitoring and control. However, most of the existing methods were designed for univariate signals and, thus, are not effective in handling multivariate signals. In this paper, we propose an efficient online steady-state detection method for multivariate systems through a sequential Bayesian partitioning approach. The signal is modeled by a Bayesian piecewise constant mean and covariance model, and a recursive updating method is developed to calculate the posterior distributions analytically. The duration of the current segment is utilized for steady-state testing. Insightful guidance is also provided for hyperparameter selection. The effectiveness of the proposed method is demonstrated through thorough numerical and real case studies. Note to Practitioners —This paper addresses the problem of online steady-state detection of systems captured by multivariate signals. Existing approaches often monitor each signal independently, and the system is claimed steady when all signals reach steady state. These methods have many shortcomings, such as failing to consider the correlations among signals and suffering the multiple testing problems. In this paper, we propose a novel joint monitoring approach, where the multivariate signal is sequentially partitioned into segments of constant mean and covariance through an online Bayesian inference scheme, and once the current segment duration is sufficiently large, the signal is considered steady. We also provide several insightful guidelines to select appropriate hyperparameters under different scenarios. The proposed approach is much more accurate and robust than existing ones. However, this method may face prohibitive computational cost and ill-posed covariance inversion problem when there are hundreds or even thousands of variables in the system. In future research, we will develop efficient distributed monitoring and data fusion techniques to overcome these challenges.