Dynamic multivariate threshold optimization and alarming for nonstationary processes subject to varying conditions

Abstract

For the alarm system of nonstationary industrial processes, the conventional alarm thresholds configured for one single operational zone often result in frequent false and missed alarms. Besides, these univariate thresholds neglect interactions among process variables. To address these issues, this paper proposes a novel dynamic multivariate alarm threshold optimization algorithm for nonstationary processes subject to varying conditions. Firstly, the process correlation variations can be identified by Toeplitz inverse covariance-based clustering method, pointing to the changes of operating conditions. Each condition can be structurally interpreted by an inverse covariance matrix of the multivariate Gaussian distribution, revealing similar within-time and cross-time variable interactions. Therefore, it provides a promising foundation to capture the conditional Gaussian distribution and design the corresponding thresholds of each variable, which finely covers the current normal operational zone. Then, offline threshold optimization and online alarming strategy are developed and discussed in detail, which can timely adapt the model to varying conditions, promoting accurate and sensitive alarming performance. Finally, the validity of the proposed threshold is demonstrated on both continuous and batch processes with typical nonstationary characteristics. Results show that the proposed threshold can effectively adapt to varying conditions and aggregate multivariate information, thus reducing nuisances and ensuring the reliability of the alarm system as well.