Statistical process fault isolation using robust nonnegative garrote

Highlights

• Multivariate fault isolation methods are proposed based on NNG and R-NNG.

• The R-NNG-based method is robust to the outliers in historical process data.

• Process variables are arranged according to their responsibility to the fault.

• The isolation results are informative for enhancing process understanding.

Abstract

Fault isolation is an essential procedure in multivariate statistical process monitoring, which is used to locate the detected fault. Fault isolation identifies the crucial variables responsible for the detected fault. Accurate isolation results are useful for process engineers in diagnosing the root cause of the fault. Recent studies have revealed the equivalence between the fault isolation task and the variable selection problem in discriminant analysis. Inspired by this idea, a nonnegative garrote-based fault isolation strategy is developed to identify the criticality of each process variable to the detected fault, which is further revised to a more robust version by adopting a robust nonnegative garrote. The critical variables can be identified even when the historical process data are contaminated by outliers using the method proposed in this study. The Tennessee Eastman process was used to illustrate the validity of the proposed method.

Introduction

In the last few decades, multivariate statistical process monitoring (MSPM) in modern industrial processes has garnered increased attention due to the requirements for plant safety, product quality, and economics [1], [2], [3]. As discussed in [4], process monitoring consists of four aspects: fault detection, isolation (identification), root cause diagnosis, and process recovery. Fault detection investigates if a fault has occurred in the process. Fault isolation locates the detected fault and identifies the process variable critical to the fault. Root cause diagnosis aims to determine the root cause of the observed process abnormality by using causality analysis techniques, such as Granger causality test, transfer entropy, and Bayesian networks [5], [6], [7], [8], [9]. Then, the effect of the fault can be removed by process recovery. It is obvious that fault isolation is an important step in connecting fault detection to root cause diagnosis, which is the focus of this research work.

There have been a number of classical fault isolation methods. The Mason, Young and Tracy (MYT) decomposition can be applied to fault isolation by dividing the T² statistic into a limited number of orthogonal items [10]. Despite of its good statistical properties, its practical use in industrial processes can be difficult, because of the huge number of decompositions to be considered [11]. Comparing to the MYT decomposition, contribution plots [12,13] and reconstruction analysis [14,15] are more popular in industrial applications. Contribution plots method isolates the faulty variables by comparing the contribution of each process variable to the monitoring statistic with a predetermined control limit. However, a phenomenon called smearing effect, which means that the faulty variables often influence the contributions of non-faulty variables, limits the effectiveness of this method [16,17]. The cause of smearing effect has been expounded upon in the literature [18]. Reconstruction analysis method can avoid smearing, which is based on the assumption that the candidate fault directions can be acquired. In this method, the faulty variables are isolated by minimizing the reconstructed monitoring statistic along these candidate directions. To relax the requirement of the candidate fault directions, the branch and bound (B&B) algorithm is utilized to locate the faulty variables in reconstruction analysis [19], [20], [21]. However, the computational burden of this algorithm is quite high, especially when there are many variables involved. Therefore, this method is not suitable for online applications. To solve this, the penalized reconstruction-based multivariate contribution analysis method was proposed to improve the efficiency of the fault isolation algorithm [22], [23], [24].

Most recently, Kuang et al. [25] and Yan et al. [26] revealed the equivalence between the problems of multivariate fault isolation and variable selection in discriminant analysis. They illustrated their idea with algorithms based on least absolute shrinkage and selection operator (LASSO). These methods avoid smearing effect and is computationally efficient for online applications, eliminating the need for indicating historical failure data or candidate failures. However, there is no guarantee regarding robustness when the historical normal operating data are contaminated by outliers. Other advanced statistical fault isolation methods, including reconstruction-based contribution [27], modified contribution plot [28], parsimonious reconstruction [29], etc., were not designed for robust fault isolation either.

The problem of robustness has been intensively studied in the field of fault detection [30], [31], [32], [33] but seldom considered in fault isolation. It is commonly assumed that the outliers are identified and removed during the fault detection step before conducting fault isolation. However, sometimes outliers can be carriers of valuable information. Hence, eliminating them could cause information loss during fault isolation. Inspired by the study of [25], this study proposes a nonnegative garrote (NNG)-based fault isolation method, which is further revised to a more robust version using a robust NNG (R-NNG) algorithm. A comparative performance analysis of the LASSO-based fault isolation methods, NNG, and R-NNG is performed using the Tennessee Eastman (TE) process simulation. The results indicate that the proposed R-NNG based fault isolation method outperforms the other two methods.

The rest of this paper is organized as follows. In Section 2, the relationship between fault isolation and variable selection in discriminant analysis is discussed. In Section 3, the NNG and R-NNG-based fault isolation algorithms are proposed. In Section 4, two simulation case studies are used to compare the isolation performance of LASSO, NNG, and R-NNG. Section 5 provides more discussions and concludes this paper.