Robust Online Monitoring for Multimode Processes Based on

Ind. Eng. Chem. Res. 2008, 47, 4775–4783

4775

Robust Online Monitoring for Multimode Processes Based on Nonlinear External Analysis Zhiqiang Ge, Chunjie Yang,* Zhihuan Song, and Haiqing Wang State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Zhejiang UniVersity, Hangzhou 310027, Zhejiang, China

A robust online monitoring approach based on nonlinear external analysis is proposed for monitoring multimode processes. External analysis was previously proposed to distinguish faults from normal changes in operating conditions. However, linear external analysis may not function well in nonlinear processes, in which correlations between external variables and main variables are generally nonlinear. Under the consideration of real-time monitoring, a moving window is used for sample selection and least-squares support vector regression is used as the model structure of nonlinear external analysis. When the influence of external variables is removed, the filtered information of main variables is extracted and monitored by a two-step independent component analysis-principal component analysis strategy. In addition, to improve the performance of modeling and monitoring, a robust scheme is developed. A benchmark study of the Tennessee Eastman process shows the efficiency of the proposed method. 1. Introduction During the last few decades, multivariate statistical process control (MSPC) has received great attention for process monitoring. MSPC can compress the high-dimensional process variables into a low-dimensional latent variable space. Particularly, multivariate projection methods such as principal component analysis (PCA), partial least-squares (PLS), and independent component analysis (ICA) are widely used.1–5 However, the current MSPC approaches have problems when applied to processes with multiple operating modes. In fact, industrial processes always change frequently due to fluctuations in raw materials, set-point changes, and unwanted disturbances. The application of traditional MSPC techniques to a process with multiple operating modes can cause false alarms, even when the process is under another steady-state nominal operating mode. It is difficult to apply MSPC in multiple mode processes, since the current techniques are based on the assumption that the process has only one nominal operating region. To solve this problem, adaptive PCA and PLS methods have been proposed.6–8 These approaches are carried out blindly, which means that continuous updating is performed whether a process change has been identified. Besides, recursive PCA (RPCA) fails to distinguish process operating mode changes from process faults. Alternatively, model library-based methods have been introduced.9–11 Predefined models match their corresponding operating modes. However, the transitions between two operating modes are always false-alarmed. Recently, process knowledge was incorporated into MSPC for time-varying process monitoring.12,13 Unfortunately, process knowledge is difficult to obtain from the process. Kano et al.14 proposed a novel method for multimode process monitoring, which is based on external analysis. Process variables are divided into two parts, external variables and main variables. Variables which represent operation mode change are regarded as external variables. When the part explained by external variables in the main variables is removed, the rest of the information from the main variables * To whom correspondence should be addressed. Tel.: +86-57187951442-808. Fax: +86-571-87951921, E-mail: [email protected]. edu.cn.

can be monitored, despite whether the operating condition changes or not. Therefore, this method is robust to operating mode changes and can also distinguish mode changes from process faults. However, several issues arise with this method. First, it cannot be carried out online, since it is an offline algorithm according to the reference literature.14 Second, the previous method used the conventional least-squares method for regression between the external main variables. The singularity problem will possibly be caused when the variables are highly correlated. Besides, modern industrial processes are mainly nonlinear. The monitoring performance will be deteriorated when a linear external analysis is applied. To overcome the nonlinear shortcoming of MSPC, several nonlinear extensions of PCA were reported. Kramer15 developed a nonlinear PCA method based on the autoassociative neural network. Dong and McAvoy16 proposed a nonlinear PCA by combining the principal curve and the neural network. Hiden et al.17 used genetic programming to address the same problem. Support vector regression (SVR) has been widely used for nonlinear function regression and system identification18 in the past decade. Recently, least-squares SVR (LSSVR) has been developed.19 Since its computation is more efficient than SVR, online process modeling is possible. There are also many applications of SVR/LSSVR in the process monitoring area. Generally, MSPC techniques are derived from a database usually containing some outliers. These outliers can distort the distribution of multivariate data and often lead to a deceptive result. To minimize the adverse effect of outliers, the robustness problem has been already issued throughout MSPC techniques. Two categories of robust algorithms were reviewed and compared in the reference.20 Jin et al.12 proposed a robust recursive PCA modeling method for adaptive process monitoring. Recently, Lee et al.21 gave a new scheme of robust PLS method for the monitoring of an industrial wastewater treatment process. The proposed robust method is categorized into two approaches, the hard threshold approach and the soft threshold approach. In this paper, we focus on developing a new robust online monitoring scheme. In the new proposed method, nonlinear information between the external variables and the main variables is extracted by LSSVR. After the influence of external

10.1021/ie071304y CCC: $40.75  2008 American Chemical Society Published on Web 06/14/2008

4776 Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008

Figure 1. Description of external analysis.

variables has been removed, a two step ICA-PCA information extraction and monitoring strategy is carried out. A robust online LSSVR regression and process monitoring strategy is also developed. The rest of this paper is structured as follows. In Section 2, the nonlinear external analysis is demonstrated. Then the two-step ICA-PCA information extraction and monitoring strategy is briefly described in Section 3, followed by the development of a robust online algorithm in the same section. A Tennessee Eastman (TE) benchmark case study is given in Section 4. Finally, some conclusions are made. 2. Nonlinear External Analysis Based on LSSVR Generally, changes in the operating condition are assumed to be brought from the outside of the process and should be distinguished from process faults.14 These changes include process inputs such as a feed flow rate, set-point change of controllers, and so on. The monitored process variables can be classified into two groups.14 The first group is referred to as external variables, which consist of variables related to operating condition changes. Other variables are regarded as main variables. The variations of operating conditions are reflected in the external variable. Changes in external variables should not be considered as process faults. Therefore, both the changes in external variables and their influences on main variables should be distinguished from process faults. Hence, the information of main variables can be decomposed into two parts as follows:14 the part explained by external variables and another unexplained part. To distinguish operating condition changes from process faults, external analysis can be carried out to remove the influence of external variables. The concept of this external analysis method is illustrated in Figure 1. Consider a data matrix Z ∈ Rn×m, where n and m are numbers of samples and variables, respectively. Due to external analysis, m variables can be classified into two parts. Suppose mu variables are classified as external variables, and my variables are classified as main variables, and thus mu + my ) m. The original data matrix can be decomposed as Z ) [Y U] (1) where Y consists of main variables and U consists of external variables. As demonstrated above, the data matrix Y of main variables should be decomposed into two parts, a part explained by external variables and another unexplained part. To remove the influence of external variables, some regression analysis tools can be used. For linear processes, multiple linear regression tools can be used. However, when process variables are highly correlated, there is the possibility of a singularity problem. In addition, modern industrial processes are mostly nonlinear. Hence, an efficient nonlinear regression tool should be incorporated. SVR is a powerful machine-learning tool and especially useful for classification and prediction in small sample cases.18 This

approach motivated by statistical learning theory led to a class of algorithms characterized by the use of nonlinear kernels, high generalization ability, and the sparseness of the solution. Unlike the classical neural network approach, the SVR formulation of the learning problem leads to quadratic programming (QP) with a linear constraint. However, the size of the matrix involved in the QP problem will become very large. Hence, to reduce the complexity of optimization processes, LSSVR is proposed to obtain a linear set of equations instead of a QP problem in the dual space. The formulation of LSSVR is introduced as follows.19 Consider a given train data set {ui, yi}i ) 1,2,... N, with input data ui ∈ Rn and output data yi ∈ R. The following regression model can be constructed by using nonlinear mapping function φ( · ): y(u) ) wTφ(u) + b

(2)

where w is the weight vector and b is the bias term. By mapping the original input data into a high-dimensional space, the nonlinear separable problem becomes linearly separable in space. Then the following cost function is formulated in the framework of empirical risk minimization: N

∑

C 1 2 e min J(w, b, e) ) |w|2 + 2 2 i)1 i

(3)

subject to equality constraints yi ) 〈w, Φ(ui)〉 + b + ei,

i ) 1, ... N

(4)

where ei is the random error and C is a regularization parameter in determining the trade-off between minimizing the training errors and minimizing the model complexity. To solve this optimization problem, the Lagrange function is constructed as N

L(w, b, e, R) ) J(w, e) -

∑ R {w φ(u) + b + e - y } T

i

i

i

i)1

(5) where Ri is the Lagrange multiplier. The solution of eq 5 can be obtained by partially differentiating with respect to w, b, ei, and Ri and it also can be written as

[

0 1N

1NT Σ+

1 I C

][ ] [ ] b 0 ) r y

(6)

where 1N ) [1 · · · 1 ]T ∈ RN, r ) [R1 · · · RN ]T ∈ RN, y ) [y1 · · · yN ]T ∈ RN , I ∈ RN×N, Σij ) K(ui, uj) ) 〈φ(ui), φ(uj)〉, ∀ i, j ) 1, ..., N (7)

Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4777

Finally, b and Ri can be obtained by the solution to the linear system b^ )

-1

-1

1 (Σ + C IN) y T

(8)

1T(Σ + C-1IN)-11

^ ^) R ) (Σ + C-1IN)-1(y - 1b

(9)

According to Mercer’s theorem, the resulting LSSVR model can be expressed as N

f(u) ) 〈w, φ(u)〉 + b )

∑ R K(u , u) + b i

i

E ) T · PT + F

where T is the score matrix, P is the loading matrix, and F is the residual matrix after the analysis of PCA. Combining the two steps together, original data set V can be recalculated as V ) A · Sˆ + T · PT + F

Y ) f(U) + V

(10)

(11)

N

f(U) ) 〈w, φ(u)〉 + b )

∑ R K(u , u) + b i

i

(12)

i)1

where the V matrix is defined as: V ) Y - f(U)

(13)

As a result, the data matrix V is robust to changes of operating conditions. Its variation is only sensitive to process faults or unmeasured disturbances. Therefore, the monitoring information is focused on data matrix V, which will be analyzed in the following section. 3. Robust Online Process Monitoring Based on Nonlinear External Analysis 3.1. Two-Step ICA-PCA-Based Information Extraction and Monitoring Strategy. The traditional MSPC approaches do not always function very well, since their achievable performance is limited by the assumption that monitored variables are of a Gaussian distribution. In fact, some of the process variables are of non-Gaussian distribution. ICA can reveal more meaningful information in the non-Gaussian data than PCA. A number of applications of ICA have been reported.22 Lee et al.4,5 used ICA for process monitoring and extended it to dynamic and batch processes. Kano et al.23 developed a unified framework for MSPC, which combined PCA-based SPC and ICA-based SPC. Our previous work also proposed a two-step information extraction strategy based on ICA-PCA.24 Therefore, only a brief description is given in the present paper. Given the data matrix V, ICA is carried out in the first step to extract the non-Gaussian information. Therefore, V could be decomposed as follows: V ) A · Sˆ + E

(14)

where Sˆ is the independent component matrix and E is the residual matrix after the ICA procedure. In the second step, PCA is used to model the Gaussian information in the residual matrix E. Thus, E is decomposed as

(16)

After both the Gaussian and non-Gaussian information has been extracted, three statistical descriptions of I2, T2, and squared prediction error (SPE) as well as their corresponding control limits can be established for monitoring purposes.24 I2 ) ST · S

i)1

where K(ui, u) is the nonlinear kernel function. In comparison with some other feasible kernel functions, the radial basis function (RBF) is a more compact supported kernel and is able to reduce the computational complexity of the training process and improve the generalization performance of LSSVR. As a result, the RBF kernel is selected as the nonlinear kernel function in this paper. To achieve a high level of performance with LSSVR models, some parameters have to be tuned, including the regularization parameter C and the kernel parameter. Therefore, the main data matrix Y can be decomposed into two parts:

(15)

k

T2 )

(17)

t2i

∑ λ e k(nn --k1) F

(18)

k,(n-k),R

i

i)1

SPE ) f · fT ) e(I - PPT)eT e SPER

[

cR√2θ2h02 θ2h0(h0 - 1) SPER ) θ1 · 1 + + θ1 θ2 1

]

(19) 1⁄h0

(20)

m where k is the number of principal components, θi ) ∑j)k+1 λji 2 for i ) 1,2,3, h0 ) 1 - [(2θ1θ3)/(3θ2 )], R is the significance level, and cR is the normal deviate corresponding to the upper 1 - R percentile. 3.2. Robust Online Monitoring Strategy. To carry out the proposed algorithm online, an adaptive method should be introduced. As mentioned in the first section, there are several papers reported on adaptive PCA and PLS models which are recursively updated using newly incoming data. In the present paper, the LSSVR model is recursively updated using newly incoming data. When process data samples become very large, the model development will be time-consuming and difficult to be carried out online. To overcome this problem, a moving window strategy can be used. Due to the merit of LSSVR, only a small number of train samples are needed for model development, which is also beneficial for online implementation. While these adaptive methods are proposed and successfully used for the modeling and monitoring of various industrial processes, it has been pointed out that these models could become seriously deteriorated when a considerable number of outliers were used in the model updating procedure. Several authors have proposed robust multivariate methods. In the present paper, a new robust method is proposed, which integrates Gaussian and non-Gaussian information together. The distinct feature of the proposed method is that incoming outliers are preliminarily screened to maintain the robustness of the regression model. In order to screen the outliers, a combined monitoring index is proposed as follows:

Ω)

I2 Ilim

+ 2

T2 SPE + Tlim2 SPElim

(21)

where Ω is the combined monitoring index, Ilim2, Tlim2, and SPElim are corresponding confidence limits of I2, T2, and SPE. The distribution of the combined monitoring index Ω can be determined by kernel density estimation,25 and thus the statistical confidence limit of the combined monitoring index Ωlim can also be calculated. Therefore, each newly incoming observation can be tested whether it is an outlier or not. However, process faults should be distinguished from outliers. In the present paper, a process fault is considered to be detected if 5 Ω values continuously exceed Ωlim. On the basis of the idea of Lee et al.,21 the present robust method can also be categorized into two different approaches,


Figure 2. Flow chart of independent component analysis-principal component analysis (ICA-PCA) monitoring model development. Table 1. Monitoring Variables in the TE Process no.

measured variables

no.

measured variables

1 2 3 4 5 6 7 8 9 10

A feed D feed E feed A and C feed recycle flow reactor feed rate reactor pressure reactor level reactor temperature purge rate

12 13 14 15 16 17 18 19 20 21

11

product separator temperature

22

product separator level product separator pressure product separator underflow stripper level stripper pressure stripper underflow stripper temperature stripper steam flow compressor work reactor cooling water outlet temperature separator cooling water outlet temperature

according to the rejection threshold for the screening of outliers. In the hard threshold approach, all data identified as outliers are simply eliminated and thus only normal data are used for model updating. In another soft threshold approach, all incoming data including outliers are used for model updating. Therefore, a weighted function should be used to suppress the adverse effect of outliers in model updating. In Lee’s study, the weight was calculated from the combined monitoring index, which can also be carried out in the present paper. Because the results of the two approaches are similar, only the hard threshold approach is carried out in this paper. The implementation of the proposed method consists of two procedures, monitoring model development and robust online monitoring. In the monitoring model development procedure, a normal operating data set is used. As a result, after the influence of external variables is removed, an ICA-PCA monitoring model is developed. The following summarizes the construction procedures of the ICA-PCA monitoring model: (1) Acquire an operating data set Z during normal process and scale the data; (2) Build the LSSVR regression model between external variables U and main variables Y; (3) Remove the influence of external variables, and V is acquired; (4) Develop ICA-PCA monitoring model based on V, calculate statistical confidence limits Ilim2, Tlim2, SPElim, and Ωlim. The flow chart of the ICA-PCA monitoring model development is shown Figure 2. The procedures of the robust online process monitoring strategy are summarized as follows: (1) For a new incoming sample data znew, using the same scaling method used in the modeling step; (2) Split the new data into external variable part unew and the main variable of ynew. A moving window is used to select train samples of the LSSVR regression model; (3) Build LSSVR regression model to remove the influence of external variables; thus, the unexplained information is obtained as vnew ) ynew - f(unew); (4) Calculate the statistical values of the new sample data; include Inew2, Tnew2, SPEnew, and Ωnew;

(5) If none of these statistics exceed their corresponding limits, return to step 1; if the statistics are continuously beyond their corresponding limits, some kind of fault is detected; otherwise, go to step 6; (6) If the Ω value of the new data sample exceeds its corresponding limit, an outlier is detected. Therefore, this data sample is eliminated in the next recursive LSSVR modeling step. The flow chart of the robust online monitoring procedures is shown in Figure 3. 3.3. Monitoring Algorithm Analysis. The proposed method is not only online adaptive but also robust. For the demands of online monitoring, the conventional monitoring methods should be modified to adapt process changes. Meanwhile, online monitoring is also useful for fault prediction and product improvement. This paper is focused on monitoring nonlinear multimode processes, in which the correlations between the external the main variables are nonlinear. First, the relation between these two categories of variables is modeled by LSSVR. Then the ICA-PCA monitoring model is built. When the method is carried out online, a new LSSVR model is built according to the new observation and the updating moving window. The influence of external variables is removed by the LSSVR model, and then the unexplained information is monitored by the ICAPCA model. However, process outliers always deteriorate the performance of adaptive methods. In the present paper, the new updating observation is screened before it is updated in the moving window. If the observation is judged as an outlier, the moving window will not be updated, and the LSSVR model remains the same as the last step. When observations are continuously judged as outliers, it can be inferred that some fault has happened in the process and advanced operation should be implemented. 4. Case Study of the Tennessee Eastman (TE) Process 4.1. Simulation and Results. In this section, the performance of the proposed method is tested through the TE process.26 As a benchmark simulation, the TE process has been widely used to test the performance of various monitoring approaches.27 This process consists of five major unit operations: a reactor, a condenser, a compressor, a separator, and a stripper. The control structure is shown schematically in Figure 4, which is the second structure listed in the work of Lyman and Georgakist.28 The TE process has 41 measured variables (22 continuous process measurements and 19 composition measurements) and 12 manipulated variables and a set of 21 programmed faults is introduced to the process. The details on the process description are well explained in a book of Chiang et al.27 In this paper, 22 continuous process variables are selected for monitoring, which are listed in Table 1. The simulation data which we have generated were separated into two parts, the training data sets and the testing data sets, and they consisted of 1000 observations for each operation mode and


Figure 3. Flow chart of robust online monitoring procedures.

Figure 4. Control system of the TE process.

their sampling interval was 3 min. The TE process could simulate six operating modes, and two of them (mode 1 and

mode 3) are chosen for simulation of the mode change in the present paper. The size of the moving window for train


Figure 5. Monitoring results of normal operating mode: (a) method 1; (b) method 2; (c) method 3; (d) method 4; (e) method 5.

sample selection is chosen as 100, which is 1/10 the number of total observations. The parameters chosen in the modeling and online monitoring procedures are as follows: the regularization parameter C ) 50 and the kernel parameter is 0.01, the number of independent components (IC) is 5, and the number of principal components (PC) is 12. In order to

test the fault detection performance of the new proposed method, two fault operating modes are also simulated. Among the list of monitoring variables, process inputs nos. 1-4 are considered external variables. Therefore, the rest of the 18 variables are considered main variables. According to the procedures given in Section 3, the ICA-PCA monitoring


Figure 6. Monitoring results of operating mode change: (a) method 1; (b) method 2; (c) method 3; (d) method 4; (e) method 5.

model is developed. In order to show the nonlinear improvement of the proposed method (method 1), linear external analysis with ICA-PCA model (method 2) is developed. To reveal the efficiency of ICA for non-Gaussian information extraction and monitoring, nonlinear external analysis with

PCA model (method 3) is built. Besides, an ordinary nonlinear external analysis model (method 4) is built without robustness. An ICA-PCA monitoring model without external analysis (method 5) is also developed for comparison. The simulation results of normal operating mode (mode 1) and


Figure 7. Monitoring results of fault operating mode: (a) fault 1; (b) fault 2.

mode change are shown in Figures 5 and 6. All dashed lines represent 99% confidence control limits. For simplicity, the five methods are demonstrated as method 1, method 2, method 3, method 4, and method 5 in the rest of the paper. The monitoring results of mode 1 are shown in Figure 5. Results of methods 1-5 are shown in Figure 5 parts a-e, respectively. Since the models are developed in a single operating mode, all five methods have given good results. It can be concluded that the new proposed method does not lose the monitoring efficiency of a single normal operating mode. However, there is a clear peak at around the 800th sampling point in Figure 5a-d, which corresponds to the nonlinear external analysis related methods. It can be inferred that the regression performance may deteriorate during this period. However, the robust method still cannot correct it. Further study should be incorporated to identify the problem and improve it efficiently. When the process operating mode changes (from mode 1 to mode 3 in TE process) after the 1000th sample, the monitoring results of the five methods are totally different from each other. Correspondingly good results are given by method 1, which are shown in Figure 6a. Although several false alarms occurred, especially in the T2 chart, the results have been greatly improved compared with those of the other methods. The monitoring results of method 2 are shown in Figure 6b. When the operating

mode changes, most of the three statistical values exceed their corresponding confidence limits, which means that some faults or unmeasured disturbances have happened in the process. Therefore, linear external analysis may not function well when a nonlinear process is monitored. On the other hand, the LSSVR model integrated in nonlinear external analysis is efficient for nonlinear regression between external variables and main variables. Figure 6c gives the monitoring result of method 3, which is without ICA; thus, non-Gaussian information is mixed in with Gaussian information. As seen in Figure 6c, there are several false alarms in the SPE monitoring chart, which means that the built model is somewhat unreasonable. This is because the non-Gaussian information is not well extracted and separated from the Gaussian information. By the use of a Gaussian method to model mixed information, inevitable error may be generated. However, there are also some false alarms in the monitoring charts of the proposed method. The superiority of the proposed method over method 3 is not very obvious. It can be inferred that the non-Gaussian information does not play an important role in the chosen process variables (main variables). In order to show the improvement of the robust method, the monitoring results of method 4 are shown in Figure 6d. The monitoring performance is seriously decreased compared with that of method 1, since the SPE chart is mostly false alarmed when the process operating mode changes. Hence, the regression performance could be seriously deteriorated when outliers are used for modeling. Finally, Figure 6e gives the monitoring results of method 5, which is carried out without external analysis. It fails to judge the process to be normal. On the other side, the operating mode change is judged as a process fault or some kind of unmeasured disturbance. It is noted that some false alarms have happened in all five methods, especially in the SPE statistic. Louwerse and Smilde29 suggested the use of the 99.9% confidence limit for SPE statistical monitoring. However, considering the consistency of the monitoring statistic confidence and without any efficiency loss of the proposed method, the 99% confidence limit is still used in the present paper. To test the fault detection ability of the new proposed method, two fault modes are simulated in the TE process. In the first fault, the reactor cooling water inlet temperature is randomly changed. The second fault is an unknown fault that happened in the TE process. Their monitoring results are shown in Figure 7. Both of the faults are correctly detected since the corresponding confidence limits are continuously trigged. Simulation results of other methods are not shown in the present paper, however, they can also detect the two faults correctly. When the fault and process change happen at the same time, all the five methods can detect the introduced faults. Due to the length of the paper, their simulation results are not shown either. Although it can be inferred from this simulation study that the proposed method has little superiority in fault detection, there are potential advantage of the proposed approach for fault detection. Consider a special case when a mode change and a fault occur simultaneously, and the effects of the mode change and the fault impact all the variables used for MSPC in the opposite directions with the same magnitudes. Theoretically, traditional methods will not be able to detect the fault, since there are no changes in any monitored variables. However, using our proposed method, the fault could potentially still be detected, because the impact of mode change is removed first, so the effect of fault could be monitored. 4.2. Discussion and Analysis. One of the important issues of this external analysis method is the choice of external variables. Although in many cases they can be easily identified by set-point changes, process input changes and other factors, they may be difficult to locate in large systems such as plant-wide processes.


That is because in these processes, the named external variables are always not as apparent as those in simple processes. In some cases, it is very hard to pick up the external variables, since some external variables not only cause process changes but also result in some faults if they are changed unreasonably. Additionally, in many processes, only when several external variables change together will the process will be considered as an operating mode change. If only one or two of them change, they may be considered as disturbances or process faults. So the choice of external variables is very important to the proposed method. If they are chosen appropriately, the efficiency of the proposed method will be enhanced and the monitoring performance will also be greatly improved. However, so far as we know, this is mainly implemented by experience and process knowledge. How to choose the external variable automatically may be a challenge work in this area and will also be one of our research interests in the future. Another important issue is related to online modeling and process monitoring. In the present paper, the LSSVR model is updated due to the moving window when a new observation is obtained. Because the LSSVR method is efficient with small training samples, the size of the moving window can be made small. Therefore, compared with the large data modeling method, the online LSSVR modeling method is less time-consuming. Besides, before the updating of the moving window, the available observation is previously screened according to the robustness of the method. This improvement guarantees that normal modeling samples are selected, and thus, the correct LSSVR model will be constructed. However, according to Section 2, some LSSVR parameters have to be tuned, including the regularization parameter C and the kernel parameter. These parameters will greatly influence the quality of the model, and the performance of the online monitoring will also be impacted. Because this is still an open question in the machine learning area, further discussion and research is not considered in this paper, and one can refer to the corresponding references if interested in this issue. 5. Conclusions In the present paper, a robust online monitoring approach is proposed for nonlinear multimode process monitoring, which is based on nonlinear external analysis. Due to the limitation of the linear external analysis, the nonlinear correlation of the process between external variables and main variables is modeled. Meanwhile, an online monitoring strategy is developed. In order to guarantee the real-time performance, a moving window is used for sample selection and LSSVR is used as the model structure of nonlinear external analysis. After the influence of external variables is removed, the filtered information of the main variables is extracted and finally monitored by a two-step ICA-PCA strategy. Additionally, a robust scheme is developed to improve the modeling and monitoring performance. A benchmark study of TE process shows that the new proposed method gives marked improvement over the conventional methods in the monitoring of nonlinear multimode processes. Acknowledgment This work was supported by the National Natural Science Foundation of China. (Grant No. 60774067).

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ReceiVed for reView September 28, 2007 ReVised manuscript receiVed March 30, 2008 Accepted April 7, 2008 IE071304Y

Robust Online Monitoring for Multimode Processes Based on

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