Penalized Reconstruction-Based Multivariate Contribution Analysis for Fault Isolation

Abstract

-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 analysed and this usually results in a combinatorial optimisation 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 small magnitude. In contrast to the original RBMCA, this penalized solution includes two steps. penalized reconstruction is used in the first step to obtain a more compact set of faulty variables. Then, the original RBMCA with 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.

Root cause analysis in multivariate statistical process monitoring: Integrating reconstruction-based multivariate contribution analysis with fuzzy-signed directed graphs

“…However, the optimisation problem could have multiple solutions with similar objective values, and thus it does not guarantee to find the actual root cause or faulty variables. Since the present study is focused on the integration of fault isolation with SDG for fault diagnosis, the reader is referred to more detailed investigation of the fault isolation accuracy in (He et al, 2013). …”

“…A BnB algorithm was proposed to efficiently solve the combinatorial optimisation problem. Later, an L 1 penalty was introduced to the variable reconstruction step of RBMCA (thus named PRBMCA), before using the BnB algorithm (He et al, 2013). PRBMCA tends to reduce the number of isolated faulty variables thus to give clearer interpretation of the results.…”

“…It was observed that RBMCA could isolate a large number of process variables when the fault magnitude is small or moderate, even with the constraint on the number of variables in eq. (3) (He et al, 2013). This is undesirable in practice, since it creates difficulty for the process engineers to find the underlying cause from many responsible variables.…”

“…(5) can be solved by using quadratic programming (He et al, 2013). It was demonstrated that both the computational efficiency and the accuracy of fault isolation have been significantly improved by introducing the penalty in RBMCA (He et al, 2013).…”

“…Besides 22 continuous measured variables and 11 manipulated variables (MV), five composition measurements which presented in control loops are included. Out of the various process disturbances, Table 2 lists the seven typical faults that can be detected by PPCA (He et al, 2013), since PPCA has been chosen to illustrate the fault diagnosis results. As discussed previously, other statistical monitoring models can also be used within the PRBMCA-SDG framework, though a comprehensive exploration of alternative monitoring methods is outwith the scope of this study.…”