Locality preserving discriminative canonical variate analysis for fault diagnosis. (2nd September 2018) - Lu, Qiugang; Jiang, Benben; Gopaluni, R. Bhushan; Loewen, Philip D.; Braatz, Richard D.
Highlights: We proposed a method known as discriminative canonical variate analysis that combines the canonical variate analysis (CVA) and Fisher discriminant analysis (FDA) for fault classification. The proposed method can preserve the capability of CVA in addressing high-dimensional process data with serial correlations and the merits of FDA for distinguishing faults from different classes. The proposed discriminative CVA can maximize the within-class mutual canonical correlations (between past and future information vectors) and minimize the between-class mutual canonical correlations. Furthermore, we incorporate the idea of locality preserving projection into our discriminative CVA formulation to enhance its ability in handling nonlinearities in the data with the form of local manifolds. By exploring the local structures, we can greatly enhance the performance of our method in fault classification. We demonstrate the process of converting the locality preserving discriminative CVA into a generalized eigenvalue problem, which admits efficiently and stable numerical solutions. We compare our method with the existing methods, such as FDA, dynamic FDA, CVA-FDA, localized DFDA, in fault classification through two case studies from the Tennessee Eastman process. It is shown that our method can give better classification performance than the other three methods. Abstract: This paper proposes a locality preserving discriminative canonical variate analysis (LP-DCVA) scheme for fault diagnosis. The LP-DCVA method provides a set of optimal projection vectors that simultaneously maximizes the within-class mutual canonical correlations, minimizes the between-class mutual canonical correlations, and preserves the local structures present in the data. This method inherits the strength of canonical variate analysis (CVA) in handling high-dimensional data with serial correlations and the advantages of Fisher discriminant analysis (FDA) in pattern classification. Moreover, the incorporation of locality preserving projection (LPP) in this method makes it suitable for dealing with nonlinearities in the form of local manifolds in the data. The solution to the proposed approach is formulated as a generalized eigenvalue problem. The effectiveness of the proposed approach for fault classification is verified by the Tennessee Eastman process. Simulation results show that the LP-DCVA method outperforms the FDA, dynamic FDA (DFDA), CVA-FDA, and localized DFDA (L-DFDA) approaches in fault diagnosis.