A multigroup framework for fault detection and diagnosis in large-scale multivariate systems

Abstract

Abstract In the multivariate system, a fault is often caused only by a few variables. However, in traditional fault detection and diagnosis (FDD) methods, all of variables are included in the fault detection index. In this case, the effect of fewer faulty variables on the fault detection index may be weakened by the introduction of a larger number of fault-free variables. Consequently, the FDD performance is reduced. To address this problem, this paper proposes a multigroup FDD framework for large-scale multivariate systems. This framework is based on three new approaches: a variable grouping algorithm, and two methods for the statistical analysis of multivariate data in the form of variable groups, called group-wise sparse principal component analysis (GSPCA) and inter-group canonical correlation analysis (IGCCA). The variable grouping algorithm generates optimal variable groups by maximizing variable correlations within groups while minimizing variable correlations among groups. The GSPCA produces a set of group-wise sparse components. Each component has nonzero loadings only for variables in one group, and thus it explains variable correlations in the corresponding group. Different from GSPCA, the IGCCA can extract the maximum correlations between variable groups. The multigroup FDD framework consists of two parts: the intra-group FDD based on a joint T 2 statistic that is defined using components of GSPCA, and the inter-group FDD based on a T 2 statistic that is defined using the residuals generated by IGCCA. Two case studies are used to illustrate advantages of the multigroup FDD framework.