Sparse analysis based fault deviations modeling and its application to fault diagnosis

In the fault process, some specific variables will be disturbed significantly and cover much fault information, while some irresponsible variables still keep similar relations with those of normal condition. Therefore, this paper proposes a sparse relative discriminant fault deviations (SRDFD) modeling algorithm which can extract fault directions and isolate faulty variables simultaneously to improve fault diagnosis performance. In the proposed algorithm, a sparse objective function is formulated by bringing an L1 penalization to the objective function of fault degradation oriented FDA (FDFDA) algorithm, which improved the traditional FDA algorithm by further considering the relative variations of variance between fault data and normal data. The proposed objective function is not convex, so that the minorization-maximization approach is used to efficiently optimize it. Then soft threshold operator is performed for analytic solutions. The extracted sparse directions and the corresponding loadings are used as reconstruction models to eliminate fault deviations. Online fault diagnosis is then conducted by finding the correct reconstruction models which can best eliminate the out-of-control monitoring statistics. The performance is verified by the pre-programmed faults of Tennessee Eastman (TE) benchmark process.