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 ${\mathit{T}}^2$ statistic that is defined using components of GSPCA, and the inter-group FDD based on a ${\mathit{T}}^2$ statistic that is defined using the residuals generated by IGCCA. Two case studies are used to illustrate advantages of the multigroup FDD framework.

在多变量系统中，故障通常仅由几个变量引起。但是，在传统的故障检测和诊断（FDD）方法中，所有变量都包含在故障检测索引中。在这种情况下，可以通过引入更多的无故障变量来减弱较少的故障变量对故障检测指标的影响。因此，FDD性能降低。为了解决这个问题，本文提出了一种用于大型多元系统的多组FDD框架。该框架基于三种新方法：一种变量分组算法，以及两种用于以变量组形式对多变量数据进行统计分析的方法，称为逐组稀疏主成分分析（GSPCA）和组间规范相关分析（ IGCCA）。变量分组算法通过最大化组内的变量相关性同时最小化组间的变量相关性来生成最佳变量组。GSPCA产生一组按组的稀疏分量。每个分量仅对一组变量具有非零载荷，因此，它解释了相应组中的变量相关性。与GSPCA不同，IGCCA可以提取变量组之间的最大相关性。多组FDD框架包括两个部分：基于联合的组内FDD 因此，它解释了相应组中的变量相关性。与GSPCA不同，IGCCA可以提取变量组之间的最大相关性。多组FDD框架包括两个部分：基于联合的组内FDD 因此，它解释了相应组中的变量相关性。与GSPCA不同，IGCCA可以提取变量组之间的最大相关性。多组FDD框架包括两个部分：基于联合的组内FDD${\mathit{Ť}}^{\mathrm{2个}}$ 使用GSPCA组件和基于以下内容的组间FDD定义的统计信息： ${\mathit{Ť}}^{\mathrm{2个}}$使用IGCCA生成的残差定义的统计量。通过两个案例研究来说明多组FDD框架的优势。