Abstract
Isolating faulty variables is play an important role in multivariate statistical process monitoring (MSPC), which discover the source of the detected fault and ensure the safe and efficient operation of manufacturing and chemical industries. However, the MSPM is difficult to analyze the influences of multiple variables on monitoring statistics and relatively limited to isolate faulty variables. The most popular technique for fault isolation is contribution plots. Although easy to use, contribution plots often suffer from “smearing” effect and yield misleading results. Reconstruction analysis is another type of isolation method, which re-calculates the values of process variables and monitoring statistics along certain candidate “faulty directions”. Such method requires the candidate “faulty directions” to be known, which may not be satisfied in industrial applications. A branch and bound (BAB) algorithm was proposed to address the fault isolation problem by solving a combinatorial optimization problem. However, the computational burden of BAB is heavy. In addition, reconstruction analysis may lead to inaccurate results when the number of variables is large, as shown in this paper. To solve the mentioned problems of the existing methods, this paper proposes to conduct fault isolation via penalized discriminant analysis. In industrial processes, the process can be divided into a continuous process and batch process, and each process have unique characteristics. According to the process method, we propose two kind of fault isolation method, respectively, for a continuous process and batch process. The basic idea is as follows. The goal of fault isolation is to identify variables responsible for the detected process abnormality. In other words, the variables to be isolated are those discriminating the normal process measurements and the fault samples. In a sense, isolating faulty variables is equivalent to identifying discriminating variables in a two-class problem, with the normal operation data regarded as belonging to one class and the data corresponding to the detected fault as belonging to the other class. Added a penalty term of discriminant analysis can reach the effect of variables selection. Since the proposed method can be solved efficiently using state-of-the-art algorithms, the problem of computational burden is avoided. Instead of just offering a suggested set of faulty variables, the proposed method provides more information on the relevance of process variables to the detected fault, which facilitates the subsequent root cause diagnosis step after isolation. The benchmark Tennessee Eastman (TE) process and injection molding process are used as a case study to illustrate the effectiveness of the proposed method. The results show that, comparing to the existing methods, the penalized discriminant analysis method is more information-rich and easier to calculate.