Exponential Local Fisher Discriminant Analysis with Sparse Variables Selection: A Novel Fault Diagnosis Scheme for Industry Application

Abstract

Local Fisher discriminant analysis (LFDA) has been widely applied to dimensionality reduction and fault classification fields. However, it often suffers from small sample size (SSS) problem and incorporates all process variables without emphasizing the key faulty ones, thus leading to degraded fault diagnosis performance and poor model interpretability. To this end, this paper develops the sparse variables selection based exponential local Fisher discriminant analysis (SELFDA) model, which can overcome the two limitations of basic LFDA concurrently. First, the responsible faulty variables are identified automatically through the least absolute shrinkage and selection operator, and the current optimization problem are subsequently recast as an iterative convex optimization problem and solved by the minimization-maximization method. After that, the matrix exponential strategy is implemented on LFDA, it can essentially overcome the SSS problem by ensuring that the within-class scatter matrix is always full-rank, thus more practical in real industrial practices, and the margin between different categories is enlarged due to the distance diffusion mapping, which is benefit for the enhancement of classification accuracy. Finally, the Tennessee Eastman process and a real-world diesel working process are employed to validate the proposed SELFDA method, experimental results prove that the SELFDA framework is more excellent than the other approaches.