Nonstationary Industrial Process Monitoring Based on Stationary Projective Dictionary Learning

Industrial data generally exhibit nonstationary features due to load changes, external disturbances, etc., which raise great challenges for process monitoring. Most existing methods for nonstationary process monitoring use a two-stage strategy, where stationary series are obtained via preprocessing, followed by feature extraction and modeling for the stationary series. However, the two-stage strategy treats preprocessing and feature extraction separately, which would obtain suboptimal features. This article develops the stationary projective dictionary learning (SPDL) method for monitoring nonstationary industrial processes. Specifically, nonstationary data are projected into a stationary subspace, overcoming the disadvantages of nonstationarity and improving the representation ability of the dictionary. Then, considering process data usually have temporal correlations, a novel self-expression constraint term is added to optimize the features so that it can describe the process data accurately. Finally, an iterative approach is proposed for joint optimization of the projection matrix and the dictionary, and the formulas for parameter estimation are derived in detail. After the projection matrix and the dictionary are obtained, the nonstationary data are projected and reconstructed, and the reconstruction error is adopted to design the monitoring statistic. Case studies on a numerical example, a nonstationary continuous stirred tank reactor (CSTR), and an industrial roasting process reveal that the proposed method is suitable for nonstationary industrial process monitoring.