Fisher Discriminative Sparse Representation Based on DBN for Fault Diagnosis of Complex System

Fault detection and diagnosis in the chemical industry is a challenging task due to the large number of measured variables and complex interactions among them. To solve this problem, a new fault diagnosis method named Fisher discriminative sparse representation (FDSR), based on deep belief network (DBN), is proposed in this paper. We used DBN to extract the features of all faulty and normal modes. Features extracted by the DBN were used to learn subdictionaries, then the overcomplete dictionary was constructed by cascading all subdictionaries in order, and each dictionary atom corresponded to class labels. The Fisher discrimination criterion (FDC) was applied to the dictionary learning to ensure smaller within-class scatter but greater between-class scatter. The quadratic programming method was applied to estimate the sparse coefficients simultaneously class by class. Therefore, both the reconstruction error and sparse coefficients were discriminative, so that the reconstruction error after sparse coding can be used for pattern classification. An experiment performed on the Tennessee Eastman (TE) process indicated that compared with the traditional monitoring methods, the FDSR based on DBN produced more interpretable results and achieved superior performance for feature extraction and classification in the field of complex system fault diagnosis. T-distributed stochastic neighbor embedding (t-SNE) appropriately visualized the performance of the proposed method and produced reliable fault diagnosis results.