Penalized Reconstruction-Based Multivariate Contribution Analysis for Fault Isolation

Contribution analysis in multivariate statistical process monitoring (MSPM) identifies the most responsible variables to the detected process fault In multivariate contribution analysis, the main challenge of fault isolation is to determine the appropriate variables to be analyzed, and this usually results in a combinatorial optimization problem. Reconstruction based multivariate contribution analysis (RBMCA) is a generic framework to solve this problem. This paper derives a sufficient condition for the isolatability of faulty variables when using RBMCA. In addition, a penalized RBMCA (PRBMCA) framework is developed to enhance the effectiveness and efficiency of fault isolation, especially for process faults with a small magnitude. In contrast to the original RBMCA, this penalized solution includes two steps. L-1-penalized reconstruction is used in the first step to obtain a more compact set of faulty variables. Then, the original RBMCA with a branch and bound algorithm is implemented to further narrow down the faulty variables. The PRBMCA framework is a generic formulation in that it is applicable to various MSPM models. The effectiveness and computational efficiency of the proposed methodology is demonstrated through a numerical example and a benchmark problem of the Tennessee Eastman process.