A supervised multisegment probability density analysis method for incipient fault detection of quality indicator
Introduction
In industrial process, the operation state may deviate from its normal state due to the environment disturbance, equipment aging and some other interferences. In order to ensure the process safety and efficiency, a reliable operating state monitoring system has playing an important role nowadays [1], [2], [3], [4].
With the rapid development of the distributed control system and computer technology, massive industrial operating data can be measured, stored and analyzed in time, and the data-driven process monitoring has received much attentions [5], [6], [7], [8]. For dealing with the high-dimensional coupling process variable, the multivariate statistical process monitoring (MSPM) has obtained widely research and application, such as the principal component analysis (PCA) [9] and independent component analysis (ICA) [10] algorithms. Li et al. proposed a process monitoring method using multiple correlation regression, which can integrate the multiple correlation of a variable with other variables, and two statistics are introduced for the fault detection [11]. In order to reduce the negative effect of the invalid and redundant information in process variables, a multigroup framework is introduced for the large-scale multivariate system, and the inter-group and group-wise information could be extracted concurrently [12]. In these algorithms, the original high-dimensional modeling data is projected into a new feature space, and the corresponding monitoring statistics and control limit are constructed. Motivated by the actual process monitoring requirements, various improved or extended algorithms are proposed, which can be used to deal with the nonlinear, dynamic, non-Gaussian, multi-subblock and some other problems contained in the industrial process [13], [14], [15], [16].
Generally, only the process measurement variables are used for modeling in above unsupervised algorithms, and the fault alarm will be triggered if the process variables deviate from the original state. However, because of the system feedback and self-regulating ability, the disturbance in process variables may not be directly reflected in the quality indicator. Therefore, traditional unsupervised model may bring more false alarms. As the quality indicator may be unavailable in real time, the supervised modeling and monitoring methods which can extract the indicator-related information from the process variable have become a research hotspot in recent years [17], [18].
Linear regression and orthogonal decomposition are the effective methods for extracting the indicator-related information. Wang et al. proposed a kernel direct decomposition method and performed singular value decomposition on the covariance matrix between the process variable and the performance indicator [19]. Jiao et al. combined the data matrix augmentation and least squares (LS) methods to realize the indicator monitoring for dynamic process [20]. Ding et al. proposed the principal component regression (PCR)-based indicator monitoring method, which had been applied in the industrial strip hot rolling mills process [21]. Wang et al. proposed the linear and nonlinear PCR method for the nonlinear process indicator monitoring [22]. In order to realize the parallel monitoring of the indicator additive and multiplicative faults, a parallel dynamic PCR algorithm was put forward [23].
Partial least square (PLS) has also been widely used in the indicator-related process monitoring [24]. Yin et al. proposed the improved PLS (IPLS) algorithm, and the original process variable space was divided into the KPI-related and KPI-unrelated parts [25]. Zhou et al. proposed the total PLS (TPLS) algorithm, which further divided the process variable into four subspaces [26]. In the efficient PLS (EPLS) algorithm, the indicator-related and indicator-unrelated faults could be detected simultaneously [27]. The recursive concurrent projection to latent structures (RCPLS) algorithm presented by Hu et al. had achieved the online adaptive update of the indicator monitoring model [28]. Recently, canonical correlation analysis (CCA) and the deep learning methods are also successfully applied in the process variable decomposition and indicator-related monitoring [29], [30], [31]. In addition to the indicator-related monitoring algorithm, the performance-similarity-based method has also been used in the indicator state assessment. For pursuing optimal comprehensive economic benefit, a performance-similarity-based operating performance assessment method is presented, and the non-optimal cause could be identified based on the variable contributions [32]. In order to improve the robustness and sensitivity of the assessment method, the optimality related variations were extracted from each steady performance grade, and the similarities between the online data and each performance grade were calculated for the state assessment of the performance indicator [33].
Since the incipient fault is usually covered by the process variation or noise, the fault alarm will not be triggered until the variables deviate from the normal state significantly. To avoid this problem, incipient fault detection has drawn more and more attentions, in recent reports, the data smoothing, Kullback–Leibler divergence and dissimilarity analysis have been widely used in the incipient fault detection. Ji et al. introduced two representative smoothing techniques, moving average (MA) and exponentially weighted moving average (EWMA), into the multivariate statistical process monitoring, which had higher sensitivity for the incipient fault [34]. Cheng et al. proposed the moving average residual difference reconstruction contribution plot (Mard-RCP) method, which could improve the diagnosis accuracy of the incipient fault through manipulating the signal-to-noise ratio properly [35]. In order to detect the incipient fault in complex dynamic system, the subspace identification and Kullback–Leibler divergence methods were used between the reference dataset and the online data [36]. Chen et al. proposed a Kullback–Leibler divergence and independent component analysis based method to perform the incipient fault detection [37]. In order to improve the fault sensitivity of the traditional canonical variate analysis indices, the canonical variate dissimilarity analysis (CVDA) method was proposed [38]. Through integrating the CVDA and the mixed kernel principal component analysis (MKPCA) algorithms, an incipient fault detection method for nonlinear process was put forward [39].
The above methods have higher sensitivity to the process variation, which perform better in the incipient fault detection. Nevertheless, these methods still exist some shortcomings. The additive fault such as the step change in process operating parameters will change the operation mean point, while the multiplicative fault such as the random variation in operating parameters will change the variable variance or covariance. The data smoothing technology such as sliding average method applies the variable mean value in each moving window for the process modeling and monitoring, and the data fluctuation information will be lost during the average calculation. Therefore, the data smoothing technology may fail when multiplicative fault occurs. In the Kullback–Leibler divergence and dissimilarity analysis methods, the probability density calculation imposes a prior assumption on the data distribution, which may be unreachable in the actual process. Besides, the quality indicator is the focus of process operation, but the research on the indicator-related incipient fault is relatively insufficient.
Motivated by the above problems, a novel indicator-related process monitoring method named supervised multisegment probability density analysis (S-msPDA) is proposed for the incipient fault detection. Firstly, the core process variables are selected based on the mutual information, and the regression model is constructed between the core process variable and the quality indicator. Through the regression coefficient decomposition and the subspace division, the indicator-related information can be extracted from the process variable. Afterwards, the multiple segment probability density estimation method is presented, and the data density can be estimated without prior distribution restriction. According to a symmetric divergence index, the distinction between the online sample and the offline modeling sample can be evaluated.
The main contributions of this paper include:
(1) A novel supervised multisegment probability density analysis algorithm is proposed, which can achieve the online incipient fault detection for the quality indicator.
(2) A supervised feature analysis method is presented to extract the indicator-related information from process variable.
(3) A data distribution interval extension and subsegment division method is introduced for the probability density estimation of the indicator-related latent variable.
(4) A symmetric divergence index is presented to evaluate the distribution discrepancy between the online sample and the reference sample set, which has high sensitivity for the incipient fault.
The remaining parts of this paper are organized as follows. In Section 2, a definition of the indicator incipient fault is introduced. The S-msPDA algorithm and the corresponding incipient fault detection method are put forward in Sections 3 Supervised multi-segment probability density analysis, 4 S-msPDA based incipient fault detection for quality indicator respectively. In Section 5, a numerical example and the Tennessee Eastman process are used to illustrate the effectiveness of the proposed method. Finally, the conclusions are given.
Section snippets
Definition of the incipient fault in process quality indicator
The incipient fault usually has lower fault-signal ratio or fault–noise ratio, which is difficult to detect in time. In this section, a definition of the indicator incipient fault is presented.
Suppose that the quality indicator in normal state is defined as where is the quality indicator without noise, is the noise signal. After the fault occurs, the quality indicator will change into or which represent the additive fault and multiplicative fault respectively.
Core process variable selection
Nowadays, numerous process measurement variables are available in the distributed control system. However, some process variables can hardly affect the quality indicator, which play a negative role in the indicator monitoring. Therefore, the indicator-related core variables should be selected firstly.
Suppose that the modeling data are and , which represent the process variable and quality indicator respectively. The data matrices are constructed as
S-msPDA based incipient fault detection for quality indicator
In this section, the S-msPDA based incipient fault detection method is introduced, which includes the offline modeling step and the online monitoring step.
Numerical example
For demonstrating the effectiveness of the proposed method, a numerical model is constructed as follows where , , obey the uniform distribution , and , , , obey the normal distribution , and . obey the normal distribution . Firstly, 1000 normal samples are
Conclusion
In this paper, a novel monitoring algorithm named supervised multisegment probability density analysis is proposed to detect the incipient fault in quality indicator. Based on the mutual information, the core process variables are selected for the modeling and monitoring. After building the regression model between the core process variable and the quality indicator, the indicator-related information can be extracted through the regression coefficient decomposition. Afterwards, multiple data
CRediT authorship contribution statement
Yang Tao: Conceptualization, Methodology, Software, Validation, Writing – original draft, Visualization, Funding acquisition. Hongbo Shi: Conceptualization, Methodology, Funding acquisition, Project administration, Supervision, Writing – review & editing. Bing Song: Conceptualization, Methodology, Writing – review & editing, Funding acquisition. Shuai Tan: Conceptualization, Methodology, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant 62103149, Grant 62073140 and Grant 62073141, in part by National Natural Science Foundation of Shanghai under Grant 19ZR1473200.
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