Sparse Exponential Discriminant Analysis and Its Application to Fault Diagnosis

Discriminant analysis, as a popular supervised classification method, has been successfully used in fault diagnosis, which, however, involves a linear combination of all variables, and thus may result in poor model interpretability and inaccurate classification performance. In this paper, a sparse exponential discriminant analysis (SEDA) algorithm is proposed for addressing those issues. The sparse discriminant model is developed by introducing the penalty of lasso or elastic net into the exponential discriminant analysis algorithm, so that the key variables responsible for the fault can be automatically selected. Since the formulated model is nonconvex, it is recast as an iterative convex optimization problem using the minorization-maximization algorithm. After that, a feasible gradient direction method is developed to solve the optimization problem effectively. The sparse solutions indicate the key faulty information to improve classification performance, and thus distinguish different faults more accurately. A simulation process and a real industrial process are used to test the performance of the proposed method, and the experimental results show that the SEDA algorithm can isolate the faulty variables and simplify the discriminant model by discarding variables with little significance.