Clustering-Based Hybrid Soft Sensor for an Industrial Polypropylene

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PROCESS DESIGN AND CONTROL Clustering-Based Hybrid Soft Sensor for an Industrial Polypropylene Process with Grade Changeover Operation Minjin Kim,† Young-Hak Lee,‡ In-Su Han,† and Chonghun Han*,§ Department of Chemical Engineering, Pohang University of Science and Technology, and ISYSTECH Company Ltd., San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, South Korea, and School of Chemical Engineering and Automation and Systems Research Institute and Institute of Chemical Processes, Seoul National University, Shillim-dong, Kwanak-gu, Seoul 151-742, South Korea

A new methodology is proposed to design a soft sensor for a polypropylene (PP) process with grade changeover operation. In contrast to the general polyolefin process, the PP process usually produces more than 100 different grades of products. Its reaction mechanism, based on seven catalysts, is so complex that neither mechanistic nor empirical models have been successful in describing full-scale industrial applications. The proposed methodology was developed based on the hybrid modeling of novel clustering and black-box and mechanistic models. Clustering based on critical to quality enables the soft sensor to handle the complexity of many different grades. Hybrid modeling offers good predictive power for transient behaviors as well as normal behaviors. The methodology also allows us to reduce the cost of building and updating the model. The developed soft sensor was successfully applied to a real industrial process. The accurate and reliable monitoring of the melt index in the PP process helped to significantly reduce the amount of off-specification product generation. Introduction Polypropylene (PP) is widely used to produce various products, such as films, injection moldings, stretched tapes, fibers, sheets, blow moldings, and pipes. Each product requires a unique specification, and to meet these different demands, the PP manufacturing industry has been forced to produce about 100 different grades of high-quality PP. However, to maximize cost savings, by operating on a large scale, many different grades have to be produced in a single PP manufacturing process. This requires a special process operation called grade changeover operation, during which the operating conditions are changed. These grade changes often result in relatively long settling times because the grade transition requires drastic and simultaneous changes in different inputs, and the dynamics of each input is complicated. Consequently, significant amounts of off-specification polymers are produced during transition operations. It is very important to minimize the amount of off-specification polymer products by reducing grade transition times, to minimize the production cost of PP. If we could monitor the melt index (MI), then this would enable the quality of the PP to be characterized * To whom correspondence should be addressed. Tel.: +822-880-1887. Fax: +82-2-888-7295. E-mail: [email protected]. † Pohang University of Science and Technology and ISYSTECH Co. Ltd. ‡ School of Chemical Engineering and Automation and Systems Research Institute, Seoul National University. § School of Chemical Engineering and Institute of Chemical Processes, Seoul National University.

in real time and, consequently, grade transition times could be greatly reduced because it would be possible to determine more precisely the time at which the grade changeover is completed. Unfortunately, however, the MI is difficult to measure on a real-time basis during a grade transition. This problem makes the quality control of PP processes more difficult if not impossible and thereby causes enormous economic losses because of the excessive amount of off-specification PP products that are generated. Hence, a soft sensor is needed that can calculate the MI from the real-time process data. Soft sensors have been successfully applied to a wide variety of polymerization reactors. Ohshima and Tanigaki1 provided an extensive review of the models that have been developed for estimating the various polymer properties, including the MI, density, and molecular weight. In the case of a polymer process that involves a grade changeover operation, mechanistic models are often used together with empirical and/or black-box models.1 These mechanistic model based soft sensors focus on the mechanistic relationships to cover the complex process characteristics resulting from the presence of multiple grades. Several mechanistic model based soft sensors2-5 have been successfully developed for the assessment of the properties of various polyolefins, such as linear low-density polyethylene (LLDPE), high-density polyethylene (HDPE), and polystyrene (PS). McAuley and MacGregor2 developed a mechanistic model based soft sensor for the online estimation of the MI of the LLDPE process. Since then, several studies3-5 have been conducted in an attempt to simplify their model using new empirical relationships and to reduce

10.1021/ie049803b CCC: $30.25 © 2005 American Chemical Society Published on Web 12/15/2004

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Figure 1. Schematic of the PP process.

the computational burden in the case of HDPE. It has been reported that the estimation performances of these models were sufficient for them to be applied to their target processes because these rigorous models based on first principles represent well the reaction mechanism. However, these previous approaches are not appropriate when it comes to building a good soft sensor for the industrial PP process. This is because the PP process is extremely complex and varied, involving more than 100 grades of PP, 7 types of catalysts, and 2 kinds of reactors (liquid and vapor phases). In addition, several recycle loops are employed to recover the unreacted monomer. Consequently, because the reaction mechanism changes significantly depending upon the grade being produced, the type of catalyst, the kind of reactor, and the effects of the recycle loops, it is very difficult to derive a modeling equation from their mechanistic relationships. For this reason, studies on the reaction mechanism for PP are few and far between and few experimental results have been reported. In this study, we propose a design methodology for a soft sensor that has a good estimation performance regardless of the operational complexity arising from the presence of multiple grades in the industrial PP process. This methodology is validated through its industrial application to the PP process. Process Description of the PP Process A novel soft sensor was developed for the PP process of Samsungatofina located in Seosan, Korea. This process is capable of manufacturing about 220 000 tons of PP/year and provides a wide range of PP grades, covering homopolymers, block copolymers, and random copolymers. Homo-PP grades make them suitable for applications such as packaging films, injection-molded household items, and woven bags. The block copolymer grades are widely used for industrial applications in the electronic and automobile industries, while the random copolymer grades are widely used in household and medical products. Figure 1 shows a simplified schematic diagram of this PP process, which consists of five major unit processes: the catalyst process, polymerization, drying, pelletizing, and other related utilities. In the catalyst process, a small amount of propylene is prepolymerized with the main catalyst and the cocatalyst to increase the stability of the catalysts, and this prepolymerized propylene is then supplied to the first reactor with the solvent. The polymerization reaction takes

place in the liquid phase in the first and second reactors and is completed in the vapor phase in the third and fourth reactors. Propylene, ethylene, and hydrogen are fed into each reactor on a regular basis. The reactants are polymerized into PP by sequential or parallel polymerization. The slurry product from the final reactor goes through the dryer and the pelletizer, and ultimately PP is produced. Depending on the grade of the polymer products, the ratio of the reactants and the catalyst entering into the reactors is varied to control the MI. The operators decide the setpoints of the controllers for the ratio of the reactants and the reactor temperature and pressure by monitoring the MI being measured every 8 h. The target PP process produces more than 100 polymer grades, with the grade being changed more than 10 times a month. However, it is difficult to determine the exact time at which the grade change is completed and the on-specification product begins to be produced. The grade transition period determined by the operators usually contains a certain amount of leeway, so that it is longer than really necessary to prevent the onspecification product from being degraded by offspecification PP because the MI cannot be measured in real time and its tolerance is rather large. Therefore, significant amounts of the on-specification product are inevitably included in the off-specification polymer during grade transition operations. The online soft sensor developed in this study has a good estimation accuracy during both transition and normal operations, thus allowing the MI to be monitored continuously and thereby determined when the transition from one grade to another grade has been completed. In this way, the amount of the off-specification product can be greatly reduced, by closing the gap between the determined transition period and the actual transition period. Difficulty in Developing a Soft Sensor for PP The main objective of this work is to develop an online soft sensor with a good estimation performance for the industrial PP process. Figure 2 shows the variation in the MI of the PP arising from the frequent grade changes over a period of 5 months. Approximately 100 grades are produced and there are about 60 grade transitions during this period. The estimation accuracies of the previous approaches are significantly reduced for the PP process because of the complex process characteristics that result from the extremely large number of grades and frequent grade changes. We explain the reasons for this reduction in detail below through several representative approaches. Several mechanistic model based soft sensors2-5 were developed: a soft sensor using a two-step modeling structure, which consists of the instantaneous MI model and the cumulative MI model. Their cumulative MI models were derived from the mechanistic relationship between the instantaneous and cumulative polymer properties in the reactor. Their instantaneous MI models were derived by incorporating the reaction kinetics models with the empirical relationship between the MI and process variables. The instantaneous MI models are formulated in the form of a linear combination of concentration ratios involving hydrogen, ethylene, propylene, 1-butene, and the cocatalyst. The coefficients of these models are estimated based on the empirical correlation derived from steady-state plant data.

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Figure 2. Plot for the MIs of the training data for the fourth reactor.

In the polyolefin process, it is well-known that the MI is strongly affected by the concentration ratio of hydrogen to the monomer (e.g., propylene or ethylene).1 However, in the PP process, it is very difficult to obtain an appropriate mechanistic relationship that allows the MI to be estimated from the concentration ratios because the relationship varies irregularly according to the grades that are produced. Additionally, discovering these complex relationships incurs considerable cost and time because of the experimental plant tests involved. Therefore, the previous approaches are not appropriate to the PP process. For practical use in the PP process, the approaches also have certain limitations. In particular, online analyzer errors cause the estimates obtained from these models to differ from the actual measurements because online analyzers that measure the concentration in the reactors (especially in vaporphase reactors) frequently do not work properly and sometimes even fail altogether. With the PP process, new grades are produced about 10 times a year in order to meet the customer’s diverse needs. Sometimes new catalysts are developed to improve the productivity and reduce the operating costs. These changes require frequent model updates, which take a significant amount of time and incur additional costs. Therefore, if we were to adopt the mechanistic model based approaches for the PP process, additional cost and time would be needed to maintain the soft sensor. Proposed Clustering-Based Hybrid Soft Sensor Architecture of the Clustering-Based Hybrid Soft Sensor. To develop a soft sensor with a good prediction accuracy, irrespective of the number of grades and which is not affected by the frequent changes in the PP process, we propose a novel clustering-based hybrid soft sensor, as shown in Figure 3. The proposed soft sensor also comprises the instantaneous MI model and cumulative MI model. However, novel instantaneous MI models for each reactor and a new cumulative MI model for the reactors connected in series are proposed to improve the estimation performance for the MI of the PP discharged from the last reactor. In the first step, we cluster the overall operation into a transition operation and three kinds of normal operations at every reactor using a critical to quality (CTQ) based clustering method to handle the complex relationships arising from the existence of multiple grades and frequent grade changes. In the second step, we develop the instantaneous MI model based on clustered operational groups for each reactor and the cumulative MI

Figure 3. Architecture of developing the proposed clusteringbased hybrid soft sensor.

model, which is applicable to the reactors connected in series. The local-based instantaneous MI model consists of three local partial least-squares (PLS) models and one global PLS model. The instantaneous MI model shows an excellent ability to estimate the MI in the case of normal operations, by using local models for each relationship that are clearly clustered by the CTQ-based clustering method. This good estimation accuracy in the case of normal operations is the main factor that helps to reduce the amount of on-specification product included in the off-specification polymer during grade transition operations, by allowing the time at which the grade change is completed to be determined. The global model estimates the instantaneous MI for the transition operation. The cumulative MI model is developed by expanding Ogawa’s cumulative MI model,3 which applies only to a single reactor, into a general form of the cumulative MI model, which can be applied to several reactors in series, as in the case of the PP process. In particular, the proposed cumulative model allows us to improve the estimation performance during transition operations, as well as to easily update the model, by newly calculating the steady-state gain when the grade changes. The details of the instantaneous MI and cumulative MI models will be explained in the section on model development. Data Acquisition and Handling. The first step in modeling is to obtain a set of training data and testing data from the target process. The training data set is used to build the model, and then the testing data set is used to validate it. The quality variables of interest are the MIs of the PP discharged from each reactor. A


Figure 4. Plot for the MIs of part of the training data with grade information for the fourth reactor.

total of 86 key operational variables are selected as the inputs of the proposed soft sensor out of a total of 114 operational variables concerned with the conditions in the four reactors and the catalysts. These variables comprise 32 flow rates, 28 temperatures, 18 pressures, and 8 tank levels. The quality variables are measured by analysis of the laboratory samples drawn from each reactor every 8 h. However, it is difficult to measure the MI at frequent and regular sampling intervals while the operational variables are measured every minute. Because the quality variables are measured much less frequently than the operational variables, moving averages of the measurements of the operational variables were taken over an 8 h period preceding each sampling time for the quality variables. Then a principalcomponent analysis (PCA)6 was employed to eliminate statistical outliers that might result from faulty measurements or abnormal operation. Finally, we obtained a total of 635 training data over a period of 5 months and a total of 77 testing data during the following 1 month period. The training and testing data were scaled and mean-centered before modeling and validation, respectively. CTQ-Based Clustering. There are several quality variables for PP such as the MI, flexural modulus, izod impact strength, vicat softening point, and so on. However, the most critical quality variable that determines the flow properties and other mechanical properties of the PP is the MI,7,8 which is defined as the mass rate of extrusion flow through a specified capillary under prescribed conditions of temperature and pressure. Figure 4 shows the MI for part of the training data together with the grade information of the observations. There are nine different grades, but not all of them are significantly different from each other and some grades have very similar MIs. Thus, these grades are roughly clustered into three representative groups according to their MIs, and groups 1-3 correspond to the low, medium, and high levels of the MI, respectively. Physically, the uses of PP differ according to the level of the MI: PP with a low MI is used for stretch and blow treatment, sheets, and pipes, that with a medium MI is used for film and injection treatment, and that with a high MI is used for coating and injection treatment. In operation, standard operational modes of PP are different according to the level of the MI: PP with each level of the MI is produced by the different concentration

Figure 5. PC1 and PC2 two-dimensional plot based on the PCA model for the fourth reactor.

ratios of hydrogen to the monomer and the different types of catalyst. Therefore, the predictive ability of a soft sensor can be greatly improved when the soft sensor consists of the local models developed based on each standard operational mode. However, previous clustering methods9,10 do not clearly discriminate these operational modes when they are applied to the PP process. Figure 5 shows that the previous PCA-based clustering method10 has a poor clustering performance for the PP process: the group of the medium MI overlaps with the group of the high MI. The previous clustering methods are performed based on the operational similarity in the feature space reduced from the multivariate operational variables. In the case of the PP process, the operational variables are not observable enough to discriminate operational differences of three operational modes based on the operational similarity. In such a case, the proposed MI-based clustering method shows a good clustering performance because the standard operational mode is previously given for each level of the MI. As shown in Figure 6, the three regions with high density indicate the normal operational groups and the remaining regions with low density indicate the transition operations. Using the boundary of on-specification for the grades included in each group, the normal operational bounds of groups 1-3 are found to be 0-2 (G41), 7-14 (G42), and 21-31 (G43), respectively. Finally, we successfully cluster the 100 grades into 3 groups according to their bounds of MI.

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MIM, MIA, MIB, and MIC are the MIs of the mixture and polymers A-C, respectively. wA, wB, and wC are the weight fractions of polymers A-C in the mixture, respectively. The following equation is the material balance derived for the four reactors connected in series under the assumption that there is no net accumulation of polymer during a short period of time, ∆t:

Hl(t+∆t) ) Hl(t) + Il(t) ∆t + Rl(t) ∆t - El(t) ∆t (3)

Figure 6. Histogram of the MI for the fourth reactor using its training data.

Instantaneous MI Model Development. As a result of the clustering process, groups 1-3 have a total of 125, 242, and 226 training data that are used for building local PLS models 1-3, respectively. The proposed instantaneous MI model is based on the static relationship between 86 operational variables and the instantaneous MI under the assumption that the instantaneous and cumulative MIs are the same during normal operation. The estimation accuracy of the localbased instantaneous MI model is much better than that of the single model for the PP process with three kinds of operational modes. However, local models are not suitable to represent transient behaviors. The instantaneous MI in the transition region is estimated by the global PLS model using all 635 training data because the global PLS model explains the transient behaviors, i.e., the variation among the three clustered groups. Each PLS model is given by

Blk ) [(Xlk)TXlk]-1(Xlk)TMIlk

(1)

for k ) 0-3, where Xlk and MIlk are the training data matrices of the modeling inputs and outputs, respectively, for the lth reactor and the kth PLS model (the 0th PLS model is a global model) and Blk is a matrix of regression coefficients determined from the training data for the lth reactor and the kth PLS model. For the instantaneous MI model, PLS is selected as the optimal modeling method, considering its accuracy and simplicity in the case of the instantaneous MI model. PLS is a good method for building inferential models because the target process has a large number of operational variables that are strongly correlated with one another.11,12 Moreover, PLS typically provides more robust and reliable models than ANNs when the data are noisy and highly correlated with each other.11,12 A PLS-based soft sensor can be built and maintained with much less cost and time because of the updating facility of the PLS model. Additionally, it is easy to gather a large number of measurements to develop a PLS model because all of the operational variables are measured every 1 min in the field and automatically collected by the real-time database system. Cumulative MI Model Development. Equation 2 is empirically used to predict the MI of the mixture when three polymers, A-C, are mixed together, where

log(MIM) ) wA log(MIA) + wB log(MIB) + wC log(MIC) (2)

where l is the index of the reactor. For l ) 1-4, Hl(t), Il(t), Rl(t), and El(t) are the polymer holdup at the reactor, the polymer entering into the reactor, the polymer reaction rate, and the production rate for the lth reactor at time t, respectively. Il(t) ∆t is the amount of polymer that entered from the previous reactor; Rl(t) ∆t is the instantaneously generated polymer; and El(t) ∆t is the cumulative amount of polymer discharged during a short period of time, ∆t. Then, the MI of the cumulative polymer at time t + ∆t for each reactor connected in series can be derived using eq 2 to yield

log[MIlc(t+∆t)] ) Il(t) ∆t l

H (t+∆t)

Rl(t) ∆t Hl(t+∆t)

log[MIlc-1(t)] +

log[MIli(t+∆t)] + Hl(t) - El(t) ∆t l

H (t+∆t)

log[MIlc(t)] (4)

where MIli(t) and MIlc(t) are the instantaneous and cumulative MIs for the lth reactor at time t, MIl-1 c (t) is the cumulative MI for the previous reactor of the lth reactor at time t, and MI0c (t) is zero for the feed stream. However, it is difficult to estimate the exact values of Hl(t), Rl(t), Il(t), and El(t) in each reactor. Therefore, eq 5 is obtained by substituting λl1 and λl2 for [Rl(t) ∆t]/Hl(t+∆t) and [Il(t) ∆t]/Hl(t+∆t) in eq 4, respectively, under the assumption that the dynamic behavior of the process is linear. It is assumed that the initial

log[MIlc(t+∆t)] ) λl1 log[MIli(t+∆t)] + l l l λl2 log[MIl-1 c (t)] + (1 - λ1 - λ2) log[MIc(t)] (5)

cumulative MI in the first reactor, MI1c (1), is identical with the initial instantaneous MI, MI1i (1). MI1c (t+∆t) is easily calculated using only MI1c (t) and MI1i (t+∆t), which are estimated using the proposed instantaneous MI model. For l ) 2-4, the values of MIlc(t+∆t) are also easily calculated using MIlc(t), MIli(t+∆t), and the prel viously estimated value of MIl-1 c (t). λ1 is the weight fraction of the instantaneous polymer newly produced in the lth reactor. λl2 is the weight fraction of the polymer arriving from the previous reactor. λl changes as a function of the grade being produced in normal operations, as well as depending on the starting and ending grades in transition operations. However, it is impossible to decide λl for all of the cases and, therefore, we estimate the appropriate value of λl based on the three groups clustered in the clustering step: there are seven cases, made up of the three kinds of normal operations (groups 1-3) and the four types of grade changes, such as “group 1 f group 2”, “group 2 f group 3”, “group 3 f group 2”, and “group 2 f group 1”. We exclude the case of “from group 1 to group 3” or “from group 3 to group 1” because the grade change is


M ˆ Ili(t) ) xl(t) Blk

(9)

ˆ Ili(t)] + λl2 log[M ˆ Il-1 log[M ˆ Ilc(t)] ) λ1l log[M c (t-∆t)] + ˆ Ilc(t-∆t)] (10) (1 - λl1 - λl2) log[M ˆ Ilc(t) are the estimates of the inwhere M ˆ Ili(t) and M stantaneous and cumulative MIs, respectively, at time t for the lth reactor. Finally, the cumulative MI of the PP discharged from the fourth reactor is estimated using eq 10 for each of the four reactors in turn. Validation of the Clustering-Based Hybrid Soft Sensor

Figure 7. Procedure used to estimate the MI of the PP discharged from the fourth reactor using the proposed clustering-based hybrid soft sensor.

performed in both directions, group 1 f group 2 f group 3 or group 3 f group 2 f group 1, in order to prevent process instability due to steep changes. For every case, the value of λl is determined by minimizing the rootmean-squared errors (RMSEs) between the MI measured by the analyzer and the MI estimated by eq 5. The cumulative MI model can be updated by calculating the optimal value of λl again from the MI data, which is obtained from the new operational condition when the transient behaviors become different from the past or new grades and/or catalysts are applied. MI Estimation Using a Clustering-Based Hybrid Soft Sensor. Figure 7 shows the procedure used to estimate the cumulative MI of the PP discharged from the fourth reactor using the operational data. The proposed soft sensor consists of the instantaneous MI model, which includes three local PLS models and one global PLS model, and the cumulative MI model for each reactor. Before the estimation of the instantaneous MI, we should decide which PLS model is appropriate for the current operational data, based on the MI value. However, the MI cannot be measured every 1 min and, consequently, we estimate the preliminary instantaneous MI from the current operational data using the global PLS model. The global PLS model estimates the preliminary instantaneous MI well enough to determine which local PLS model should be used to estimate the instantaneous MI.

MIl0(t) ) xl(t) Bl0

(6)

for the lth reactor, where MIli0(t) is the preliminary instantaneous MI at time t, which is obtained using the global PLS model, and xl(t) is the operational data at time t. If MIli0(t) belongs to one of the regions corresponding to the three clustered groups, the corresponding local PLS model is chosen to estimate the instantaneous MI. Otherwise, the preliminary instantaneous MI is used as the instantaneous MI.

MIli0(t) ∈ Glj f k ) j otherwise f k ) 0 Glj

As mentioned above, the previous approaches cannot be used to develop a soft sensor for PP because of the difficulty in deriving the mechanistic model. Therefore, the performance of the proposed soft sensor in terms of its estimation accuracy was compared with that of the conventional black-box models, including PLS, ANNs, and neural network partial least squares (NN-PLS). PLS has been widely used as a powerful modeling method for constructing linear models from laboratory and field measurement data.11,13-15 ANNs are widely used for modeling of the nonlinear behaviors of a process because they allow a great deal of flexibility in deciding the model structures.13,16-18 NN-PLS algorithms19,20 are hybrid models that combine linear PLS with ANNs. In NN-PLS, the ANNs capture the nonlinearity, while PLS allows the PLS projection to be maintained to obtain a robust generalization property. In the case of PLS and NN-PLS modeling, the total number of latent variables, a, is determined by means of cross-validation.6 Then, for the ANN modeling, the MI is modeled by employing a feed-forward network with one hidden layer, for which the best number of nodes in the hidden layer has been found to be 2. The transfer function for each hidden node is the sigmoidal function represented by f(1) i (z) ) 1/[1 + exp(-z)], while that for the output node is the pure linear function, f (2)(z) ) z. The weights and biases in this type of feed-forward network are determined from a back-propagation training algorithm.21 Conventional Black-Box Models. Table 1 shows the estimation performances of the three black-box models and the proposed soft sensor, including the instantaneous MI and cumulative MI models, based on the RMSEs between the measured and estimated MIs. The conventional black-box models, including the linear and nonlinear models, showed poorer performances than the proposed models. The PLS, ANN, and NN-PLS models have RMSEs of 3.78, 4.81, and 3.90 for the testing data, respectively. The PLS model cannot capture highly nonlinear behaviors arising from many different grades, as shown in Figure 8a. The estimates of the ANN model significantly deviate from the measurements, as shown in Figure 8b. The poor estimation performance of the ANN model can be explained by the Table 1. RMSEs for the Conventional Black-Box Models and the Proposed Soft Sensor

(7) (8)

is the bound of MI for the jth for j ) 1-3, where clustered group for the lth reactor.

RMSE modeling method PLS ANNs NN-PLS clustering-based hybrid soft sensor

training data testing data 3.73 4.54 3.61 1.37

3.78 4.81 3.90 1.58

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Figure 8. (a) For the PLS method, the measured and estimated MIs of the PP discharged from the fourth reactor. (b) For the ANN method, the measured and estimated MIs of the PP discharged from the fourth reactor. (c) For the NN-PLS method, the measured and estimated MIs of the PP discharged from the fourth reactor. (d) For the proposed soft sensor, the measured and estimated MIs of the PP discharged from the fourth reactor.

lack of training data. When using ANNs, it is not easy to determine the optimal structure and parameters for complex characteristics such as the PP process because of the existence of many local minima.21 A considerable amount of data are required to obtain a good training performance in the case of ANNs when there are many input variables.13,21 It is noteworthy that the ratio of the measurements to the input variables is only about 7.36 for the PP polymerization process. Generally, NN-PLS can obtain a better performance even when the training data are sparse and the ratio of the measurements to the input variables is small because the number of input nodes to be trained is smaller than that of ANNs. However, the NN-PLS model yields a bad performance, as shown in Figure 8c, because its modeling structure is not able to exactly explain the operational complexity because of the existence of multiple grades and frequent grade changes. Clustering-Based Hybrid Soft Sensor. The cumulative MI model has an RMSE of 1.58 for the testing data, as shown in Table 1, which is much better than that of any of the conventional black-box models. The estimation performance in the transition operation is even more highly improved by supplementing the cumulative MI model with the instantaneous MI model. Most of the estimated MIs track the measured ones very closely throughout the transition operations, as well as during normal operation, as shown in Figure 8d. Industrial Application Results and Discussion The developed soft sensor was applied to the PP process of Samsungatofina for the purpose of monitoring

Figure 9. Industrial application results using the proposed clustering-based hybrid soft sensor.

and controlling the MI of the PP discharged from the fourth reactor on a real-time basis. The company was able to reduce the amount of off-specification PP products during the grade transitions by 30%. Figure 9 shows the MI estimated every 1 min by the developed soft sensor using the proposed approach, as compared with the MI measured every 8 h during the 10 day period of operation. This accurate and continuous monitoring helped shorten the transition region, by allowing the appropriate time at which the MI of the


target grade is within the on-specification bounds to be determined. As shown in Figure 9, we can clearly discern the point at which the MI changes from a steep slope to a gentle slope by monitoring the estimated MI every 1 min. Additionally, the actual grade transition time was gradually reduced by helping the operators adjust the operating conditions so that the MI of the target grade reaches the desired specification rapidly and stably. In the future, it is expected that it will be possible to control the MI in a more stable manner, according to the desired specification in the case of normal operations, because the developed soft sensor has a good performance even during normal operations. Conclusion We proposed a novel methodology that allowed us to develop a soft sensor with a good performance for the industrial PP process, despite the production of many different grades of PP. The proposed soft sensor comprises CTQ-based clustering, a local-based instantaneous MI model, and an expanded cumulative MI model. First, we successfully handle the complex relationships arising from the multiple grades by clustering the overall operations into several subgroups with a CTQ-based clustering method. This method is especially effective at improving the operational similarity in each clustered group, thereby improving the accuracy of the inferential models. Second, the instantaneous MI model, which consists of one global and three local PLS models, greatly improves the estimation performance in the case of normal operations. Third, the cumulative MI model is developed by expanding the existing cumulative MI model, and this cumulative model improves the interpretation capability of the transient behaviors. The proposed soft sensor is validated by applying it to the industrial PP process of Samsungatofina. On the basis of the results of the assessment using the testing data set, we found that the proposed soft sensor gives an excellent estimation accuracy during both normal and transition operations. The results show that the online monitoring of the estimated MI using the proposed soft sensor contributes to a significant reduction in the amount of off-specification PP products, with this reduction amounting to 30% during the grade transitions. The accurate and continuous monitoring of the MI allowed the operators to reduce the actual transition time. In addition, the proposed soft sensor can overcome practical problems, such as frequent model updates and online analyzer errors. In this study, it was built and updated with a relatively small amount of effort and, therefore, the cost of building and maintaining the model is much lower than that of previous models. It is not affected by analyzer errors because it does not use the measurements of the online analyzer, which frequently cause trouble. Therefore, it is expected that the clusteringbased hybrid soft sensor can be widely applied to many other PP processes with operational complexity caused by the existence of a large number of grades. Acknowledgment This work was financially supported by the Korea Science and Engineering Foundation through the Advanced Environmental Biotechnology Research Center at Pohang University of Science and Technology, and the authors gratefully acknowledge the support pro-

vided by the process engineers, Jinsuk Lee, Woo Kyoung Kim, and Kun Lo, at Samsungatofina, Korea. Nomenclature English Symbols Blk ) matrix of regression coefficients for the lth reactor and the kth PLS model El(t) ) polymer production rate for the lth reactor at time t Glj ) bound of MI for the lth reactor and the jth clustered group Hl(t) ) polymer holdup at a reactor for the lth reactor at time t Il(t) ) polymer entering into a reactor for the lth reactor at time t MIA ) MI of polymer A MIB ) MI of polymer B MIC ) MI of polymer C MIM ) MI of the polymer mixture MIlc(t) ) cumulative MI for the lth reactor at time t M ˆ Ilc(t) ) estimate of the cumulative MI for the lth reactor at time t MIli(t) ) instantaneous MI for the lth reactor at time t M ˆ Ili(t) ) estimate of the instantaneous MI for the lth reactor at time t MIli0(t) ) preliminary instantaneous MI for the lth reactor at time t MIlk ) training data matrix of modeling outputs for the lth reactor and the kth PLS model Rl(t) ) polymer reaction rate for the lth reactor at time t ∆t ) short period of time wA ) weight fraction of polymer A wB ) weight fraction of polymer B wC ) weight fraction of polymer C Xlk ) training data matrix of modeling inputs for the lth reactor and the kth PLS model xl(t) ) operational data for the lth reactor at time t Greek Symbols λl1, λl2 ) weight fractions of the instantaneous polymer newly produced in the lth reactor and that of the polymer arriving from the previous reactor Subscripts j ) index of the clustered group k ) index of the PLS model l ) index of the reactor

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Received for review March 13, 2004 Revised manuscript received October 22, 2004 Accepted November 1, 2004 IE049803B

Clustering-Based Hybrid Soft Sensor for an Industrial Polypropylene

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