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Review of recent research on data-based process monitoring Zhiqiang Ge, Zhihuan Song, and Furong Gao Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie302069q • Publication Date (Web): 17 Feb 2013 Downloaded from http://pubs.acs.org on February 25, 2013

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Industrial & Engineering Chemistry Research

Review of recent research on data-based process monitoring Zhiqiang Gea∗∗, Zhihuan Songa, Furong Gaob a

State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Department of Control Science and Engineering, Zhejiang University, Hangzhou, China

b

Department of Chemical and Biomolecular engineering, The Hong Kong University of Science and Technology, Hong Kong

Abstract Data-based process monitoring has become a key technology in process industries for safety, quality and operation efficiency enhancement. This paper provides a timely update review on this topic. Firstly, the natures of different industrial processes are revealed with their data characteristics analyzed. Secondly, detailed terminologies of the data-based process monitoring method are illustrated. Third, based on each of the main data characteristics that exhibits in the process, a corresponding problem is defined and illustrated, with review conducted with detailed discussions on connection and comparison of different monitoring methods. Finally, the relevant research perspectives and several promising issues are highlighted for future work.

Keywords:

Data-based process monitoring; Multivariate statistical process control; non-Gaussian;

Nonlinear; Time-varying; Multimode; Dynamic; Batch processes.

∗

Corresponding author:

E-mail address: [email protected] (Ge Z.) -1-

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Contents 1. Introduction ................................................................................................................................................. 4 2. Industrial processes and data characteristics ............................................................................................... 7 2.1. Industrial processes .......................................................................................................................... 7 2.1.1. Continuous processes ............................................................................................................ 7 2.1.2 Batch processes ...................................................................................................................... 7 2.2. Data characteristics in the process industry...................................................................................... 8 2.2.1. High dimensionality .............................................................................................................. 8 2.2.2. Non-Gaussian distribution ..................................................................................................... 9 2.2.3. Nonlinear relationships.......................................................................................................... 9 2.2.4. Time-varying and multimode behaviors .............................................................................. 10 2.2.5. Data auto-correlations ......................................................................................................... 10 2.2.6. Three-way dimensional data in batch processes .................................................................. 11 2.2.7. Other data characteristics .................................................................................................... 11 3. Data-based process monitoring methodology ........................................................................................... 12 3.1. Data inspection and selection ......................................................................................................... 13 3.2. Data pre-processing ........................................................................................................................ 13 3.3. Model selection, training and validation ........................................................................................ 14 3.4. Online process monitoring ............................................................................................................. 15 3.4.1. Fault detection ..................................................................................................................... 15 3.4.2. Fault diagnosis..................................................................................................................... 15 3.4.3. Fault reconstruction ............................................................................................................. 16 3.4.4. Fault identification .............................................................................................................. 16 3.5. Fault isolation and process recovery .............................................................................................. 17 3.6. Model maintenance ........................................................................................................................ 17 3.7. Other related methodologies .......................................................................................................... 17 4. State-of-the-art of data-based process monitoring..................................................................................... 18 4.1. Non-Gaussian process monitoring ................................................................................................. 18 4.1.1. Problem statement ............................................................................................................... 18 4.1.2. Independent component analysis ......................................................................................... 19 4.1.3. Gaussian mixture models .................................................................................................... 20 4.1.4. Support vector data description ........................................................................................... 21 4.1.5. Discussions, connections, and comparisons ........................................................................ 21 4.2. Nonlinear process monitoring ........................................................................................................ 23 4.2.1. Problem statement ............................................................................................................... 23 4.2.2. Principal curves and neural networks .................................................................................. 24 4.2.3. Kernel-based methods ......................................................................................................... 24 4.2.4. Linear approximation approaches ....................................................................................... 25 4.2.5. Discussions, connections, and comparisons ........................................................................ 26 4.3. Time-varying and multimode process monitoring.......................................................................... 27 4.3.1. Problem statement ............................................................................................................... 27 -2-


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4.3.2. Adaptive/Recursive methods ............................................................................................... 28 4.3.3. Multi-model methods .......................................................................................................... 29 4.3.4. Soft modeling methods ........................................................................................................ 29 4.3.5. Local-learning and robust methods ..................................................................................... 30 4.3.6. Discussions, connections, and comparisons ........................................................................ 31 4.4. Dynamic process monitoring.......................................................................................................... 32 4.4.1. Problem statement ............................................................................................................... 32 4.4.2. Dynamic MSPC methods .................................................................................................... 33 4.4.3. Time-series analysis methods .............................................................................................. 34 4.4.4. State-space model based methods ....................................................................................... 35 4.4.5. Discussions, connections, and comparisons ........................................................................ 35 4.5. Batch process monitoring ............................................................................................................... 36 4.5.1. Problem statement ............................................................................................................... 36 4.5.2. Multiway monitoring methods ............................................................................................ 37 4.5.3. Phase-based methods........................................................................................................... 38 4.5.4. Two-dimensional dynamic monitoring methods ................................................................. 39 4.5.5. Discussions, connections, and comparisons ........................................................................ 39 4.6. Summary ........................................................................................................................................ 40 5. Research perspectives ............................................................................................................................... 41 5.1. Monitoring of complex dynamic processes .................................................................................... 41 5.2. Plant-wide process monitoring ....................................................................................................... 43 5.3. Transition process monitoring ........................................................................................................ 43 5.4. Probabilistic process monitoring .................................................................................................... 44 5.5. Model combination and complementation ..................................................................................... 45 5.6. Multi-data fusion for process monitoring ....................................................................................... 46 5.7. Other promising issues ................................................................................................................... 46 6. Conclusions ............................................................................................................................................... 47 Acknowledgement......................................................................................................................................... 47 References ..................................................................................................................................................... 48

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1. Introduction In modern industries, process safety and product quality are two important issues of interest. Process monitoring is a widely adopted tool for process safety and quality enhancement. In many occasions, process monitoring is also simply termed as fault detection and diagnosis, although the terminology of process monitoring is much more common in practice. Generally, process monitoring can be divided into three categories: model-based methods, knowledge-based methods and data-based methods. Among these three types of method, the model-based method is the most traditional one, it has initially been used for fault detection and diagnosis in aerospace, engine and power systems. Compared to other two methods, the model-based method is based on exact process models, for example, the first-principle of physical/chemical relationships between different variables. As a result, they tend to give more accurate results than other two methods as long as the system model is reliable. However, as modern industrial processes become more and more complicated, the characterization of first-principle models also becomes much more difficult, costly, and sometime it is even impossible to build such models. On the other hand, knowledge-based methods are based on the available knowledge of the process behavior and the experience of expert plant operators. The monitoring results provided by these methods tend to be more intuitive. However, the creation of the process knowledge base is always a time consuming and difficult operation requiring the long term accumulation of expert knowledge and experiences. Although there are limitations of the model-based and knowledge-based methods, they are still popular in particular areas, especially those in which process models can be easily obtained or the process knowledge has been readily accumulated. Compared to the aforementioned two types of process monitoring methods, data-based process -4-


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monitoring methods have no requirement of the process model and the associated expert knowledge. It has become more and more popular in recent years, especially in those complex industrial processes/systems whose models and expert knowledge are difficult to build and obtain in practice. Due to the wide utilization of the distributed control system (DCS) in modern industrial processes, large amounts of data have been recorded and collected. Those data contain most process information and therefore can be used for modeling, monitoring, and control. Besides, in the past years, a significant progress has been made in the data-mining and processing area, which can provide new technologies for the utilization of process monitoring. More detailed descriptions and discussions of different types of process monitoring methods can refer to the three parts review papers by Venkatasubramanian et al.1,

2, 3

which were published in 2003.

Previously, three books have been published on the topic of data-based methods for process monitoring and control, which are: (1) Wang4, Data Mining and Knowledge Discovery for Process Monitoring and Control; (2) Russell et al.5 , Data-driven Techniques for Fault Detection and Diagnosis in Chemical Processes; (3) Chiang et al.6, Fault Detection and Diagnosis in Industrial Systems. Whilst Wang introduced some data-mining technologies into process monitoring and control, Russell et al.5 is mainly concerned with the traditional Multivariate Statistical Process Control (MSPC) methods for process monitoring. Later, Chiang et al.

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extended data-based process monitoring to incorporate model-based and knowledge-based

methods. More recently, Qin7 summarized the previous works on the topic of MSPC, such as fault detection, reconstruction, and diagnosis. MacGregor et al.8 gave an overview of the important concepts behind latent variable models for process analysis, monitoring and control. Kano9 provided a recent development and application of data-based process monitoring, control and quality improvement methods in steel industries. Yao and Gao10 gave a recent survey on multistage/multiphase statistical modeling methods for batch processes. Zhang and Zhang11 also reviewed recent developments of multivariate -5-



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statistical techniques for industrial process monitoring, fault diagnosis and quality prediction. However, it should be noted that the traditional Multivariate statistical based method has several inherent limitations. For example, the calculations of monitoring statistics and their control limits of the principal component analysis (PCA) and partial least squares (PLS) methods are made under the assumption that the process data are Gaussian distributed. Also, they require the process variables are linear correlated, and the process is operated under a single stationary condition. In practice, however, most of these assumptions can be easily violated. Therefore, in the past years, various improvements of the traditional MSPC-based process monitoring methods have been made, and many other data-based methods have also been introduced for process monitoring, such as independent component analysis (ICA), Gaussian mixture models (GMMs), artificial neural networks (ANN), support vector machines (SVM), support vector data description (SVDD), among others. Nevertheless, a systematic review on these recently developed data-based process monitoring has not been reported yet. The motivation of this survey paper is to provide such an overview of data-based process monitoring methods that have been developed in the past years, especially since 2003. The remainder of this paper is organized as follows. In section 2, the data characteristics in the process industry are explored and analyzed. A systematical illustration of the data-based process monitoring terminology is provided in section 3, which is followed by a detailed review of recent developments of data-based process monitoring methods in section 4, performing through various aspects, e. g. non-Gaussian monitoring, handling nonlinear process data, monitoring for time-varying industrial processes, etc. In section 5, detailed research perspectives and some additional promising issues are demonstrated. Finally, conclusions of this survey paper are made.

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2. Industrial processes and data characteristics In this section, two types of industrial processes are introduced, followed by detailed analyses of different data characteristics in these processes.

2.1. Industrial processes 2.1.1. Continuous processes

Continuous process is a traditional type of industrial processes, which has been widely used in sectors of chemical, petrochemical, and metallurgical engineering. As its name suggests, the continuous process is always operated through a continuous way. That is, after the process has been started up, it is operated around the optimal state in most time, and produce constant outputs. The systematic flowchart of a typical continuous process is shown in Figure 1, which is a distillation process. Actually, in the initial stage of data-based process monitoring, most application studies were carried out in the continuous process, for example, the continuous process was the initial research objective of the MSPC method. [Figure 1 about here]

2.1.2 Batch processes

Batch process is a kind of processes which have finite operation durations, and the production strictly follows the recipe of the process specification. Compared to the continuous process, the set-point of the batch process always changes, which means the process is often operated under different process conditions. Therefore, while the continuous process can hardly produce different types of products in the same process, various grades of products can be manufactured in a single batch process. Many processes in specialty -7-



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chemistry, plastic engineering, food engineering and biochemistry industries are all of this type. Similarly, a representative batch process is shown in Figure 2, which is a typical injection molding machine in the plastic engineering area. [Figure 2 about here] In contrast to the continuous process, any process which is not operated through a continuous way can be termed as the batch process. Here, all terminologies of the batch, semi-batch or discontinuous processes are called as batch process. In term of data-based process monitoring, the batch process modeling should deal with an additional dimension of the data variation, namely the batch-to-batch variation. To this end, batch process monitoring is sometimes considered to be more complicated than the continuous process monitoring approach. However, in the rest of this paper, most of the demonstrated terminologies and methodologies can be used for both of these two kinds of process.

2.2. Data characteristics in the process industry In this subsection, the main critical data characteristics in the process industrial are analyzed, given as follows.

2.2.1. High dimensionality

Modern industrial processes always consist of various components, parts or operation equipments, and each of these parts may has a significant number of measured variables. As a result, the whole process may generate a large number of high dimensional data samples. How to handle these high dimensional process datasets is a challenge for data-based modeling approaches. Fortunately, we do not have to generate the monitoring chart for each process variable, which is totally cumbersome and inefficient. Instead, by using -8-


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multivariate data analysis and processing approaches, such as PCA and PLS, the dimensionality of the process dataset can be significantly reduced, while the main data information still remains. Besides, the problem of co-linearity can also be solved simultaneously, since both PCA and PLS result in uncorrelated latent variables from the original dataset. Therefore, based on the reduced variable space, process monitoring can be carried out more easily, and in most cases the data visualization also becomes available.

2.2.2. Non-Gaussian distribution

It is mentioned that the traditional MSPC method such as PCA-based process monitoring approach has inherently assumed that the process data follow Gaussian distribution, due to the calculation of the monitoring statistics and their control limits. In practice, however, this assumption can hardly be satisfied. Actually, most process variables do not exactly follow the Gaussian distribution, which may due to the non-Gaussian noise, feedback control systems, different data transformations, etc. Figure 3 show comparative results of a standard Gaussian distribution variable and a non-Gaussian distribution variable. For a Gaussian process variable, the first and second order statistics can sufficiently describe it. However, higher order statistics should be incorporated to depict the non-Gaussian process variable. Detailed monitoring methods for those processes which have non-Gaussian variables are discussed in section 4.1. [Figure 3 about here]

2.2.3. Nonlinear relationships

Nonlinear relationships among different process variables are very common in the process industry, as well as between the process variables and the quality variables. A typical linear correlation and a nonlinear correlation between two variables are shown together in Figure 4. While the linear relationship of the data

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can be easily captured by the traditional MSPC method, the data nonlinearity is difficult to model. Different processes may have quite different nonlinear relationships among process variables. Therefore, it is difficult to construct a unified nonlinear model for process monitoring. In the past years, different kinds of nonlinear models have been developed, with their corresponding statistics constructed for process monitoring. Detailed reviews of nonlinear process monitoring methods are provided in section 4.2. [Figure 4 about here]

2.2.4. Time-varying and multimode behaviors

Due to the fluctuations of process raw materials, slowing shift of the set-points, aging of the main components of the process, seasoning effects, among others, the operating condition of industrial processes may changes frequently. In batch processes, particularly, the change of production grades is subjected to the demand of the market. As a result, the condition of the batch process may be often switched among different operation modes. For those processes which are slow-varying or have multiple operating conditions, it is difficult to apply the traditional MSPC methods, since they are based on the assumption that the process has only one stable operating region. Therefore, problems will arise when those techniques are applied to varying processes. To improve the monitoring performance for those processes, different methods have been proposed in the past years, detailed reviews of which will be illustrated in section 4.3.

2.2.5. Data auto-correlations

In practice, some process variables may show dynamic behaviors, that is, different sampling points of each variable are auto-correlated with each other. This time-series correlation of the variable may due to the inherent of the process, feedback control systems, time correlation of process noises, etc. To eliminate the

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dynamic effect of the process data, a simple way is to use a big sampling interval, thereby weakening the correlation between different sampling data. However, this method may lose significant data information, and the relationships among different process variables may also be distorted. Particularly, when the fault only influences the dynamic change of the process variables, the monitoring performance will be seriously deteriorated if the dynamic relationships have not incorporated for modeling. Similarly, various research studies have been carried out in the past years, we will give a thorough review on this topic in section 4.4.

2.2.6. Three-way dimensional data in batch processes

In batch processes, the dataset is often expressed as a three-dimensional manner, with an additional batch direction. Usually, this three-way dataset is unfolded into a two-dimensional dataset, based on which a monitoring model is then developed. A typical three-way dataset of the batch process and the widely used batch-wise unfolding method is given in Figure 5. For process monitoring, the traditional PCA and PLS models have been extended to their multiway counterparts: multiway PCA (MPCA) and multiway PLS (PLS). Since 1990s, research works on these multiway model based batch process monitoring approaches have been widely acknowledged and extended to other more complicated situations, e.g. nonlinear batch process, dynamic batch process, etc. The state-of-the-art of batch process monitoring will be demonstrated in section 4.5. [Figure 5 about here]

2.2.7. Other data characteristics

Except for the mentioned data characteristics above, there are also other data characteristics which may significantly influence the performance of the monitoring method. For example, due to the malfunction of a

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hardware sensor, maintenance of a part of the process, real-time database failure, among others, there is a certain probability that some of the sensors will occasionally fail to provide measurements. In such missing data situations, the normal operation region of the monitoring model may be distorted if the missing data of some important process variables have not been well fixed. Various methods for dealing with missing data have been developed12,

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. Outliers are another type of the data abnormality, which are also very common

in practice. Actually, outlier detection is a part of the data pre-processing procedure, which remains very critical for data-based process modeling. Sometimes, several outliers or even a single outlier may have great negative effect on the statistical data-based model. In the past years, lots of works have been done on the outlier detection issue, including several reviews14,

15, 16

. Besides, the process data may also show

multi-scale characteristic, inconsistent sample rates, measurement delay, etc. All of them should be considered when constructing the data-based monitoring model. Furthermore, it should be noticed that the process may simultaneously exhibit several data characteristics that mentioned above.

3. Data-based process monitoring methodology In this section, detailed illustrations of methodology issues and implementation procedures of the typical data-based process monitoring method are provided. Those methodologies and implementation procedures are general and thus can be used for both of the continuous and batch processes, as well as in different application areas. An overview of the data-based process monitoring methodology is presented in Figure 6. [Figure 6 about here]

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3.1. Data inspection and selection This is an initial step for data-based process monitoring, the aim of which is to get an overview of the process data and select the most appropriate data for modeling. Typically, in this step, the process data structure is examined, different data characteristics are analyzed, the operating region of the current process is identified, and the modeling and evaluation datasets are determined. For continuous processes, it is important to identify the parts of process data which are collected under the stationary condition. This is because in most time the continuous process runs under a stable operating condition. In contrast, the situation is different for batch processes, since they usually have no steady-states. As a result, the modeling dataset should be determined by selecting the most representative batches in the process. Generally speaking, data inspection and selection is an important step for data-based process monitoring, because the following steps are all based on this step. If an inappropriate dataset has been selected for model construction which cannot well represent the operating condition of the industrial process, then the monitoring system may result in various false alarms or miss to detect the process fault.

3.2. Data pre-processing Data pre-processing is also a critical step for data-based process monitoring. The aim of this step is to transform the original data to more appropriate manner, which can be efficiently used for modeling. By taking the traditional PCA method for example, different data samples are always normalized to zero means and unit variance. In this way, the scales of different process variables can be eliminated, therefore, the PCA model will not be inclined to any one of the process variables. For different purposes, there are also other data-scaling and transformation methods. For example, to handle the three-way batch process dataset,

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it is always unfolded through the batch direction. In order to remove the mean trajectory of different batches, a batch normalization procedure is typically carried out for the unfolded two-dimensional dataset. Besides, we may also have to handle missing data, outliers and gross errors in the dataset, all of which are very common in practice.

3.3. Model selection, training and validation Based on the data characteristic analysis and evaluation results, we can determine the complexity of the process monitoring model, e.g. which type of model is used for modeling, how complex of the model structure should be, and so on. For example, if the data relationship is linear and most process variables are Gaussian distributed, we can simply select the PCA or PLS model; If some of the process variables are non-Gaussian, then a kind of non-Gaussian modeling approach should be employed, such as ICA; Or if the relationships between different process variables are nonlinear, some nonlinear modeling methods such as ANN and SVM can be incorporated. Since the model can be considered as the engine of data-based process monitoring, selection of the optimal model type is of critical importance. Up to now, however, there is no theoretical criterion for model selection. Instead, the model is often selected by experience or determined through an ad hoc manner. Once the type of the model has been selected, the next step is to train the model based on the process data, and evaluate it for its efficiency. In this stage, different models have their own training algorithms. Before putting the model for online utilization, the performance should be evaluated. Therefore, the process dataset is often divided into two parts: training dataset and testing dataset. However, in some particular situations, the industrial process may not be able to provide sufficient data for model training and evaluation. In this case, it is useful to apply the cross-validation technique or resort to some re-sampling - 14 -


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methods, such as bagging17 and boosting18.

3.4. Online process monitoring After the data-based model has been built, appropriate statistics are constructed for online monitoring. For example, two monitoring statistics T 2 and SPE are typically constructed in the traditional PCA-based monitoring method. Besides, when a possible fault has been detected in the process, the next step is to diagnosis it (trying to find the root cause of this fault), reconstruct its direction and magnitude, and identify the fault type. Detailed descriptions of these issues are given as follows.

3.4.1. Fault detection

Fault detection is an initial step for process monitoring, based on which we can judge if an abnormal event happens in process or not. If the values of the monitoring statistics have exceeded their corresponding control limits, a fault alarm should be triggered. In order to guarantee the reliability of the process system, reducing both of the false alarm rate and the missing alarm rate has always been the first aim of the fault detection approaches.

3.4.2. Fault diagnosis

After a fault has been detected in the process, we may want to know which part or which component of the process is abnormal. This leads to the fault diagnosis method, which can provide the root cause of the detected fault. Typically, the diagnosis result can be located to a small part of the process or even to an exact sensor/actuator. However, different process variables are always correlated, and the fault may influence various variables and propagate to other parts of the process. Hence, how to provide an accurate fault diagnosis results is still a challenge work in the process monitoring area. - 15 -



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Actually, the task of fault diagnosis is extremely easy in the era when the process monitoring is mainly carried out by single variable monitoring charts. That is, each process variable has its own monitoring chart, and the up/low control limit has been well defined. Therefore, as long as the control limits have been violated, the fault can be easily detected and diagnosed. However, if the number of process variables is very large, the single variable monitoring approach will become cumbersome, and also the correlations between process variables cannot be captured. That is why single variable monitoring should be updated to the widely used multivariate variable monitoring method today. However, while fault detection becomes much easier for multivariate variable monitoring, the fault diagnosis becomes much more difficult. Hence, to some extent, fault detection and fault diagnosis are paradoxical to each other.

3.4.3. Fault reconstruction

After detection of a process fault, the aim of fault reconstruction is to explore its direction and magnitude. When a fault has been reconstructed, the normal value of the faulty data sample can be recovered. Also, we can examine the detailed information of the fault, which is very helpful for the following fault isolation and process recovery steps. Besides, the fault reconstruction is quite important especially when this faulty variable is used for some other purposes, such as process control, soft sensor modeling, quality prediction and so on. Without fault reconstruction, the results could be distorted and even cause another fault in the process.

3.4.4. Fault identification

Typically, the industrial process always has various types of faults. Therefore, when a fault has been detected from the process, we may want to know which type it belongs to. The information of the fault type

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is very useful because it can help the operator to quickly understand the fault, and find the appropriate maintenance strategy to get the process back into the normal condition as soon as possible. Generally, the fault identification issue can be regarded as a pattern match and recognition problem. Therefore, different data-based pattern analysis methods can be used for the fault identification purpose.

3.5. Fault isolation and process recovery After the detailed information of the detected fault has been explored, it should be further isolated from other parts of the process. It is important that the process should not be significantly impacted when the fault is isolated. Then, an experienced operator tries to repair it, and resume the process as operating in the normal condition.

3.6. Model maintenance Conventionally, when the process monitoring model has been built, it keeps fixed in the process. However, due to the slow drift and other changes of the process data, the monitoring performance of the model may be degraded, as a result, a significant number of fault alarms may happen in the process. Therefore, it is necessary to evaluate the feasibility and efficiency of the process monitoring model periodically. In the past years, different kinds of model maintenance methods have been developed, such as recursive/adaptive modeling methods, moving-window approaches, multi-models methods and so on. Detailed explorations of the monitoring method for time-varying processes are provided in section 4.3.

3.7. Other related methodologies Furthermore, there are other related methodologies which may also play important roles in data-based - 17 -



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process monitoring. Some of these related methodologies are listed as follows: (1) Variable selection; (2) Sensor network design; (3) Data clustering and analysis; (4) Fault mode analysis; (5) Fault propagation path tracking;

4. State-of-the-art of data-based process monitoring In this section, the state-of-the art of data-based process monitoring is examined through several different viewpoints.

4.1. Non-Gaussian process monitoring 4.1.1. Problem statement

In practice, as we know, not all of the process variables are Gaussian distributed, some of them may follow different kinds of non-Gaussian distributions. In this case, the traditional PCA and PLS based monitoring methods may not function very well. When constructing T2 and SPE statistics for process monitoring, the calculation of their control limits should be made under the assumption that the latent variables are Gaussian distributed. Otherwise, the control limits may be inaccurate, thus unable to represent the boundary of normal operation region of the process. Therefore, when the data are not Gaussian distributed, the monitoring results based on PCA/PLS may be misleading or cause false alarms. To improve the monitoring performance of those non-Gaussian processes, several kinds of methods have been

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developed in the past years, such as independent component analysis, Gaussian mixture models, support vector data description, etc, detailed reviews of which are given as follows.

4.1.2. Independent component analysis

Independent component analysis is an emerging technique for finding independent latent components from the measured process variables. What distinguished ICA from PCA is that it looks for components that are both statistically independent and non-Gaussian. While PCA can only impose independence up to second-order statistics information, ICA involves higher-order statistics of the data. Therefore, ICA may reveal more meaningful information in the non-Gaussian data than PCA. For the process monitoring purpose, ICA was first introduced by Li and Wang19 and Kano et al20. Later, Kano et al.21 developed a unified framework for MSPC, which combined PCA-based SPC and ICA-based SPC. Lee et al.22 also developed a process monitoring method based on the ICA method, in which three statistics have been used for process monitoring. Different from the single independent component based monitoring approach, the information of various independent components have been integrated into the three statistics. More recently, the ICA-based process monitoring method has been modified and improved, such as Lee et al.23, Zhang and Zhang24, 25, Wang and Shi26. A two-step ICA-PCA based monitoring approach has been proposed both fault detection and identification by Ge and Song27, and then adopted for time-varying and batch process monitoring28,

29

. Other applications of the ICA based process monitoring methods include Albazzaz and

Wang30, Zhang and Qin31, Kim and Yoo32, Tian et al.33, Huang and Chiu34, Ge et al.35, Hsu et al.36, Stefatos and Ben Hamza37, Odiowei and Cao38, among others. Although the ICA model has been successfully introduced for process monitoring, there are several shortcomings which may make this method cumbersome for practice utilization. First, due to the random - 19 -



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initialization of most ICA algorithms, the extracted components may be different from each running time, which will lead to various monitoring results. Therefore, the monitoring performance of the ICA-based method is unstable, which could cause confusions to the process engineer. Second, the number selection of retained independent components is still an open question. Although several methods have been developed for number selection of the independent components, they have their own advantages and disadvantages. Therefore, it is quite difficult to set a critical rule for selection of the independent components in the ICA method. Third, how to measure the importance of each independent component for the process monitoring purpose is also a difficult task so far. Besides, the control limit of the ICA-based monitoring statistic is difficult to determine, due to the non-Gaussian distribution of the extracted independent components.

4.1.3. Gaussian mixture models

Another commonly used method for non-Gaussian process monitoring is known as Gaussian mixture model (GMM). The main idea of this method is due to the assumption that the dataset of a complex industrial process can be described by several local linear models. To learn the GMM model, the Expectation-Maximization (EM) algorithm is often employed to determine the multiple parameters in the GMM model. In order to reduce the dimensionality of the process data, the GMM model is sometimes combined with the traditional PCA model, which leads to a mixture form of the PCA model. Chen and Liu proposed a mixture PCA model based method for process monitoring and extracting fuzzy rules from the process data39,

40

. Choi et al.41 proposed a Gaussian mixture model via PCA and discriminant analysis,

based on which both fault detection and identification can be efficiently carried out. Later, a Maximum-Likelihood PCA modeling framework was proposed for non-Gaussian process monitoring42, and has been extended to a more general form, which is called as Maximum-likelihood mixture factor analysis - 20 -


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model43. Other applications of the GMM models for process monitoring include Thissen et al.44, Yu and Qin45, Chen and Zhang46, Wen et al.47, etc.

4.1.4. Support vector data description

Recently, the well-known one-class classification method: support vector data description has been introduced for process monitoring. The goal of SVDD is to define a boundary around normal samples with a volume as small as possible. By introducing kernel functions, SVDD can adapt to the real shape of samples and find flexible boundary for process monitoring. In this method, there is no restriction that the process data should be assumed to be Gaussian. Therefore, SVDD has been considered as a promising method for non-Gaussian process monitoring. Liu et al.48 and Ge et al.49 used the SVDD model to determine the control limit of the independent components generated from ICA. Compared to the traditional ICA-based process monitoring which typically incorporated a kernel density estimation procedure, the SVDD-based method is more computationally efficient, which relies on a quadratic programming cost function. Cho50 dealt with the data description and noise filtering issues based on the SVDD model, and applied it for fault detection. Ge et al.51 further proposed an SVDD based reconstruction algorithm for sensor fault identification and isolation. Compared to the reconstruction based methods that been developed upon the PCA model52,

53, 54, 55, 56

, the SVDD based method can efficiently handle the

non-Gaussian process fault. More recently, the SVDD based monitoring method has been extended in dynamic and batch processes57,

58

.

4.1.5. Discussions, connections, and comparisons

Except the above three types of non-Gaussian process monitoring methods, there are also other

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methods that have been developed which are also able to handle the non-Gaussian data information. For example, the non-parametric probability density estimation methods59,

60, 61

, kernel-based methods such as

support vector machine, multi-scale statistical modeling methods62, and so on. Although those methods have been developed separately, they are actually highly related with each other. For example, when we use the ICA model for non-Gaussian process monitoring, the control limit of the monitoring statistic is usually determined by some kind of non-parametric probability estimation approach, e. g. Histogram, kernel density estimation, etc. Kernel-based methods such as support vector machine, SVDD, and kernel density estimation can share a common kernel function when they are used for non-Gaussian process modeling, monitoring or control limit calculation. Particularly, the SVDD method can be considered a special form of support vector machine, which is also known as one-class support vector machine. Compared to the commonly used support vector machine, the main feature of the SVDD method lies in its one-class classification property, which means only two classes of the data are focused in this method, corresponding to the normal and abnormal data patterns. When a large number of process variables are incorporated for process monitoring, the ICA model can be combined with the GMM model, which is used for dimensionality reduction of the process variables. In this case, the construction of the GMM model becomes much easier. However, with the additional dimensionality reduction step, fault diagnosis may become much more difficult. Besides, in order to facilitate the calculation of the control limit for the ICA-based process monitoring method, SVDD has been combined with ICA. After the independent components have been extracted from the non-Gaussian process data, they are modeled by the SVDD method, providing easier control limit determination and more accurate monitoring results. Based on the current research status, it has shown that ICA, GMM and SVDD are three of the most widely used and promising methods for non-Gaussian process monitoring. Detailed comparative - 22 -


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advantages and disadvantages of these three different methods are listed in Table 1. However, with more and more combinations and emergencies of different non-Gaussian data modeling techniques, it can be expected in the near future that the monitoring performance could be further improved, including fault detection speed, fault classification rate, fault diagnosis accuracy, etc. [Table 1 about here]

4.2. Nonlinear process monitoring 4.2.1. Problem statement

Traditionally, it has been assumed that the relationships among different process variables are linear correlated with each other. Actually, this assumption is valid in quite a large number of industrial processes. This is because a lot of industrial processes focus on producing a stable production, which often operated under a small region of steady condition. Therefore, even if the relationships among process variables are nonlinear, they can be linearized around this steady condition. However, with the rapid development of modern process industry, some of them may be operated under various conditions, and the relationships among different process variables also become more complicated. In this case, the linear modeling approach may not function very well. Compared to the linear process, it is more difficult to detect the fault in nonlinear processes. The fault behavior may become more complex and sometime even be smeared in the process. Due to different types of nonlinear relationships among process variables, it is difficult to construct a unified nonlinear model for process monitoring. As a result, there is no method that performs well in all industrial processes. One method can obtain good monitoring performance in one process may not function well in another process. In the past years, process monitoring for nonlinear processes has become a hot research aspect in this area. Thus, different kinds of nonlinear models have been developed, - 23 -



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with their corresponding process monitoring schemes. Detailed reviews of these methods are provided as follows.

4.2.2. Principal curves and neural networks In order to generalize the traditional PCA method for nonlinear process monitoring, Kramer 63 developed a nonlinear PCA method based on the auto-associative neural network. Based on this method, a nonlinear dimensionality reduction is able to carry out. Dong and McAvoy64 proposed a nonlinear PCA by combining the principal curve and the neural network. In this method, a five-layer neural network has been designed, which is also known as the double three-layer neural network. The scores of the nonlinear principal components were calculated by the principal curve. To determine whether the linear or nonlinear method should be used for process monitoring, Kruger et. al.65 proposed a nonlinearity measure for principal component. A hybrid neural network model has been developed for rule generation of the process, and was also used to fault detection and diagnosis66. To enhance the process monitoring performance, the ensemble learning method has been combined with neural network and used for on-line monitoring of process mean and variance shifts67. For fault diagnosis of the Tennessee-Eastman benchmark process, a hierarchical neural network based on fuzzy clustering method has been designed68. Other nonlinear process monitoring methods related to principal curves and neural networks have also been developed in the last years69,

70, 71, 72, 73

.

4.2.3. Kernel-based methods

Recently, the kernel learning method has been introduced in this area, and also combined with some traditional method such as PCA and PLS for nonlinear process monitoring. For example, a nonlinear

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process monitoring method based on kernel PCA (KPCA) has been proposed74,

75

. By introducing a kernel

function, the nonlinear mapping and the inner product computation can be avoided. Similar to the conventional PCA method, two monitoring statistics have been constructed to monitor the systematic and the noisy part separately. An improved KPCA monitoring method has been developed, which is combined with the technique of local approach76. In this method, the nonlinear and non-Gaussian data characteristics can be handled simultaneously. Alcala and Qin77 developed a reconstruction-based contribution approach based upon the KPCA model. Cheng et al.78 used the adaptive KPCA model to monitor the small disturbance of the nonlinear process. Similarly, the kernel learning methods have also been combined with both PLS and ICA for nonlinear process monitoring79,

80, 81

. Zhang82 improved the kernel ICA model and

combined with SVM for fault detection and diagnosis of nonlinear processes. A multiscale kernel PLS model has also been developed for fault diagnosis of nonlinear processes83. Besides, several developed kernel methods have been extended for monitoring of batch processes29,

84

. Other related kernel-based

methods that have been developed for nonlinear process monitoring include Ge and Song85, Bouhouche et al.86, Ge and Song87, Saravanan et al.88, Ge and Song89, etc.

4.2.4. Linear approximation approaches

Another type of nonlinear process monitoring methods is based on linear approximation approaches. In this method, the nonlinear space is approximated by several local linear models. A detailed illustration of the nonlinear generalization of the principal component analysis model is given in Kerschen and Golinval90, which discussed the model structures from global to local approaches. More recently, a linear subspace method has been proposed for nonlinear process monitoring91. The first step of this method is to divide the nonlinear process into several linear subspaces, which is based on the PCA decomposition. Due to the - 25 -



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uncorrelated nature of principal components, a linear subspace is constructed through each one of the principal component directions. As a result, a good property of the diversity of linear subspaces has been obtained, which is important to the linear approximation approach. For nonlinear fault detection and diagnosis, the linear subspace method has been integrated with Bayesian inference. Compared to the neural network and kernel-based methods, the linear approximation approach is much easier to implement. However, the nonlinear modeling efficiency of this method may be limited in specific cases. Furthermore, the linear subspace method has been extended to the two-dimensional case92, in order to handle the multimode problem in the nonlinear process.


Furthermore, there are also other alternative nonlinear process monitoring methods that have been developed in the past years. For example, Cheng and Chiu93 proposed a just-in-time-learning based PCA model for nonlinear process monitoring, Maulud et al.94 developed a multi-scale orthogonal nonlinear strategy, Wang et al.95 combined the neural network based nonlinear PCA model with the local approach for fault detection and diagnosis in nonlinear processes. Besides, the Gaussian mixture models which are reviewed in section 4.1.3 can also be used for nonlinear process monitoring. In fact, the GMM model can be considered as a particular form of the linear approximation approach. Each single Gaussian component can be considered as a linear model in the GMM method, as a result, the combination of the various Gaussian components can be used for approximation of the nonlinear process. Compared to the nonlinear modeling method such as neural network, kernel-based model, the implementation of the linear approximation method is much easier. While the nonlinear modeling method needs to determine several key parameters, the determination of the linear approximation method seems - 26 -


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much more straightforward. Therefore, compared to the nonlinear method, modeling interpretation will be much easier for the linear approximation method. However, it should be noted that the nonlinear modeling method can be used in a much wider application field than the linear approximation method. This is because it is more flexible for the nonlinear modeling function to match different nonlinear relationships of the industrial process. Detailed comparisons of advantages and disadvantages of the three main types of nonlinear process monitoring methods are listed in Table 2. [Table 2 about here] It is worth to notice that although different types of nonlinear models have been developed for process monitoring, linear models still play a critical role for both academics and industrial engineers. Since a lot of industrial processes are designed for the production of a product about a fixed set of conditions and there is only limited variation about these conditions, in this case, linear models will perform very well. This is why the linear monitoring methods such as PCA and PLS are still very popular today. However, with the increase requirements of multiple products and operation conditions, the variations of the industrial process become more and more significant, and the relationships among different process variables become much more complicated as well. In this situation, it is quite necessary to incorporate the nonlinear modeling method, which will not only improve the modeling accuracy of the variable relationships, but also to make the monitoring performance better for the industrial processes.

4.3. Time-varying and multimode process monitoring 4.3.1. Problem statement

While the traditional PCA/PLS method assumed that the industrial process operated under a single steady condition, the operation condition of modern industrial processes may be varying from time to time, - 27 -



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or switched from one operation condition to another. In fact, due to fluctuations in raw materials, set point changes, aging of equipments, and seasoning effects, the operation condition of industrial processes change frequently in practice. Besides, with the great market competition from outside, high quality and various types of products are strongly desired in the process industry. In this situation, the application of a stable monitoring approach to those processes may cause false alarms, even when the process is operated under another steady-state nominal operating mode. In order to keep the industrial process under control, the monitoring method should be updated according to the change of the operation condition. On the other hand, when the process consists of several different operation conditions, the multimode process monitoring method should be developed. In the past years, to solve the time-varying and multimode problems, different methods have been developed, such as adaptive learning techniques, multi-model approaches, soft modeling methods, among others. Detailed reviews of these methods are provided as follows.

4.3.2. Adaptive/Recursive methods

When the process is slow-varying, many adaptive and recursive monitoring approaches have been developed. For example, Dayal and MacGregor 96 proposed a recursive exponentially weighted PLS method for adaptive control and prediction in industrial processes, Qin97 developed a recursive PLS method for adaptive process monitoring, Li et al.98 presented an adaptive monitoring strategy which incorporated a recursive PCA (RPCA) to update the monitoring model. Wang et al.99 also built a recursive PLS model for adaptive monitoring of complex industrial processes. Later, a fast moving window PCA approach was developed for improve the monitoring efficiency of time-varying processes100. In this method, an N-step-ahead horizon strategy was proposed to avoid fault accommodation in adaptive process - 28 -


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monitoring. Jin et al.101 proposed a robust recursive PCA model for monitoring time-varying processes. For monitoring of nonlinear time-varying processes, a moving window approach has been developed upon the kernel PCA model102. Also, to improve the monitoring performance for time-varying processes, several efficient techniques have been illustrated, such as Elshenawy et al. 103 and Jeng 104 . Other adaptive, recursive or moving window research works related to time-varying process monitoring include Choi et al.105, Yoo et al.106, Xiao and Yang107.

4.3.3. Multi-model methods

For those industrial processes which have multiple modes, and the operation condition is always switched from one operation modes to another, different multi-model methods have been developed for process monitoring. Sometimes, this type of method is also called as the model library based approach, in which predefined models match their corresponding operation modes of the process. A real-time monitoring approach has been developed for multimode processes by Hwang and Han108, Zhao et al.109 developed a multiple PCA model based method for monitoring processes with multiple operation modes. Based on the defined PCA similarity factor, Singhai and Seborg110 evaluated a pattern matching method in the Tennessee Eastman benchmark process, which can also be regarded as a multi-model approach. Yoo et al.111 designed a multi-model statistical process monitoring and fault diagnosis method for a sequencing batch reactor. A similar pattern matching method has been developed for process analysis, monitoring and quality evaluation in batch processes112.

4.3.4. Soft modeling methods

For some multimode processes, the transition period between two different operation modes should

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also be modeled and well monitored. However, the traditional multi-model method may ignore the data information in the transition period of two operation modes, since most of them are based on hard partition of process conditions. To improve the monitoring performance for those particular multimode processes, several multi-model alike methods have also been developed. In contrast to the hard multi-model methods, most of the developed methods are based on probabilistic models, which are named as soft modeling methods in the present paper. For example, the methods which are based on the Maximum-Likelihood PCA and FA models can be efficiently used for monitoring multimode processes42, 43. Yu and Qin45 developed a multimode process monitoring method based on the GMM model, Ge and Song 113 improved the conventional probabilistic PCA model and extended it to the mixture form for multimode process monitoring. Besides, the Bayesian inference and combination strategy has also been introduced to connect various monitoring models developed in different operation modes of the process114.

4.3.5. Local-learning and robust methods

Another type of monitoring methods for time-varying and multimode processes is known as the local-learning method. In this method, both of the modeling construction and process monitoring are carried online. Therefore, each time a data sample is available, the first step of the local-learning method is to search some similar data samples in the historical database. Then, based on the obtained similar dataset, an online model is intended to be developed for online process monitoring of that particular data sample. After that, the model is discarded and the procedures are repeated for the next data sample. A typical local-learning method is known as just-in-time-learning model, which has been used for nonlinear process monitoring93. However, utilization of this method for time-varying process monitoring is also straightforward. Later, the similar local-learning idea was adopted by Ge and Song28 for online monitoring - 30 -


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of nonlinear time-varying and multimode processes, which was known as adaptive local model approach. Besides, several robust modeling strategies have also been developed for monitoring of multimode processes. For example, Kano et al.115 developed an external analysis based method, and combined with ICA for process monitoring. Similarly, Ge et al.116 proposed a robust online multimode process monitoring method, which was based the nonlinear extension of the external analysis method. In this method, the operation mode information is related to the external variables, and other process variables are referred as main variables. By constructing a relationship between these two types of variables, the influence of the operation mode change can be efficiently removed from the main process data information. As a result, a robust process monitoring can then be developed, which is not sensitive to the operation mode change of the process any more.


Time-varying and multimode process monitoring methods are both motivated for industrial processes in which multiple operation conditions are involved. While the time-varying process monitoring method focuses on those processes whose operation condition changes frequently, e. g. from time to time, the multimode process monitoring method usually handle those processes which have several stable operation conditions, and switches from one to another. Generally, the adaptive and recursive modeling method, such as adaptive PCA/PLS, recursive PCA/PLS methods are mainly used for time-varying process monitoring purpose, while the multi-model and soft modeling methods are mainly focused on monitoring multi-mode industrial processes. However, there are also research works that applying adaptive and recursive models for multimode process monitoring. In this case, false alarms will be inevitable during the model updating in the switching process of two adjacent operation conditions. Compared to the multi-model monitoring - 31 -



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method, the soft modeling method is able to incorporate the transition period of two operation modes. In some situations, when the transition period of two operation modes is significant, the soft modeling method is much more appropriate than the multi-model based monitoring method. It is worth to note that the GMM model which has been used for non-Gaussian and nonlinear process monitoring can also be used for multi-mode process monitoring, which is classified in the soft modeling method. In this method, each Gaussian component corresponds to one operation condition of the process. When combined with other data modeling method, various kinds of GMM-type monitoring methods have been constructed in the past years. In contrast, the local-learning and robust methods are comparatively new. While the local-learning method can be used for both time-varying and multi-mode process monitoring, the robust method is particularly designed for multimode processes. Under both of the local-learning and robust modeling frameworks, various data modeling methods can be incorporated, based on which different time-varying or multi-mode process monitoring methods can be formulated. For the robust monitoring method, it is worth to point out that this method is able to differentiate new operation modes and the fault conditions of the process, as long as the external variables are correctly separated from the process variables. Table 3 shows the detailed comparisons of advantages and disadvantages of various time-varying and multimode process monitoring methods. [Table 3 about here]

4.4. Dynamic process monitoring 4.4.1. Problem statement

Due to the feedback control systems which are widely used in modern industrial processes, the - 32 -


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influence of random noises and process disturbances, the dynamic data behavior is often presented in both input and out variables of the process. However, most of the traditional data-based monitoring methods are based the assumption that the process data sample is sampling independent to each other. Actually, subjected to the dynamic data behavior, the data sample obtained at the present time may be correlated with the ones sampled before and after the present time. For different industrial processes and operation conditions, the dynamic steps may be different from each other. If the dynamic information of the process data is not incorporated into the monitoring model, we may obtain a misleading result. Thus, changes of dynamic relationships among process variables cannot be efficiently explored, which may cause a severe malfunction to the process. Besides, due to the dynamic relationships, the fault may also be distorted or smeared by random noises and other disturbances. Sometimes, even the fault can be detected, the fault behavior has been changed significantly and it may also cause a large detection delay to the monitoring system. In order to improve the monitoring performance in dynamic industrial processes, significant research efforts have been made in the past years, detailed reviews of which are demonstrated as follows.

4.4.2. Dynamic MSPC methods A dynamic form the PCA model was developed early by Ku et al.117 for disturbance rejection and isolation in the industrial process. The first step of this method is to augment the modeling dataset by incorporating several time-lagged data samples of each variable. By constructing the PCA model upon this augmented data matrix, the auto-correlation of the process data can be extracted. Actually, before the work of dynamic PCA, a similar form of the dynamic PCA/PLS model has already been formulated in batch processes, which is known as mutilway PCA or multiway PLS. We will make a detailed discussion in section 4.5. Chen and Liu118 developed and compared two dynamic MSPC methods for online batch - 33 -



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process monitoring, which are based on PCA and PLS, respectively. Choi and Lee119 extended the dynamic PCA idea to the kernel PCA model, and proposed a nonlinear dynamic process monitoring method. Jia et al.84 applied the dynamic kernel PCA model for online batch process monitoring purpose. Based on two-dimensional dynamic kernel PCA and two-dimensional dynamic kernel Hebbian algorithm, Zhang et al.120 proposed a statistical analysis and adaptive technique for dynamic process monitoring. Similarly, several other dynamic forms of the PLS model have also been developed for fault diagnosis, e. g. Lee et al.121, Lu and Wang122. More recently, the idea of the conventional dynamic MSPC method has been extended to the ICA model. For example, Stefatos and Ben Hamza37 has developed a fault detection and diagnosis based on the dynamic ICA model, Hsu et al.36 also proposed a dynamic ICA based process monitoring method.

4.4.3. Time-series analysis methods

Although the dynamic MSPC method has been widely used for process monitoring of dynamic processes, Kruger et al.123 demonstrated that the traditional dynamic PCA method may not be able to model the dynamic information of the process data. Furthermore, it will even introduce some additional dynamic behavior into the process dataset, which is harmful to the process monitoring algorithm. Instead, by incorporating the autoregressive model, Kruger et al.123 proposed a dynamic process monitoring method called improved PCA, based on which the auto-correlation of the process data has been successfully extracted. Later, Choi et al. 124 proposed a new dynamic monitoring model based on a multivariate autoregressive model and multiway PCA for monitoring dynamic batch processes. The results of case studies indicated that the new methods have provided better monitoring performance than the traditional methods. - 34 -


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4.4.4. State-space model based methods

Another main type of dynamic process monitoring methods is referred as the state-space model based methods, which is often combined with subspace identification algorithms. The main advantage of this method is that auto-correlation and cross-correlation among the process data can be modeled simultaneously. Xie et al.125 investigated different dynamic process monitoring methods, including the dynamic PCA method, the autoregressive model based method, and the subspace identification based method. As a result, the subspace identification based method turned out to be the most promising method for dynamic process monitoring126. Yao and Gao127 extended the subspace identification model to the batch process, and proposed a two-dimensional dynamic monitoring method. More recently, the state-space model has also been incorporated with the ICA model for nonlinear dynamic process monitoring38, and combined with the local approach for fault detection of non-Gaussian dynamic systems57.


Besides, in the past years, there are also several other methods that have been developed for dynamic process monitoring. For example, Chen and Liao128 combined neural network with the PCA model for dynamic process fault monitoring, Alabi et al.129 proposed an online dynamic process monitoring method by using wavelet-based generic dissimilarity measurement, Hu and Yuan130 provided a dynamic multiway neighborhood preserving embedding method for statistical monitoring of fed-batch processes, and Odiowei and Cao131 designed a nonlinear dynamic process monitoring approach based on canonical variate analysis and kernel density estimations. Among all of the developed dynamic process monitoring methods, the dynamic MSPC-type methods such as dynamic PCA and dynamic ICA may be the simplest ones. By extending the process data matrix - 35 -



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with more correlated data samples, the dynamic MSPC model can be easily formulated. One critical issue of this method is the determination of the dynamic step of the data matrix, which in some cases may significantly influence the monitoring result. Although there are several methods that have already been developed for selection of the dynamic step, it is still an open question that requires more investigations in the future work. Compared to the time-series analysis method, the main feature of the state-space modeling method is that it can simultaneously model auto-correlations and cross-correlations among different process variables. When the dynamic feature of the process is complicated and crossly reflected in different variables, the state-space modeling method is particularly useful. Similarly, both of the time-series analysis method and the state-space modeling method can be combined with traditional MSPC method. As a result, various types of time-series analysis and state-space MSPC monitoring models can be constructed, which may receive unexpected effects in particular industrial processes. Detailed analyses of advantages and disadvantages of different dynamic process monitoring methods are given in Table 4. [Table 4 about here]

4.5. Batch process monitoring 4.5.1. Problem statement

Different from the continuous process, batch processes are always more complicated, due to frequent start-ups and shut downs, non-stationary operation conditions, nonlinear and dynamic data behaviors, and many batch processes are also operated under multi-phases or have various operation stages. Therefore, it seems more difficult to carry out the monitoring tasks in batch processes. Since the pioneer works of Nomikos and MacGregor in 1990s132,

133

, batch process monitoring has become a hot research spot, and - 36 -


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will still play an important role in batch process engineering areas, such as pharmaceutical engineering, food engineering, biological engineering and etc. The following subsections give a detailed review of batch process monitoring methods that have been developed up to date.

4.5.2. Multiway monitoring methods

Multiway PCA and Multiway PLS are two of the most traditional batch process monitoring methods, which have still been widely used and researched in both industry and academy. Chen and Liu118 incorporate the dynamic monitoring algorithm upon the multiway PCA and multiway PLS methods, Kourti134 provided a detailed statistical analysis and monitoring result discussions on start-ups and grade transitions for the continuous process which are very similar to the case in batch processes, Chen and Chen 135 developed a novel technique for on-line batch process monitoring, which is based on the wavelet-based multi-hidden Markov model tree (MHMT) and multiway PCA method. For those batch processes which have non-Gaussian data information, the multiway modeling method has been extended to the ICA model. For example, multiway independent component analysis method has been proposed for batch process monitoring136, Albazzaz and Wang30 also incorporated the ICA model for batch process monitoring. Besides, the multiway PCA and multiway ICA methods have both been extended to their nonlinear cases, precisely, the multiway kernel PCA and multiway kernel ICA methods have been developed for nonlinear batch process monitoring. However, it is worth to notice that the traditional batch-wise unfolded PCA and PLS methods also have the ability to capture the nonlinearity and time varying nature of batch processes. This is because they have different loadings for each variable at every time point throughout the batch. As a result, they can effectively provide locally linear models at every time point throughout the batch, which can be considered as a particular form of the nonlinear monitoring - 37 -



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model. To study and evaluate of different multiway batch process monitoring methods, several research works have been carried out. For example, Ramaker et al.137 studied the fault detection properties of global, local and time evolving models for batch process monitoring. Ferreira et al.138 studied various multiway multivariate techniques for data modeling through an industrial fermentation process. A critical evaluation of different batch process monitoring approaches was provided by Sprang et al.139. Besides, Camacho et al.140 gave a detailed analysis and exploration of different statistical data-based methods for batch process monitoring.

4.5.3. Phase-based methods

Recently, a multiphase behavior has been recognized in many batch processes. During the past several years, various multiphase batch process monitoring have been proposed. Undey and Cinar141 illustrated the multistage and multiphase statistical monitoring methods in batch processes. Muthuswamy and Srinivasan142 developed a phase-based supervisory control algorithm for a fermentation batch process. Lu et al.143 proposed a novel sub-PCA modeling method for multiphase batch process monitoring, based on which the batch process can be automatically determined into different phases. Zhao et al.144 studied an adaptive monitoring method for batch processes under the limited modeling data case. Camacho et al.145 presented a multiphase data analysis framework for batch processes. Zhao et al.146 proposed a subspace separation algorithm for multiphase batch process monitoring, based on which both quality analysis performance and process comprehension have been improved. More investigation of the phase-based method for batch process monitoring can be found in the recent survey paper10.

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4.5.4. Two-dimensional dynamic monitoring methods

To handle the dynamic data behavior, the batch process has an additional dynamic dimension, which is through the batch direction. Therefore, a two-dimensional dynamic PCA method has been proposed for batch process monitoring, which can efficiently model the dynamic data information through both of the two dimensionalities147. Yao and Gao148 developed a score space based two-dimensional dynamic PCA method for batch process monitoring. Later, the subspace identification scheme was employed for two-dimensional dynamic modeling of the batch process127, and the traditional two-dimensional dynamic PCA model was also extended to multiphase batch processes149. More recently, the non-Gaussian data information of the batch process has been incorporated into the two-dimensional dynamic monitoring method, which is based on the mixture Gaussian model47.


Compared to the continuous process, the batch process is inherently nonlinear, time-varying, and often has a strong dynamic data behavior. Although the mutliway method has the ability to handle these data characteristics, it may not always perform very well, especially when the batch process has several distinct phases. Furthermore, different phases may have different data behaviors, e. g. different nonlinear relationships, different dynamic steps, and different data distributions. In this case, those different phases should be considered separately, for example, by using different models, different monitoring schemes, different dynamic steps, etc. Also, the transition period between two adjacent phases in the batch process should be paid particular attentions, which may have significant effect on the monitoring performance of the whole batch process. Compared to various phases, the data obtained from the transition period may have more significant nonlinear and dynamic behaviors, thus should be modeled separately. If we put the - 39 -



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multimode problem and the multi-phase problem together, it can be easily found that they are quite similar. Therefore, those monitoring methods which have been developed in multimode continuous processes may be made useful in multiphase batch processes. Also, various dynamic monitoring methods that have been developed for continuous processes may be migrated in batch processes. Particularly, they can be combined with two-dimensional dynamic monitoring methods, in order to further enhance the monitoring performance for the batch process. So far, ongoing research studies for all of the above three types of batch process monitoring methods have being carried out. More recent related works include Gunther et al.150, Faggian et al.151, Berber et al.152, Alvarez et al.153, Chen and Jiang154, He and Wang155, Yu156, and so on. To examine the advantages and disadvantages of different types of batch process monitoring methods, please refer to the recent critical evaluation and survey papers139, 140, 10.

4.6. Summary After specifically reviewing the data-based process monitoring method thought different fundamental problems, a summarized overview of various data-based process monitoring methods and some additional comments are provided in this subsection. Generally, a complex industrial process always has various data characteristics, such as non-Gaussian data distribution, nonlinear variable relationships, dynamic data correlations, and the operating condition of the process may also changes. So far, as have been demonstrated, separated research works have been carried out for solving those specific problems in both of the continuous and batch processes. However, a good process monitoring system should be able to deal with various data behaviors simultaneously. During the past years, many research works have already been carried out for dealing with two or more main - 40 -


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characteristics of the process data. For example, to monitor the non-Gaussian process under nonlinear variable relationships, the ICA model has been incorporated with the kernel method. Also, the non-Gaussian process monitoring approaches have been extended to their adaptive or multi-model forms, based on which the time-varying data characteristic of the process can be modeled simultaneously. In order to deal with the nonlinear variable relationship in time-varying processes, the kernel PCA model has been incorporated with the moving window approach, and several Gaussian mixture models have also been developed. Besides, there are also several other works that have been developed for dealing with nonlinear, non-Gaussian and time-varying data behaviors simultaneously. Therefore, although we have divided the data-based process monitoring methods into different categories according to various fundamental problems, many of them are intercrossed in different categories. Besides, for batch process monitoring, four different categories of data-based monitoring methods have also been overlapped and combined with multiway modeling approaches. A systematic overview of different data-based process monitoring methods is illustrated in Figure 7. [Figure 7 about here]

5. Research perspectives Over the last 20 years, data-based process monitoring has been receiving continuous attentions from both academy researchers and practicing engineers. Based on the literature survey given in section 4, some research perspectives can be revealed and several promising issues are also discussed in this section.

5.1. Monitoring of complex dynamic processes Compared to other three fundamental problems, there are much less works on the dynamic process - 41 -



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monitoring issue, especially combined with other data characteristics, e. g. dynamic non-Gaussian processes, nonlinear dynamic processes, time-varying dynamic processes, etc. Since the dynamic data behavior is very common in practice, and also important to the process control system, it should be well considered in the process monitoring system. Although there are several methods that have been proposed to monitor complex dynamic processes, such as for the dynamic non-Gaussian process, more research investigations need to be carried out on this topic. Besides, the incorporation of some new nonlinear dynamic modeling approaches may be of particular interest for process monitoring. When the process exhibits several different data behaviors, the fault diagnosis and identification will become much more difficult, because the root cause of the fault is difficult to locate, and a more complex fault propagation network may be caused. Therefore, for those complex dynamic processes, fault diagnosis and identification should be carefully carried out. It will be greatly helpful if some prior process knowledge and experiences of operation experts can be incorporated for utilization. For Batch processes, dynamic data behavior is also an important issue. So far, the multiway modeling method has been extended to dynamic forms, and several two-dimensional dynamic monitoring schemes have also been constructed. However, most of them have not considered more complex data characteristics, for example, how to handle the non-Gaussian data behavior in dynamic batch processes? How to develop a nonlinear dynamic monitoring model for multiphase batch processes? How to extend the existing dynamic model to the multi-model form? Generally speaking, compared to the continuous process, dynamic monitoring in batch processes is more difficult, which on the other hand, also provides great opportunities for future research.

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5.2. Plant-wide process monitoring With the increasing development of modern industry, more and more operation units and equipments have been incorporated into the process. As a result, a large-scale type of processes has been generated, which are known as plant-wide processes. Compared to the traditional process, monitoring of those plant-wide processes is much more difficult, for example, a fault happens in one unit may be smeared by another equipment. Even if the fault has been successfully detected, it is very difficult to locate its root causes. Therefore, how to develop efficient monitoring methods for plant-wide processes is considered to be a challenge in this area. Existing methods for plant-wide process monitoring are mainly resorted to the multi-block statistical modeling approaches, such as MacGregor et al.157, Westerhuis et al.158, Qin et al.159, Smilde et al.160, Choi and Lee161, Cherry and Qin162, Kohonen et al.163, Ge and Song164, Zhang et al.81, and so on. However, there are still many issues that remain unexplored, for example, how to divide the plant-wide process into different sub-blocks without the process knowledge? How to efficient combine the monitoring results in different sub-blocks? How to analysis the fault propagation path in plant-wide processes? Besides, the relationships among different parts of the process also deserve further researches.

5.3. Transition process monitoring Typically, transition is a period time that the process changes from one operating condition to another, in which the operating condition is unstable, data may show high nonlinearities and have significant dynamic effects. Therefore, it is more difficult to monitor these transition processes. In practice, transitions are very common in both continuous and batch processes. In the continuous process, start-ups of the process equipment, shut-downs of the process system, and transition periods between two operation modes

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can all be considered as the transition process. In contrast, there are even more transitions in the multiphase batch process, e.g. gradual transitions between two adjacent steady phases. In these phase transition periods, the process dynamic behaviors are more complex than those in steady phases. If the abnormal events in the transition process are not well monitored, they may greatly affect the process operation safety and the quality of final products. Recently, several methods have been developed for monitoring transition processes. For example, a dynamic data analysis and statistical process control method has been developed for modeling of start-ups and grade transitions in batch processes134, Sundarraman and Srinivasan165 used an enhanced trend analysis method for monitoring transition in chemical plants, Zhao et al.166 developed a stage-based soft-transition multiple PCA modeling for batch process monitoring, Yao and Gao167 also developed a phase-based method for monitoring transitions in the batch process. More recent developments of transition monitoring methods include Ng and Srinivasan168, Natarajan and Srinivasan169, Zhao et al.170, Zhu et al.171, Ge et al.172. However, more efficient transition monitoring strategies are still expected, especially those which can be plugged into the existing monitoring system.

5.4. Probabilistic process monitoring So far, most data-based process monitoring methods are resorted to deterministic models, such as PCA, PLS, ICA, and KPCA. In practice, however, almost all process variables are contaminated by random noises. Therefore, most process measurements are inherently random variables, thus perform through a statistical manner, not the deterministic way. As a result, it is required that process monitoring should also be carried out through the statistical manner, and the monitoring decisions are made through a probabilistic way. Recently, the PCA based monitoring method has been extended to its probabilistic counterpart, which is called probabilistic principal component analysis (PPCA)173. Later, the factor analysis (FA) model has - 44 -


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been incorporated for probabilistic monitoring, which has no assumption that different process variables should share the same noise variance174, 49. More recently, both of the PPCA and FA models have been extended to their mixture form for monitoring processes with multiple operation modes43, 113. Compared to the monitoring method based on deterministic models, the main advantages of the probabilistic model based monitoring method lie in the following several points. Firstly, the combination of a probabilistic model and the Expectation-Maximum algorithm allows us to deal with missing values in the dataset, which is very practical in process data. Secondly, it is more sophisticated to extend the probabilistic model to its mixture form, thus can be used for modeling complex processes. What’s more, the probabilistic model can naturally exploit Bayesian treatment of the model. However, current research works have not sufficiently considered the nonlinear and dynamic data characteristics, and how to efficiently apply these models in batch processes is also underway. Besides, for online process monitoring, we may also want to know how safe or how well the process is operated, to what extent the process is abnormal, and how to provide a probabilistic confidence interval is also of great significance to the process.

5.5. Model combination and complementation In the past years, although different data-based process monitoring methods have been developed, each of these methods has its own advantages and disadvantages. Therefore, a method works well under one process condition might not provide a satisfactory monitoring performance under another. In other words, the efficiency of each process monitoring method may depend on the data characteristic of specific process and fault. Particularly, for those processes which have wide range of operating conditions, it is a promising idea to combine several monitoring methods together. In this case, the process monitoring performance could be enhanced by taking advantages of various methods, and the shortcoming of each method can also - 45 -



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be complemented for each other. Recently, several pieces of research works have already been carried out on this topic. For example, Ng and Srinivasan175 proposed a multi-agent based method for collaborative fault detection and identification in chemical processes. Perk et al.176 also developed an agent-based system for statistical monitoring of complex chemical processes. Nevertheless, more further research efforts are still needed towards this issue, especially on the model combination strategy and local performance analysis for different methods.

5.6. Multi-data fusion for process monitoring In most cases, the data-based model only incorporates the routinely measured process variables, such as temperatures, pressures, levels, and so on. However, in modern industrial processes, various new measurement devices have been used, which might provide additional data information of the process. For example, a spectroscopic measurement device can capture detailed chemical information during the reaction process, a camera-based image sensor is able to extract abundant data information for some particular processes, e. g. metallurgic processes. If these new data information can be incorporated, the reliability of the process monitoring system may be improved. Besides, both of the process analysis and the fault interpretation may also become much easier.

5.7. Other promising issues Furthermore, there are also other promising research issues that wroth highlighting for future work. For example, by incorporating some available process knowledge, the performance of both fault detection and fault diagnosis could be improved. Most current data-based process monitoring methods take the assumption that all process variables are sampled under the same rate. However, in many practical - 46 -


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industrial processes, various sampling rates are often used for different process variables. A commonly used data pre-processing method is to down-sample those variables with higher sampling rates, which will probably waste data information. Therefore, how to carry out process monitoring directly for multi-sampling rates data is another topic deserving further studies. Meanwhile, how to efficiently combine the data-based process monitoring system with the traditional control system is also a promising research issue, which will be greatly helpful to both continuous and batch process industries.

6. Conclusions In this paper, recent developments of data-based process monitoring methods for industrial processes have been reviewed. A detailed illustration of main terminologies of the data-based process monitoring method was provided. Based on evaluations of various data characteristics in typical industrial processes, a timely update review has been carried out through different aspects, including non-Gaussian, nonlinear, time-varying and multimode, dynamic, and batch processes. Detailed discussions of connection and comparison among different data-based process monitoring methods are demonstrated. Furthermore, several important and promising research perspectives have been highlighted for future work on the topic.

Acknowledgement This work was supported in part by the National Natural Science Foundation of China (NSFC) (61004134), National Project 973 (2012CB720500), and the Fundamental Research Funds for the Central Universities. We would like to sincerely thank the reviewers and the editor for providing useful comments and suggestions to improve our manuscript. - 47 -



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