Structured Joint Sparse Orthogonal Nonnegative Matrix Factorization for Fault Detection

Abstract

As modern industrial processes become complicated, and some faults are difficult to be detected due to noises and nonlinearity of data, data-driven fault detection has been extensively used to detect abnormal events in functional units. In order to obtain the better fault detection performance of nonnegative matrix factorization, this paper first proposes a fault detection method using the structured joint sparse orthogonal nonnegative matrix factorization. The core idea is to incorporate the graph regularization, sparsity and orthogonality constraints into the classical nonnegative matrix factorization, which enjoys stronger discriminative ability, removes redundancy of different basis vectors and improves the fault interpretability. More importantly, an optimization algorithm based on the proximal alternating nonnegative least squares is developed, which can guarantee and speed up the convergence. Finally, the effectiveness of the proposed method is demonstrated by the experiments on the benchmark Tennessee Eastman Process and two practical bearing datasets. Particularly, compared with the classical nonnegative matrix factorization, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> statistic has a gain of 33.13% for the fault IDV(16) on the Tennessee Eastman Process. The results show that the proposed model and algorithms are promising for the fault detection.