Dynamic Stationary Subspace Analysis for Monitoring Nonstationary Dynamic Processes

With the increasing demand for process safety and production efficiency, many research efforts have been made for nonstationary process monitoring in recent years. However, existing methods usually neglect dynamic characteristics of industrial processes, which may lead to misleading results. Only few literature studies address the problem of nonstationary dynamic process monitoring, and most of them are mainly based on the assumption that nonstationary variables are integrated with the same order I = 1. In order to deal with the general case, where nonstationary variables are integrated with different or higher orders, dynamic stationary subspace analysis (DSSA) is proposed in this paper. In DSSA, the time shift technique is introduced to model dynamic relationships, and an optimization problem is described to estimate the stationary projection matrix similar to stationary subspace analysis (SSA). Different from traditional SSA, the alternating direction method of multipliers is utilized to solve the optimization problem, and detailed iteration expressions are derived. After the stationary projection matrix is obtained, the Mahalanobis distance is adopted for monitoring stationary components of augmented data. The monitoring performance of DSSA is demonstrated by case studies on a simulated nonstationary dynamic process, a nonstationary continuous stirred tank reactor, and a practical ultra-supercritical power plant.