Multimode Process Monitoring Based on Mode Identification

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Multimode Process Monitoring Based on Mode Identification Shuai Tan,* Fuli Wang, Jun Peng, Yuqing Chang, and Shu Wang College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning Province, 110004 P. R. China ABSTRACT: Many industrial processes have multiple operation modes due to different manufacturing strategies or varying feedstock. Fault detection for a multimode process is a complex problem, as monitoring for both stable and transitional modes should be taken into consideration. In this paper, a novel method based on the similarity of data characteristics is proposed to realize mode identification for modeling data. Different models are developed to capture the major tendencies of process variables. Especially, the transitional regions between neighboring stable modes, which have their particular dynamic characteristics, are modeled, respectively. Online monitoring procedures are formulated on the basis of mode identification. It is more efficient than a model matching strategy using traversing method. At last, the efficacy of the proposed method is illustrated by applying it to a continuous annealing line process and the Tennessee Eastman process. Both results of real application and simulation clearly demonstrate the effectiveness and feasibility of the proposed method.

process understanding.911 On this basis, many researchers developed multiple models for multimode process monitoring.1216 The data is segmented into multiple groups that correspond to different operating modes. Different models are built for monitoring corresponding mode more exactly. The above PCA-based approaches can perform well for single Gaussians multimode model. Gaussian mixture model, which is a mixture of finite weighted Gaussian components, is also explored in multimode process monitoring recently.1721 Bayesian posterior probabilistic index describes the probability of each sample belonging to the multiple components. An integrated global probabilistic index is proposed for fault detection of multimode processes.21 When process changes from one stable mode to another stable mode, the process turns into transitional mode. The transitional mode between two stable modes leads to loss of production time, off-grade materials, and lack of reproducibility of product grades. It cannot be ignored. However, monitoring the transitional trajectory is a problem attracting increasing attention yet has not been well-solved up to now. When a large number of process data are collected, one could make use of data-based multivariate statistical analysis methods to describe the transition feature.22,23 Yew Seng Ng24 proposed a modeling technique using overlapping PCA models to ensure smooth evolution of the monitoring for transient operations. However, this method does not give a clear guideline to identify the transitional mode. Lu25 developed a stage-based sub-PCA modeling method to model and monitor multistage batch processes. Sub-PCA method divides phases with a kind of hard partition algorithm. However, many batch processes transit from one phase to another gradually. As an improvement for sub-PCA method, a soft-transition multiple PCA method is proposed.26,27 The transitional mode between two phases is identified and is expressed as a weighted sum of two phase models. Because the transitional mode has its own characteristic,

1. INTRODUCTION Fault detection and diagnosis (FDD) is a comprehensive, multidisciplinary technology including control theory, reliability theory, information theory, system theory, and other disciplines. FDD technology has been divided into two categories: one is based on the mathematical model of system to be diagnosed; the other is based on observational data processing technology. Valuable research results of fault detection and isolation based on process model have been motivated.14 A fault detection and isolation filter and controller reconfiguration is designed to solve the problem of control actuator fault detection and isolation and fault-tolerant control for a multi-input multioutput nonlinear system. During the past decades, the use of signal detection instruments and computer has received rapid development. There has been increasing interest in pursuing methods that are capable of grasping the essentials in these highly correlated data. The information is hidden inside the data in the form of combinations of variables: the latent structures.5 The dimension of the latent space is much lower than the original variable space. Models obtained from the projection of the data to the latent space have lower dimension and better statistical properties. Principal component analysis (PCA) is the most used method to discover the latent structures of the data. It has been applied to diverse processes and achieved great success in the past decade.5,6 However, PCA generally tends to behave unsatisfactorily in a process with multiple modes, which are caused as the alteration of running state and operation condition. The characteristics of variables in different modes are not the same. If one model is used to describe different modes, the rate of false positive or false negative will increase. Some efforts have been reported to approach the multimode process monitoring issue through the modified PCA/PLS methods. A united model to monitor multiproduct processes is proposed.7,8 However, this solution has good performance if and only if the variables in different modes have the similar characteristics. Kosanovich et al. pointed out a division of the data into sets that correspond to the major chemical phenomena will provide clarity and allow for interpretation based on r 2011 American Chemical Society

Received: October 8, 2010 Accepted: November 24, 2011 Revised: October 19, 2011 Published: November 24, 2011 374

dx.doi.org/10.1021/ie102048f | Ind. Eng. Chem. Res. 2012, 51, 374–388

Industrial & Engineering Chemistry Research

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a model composed with two neighboring stable models may have difficulty describing the characteristics of transitional mode perfectly. Here, fault detection method for multimode process is proposed. This paper is organized as follows. In section 2, definition and features of multimode process are introduced. In section 3, offline modeling based on mode identification is depicted. We propose a new mode identification method based on the duration and underlying process behaviors. Rather than describing the process measurements using one model, the fault detections for both stable mode and transitional mode are taken into consideration. The transitional mode with particular dynamic characteristics is described using a series of submodels. In section 4, the online analysis and mode identification procedures are formulated to enhance real-time performance of online fault detection. In section 5, practical application and simulation clearly demonstrate the effectiveness and feasibility of the proposed method.

Figure 1. Flowchart of monitoring method for multimode process.

2. BRIEF DESCRIPTION OF MULTIMODE PROCESS In industrial process, mode of manufacturing process changes due to various factors, such as alterations of feedstocks and compositions, different manufacturing strategies, fluctuations in the external environment, and various product specifications. The operating conditions, such as set points of reactor temperature and pressure, compositions of catalysts, etc., have to be adjusted to meet the production specifications. These cause various operation modes. Some of them are steady state modes, while others including grade changes, startup, shutdown, and maintenance operations are transitional ones. We take two typical processes. For example, one is continuous process: continuous annealing line process. The other is batch process: penicillin fermentation process. Continuous annealing is a heat treatment that alters the microstructure of a material causing changes in properties such as strength and hardness and ductility. Different materials need different operating conditions, which cause multiple operation modes. The additional coils connecting the different materials can be considered as transitional mode. Fermentation is the process of extracting energy from the oxidation of organic compounds. In each batch, microbe growth includes the following: latent phase, logarithmic growth phase, and stagnate phase. The data characteristics of each phase are similar and can be described using one model. The process between two phases can be considered as transitional mode. In these industries, steady state mode is the main process which occupies the most production time to yield high productivity. The steady state modes have more constant characteristics than the transitional mode. In other words, the stable mode is defined as the process with the stable characteristics which can be described using one model. Transitional mode is the transient state between two stable modes which does not play the primary role. It is the process with dynamic information. It is unsuitable to describe the transitional mode using one model. We separate the transitional mode into one or more submodes. Each transitional submode contains the similar process characteristics, which can be covered using one model. In short, the transitional mode is the process with dynamic information which needs a series of submodels to grasp more accurate dynamic details. A flowchart of monitoring method for multimode process is shown as Figure 1. It includes two parts: offline modeling and online monitoring. Mode identification also includes two parts: mode identification for offline modeling data, which is classifying

modeling data into different modes, and mode identification for online data, which is selecting the proper model for online sampling. In offline mode identification and process modeling phase, if the mode information is clear, a data-driven model can be directly developed for the corresponding period of data; otherwise, mode identification procedure is necessary to get mode information before modeling. For online application, if mode information of new data is known, then the corresponding mode model is used for process monitoring. (Batch process is of recurrence and repetition. According to time indication, monitoring model for online data is easy to select.) Otherwise, online mode identification should be conducted to match new data with one of the historical modes.

3. OFFLINE MODELING FOR MULTIMODE PROCESS 3.1. Mode Identification Algorithm for Modeling Data. Although the process variables are time-varying, fast or slow, the local covariance structure will be largely similar within the same mode. We use the sampling window instead of a single sampling as the basic unit for mode identification. In each window, the loading matrices P, representing the local covariance information and underlying process behaviors, can be used to divide the operation modes. Offline data set X(K J) has K number of observations and J number of variables. First, a cutting window with designated width H is introduced. Parameter H is the minimum stable mode duration. The massive offline data is divided into a series of data segments with H length, and the underlying characteristics of each segment are extracted. To highlight the details in mode changeovers, a smaller cut window with width L (L < H) is employed. Parameter L is minimum transitional submode duration. It is usually 23 times the number of process variables according to the modeling experience of multivariate statistical regression methods.28 The windows with the similar correlation characteristics are considered as the same mode. The detailed steps of offline mode identification are shown as Figure 2, including two parts. The first part can be seen in Figure 2, step one. J variables are measured at K time instances. Then, collected process data can be organized as a two-way matrix X(K J), which is the most popular data structure. The original data is cut into a series of segments XT = [XT1 , XT2 ,...] using cutting window with H-sample 375

dx.doi.org/10.1021/ie102048f |Ind. Eng. Chem. Res. 2012, 51, 374–388


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Figure 2. Illustration of mode identification algorithm.

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Figure 3. (a) Real variable of an ideal multimode process. (b) Real variable of an ideal multimode process.

)

)

)

)

))

)

)

)

)

length, where XT1 = [x(1), x(2), ...x(H)]JH, XT2 = [x(H + 1), ... x(H + H)]JH . Assume that the first H-window X1 belongs to a stable mode. The first H-window X1 is taken as reference window Xbase. P1, P2,... are the loading matrices of X1, X2, ..., respectively. Pbase is the loading matrices of Xbase. Note that loadings p(j)(J 1) (j = 1, ... J) are unit vectors, where P(J 1) = [p(1), p(2),...p(J)]. (i) = 0; When Pbase = Pk, Pbase Pk = ΣJi = 1 P(i) base pk oppositely, when Pbase and Pk are completely opposite, Pbase (i) = 2J. Then, the similarity degree γk = Pk = ΣJi = 1 P(i) basepk 1(( Pbase Pk )/(2J)) is defined as dissimilarity between window k and reference window. The values 0 and 1 indicate no membership and full membership, respectively. Grades between 0 and 1 indicate a partial membership. γk = 1 means Pk = Pbase, and then window k is strictly consistent with the stable mode which window Xbase belongs to. γk = 0 means Pk and Pbase are completely opposite. An adjustable parameter α is introduced as mode judgment threshold. If γk g α, then window k belongs to the same mode with window Xbase. When γk < α, a new cutting window with L-duration is switched from the beginning of window k 1. The second part can be seen in Figure 2, step two. In order to explain why the new identification with L-length window begins from the window k 1, we simply take an ideal multimode

Figure 4. Two clustering results of transition from A to B.

process with two stable modes and one transitional mode as example. A representative variable is shown as Figure 3a,b, where the bold line is transitional operation. γk < α means that Pk is dissimilar to Pbase; that is to say, the potential characteristics of window k are different from the reference window. There are two possible situations: (1) The starting point of transitional mode occurs at the first half of window k, as shown in Figure 3a. Pk1 reflects the characteristics of prior stable mode, and γk g α. Pk represents the characteristics of transitional mode and γk < α. 377



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Figure 5. Online mode identification for the d samplings.

~ 2,..., are extracted using PCA. If the similarity degree γ~k ~ 1, X X ~base, which is the loading matrix of the new between P~k and P ~ base, is equal or greater than α, then window reference window X k belongs to the mode of the reference window. Otherwise, if γ ~k < α, we consider that the window k turns into the next new transitional submode. The window k becomes the new reference window. The clustering algorithm for transitional region will go on running until cumulative duration of one transitional submode is greater than the minimum stable mode duration H. For example, there are n continuous data segments belonging to the same

(2) The starting point of transitional mode lies in the latter half of window k 1, as shown in Figure 3b. The result is also γk1 g α and γk < α. In order to get the accurate location of the starting point of transitional mode, cutting window with L-duration is reanalyzed from the window k 1. Here, assume H > 2L to ensure the first L-duration window is the stable mode. It is considered as the new reference window ~. ~ base. The residual data from window k 1 is denoted as X X ~ ~ A series of segments X 1, X 2,... can be got using L-duration cutting ~ (1), X ~ (2),...X ~ (L)]JL, X ~ T2 = [X ~ (L + 1), ~ T1 = [X window, where X ~ 1, P ~1,..., of ~ (L + 2),...X ~ (L + L)]JL. Here, the loading matrices P X 378



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Table 1. Process Variables for Continuous Annealing Line furnace section heat furnace (HF)

no.

variable

1

strip temperature in HF

2

furnace temperature of

3


4


5

furnace temperature of the fourth area in HF

6


7

furnace temperature of the SF

8

strip temperature in SF

the first area in HF the second area in HF the third area in HF

Figure 6. Flow diagram of the annealing furnace.

submode. If (n 3 L) g H, the transition ends up and turns into the next stable mode. Threshold α is key parameter determined using the trial-anderror method. The larger threshold α means the data within the same mode has greater similarity. The monitoring models based on larger threshold α can describe more process details, but too many models will increase the computing time for online mode matching and might lead to a high false alarm rate. The smaller threshold α means the judgment condition relaxed. The monitoring models based on smaller threshold α are less false positive but will be possible to mistake the fault for the normal. 3.2. Construction of Monitoring Model. 3.2.1. Modeling for Stable Mode. In different stable modes, the input profiles, conditions, process characteristics, and control strategy are quite different from each other. Different modes need different models to describe the characteristics. Assume that we get N stable modes using mode identification algorithm mentioned in part 3.1. The collected modeling data for each mode is X(m)(K(m) J) (m = 1,2,...M), where M is the number of stable mode. A(m) principal components are extracted from X(m), and the loading P(m)(J A(m)) and score matrix T(m)(K(m) A(m)) are calculated, which preserve the major relations within m-model. Traditional PCA method can detect fault for linear system using two statistics: T2 and squared prediction error (SPE). Their confidence limits can be obtained as follows: A

slow cool furnace (SCF)

9

strip temperature in SCF

10


11

the first area in SCF furnace temperature of

12


13


reheat furnace (RH)

14

strip temperature in RH

fast cool furnace (FCF) 1# overaging furnace (1OA)

15 16

strip temperature in FCF furnace temperature of

17


18

strip temperature in

19

strip temperature in

20

the second area of 1OA furnace temperature of

21


22


23


the second area in SCF the third area in SCF the forth area in SCF

the first area in 1OA the second area in 1OA the first area of 1OA

ðmÞ

ðK 1Þ F ðmÞ ðmÞ ðmÞ K ðmÞ AðmÞ A , K A , α ð1Þ

2# overaging furnace (2OA)

the first area in 2OA the second area in 2OA

^ ðmÞ ÞðX ðmÞ X ^ ðmÞ ÞT ∼ g ðmÞ χðmÞ2 SPEðmÞ ¼ eðmÞ eðmÞT ¼ ðX ðmÞ X h, α

the third area in 2OA

ð2Þ

the forth area in 2OA

Here, t(m) is the row of T(m); S(m) is the covariance matrix of T(m); ^ (m) = X(m)P(m)P(m)T is the reconstruction of X(m); g(m) = X ((v(m))/(2m(m))); h(m) = ((2m(m))/(v(m))); m(m), v(m) are the average and variance of SPE(m). 3.2.2. Modeling for Transitional Mode. Transitional process shows the gradual changeover between two neighboring modes. Regularly, at the beginning they have the underlying characteristics more similar to the previous mode, while at the end they are more similar to the next one. Previous work mostly focuses on describing the transitional process using the summation of stable models. However, this method is only suitable for a short-time transitional process whose characteristics can be described using the neighboring models. In most industries, the transitional process has its own particular characteristics which can not be covered by the stable models. In this part, the monitoring model for transitional process is modeled on the basis of a series of submodels.

)

Most variables’ responses to noise in the transitional process are so sensitive that it is difficult to control them following the ideal trajectory exactly. This will lead to different identification results for the same transitional mode. In order to keep as many details as possible, we select the transition with the maximum number of submodes as standard. Other transitions are normalized to the standard one. We simply take twice the transitions from mode A to mode B as an example. One transition is classified into three submodes, as Figure 4, case 1, shows. The other one is classified into four submodes, as Figure 4, case 2, shows. We selected case 2 as the standard transitional process in order to describe more details. P~(2) )/(2J)) is the similarity degree γ1,1 = 1 (( P~(1) 1 1 (1) (2) ~1 and P~1 , where P~(1) and P~(2) are the loading between P 1 1 379

)

T 2ðmÞ ¼ t ðmÞ ðSðmÞ Þ1 t ðmÞT ∼

ðmÞ

the fifth area in HF soak furnace (SF)



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~ (1) ~ (2) matrices of X 1 andX 1 . Then, γ1,C(C = 1, 2, 3, 4) is the simi~(2) ~(1) larity degree between P 1 and P C (C = 1, 2, 3, 4). The two matrices with the maximum similarity degree can be classified ~ (1) ~ (1) ~ (2) ~ (2) ~ (2) ~ (1) into one mode. X 1 , X 2 , X 3 are classified into X 1 , X 2 , X 3 , (2) ~ 4 , respectively. The transitional process from mode A to mode X ~ 2, X ~ 3, ~ 1, X B can be described using four reconstructed data sets X ~ X 4. PCA is applied to extract the time-dependent relation of each submode. Also, the statistic limits of T2 and SPE are obtained using eqs 1 and 2.

sampling time. If the current sampling does not go beyond any one of the control limits of time (k 1), we can conclude that the current sampling is normal. Otherwise, if one or both statistics exceed the confidence limits, there are three possible cases: (1) The mode turns into another new one from the current time. (2) It is abnormal at the current time. (3) It is a new mode unmodeled. We start hypothesis testing from case 1. Remonitoring the current k-time sampling using the new model. If it is under the new control limits, it can be considered as normal and the process monitoring is continued using the new model. Otherwise, if the current sampling goes beyond any one of the two new limits, this sampling is either abnormal (case 2) or an unmodeled mode (case 3). It needs to be judged furthermore. The detailed steps are shown in Figure 5. Step 1 follows: A new sampling x(k) new(1 J) is obtained at current time k. If the mode identification and process monitoring just depend on one sampling at time k, the result may not be robust. Then we accumulate d samplings from time (k d + 1) to time k instead. Assume that the model of time (k d) has been known. First, monitor d samplings using the model at the time (k d). T2 and SPE can be calculated by the following formulas:

4. ONLINE MONITORING OF MULTIMODE PROCESS Mode identification for online data is used to select the right model to monitor the current sampling. Assume that the mode type at time (k 1) has been known, where k is the current

ðk dÞ tnew ¼ xnew Pnew ðk dÞT ^xnew ¼ tnew Pnew 2 dÞ T Tnew ¼ tnew S1ðk tnew new SPEnew ¼ ð^xnew ^xnew Þð^xnew ^xnew ÞT

Figure 7. Mode identification using the varying-width window clustering method.

ð3Þ

Figure 8. Twenty-three variables of the modeling set. 380



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Figure 9. Monitoring results in the case of fault. (Solid line is online T2 or SPE statistic; dashed line is the 99% control limit.)

Step 2 follows: If all d samplings in the moving window exceed any one of the two control limits, the mode from time (k d + 1) turns into a new mode and the method turns into step 3. Otherwise, if one or more of d samplings is under control, we conclude that the process is normal at time (k d + 1). The mode is the same as the one at time (k d). Step 3 follows: There are two cases needed to analyze furthermore. Case one is that the mode of time (k d) is a transitional mode AB from stable mode A to stable mode B. Then the possible mode of time (k d + 1) is either the transitional submode of transitional mode AB or the stable model B. Case two is that the mode of time (k d) is stable model C. Then, the mode of time (k d + 1) is the transitional submode beginning with C. Calculating SPE values of d samplings in these models, respectively, gets SPE = (1/d)Σdi = 1SPEi of each model. The model producing the minimum SPE is adopted for time (k d + 1). Step 4 follows: Remonitoring d samplings from time (k d + 1) to time k using new limits. Step 5 follows: If d samplings all exceed any one of the new confidence limits, the process at time (k d + 1) may be an abnormality or a new mode that need not be modeled. Otherwise, it can be considered as normal.

shown in Figure 6. The inner structure of strip successively experienced the stages of grain recovery, recrystallization, grain growth, carbide precipitation, etc. The inner quality can be well improved by the stages mentioned above. Steel strip travels all furnace sections driven by a series of tension rollers. After pretreatment, the strip is heated to the required temperature using multiple heat radiation tubes (the tubes are full of combustion gas) in the heat furnace. The following soak furnace is used to heat steel evenly in order to transform crystal structure from the pearlite into austenite. Recrystallization occurs in the cooling process (including slow cool furnace, reheat furnace, and fast cool furnace), and pearlite crystal is more tiny and homogeneous. Supersaturated carbon is precipitated in the overaging process (including 1# overaging furnace and 2# overaging furnace) to improve the antistamping and antiaging properties. At last, steel strip is cooled to normal temperature quickly in the final cool section without any contribution. Here, 23 process variables are chosen as the model input shown in Table 1. In the production line, different strip properties marked with tinplate hardness (such as T-3CA, T-4CA, T-5CA, etc.) need different operating conditions. The furnace temperature and pressure, conveyer speed, etc. have to be adjusted to meet the production specifications. The multiple modes monitoring system is modeled. Here, we take two tinplate hardness processes (T-4CA and T-3CA) and the transitional processes between them (transition from T-4CA to T-3CA and transition from T-3CA to T-4CA, for example). A total of 114 800 samplings for 23 variables are generated from actual production. The modeling data matrix X(114 800 21) includes two stable modes T-4CA and T-3CA and the transitional processes between T-4CA and T-3CA. In order to achieve the effective statistical feature extraction, the sampling of window data should be two or three times more

5. ILLUSTRATION AND DISCUSSION 5.1. Annealing Furnace System. The annealing furnace is an important part for a continuous annealing line. The main processes in annealing furnace include heating (heat furnace), soaking (soak furnace), cooling (including slow cool furnace, reheat furnace, and fast cool furnace), over aging (including 1# overaging furnace and 2# overaging furnace), and final cooling, as 381



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Figure 10. Schematic diagram of the Tennessee Eastman process.

Table 3. Operating Modes of Tennessee Eastman Process

Table 2. Tennessee Eastman Process Measurements Used for Modeling no.

variable

1

A feed (stream 1)

2

D feed (stream 2)

3

E feed (stream 3)

4 5

A and C feed (stream 4) recycle flow (stream 8)

6

reactor feed rate (stream 6)

7

reactor temperature

8

purge rate (stream 9)

9

product separator temperature

10

product separator pressure

11

product separator underflow (stream 10)

12 13

stripper pressure stripper temperature

14

reactor cooling water outlet temperature

15

separator cooling water outlet temperature

mode type

reactor press set point

reactor level set point

stable mode A

2800 kPa

65%

stable mode B stable mode C

2705 kPa 2705 kPa

65% 75%

10 (95 901114 800) belong to the same mode. Transitional mode is the dynamic process which needs one or more short submodes to describe it. Then, phase 2, phase 3, and phase 4 are the submodes in the transitional region from phase 1 to phase 5. Phase 6, phase 7, phase 8, and phase 9 are the submodes in the transitional region from phase 5 to phase10. For comparison, we draw out the trajectories of 23 modeling variables X(114 800 23) in Figure 8. From the curves, it is clear that the real transitional region from T-4CA to T-3CA is [28 304 37 329]. The transitional region from T-3CA to T-4CA is [89 713 95 827]. The following conclusions are obtained from Figure 7: the phase 1 and phase 10 are T-4CA, the phase 5 is T-3CA; the transitional region from T-4CA to T-3CA is [28 35137 450]; the transitional region from T-3CA to T-4CA is [89 60195 900]. The identification result from T-4CA to T-3CA is three submodes, and the transition from T-3CA to T-4CA is classified into four submodes. The process with more fluctuation information needs more submodes to reflect the details. Modeling data of two stable modes T-4CA and T-3CA can be expressed as follows: XT4CA = [X(1); X(2)]; X(1) = [x(1); x(2);... x(28 350)]; X(2) = [(95 901); x(95 902)]; ...x(114 800)]; XT3CA = [x(37 451); x(37 452)]; ...x(89 600)]. There are three

than the number of variables at least. Here, the window length of L is determined 350. The window length of H is calculated 1050 according to the assumption H > 2L. The mode identification result of X(114 800 23) is shown in Figure 7. The process with the same statistical characteristics, whose duration length is longer than H, is stable mode. Phase 1 (127 650), phase 10 (95 901114 800), and phase 5 (37 45189 600) in Figure 7 are stable modes, where phase 1 (127 650) and phase 382



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Figure 11. Fifteen variables of the TE process modeling set.

Figure 12. Mode identification results with different thresholds α.

submodes in the transition from T-4CA to T-3CA, and five submodes in the transition from T-3CA to T-4CA. PCA models are built for each stable and transitional mode. Process monitoring is performed using another 84 800 samplings data Xonline(84 800 23) collected including four states: stable mode T-4CA; stable mode T-3CA; transition from T-4CA

to T-3CA; transition from T-3CA to T-4CA. From the 63 200th sampling time, an increscent fault was caused by the reduction of the 1# fan speed in 1OA, and this directly led to the increase of the temperature in the first furnace area of 1OA (1# overaging furnace). The fault occurs during transitional process from T-4CA to T-3CA. From the monitoring results shown in Figure 9, the 383



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Figure 13. Mode identification result of modeling data.

Figure 14. Mode identification result of the transitional mode AB.

abnormality can be clearly detected as T2 and SPE go beyond the control limit at 63 270th and 63 235th sampling time, respectively. The sampling from actual production is once per second. In order to enhance the reliability of the monitoring system, we accumulate the status of d = 35 continuous samplings. The fault is introduced from

the 63 200th sampling time. The monitoring statistic T2 and SPE have 70 and 35 s alarm delay, respectively. Annealing furnace is a large-scale continuous production line which needs a highly reliable alarm. It is rather false negative than false positive. Alarm delays of 35 and 70 s are allowable error for this production line. 384



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Figure 15. Mode identification result of the transitional mode BC.

Figure 16. Monitoring results using stage-based sub-PCA modeling method. (Solid line is online T2 or SPE statistic; dashed line is the 99% control limit.)

Vogel,29 is the simulation of a complex industrial chemical process. It has been used as a benchmark, especially for studying

5.2. Tennessee Eastman Process. The Tennessee Eastman

(TE) process simulation benchmark, presented by Downs and 385



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Figure 17. Monitoring results using soft-transition multiple PCA method. (Solid line is online T2 or SPE statistic; dashed line is the 99% control limit.)

advanced control strategies. In the past decade, it has increasingly been used to test the performance of proposed MSPC tools. Figure 10 gives the well-known flow sheet of the TEP.30 The process has five major units: a reactor, a condenser, a vaporliquid separator, a recycle compressor, and a product stripper. It involves two simultaneous gasliquid exothermic reactions that produce two desired products (G and H) and a byproduct F which is produced from two additional reactions, from four reactants A, C, D, and E. Within the process there is also an inert B. The process has 12 manipulated variables and 41 measured variables for monitoring and control. About 22 measured variables are available at significantly higher sampling frequency. For the sake of practical consideration, the 15 continuous outputs among the 22 measurements shown in Table 2 are used for monitoring, and the sampling interval is 0.01 h. The simulation programs have been implemented for 70 h, and data corresponding to a set of three stable process operations are collected. The imposed modifications are indicated in Table 3 and arise from controlled changes in reactor pressure and reactor level. The initial set points of reactor pressure and reactor level are 2800 kPa and 65%, respectively. After 20.824 h, the reactor pressure is reduced to 2705 kPa, and the process maintains the new status until the reactor level is increased to 75% at 41.546 h. After running 70 h, there are 7000 samplings including three stable modes and two transitional modes. The drift in production status causes changes in most variables. Figure 11 presents typical trends of 15 variables. As mentioned before, the value of L can be set as 23 times the number of process variables. Here, L = 30. H = 140 according to H > 2L. Tuning parameter α is established using the trial-anderror method. The results of mode identification with different thresholds are shown in Figure 12. When α = 0.8, stable modes are incorrectly divided into multiple phases. It will cause a high false alarm rate. If α = 0.65, the beginning time of transitional

mode is delayed and the range of transitional process is reduced. After extensive testing, we determine α = 0.7. The similarity degree is fed to the clustering algorithm, and we can get the number of the clusters shown in Figure 13. The results of mode identification are as follows: 12080 (stable mode A), 2081 2350 (transitional mode AB), 23514150 (stable mode B), 41514390 (transitional mode BC), and 43917000 (stable mode C). It is clear that the ending time of stable modes identified using our algorithm is almost the same with the real system. In order to analyze the dynamic characteristics, enlarged figures for transitional modes are painted. Figure 14 shows 15 variables in the transitional mode from stable mode 1 to stable mode 2. This transitional mode is classified into four submodes: submode AB_1 (phase 2: 20812110), submode AB_2 (phase 3: 21112170), submode AB_3 (phase 4: 21712230), and submode AB_4 (phase 5: 22312350). It can be observed that the method divides operations with different dynamic characteristics into different submodes: first, submode AB_1, in which the reduction of reactor pressure directly causes fluctuations of temperature variables. Reactor temperature, separator temperature, and stripper temperature are temporarily declined. In submode AB_2, reactor temperature begins to rise, and corresponding changes happen in product separator and stripper. Submode AB_3 mainly reflects the trajectories of variables in separator and stripper. In submode AB_4, major variables tend to stabilize. The identification results well reflect the whole measurement trajectory of transitional process. Another transitional example from stable mode B to stable mode C caused by the increase of reactor level is shown as Figure 15. This transitional mode is classified into five submodes: submode BC_1 (phase 7: 41514180), submode BC_2 (phase 8: 41814240), submode BC_3 (phase 9: 42414300), submode BC_4 (phase 10: 43014330), and submode BC_5 (phase 11: 43314390). In submode BC_1, the change of reactor level directly leads to the rise of product 386



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Figure 18. Monitoring results using monitoring method based on mode identification. (Solid line is online T2 or SPE statistic; dashed line is the 99% control limit.)

separator pressure and the stripper pressure. In submode BC_2, the reactor temperature, product separator pressure, and stripper pressure begin to decrease with increasing reaction time. As the feed flow continues to increase, the purge rate, product separator temperature, and stripper temperature present rising tendency in submode BC_3, while the increase of recycle flow drives the reactor feed rate and reactor temperature increase in submode BC_4. In submode BC_5, all variables tend to stablize after mild fluctuation, and reactor level reaches its set point. It is clear that these submodes agree well with the actual correlation variation. The mode identification algorithm generates reasonable mode division results, which can indeed enhance the process understanding. The principal components are selected to explain 95% of the variability of the data. The control limit is set at the 99% of the statistics which are calculated from data in normal operation. To illustrate the advantages of online monitoring based on mode identification, another two accredited methods, “stagebased sub-PCA modeling method” proposed by Lu and “softtransition multiple PCA method” proposed by Zhao, are compared with our method. An example of transitional mode considering a man-made fault is presented. Two initial values of variables, reactor pressure and level, are set at 2705 kPa and 65% for the online simulation program. After 1.88 h, the reactor level is increased to 75%. A fault is introduced at 3.50 h, which is in the transitional process from stable mode B to stable mode C. The fault is caused by step change of A/C feed rate (stream 4), which leads to the increase of C feed (stream 4) and the decrease of A feed (stream 4). At last, the flow rate of stream 4 is lower than the normal value, and most monitoring variables are out of normal ranges. The online sampling interval is 0.01 h, and a total of 470 samplings are generated. Figures 16, 17, and 18, respectively, show monitoring results using these three methods. When the reactor level changes at

1.88 h, the process begins transition from the former stable mode to the new one. It is clear that the beginning time of transitional mode is delayed in Figure 16. The transitional mode is well identified in Figures 17 and 18. The error is added at 3.50 h. From the monitoring results shown in Figure 16, the abnormality is detected at 383th and 378th sampling times, respectively. The alarm time is delayed for long time. In Figure 17, the fault is warned timely, but there are too many false alarms for the normal. The T2 and SPE in Figure 18 go beyond the control limit at 362th and 354th sampling times, respectively. The fault is detected in time. Moreover, the false alarm rate is reduced. The above application and simulation indicate that the proposed mode identification algorithm can draw the right mode information for the data. Furthermore, the monitoring model based on it is timely for fault detection not only in stable modes but also in transitional regions. The deficiencies of traditional monitoring method are remedied by our improvement.

6. CONCLUSIONS A new monitoring method for multimode process based on mode identification is proposed in this paper. Offline mode identification is proposed to partition the modeling data according to the durations and underlying process behaviors of different modes. When online monitoring, the proper model is chosen using the online mode identification method. The illustration results demonstrate that the proposed method is more reliable and effective for online monitoring. It significantly decreases the frequency of false alarms and missing alarms. ’ AUTHOR INFORMATION Corresponding Author

*Tel.: 86-24-83687434. E-mail: [email protected]. 387



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’ ACKNOWLEDGMENT This work was supported by the National Science Foundation of China under Grant 61074074, project 973 under Grant 2009CB320601.

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Multimode Process Monitoring Based on Mode Identification

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