Nonstationary Process Monitoring Using Sparse Stationary Subspace Analysis

Stationary subspace analysis (SSA) is an emerging algorithm for nonstationary process monitoring, which establishes a linear relationship between nonstationary variables and stationary components. However, the linear transformation reduces the interpretability of SSA. In this paper, a novel algorithm called sparse SSA (SSSA) is proposed to deal with this problem. The SSSA algorithm is described as a sparse optimization problem, where the $\ell_{2,1}$ norm is used to restrict the sparsity of the stationary projection matrix. After the sparse projection matrix is obtained, a monitoring statistic is developed using the Mahalanobis distance. The effectiveness of the proposed method is demonstrated by two case studies, including a numerical example and a closed-loop continuous stirred tank reactor.