Compressive sparse principal component analysis for process supervisory monitoring and fault detection. (February 2017) - Liu, Yang; Zhang, Guoshan; Xu, Bingyin
Highlights: Compressive sparse principal component analysis (CSPCA) is proposed for process supervisory monitoring and fault detection. CSPCA takes into account the effects of PCs with small scores. CSPCA establishes a connection between the resolution problem of sparse PCs and the selection problem of PCs, and both problems are solved in the unified framework. CSPCA can adaptive partially reconstruct abnormal data without prior information of the sparsity. CSPCA is a convex optimization problem. Abstract: This paper presents a novel sparse principal component analysis method, which is named the compressive sparse principal component analysis (CSPCA) . CSPCA ensures that the effects of principal components (PCs) with small scores (eigenvalues/variances) on monitoring performance are taken into account during deriving the first PCs, and measurements are adaptively compressed and partially reconstructed without prior knowledge of data sparsity. The proposed method employs the strategy of screening, reconstructing, and detecting for process supervisory monitoring. Data-screening algorithm is employed to sift out data with essential characteristics of abnormal situations at the screening stage. Data selected are adaptively compressed, and abnormal features are highlighted by the partial reconstruction algorithm at the reconstructing stage. A new SPCA is developed by introducing L 2, 1 -norm to replace the usual norm in the traditional SPCA, and is employed to analyse data reconstructed at the detecting stage. The effectiveness of the compressive sparse principal component analysis is evaluated on the Pitprops data set and the Tennessee-Eastman process with promising results.