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## Über dieses Buch

Given their key position in the process control industry, process monitoring techniques have been extensively investigated by industrial practitioners and academic control researchers. Multivariate statistical process control (MSPC) is one of the most popular data-based methods for process monitoring and is widely used in various industrial areas. Effective routines for process monitoring can help operators run industrial processes efficiently at the same time as maintaining high product quality.

Multivariate Statistical Process Control reviews the developments and improvements that have been made to MSPC over the last decade, and goes on to propose a series of new MSPC-based approaches for complex process monitoring. These new methods are demonstrated in several case studies from the chemical, biological, and semiconductor industrial areas.

Control and process engineers, and academic researchers in the process monitoring, process control and fault detection and isolation (FDI) disciplines will be interested in this book. It can also be used to provide supplementary material and industrial insight for graduate and advanced undergraduate students, and graduate engineers.

Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

## Inhaltsverzeichnis

### Chapter 1. Introduction

With the wide use of the distributed control systems in modern industrial processes, a large amount of data has been recorded and collected. How to efficiently use these datasets for process modelling, monitoring and control is of particular interest, as the traditional first-principle model-based method is difficult to use in modern complex processes, which is mainly due to the high human and resource costs or special environments. Different from the first-principle model-based method, the data-based method rarely needs any prior knowledge of the process. By extracting the useful information from the recorded process data, data-based models are also able to model the relationship between different process variables. Particularly, for process monitoring purpose, the multivariable statistical process control (MSPC)-based method has received much attention since the 1990s. The main idea of the MSPC-based monitoring approach is to extract the useful data information from the original dataset, and construct some statistics for monitoring. Most MSPC-based methods can successfully handle the high-dimensional and correlated variables in the process because they are able to reduce the dimension of the process variables and decompose the correlations between them. Therefore, MSPC has become very popular in industrial processes, especially when used for process monitoring.

Zhiqiang Ge, Zhihuan Song

### Chapter 2. An Overview of Conventional MSPC Methods

This chapter introduces some basic MSPC-based process monitoring methods, including principal component analysis, partial least squares, factor analysis, independent component analysis, and kernel principal component analysis.

Zhiqiang Ge, Zhihuan Song

### Chapter 3. Non-Gaussian Process Monitoring

Independent component analysis (ICA) has recently been introduced for the non-Gaussian process monitoring purpose. Compared to the traditional principal component analysis (PCA) method, ICA has gained more satisfactory monitoring performance for processes with non-Gaussian data information. This chapter first gives a review of different ICA-based monitoring methods, and then demonstrates a two-step ICA-PCA information extraction strategy-based monitoring method for processes which are simultaneously driven by non-Gaussian and Gaussian components. Furthermore, in order to improve the monitoring performance, both support vector data description and factor analysis model have been incorporated into the non-Gaussian monitoring framework.

Zhiqiang Ge, Zhihuan Song

### Chapter 4. Fault Reconstruction and Identification

This chapter introduces fault reconstruction and identification methods, particularly for those processes whose data follow non-Gaussian distributions. For non-Gaussian fault detection, recent work has demonstrated the effectiveness of Independent Component Analysis (ICA) to extract non-Gaussian source signal and Support Vector Data Description (SVDD) to determine control limits for associated monitoring statistics. Here, a fault reconstruction method is introduced based on the SVDD model, which is similar to the recently developed reconstruction methods upon the PCA model. For fault identification, the traditional PCA-based similarity factor is extended to the non-Gaussian case, which is developed upon the ICA model, namely ICA similarity factor. Furthermore, with the introduction of the FA model, an additional noise similarity factor has also been defined. By combining these different similarity factors, a mixture similarity factor is developed for fault identification under different situations.

Zhiqiang Ge, Zhihuan Song

### Chapter 5. Nonlinear Process Monitoring: Part 1

Conventional kernel principal component analysis (KPCA) may not function well for nonlinear process monitoring, since the Gaussian assumption of the method may be violated through nonlinear and kernel transformation of the original process data. To overcome this deficiency, a statistical local approach has been incorporated into KPCA. Through this method, a new score variable which was called improved residual in the statistical local approach is constructed. This new variable approximately follows Gaussian distribution, in spite of which distribution the original data follow. Like the traditional method, two statistics can be constructed for process monitoring, with their corresponding confidence limits determined by a $${{\chi }^{2}}$$ distribution. Besides of the improvement made on KPCA, the joint local approach-KPCA method also shows superiority on detection sensitivity, especially for small faults slow changes of the process.

Zhiqiang Ge, Zhihuan Song

### Chapter 6. Nonlinear Process Monitoring: Part 2

This chapter introduces a linear subspace and Bayesian inference-based monitoring method for nonlinear processes. Through the linear subspace method, the original nonlinear space can be approximated by several linear subspaces, based on which different monitoring sub-models have been developed. A subspace contribution index has been defined for variable selection in each subspace. Monitoring results are first generated in each subspace, and then transferred to fault probabilities by the Bayesian inference strategy. To make the final monitoring decision, subspace monitoring results are combined together with their fault probabilities. In addition, a corresponding fault diagnosis method has also been developed. To demonstrate the computationally efficiency of the new method, detailed comparisons of the algorithm complexity for different methods are provided in this chapter.

Zhiqiang Ge, Zhihuan Song

### Chapter 7. Time-Varying Process Monitoring

In this chapter, an adaptive local model-based monitoring approach is introduced for online monitoring of nonlinear time-varying processes with non-Gaussian information. To solve the time-varying problem, a just-in-time-learning (JITL) strategy is introduced. The local least squares support vector regression (LSSVR) model is built upon the relevant dataset for prediction. To satisfy the online modeling demand, the real-time problem is considered. Then, a two-step independent component analysis-principal component analysis (ICA-PCA) information extraction strategy is introduced to analyze residuals between the real output and the predicted one. A simulation case study shows that the new method gives better performance compared to conventional methods.

Zhiqiang Ge, Zhihuan Song

### Chapter 8. Multimode Process Monitoring: Part 1

Multimode process monitoring has recently received much attention. Conventional methods either assume the process data is Gaussian in each operation mode, or some process knowledge should be incorporated, which makes the methods supervised. In this chapter, a new unsupervised method is introduced for multimode process monitoring, which is based on Bayesian inference and two-step independent component analysis-principal component analysis (ICA-PCA) feature extraction strategy. ICA-PCA is first introduced for feature extraction and dimension reduction. By transferring the traditional monitoring statistic to fault probability in each operation mode, monitoring results in different operation modes can be easily combined through the Bayesian inference. After that, a fault identification method can be developed upon this monitoring framework. Through analyses of the posterior probability and the joint probability for the monitored data sample, the correct operation mode or fault scenario can both be identified.

Zhiqiang Ge, Zhihuan Song

### Chapter 9. Multimode Process Monitoring: Part 2

Nonlinear and multimode are two common behaviors that widely exist in modern industrial processes, monitoring research studies have been carried out separately for these two natures in recent years. This chapter introduces a two-dimensional Bayesian method for monitoring processes with both nonlinear and multimode characteristics. In this method, the concept of linear subspace is introduced, which can efficiently decompose the nonlinear process into several different linear subspaces. For construction of the linear subspace, a two-step variable selection strategy has been developed. A Bayesian inference and combination strategy is then used for result combination of different linear subspaces. Besides, through the direction of the operation mode, an additional Bayesian inference and combination step can be performed. As a result, a two-dimensional Bayesian monitoring approach is formulated, through which both nonlinear and multimode behaviors of the process can be well monitored.

Zhiqiang Ge, Zhihuan Song

### Chapter 10. Dynamic Process Monitoring

Dynamic is another critical behaviour of the process data, which has also caught much attention in process monitoring. Based on the previous works on dynamic process monitoring in the past years, this chapter introduces two different methods. These approaches rely on (i) recent work on independent component analysis and support vector data description that is applied to a dynamic data structure and (ii) the incorporation of the statistical local approach into a dynamic data representation. The analysis of experimental data from a gearbox system confirms (i) significant auto- and cross-correlation within and among these signals and (ii) that they cannot be assumed to follow Gaussian distributions. The application of both approaches showed that they are more sensitive to incipient faults than conventional multivariate statistical methods.

Zhiqiang Ge, Zhihuan Song

### Chapter 11. Probabilistic Process Monitoring

To monitor industrial processes through a probabilistic manner, the probabilistic principal component analysis (PPCA) method has recently been introduced. However, PPCA has its inherent limitation that it cannot determine the effective dimensionality of latent variables. This chapter intends to introduce a Bayesian treatment upon the traditional principal component analysis method for process monitoring, which can automatically determine the effective number of retained principal components. Thus, a Bayesian principal component analysis-based monitoring approach can be developed. Besides, for those processes with multiple operation modes, the Bayesian regularization method is extended to its mixture form, and a mixture Bayesian regularization method of PPCA can be further developed for process monitoring. To combine the monitoring results in different operation modes, a probabilistic strategy is employed, based on which a mode localization approach is constructed, which can provide additional information and improve process comprehension for the operation engineer.

Zhiqiang Ge, Zhihuan Song

### Chapter 12. Plant-Wide Process Monitoring: Multiblock Method

Due to the complexity of the plant-wide process, many of the present multivariate statistical process monitoring techniques lack the ability to interpret the nature of a detected fault, hence, fault identification also becomes difficult. In this chapter, a two-level MultiBlock Independent Component Analysis and Principal Component Analysis (MBICA-PCA) method is introduced. Different from the conventional multiblock method, this two-level approach can incorporate block information into the high level for global process monitoring. Through this method, the process monitoring task can be reduced and the interpretation of the process can be made more efficiently. When a fault is detected, a two-step fault identification method is developed. That is, the responsible sub-block is first identified by contribution plots, which is followed by fault reconstruction in the corresponding sub-block for advanced fault identification.

Zhiqiang Ge, Zhihuan Song

### Backmatter

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