Multimode Process Monitoring Approach Based on Moving Window

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Multi-mode Process Monitoring Approach Based on Moving Window Hidden Markov Model lin wang, ChunJie Yang, and Youxian Sun Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03600 • Publication Date (Web): 15 Dec 2017 Downloaded from http://pubs.acs.org on December 22, 2017

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Industrial & Engineering Chemistry Research

Multi-mode Process Monitoring Approach Based on Moving Window Hidden Markov Model Lin Wang, Chunjie Yang*, Youxian Sun State Key Laboratory of Industrial Control Technology, Institute of Industrial process Control, Zhejiang University, Hangzhou, Zhejiang 310027, P. R. China E-mail: [email protected] Abstract: Due to the existence of multiple operating modes, traditional fault detection techniques are ill-suited for complex industrial process. Although there are more and more literatures concerning this problem, only a few of them are based on hidden Markov model (HMM). But there is no exploration to concern the unknown mode in industrial process based on it. This artical proposes a novel process monitoring approach based on moving window HMM (MVHMM) for real-time multi-mode process monitoring with unknown mode. First, a hidden Markov model is built by training set. Instead of just considering the posterior probability of one single sample, moving window is introduced to utilize the independency of samples for improving the accuracy of on-line mode identification. Besides, an MVHMM-based threshold statistic is defined to identify the unknown mode. And various known modes which include stable modes and transitions are seperated based on Viterbi algorithm. Second, a new monitoring scheme is developed for fault detection of each mode. The effectiveness of the proposed approach is validated by Tennessee Eastman (TE) chemical process and a numerical simulation example. Key Words: Hidden Markov model, Multi-mode process, Transition process, Fault detection

1 INTRODUCTION Effective process monitoring and fault diagnosis are critical to improve plant safety, profitability and reliability.1, 2 Due to the wide utilization of sensors, a large amount of data have been collected, which promoted rapid development of data-based industrial monitoring techniques in the past several decades, such as partial least squares (PLS) and principal component analysis (PCA).3–7 Typical data-based multivariate statistical process monitoring (MSPM) method like PCA assumes that the correlation between the variables has the same process characteristics, while actual industrial production process often does not satisfy this assumption. Most of the productive processes have more than one operating mode, which means that there are multiple stable working points. And the correlation between variables of diverse stable working points is different. There are many reasons for multi-mode conditions: changes in raw materials, external environments, process loads, or equipment depreciation will alter the process conditions. Each of the above cases will cause multi-mode process. And the dominant variables and process characteristics are not always the same in each operating mode. The corresponding statistical properties of the process like mean, variance and correlation of variables are often distinct. However, the traditional MSPM methods have not well considered mode shifts. In recent years, a lot of scholars have done researches on multi-mode process. Srinvasan first estimated the Euclidean distance of the sample points to identify the mode of the sample, and then use dynamic PCA (DPCA) to approximate the sample clustering.8 Choi proposed an adaptive MSPM approach to update the mean and covariance of samples to achieve the purpose of updating the model.9 Liu developed an adaptive Takagi Sugeno fuzzy model in the subspace of PCA in order to fit the time-varying characteristics of This work is supported by the 863 Program (Grant 2012AA041709) and the National Natural Science Foundation of China (Grant No. 61290321)

multi-mode process.10 He and Wang used k-nearest neighbor (kNN) rule in multi-mode process.11 Yu combined finite Gaussian mixture model (GMM) with Bayesian inference mechanism, and successfully applied that method to continuous stirred tank heater (CSTH) process and TE process.12 Ge developed a just-in-time-learning (JITL) strategy for establishing the current monitoring model.13 The Bayesian method is widely used to distinguish different modes of samples.14 Ng chose a PCA with the least differences as the most suitable sub-model by calculating the differences between T 2 and SP E in each PCA model.15 Ge proposed a Bayesian regularization method based on probabilistic PCA (PPCA) for multi-mode process monitoring.16 Tan proposed a novel monitoring method based on the similarity of data feature, which constructs different models to obtain most of the characteristics of process variables.17 Zhu offered an adjoined multi-ICA-PCA model for multi-mode process monitoring.18 Xie combined the moving window and the Gaussian mixture model very well. The method can characterize the multi-mode process well on the one hand, and on the other hand, it can accurately identify the changes of the process and realize the online self-adaptation monitoring.19 Compared with traditional multi-mode process monitoring methods, HMM could efficiently deal with inherent uncertainty and dynamic characteristic in industrial process as a typical dynamic Bayesian network (DBN) model.20 While, dynamics and uncertainty are two main features in the process of practical production, which should be paid widespread attention.21 So HMM has been gradually used to handle the problems of multi-mode process monitoring in recent years. Yu proposed an HMM-based process monitoring approach for multi-mode and nonlinear process.22 Rashid proposed a new HMM based on ICA approach for fault detection.1 Ning proposed a HMM-SPA approach to monitor multi-mode process.23 Wang proposed a probability ratio strategy based on HMM to identify the transitions in multi-mode process.24, 25 To the best of our knowledge, there is no research on the

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Based on the Baum-Welch algorithm, the parameters λ = {A, B, π} of HMM could be decided by given sequence of hidden states, the corresponding observation sequence and the inial state probability distribution.27, 28 It is important to note that all the modes of training samples are known in advance, which means that the unknown mode only appears in the testing data. At the same time, observation probability density distribution matrix bi (Yt ) = P(Yt |qt = Si ) can be gained. The element in the matrix means the probability that current observation belongs to each operating mode. For an observation, the probability which it belongs to its own mode is far greater than the probability that it belongs to other modes. YT ∗n = {Y1 , Y2 , · · · , YT }

(7)

where T means the sequence number of observations in training set and n represents the number of variables in training set. Once HMM has been trained, the variance σt2 of posterior probability of each observation in training set can be calculated as follows: L P

σt2

= var P(Yt |qt = Si ) =

i=1

Here observation sequence in the kth moving window for testing is as follows Ykw∗n = {Yk−w+1 , Yk−w+2 , · · · , Yk }

(11)

where w signifies the width of the moving window and k signifies the moving window index. It should be noted that when moving window is used to intercept the dynamic information of the process data, it is necessary to select the appropriate window length according to the dynamic characteristics of the specific process. For a fast dynamic response process, the length of the window should be chosen shorter, which is conducive to the rapid mode identification. For some relatively slow dynamic response processes, a longer window should be selected, which could contain more complete process dynamic information. This is beneficial to accurate mode identification. After identifying unknown mode and known mode, the observation probability density distribution matrix is utilized to separate current observations into suitable operating modes. The corresponding optimum state in the kth moving win dow Q∗w = qk−w+1 , qk−w+2 , · · · , qk can be obtained by maximizing the conditional probability P (Q|Y, λ) according to Viterbi algorithm.27

(P(Yt |qt = Si ) − Pt )2 L

. (8)

Q∗w = arg max P (qk−w+1 , qk−w+2 , · · · , qk | Qw

(12) Yk−w+1 , Yk−w+2 , · · · , Yk , λ)

Pt =

PL

i=1

P(Yt |qt = Si ) L

(9)

As long as the current observation belongs to one of the known modes, the variance of posterior probability is a relatively large value. On the contrary, if the observation does not belong to any known mode, the probability which it belongs to each known mode is all a small value. Hence, its variance is tiny. Based on the above analysis, the variance of posterior probability of each observation can be an indication to identify the unknown mode. Because all the modes in training set are known, we could get the predetermined threshold Pt ∗ by minimizing the variance of posterior probability of all training samples. If the variance of posterior probability is under Pt ∗ , it may be an indication that there is an unknown mode present in the process. The threshold can be decided as follows: Pt ∗ = α ∗ min(σt2 )

(10)

where α is a tolerant parameter of Pt . Actually, it should be a particularly small value to ensure the effectiveness of threshold Pt ∗ . Instead of just considering the posterior probability of one single sample in testing set, we introduce moving window to utilize the independency of samples. At each moment, the moving window contains the dynamic measurements of each variable. By accurately analyzing the dynamic characteristics of the measured data within the window, the dynamic characteristic information of the operation process is obtained. This could avoid the shortcomings of insufficient information which is contained in a single sample, and facilitate the accurate on-line mode recognition of the samples.

where Q∗w expresses the optimal hidden state sequence for k the corresponding observation sequence Yw∗n . Here HMM is used for estimating the sequence of operation condition. Each hidden state in the sequence represents a specific operation condition. Hence, any monitoring sample can be divided into an appropriate operation condition. With the identified operation type from HMM, the operating mode is confirmed. 3.2 On-line Fault Detection Using a New Monitoring Index Scheme When there are multiple operational modes in the production process, there is no sudden change from a steady operating mode to another stable operating mode.29 Just considering the steady mode is not comprehensive, it is also necessary to take into account the gradual transition between the stable operating modes. The process characteristics of the transition mode are different from those of the steady mode. The transition mode will show a dynamic gradient trend, which is not only reflected in the change of the process variable, but also in the changes of the correlations between process variable. In the view that the process characteristics of transitions and the stable operation modes are entirely different, a new monitoring scheme is developed for multi-mode process monitoring with transitions after mode recognition. In the scheme, two kinds of monitoring indexes are build separately for process monitoring. They can be automatically switched according to the mode of sample. The new monitoring index scheme combines two kinds of probability information: multivariate Gaussian probability density and likelihood probability.




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Table 4: Process Fault for TEP Fault No. IDV(1) IDV(2) IDV(3) IDV(4) IDV(5) IDV(6) IDV(7) IDV(8) IDV(9) IDV(10) IDV(11) IDV(12) IDV(13) IDV(14) IDV(15) IDV(16-20) IDV(21)

Fault Description Step in A/C feed ratio, B composition constant (stream 4) Step in B composition, A/C ratio constant (stream 4) Step in D feed temperature (stream 2) Step in reactor cooling water inlet temperature Step in condenser cooling water inlet temperature A feed loss (step change in stream 1) C header pressure loss-reduced availability Random variation in A+B+C feed composition (stream 4) Random variation in D feed temperature (stream 2) Random variation in C feed temperature (stream 2) Random variation in reactor cooling water inlet temperature Random variation in condenser cooling water inlet temperature Slow drift in reaction kinetics Sticking reactor cooling water valve Sticking condenser cooling water valve Unknown The valve for steam 4 was fixed at the steady state position

Table 3: Six Different Operating Modes of TEP

500

mode 1 2 3 4 5 6

400

300

MGDLLP

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200

G/H mass ratio 50/50 10/90 90/10 50/50 10/90 90/10

Production rate (steam 11) 7038 kg/h G and 7038 kg/h H 1408 kg/h G and 12669 kg/h H 10000 kg/h G and 1111 kg/h H Maximum Maximum Maximum

100

0

-100 0

20

40

60

80

100

120

140

160

180

200

sample

Fig. 13: Monitoring result of HMM in case 4 of numerical example Table 2: Monitored Variables of TEP Variable No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Variable Description A feed (stream 1) D feed (stream 2) E feed (stream 3) A and C feed (stream 4) Recycle flow (stream 8) Reactor feed rate (stream 6) Reactor temperature Purage rate (stream 9) Product separator temperature Product separator pressure Product separator underflow (stream 10) Stripper pressure Stripper temperature Compressor power Reactor cooling water outlet temperature Separator cooling water outlet temperature

In Fig. 15, 16, the monitoring results of fault 4 in mode 3 are displayed seperately by PCA and proposed approach. As can be seen from the Fig. 15, obviously it is completely un-

able to monitor the occurrence of fault in the process. But in Fig. 16, which represents the detection ability of the developed approach, the fault could be detected around the 270th sample. According to the result which is gained from TEP, the developed method could effectively identify the operating mode for multimode process with transitions even when fault happened. Then we can compare its monitoring performance with the PCA in TEP simulation cases, which validates the developed method is superior to PCA in detecting the faults under multi-mode process with transitions. Table 5: Result of mode recognition of TEP method MVHMM

5

errors 33

missclassification rate 0.825%

CONCLUSIONS

A new process monitoring approach based on MVHMM for multi-mode process with unknown mode is developed in this paper. Compared with the existing works, the proposed approach takes into account the identification of unknown operating mode in industrial process for the first time. And moving window is introduced to utilize the independency of samples for improving the accuracy of on-line mode identification. Then, a new monitoring scheme is suggested after mode recognition. For stable mode, monitoring index MDGLLP which combined the multivariate Gaussian probability density and likelihood probability is used for fault detection. And monitoring index MGD is used for fault detection of transition mode. Compared with the traditional


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Off-line learning

On-line process monitoring

Training data

Testing data in the moving window

Build HMM

Calculate Pt

Calculate Threshold Pt*

Pt < Threshold

Yes

Unknown mode

No Mode recognition

Stable mode

Monitoring index LLP

Monitoring index MGD

Fault detection MGDLLP ACS Paragon Plus Environment

Transition mode

Monitoring index MGD

Fault detection MGD

Multimode Process Monitoring Approach Based on Moving Window

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