Improved canonical correlation analysis-based fault detection methods for industrial processes☆
Introduction
With increasing understanding of the intricacies present in complex, industrial plants, the ability to improve product quality, operation safety, and reliability has correspondingly increased. High-efficiency fault detection methods play an essential role in avoiding malfunctions in process equipment, predicting performance degradation, and decreasing maintenance effort. Driven by this trend, process monitoring and fault diagnosis (PM-FD) techniques have received much attention over the past decades. The most commonly encountered faults can be divided into two categories [1]:
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additive faults that only influence the mean value of the process; and
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multiplicative faults that influence the variances, covariances, or higher-order statistical characteristics of the process.
Based on the physical and mathematical knowledge of the industrial processes, the model-based methods have received considerable attention [4], [5] and found a large number of successful applications [6], [7], [8], [9]. In industrial applications, e.g. the process industry, data-driven approaches are widely applied for PM-FD due to their simple form and fewer requirements on design and engineering effort. On the other hand, the techniques for processing routine data have been significantly improved [10], [11], [12], [13], [14]. Among the numerous data-driven approaches, multivariate analysis (MVA)-based ones, with principal component analysis (PCA) and partial least squares (PLS) as representative methods, are a major part. The early work can be found in [15]. In past years, various improvements to the conventional MVA-based methods have been made to solve problems like dynamics [16], time-varying [17], [18] and nonlinearity [19], [20]. Various methods have also been introduced for process monitoring, such as independent component analysis (ICA)-based [21], [22], canonical correlation analysis (CCA)-based [23] and probabilistic MVA-based methods [24]. The reader is referred to [11], [12], [25], [26], [27], [28], [29], [30], [31] for a comprehensive literature review.
Compared with the large amount of research work focused on (incipient) additive fault detection (FD) issues [32], studies on multiplicative faults are relatively few [33]. In fact, early detection of multiplicative faults is necessary in industry. The earlier the detection, the faster can the appropriate measures be taken to avoid accidents and serious economic losses. In Zhang et al. [34], a statistical local approach was proposed to provide early warning of slight changes in the system. Furthermore, Basseville [35] developed and elaborated the key principles of the statistical local approach for application to component fault detection and isolation. Juricek [36] introduced the statistical local approach to canonical variate analysis (CVA). In Kruger et al. [37], the incorporation of PCA and the statistical local approach has been proposed to detect incipient changes in the covariance structure. In order to detect incipient fault in processes that are subject to non-Gaussian noise, Ge et al. [38] proposed a process monitoring method based on ICA and the statistical local approach. Li et al. [39] incorporated the statistical local approach into manifold-based method for process monitoring.
Taking into account the input and output data, CCA method has been developed both for static and dynamic processes [23]. This method, which deals with both input and output variables, can be viewed as an extension of the PCA and PLS methods [15], [40]. Unlike the CVA-based methods that depend on canonical variable, CCA-based methods are primarily developed based on the canonical correlation residual generator framework. The CCA-based methods are mainly characterized by their significantly simplified design procedure due to avoiding the need for system identification. However, these methods still face the same problem when coping with incipient multiplicative faults.
Therefore, this paper focuses on improving the CCA-based methods to detect incipient multiplicative faults in industrial processes. The objectives of this paper are to propose a new method that integrates the statistical local approach into the existing CCA-based methods for detecting incipient multiplicative faults, and to demonstrate the strength of the proposed method using a pilot scale continuous stirred tank heater (CSTH) and the Tennessee Eastman benchmark process (TEP).
Notation: The notation used in this paper is standard. denotes the n-dimensional Euclidean space consisting of n × 1 vectors with real components, is the set of all n × m real matrices, and diag(., …, .) is a square diagonal matrix. rank(A) denotes the rank of matrix A. A(:, i) represents the i-th column of A. In is an n × n identity matrix. E(·) is the expectation operator. denotes that x is a normally distributed random vector with mean μx and covariance Σx. χ2(m) stands for the chi-square distribution with m degrees of freedom and stands for the F distribution with m and n degrees of freedom. Let be the probability that equals α (significance level) and be the probability that equals α.
Section snippets
Background
This section seeks to propose a unified framework of CCA-based FD methods for linear static and dynamic processes. In the static case, the output is assumed to be affected only by the current measurements. In the dynamic case, the process is assumed to be running in steady state and the output can depend on past measurements. Process input and output data in a time interval are applied for the fault detection.
In Chen et al. [23], a general canonical correlation-based residual generator for
Integrating the statistical local approach into CCA for FD
The proposed method will be introduced in the next two sections. Section 3.1 derives the required basic residual, followed by a development of the FD method in Section 3.2.
On detecting incipient multiplicative faults using the T2 statistic
This section discusses two frequently considered questions related to detect incipient multiplicative fault using the T2 statistic:
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Why is the T2 statistic insensitive to incipient multiplicative faults?
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Why can the statistical local approach improve its sensitivity to incipient multiplicative fault?
Static case: application to an experimental CSTH
Consider a pilot scale, continuous stirred tank heater (CSTH). The structure of the CSTH plant is shown in Fig. 4. Water enters the tank and is heated by a heating jacket. The water then leaves the tank and is recycled to the reservoir. Let Ti, i = 1, …, 4 denote the temperature inside the stirred tank, the temperature inside the heating jacket, the input water temperature, and the temperature in the reservoir, respectively; L1 represent the water level inside the stirred tank; and F1 denote the
Conclusions
In this paper, improved CCA-based FD methods are proposed to detect incipient multiplicative faults in chemical processes. The improved methods are developed based on a statistical local approach-based residual evaluator. Although designed for both static and dynamic processes, the conventional CCA-based residual generator is only sensitive to relatively large multiplicative faults, but not incipient ones. The reasons why the T2 statistic is insensitive to incipient faults and how the
Acknowledgments
Messrs. Chen and Zhang are grateful for the financial support from the China Scholarship Council (CSC). Prof. Hu would like to thank the National Natural Science Foundation of China (Grant #61273159). The authors would like to thank Dr. C. Louen for technical support with the experiments on the CSTH.
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Part of the work was presented at the 9th IFAC Symposium SAFEPROCESS held in Paris, France, September 2015.