Long-Term Industrial Applications of Inferential Control Based on Just

Article pubs.acs.org/IECR

Long-Term Industrial Applications of Inferential Control Based on Just-In-Time Soft-Sensors: Economical Impact and Challenges Sanghong Kim,† Manabu Kano,*,‡ Shinji Hasebe,† Akitoshi Takinami,§ and Takeshi Seki§ †

Department of Chemical Engineering and ‡Department of Systems Science, Kyoto University, Kyoto, Japan § Production Technology Department, Showa Denko K.K., Oita, Japan ABSTRACT: Many research works on soft-sensors have been conducted. Although it is common practice to evaluate the estimation performance of soft-sensors by using industrial process data, few papers have reported long-term application results of process control using soft-sensors in real processes. In the present work, a practical configuration of an inferential control system was developed that integrated a commercial model predictive control (MPC) software and a just-in-time (JIT) soft-sensor. The developed system has adopted locally weighted partial least squares (LW-PLS) to build soft-sensors. LW-PLS is a kind of JIT modeling method that can cope with changes in process characteristics as well as process nonlinearity. Thus, LW-PLS helps engineers to reduce their burden of model maintenance, which has been recognized as the most serious problem in practice. The usefulness of the developed LW-PLS-based soft-sensors and inferential control systems is demonstrated through their successful industrial applications to a cracked gasoline (CGL) fractionator and a purification section for an acetyl plant. Inferential control systems have been used for more than a year at Showa Denko K.K. (SDK) in Japan. The operation cost and environmental burden have been significantly reduced. In the CGL fractionator, for example, about 0.6% of operation cost was cut successfully. In addition, the present work aims to describe challenges, revealed by the long-term applications of JIT soft-sensors: the parameter tuning, the selection of input variables, the definition of similarity in JIT modeling, the management of the database, and the assessment and enhancement of soft-sensor reliability.

1. INTRODUCTION In industrial processes, it is crucial to meet the quality requirements; however, online measurement of the quality is not always available because of unacceptable expenses of analytical instruments or long measurement/analysis delay. In such cases, soft-sensors are useful for estimating and controlling quality by using online measured variables. Multiple linear regression (MLR) is a common statistical method for developing soft-sensors. About 70% of soft-sensors are constructed by MLR according to the recent questionnaire survey of chemical process control in Japan.1 Another widely used regression method is partial least squares (PLS), which can deal with the problem of collinearity that MLR cannot. These linear modeling methods account for over 90% of the soft-sensors used in industry.1 Although this fact shows that linear models are practically useful, nonlinear modeling methods such as neural networks, 2−5 support vector regression,6−8 and nonlinear PLS9−11 have been used to construct soft-sensors for nonlinear processes. The above-mentioned questionnaire survey1 revealed that the most important problem of current soft-sensors was how to cope with changes in process characteristics and maintain high estimation accuracy for a long period of time, i.e. model maintenance. The importance of this problem has also been pointed out in other literature.12,13 When the estimation performance of a soft-sensor becomes worse with time and, hence, laborious model reconstruction is frequently required, soft-sensor applications cannot be widespread. To solve this problem, various recursive modeling methods, which update models by prioritizing newer samples, have been developed.14 However, the estimation accuracy of these methods deterio© 2013 American Chemical Society

rates when abrupt changes in process characteristics such as replacement of a catalyst and cleaning of equipment occur. This is because a query sample, for which an output estimation is required, becomes significantly different from the prioritized samples just after an abrupt change occurs. On the other hand, locally weighted regression (LWR),15 which is a kind of just-intime (JIT) modeling method, constructs a local model by prioritizing samples in a database according to the similarities to a query sample. Hence, LWR can cope with abrupt changes as well as gradual ones. In addition, it can cope with nonlinearity since it builds a local model repeatedly. Many researches on LWR have focused on the definition of the similarity to enhance the estimation accuracy.16−22 One can refer to the review papers by Kadlec et al.12,14 and Kano and Fujiwara23 for more information about the state of the art of soft-sensors. Kadlec et al.12 summarized general techniques of soft-sensor development including abnormal data detection, data preprocess, basic regression methods, and so on. Kadlec et al.14 focused on adaptive modeling techniques such as recursive methods and ensemble methods. Kano and Fujiwara23 explained the current situation of soft-sensor applications in Japan, exhaustively surveyed on input variable selection methods and JIT modeling methods, which can solve the problem of estimation performance deterioration of softsensors and also pointed out remaining problems to solve. Special Issue: John MacGregor Festschrift Received: Revised: Accepted: Published: 12346

December 16, 2012 April 8, 2013 April 11, 2013 April 11, 2013 dx.doi.org/10.1021/ie303488m | Ind. Eng. Chem. Res. 2013, 52, 12346−12356

Industrial & Engineering Chemistry Research

Article

where wr is the eigenvector of XTr ΩYrYTr ΩXr which corresponds to the maximum eigen value. 5. Derive the rth loading vector of X

This paper describes a practical configuration of an inferential control system developed at the Showa Denko K.K. (SDK) in Japan and its successful long-term application examples. The developed inferential control system can integrate a commercial model predictive control (MPC) software and a JIT soft-sensor. The developed system has adopted locally weighted partial least squares (LW-PLS),24 which is a kind of JIT modeling method that can cope with changes in process characteristics as well as process nonlinearity to reduce the burden of model maintenance. It has been stably working for more than a year and significantly reduced the operation cost and environmental burden. The rest of this paper is organized as follows. Section 2 explains the algorithm of LW-PLS. The details of the control systems and application results are shown in section 3. Section 4 discusses the challenges revealed by the long-term applications of JIT soft-sensors. Finally, this research is concluded in section 5.

pr =

(1)

yn = [yn1 , yn2 , ..., ynL ]T

(2)

qr =

(10)

YrTΩtr trTΩtr

(11)

6. Derive the rth latent variable of xq

tq , r = x qT, rwr

(12)

and finish estimation. Otherwise, set X r + 1 = X r − trprT

(14)

Yr + 1 = Yr − trq rT

(15)

xq , r + 1 = xq , r − tq , r pr

(16)

8. Set r = r + 1 and go to step 4. The number of latent variables R is usually determined by cross validation. The similarity matrix Ω in step 2 is usually defined on the basis of the Euclidean distance or the Mahalanobis distance.8,24−29 Other similarity measures proposed so far include the angle,17,30 the distance between an output estimate for a query sample derived by a global model and output measurements for samples in a database,13,16 the correlation, 18,19 and the weighted Euclidean distance (WED).20−22 Various similarity measures and their applications were surveyed by Kano and Fujiwara.23 When Ω is an identity matrix, LW-PLS becomes the same as PLS. At step 3, the weighted mean of each variable is subtracted from each column of X, Y, and xTq to make the query sample near to the origin of the multidimensional space. At steps 4−8, the latent variable t, the loading vector p, and the regression coefficient vector q are derived iteratively, and the output estimate ŷq is calculated when r = R.

where M is the number of input variables, L is the number of output variables, and the superscript T denotes the transpose of a vector or matrix. X ∈ 9 N×M and Y ∈ 9 N×L are input and output variable matrices whose nth rows are xTn and yTn , respectively. LW-PLS24 is a JIT modeling method, which does not construct a regression model off-line. Instead, X and Y are stored in a database. When an output estimation is required for a query sample xq, the similarity ωn between xq and xn is calculated, and a local PLS model is constructed by weighting samples with a similarity matrix Ω ∈ 9 N×N defined by Ω = diag(ω1, ω2 , ..., ωN )

trTΩtr

and the regression coefficient vector

2. LOCALLY WEIGHTED PARTIAL LEAST SQUARES The nth samples (n = 1, 2, ..., N) of input and output variables are denoted by x n = [xn1 , xn2 , ..., xnM ]T

X rTΩtr

(3)

In general, the output estimate ŷq ∈ 9 is calculated through the following procedure. 1. Determine the number of latent variables R and set r = 1. 2. Calculate the similarity matrix Ω. 3. Calculate Xr, Yr, and xq,r L

X r = X − 1N [x1̅ , x 2̅ , ..., xM̅ ]

(4)

Yr = Y − 1N [y1̅ , y2̅ , ..., yL̅ ]

(5)

xq , r = xq − [x1̅ , x 2̅ , ..., xM̅ ]T

(6)

N

xm̅ =

N

∑ ωnxnm/ ∑ ωn n=1

n=1

N

yl̅ =

3. INDUSTRIAL APPLICATIONS OF LOCALLY WEIGHTED PARTIAL LEAST SQUARES At Showa Denko K.K. (SDK) in Japan, soft-sensors based on LW-PLS have been applied to various processes. In the early stage of soft-sensor implementation, MLR and PLS had been mainly used. However, the company had to confront two major problems: first, the considerable cost and time required to implement soft-sensors, and second, the burden of the maintaining soft-sensors to prevent the performance deterioration. To solve these problems and increase the number of soft-sensor applications, a practical configuration of an inferential control system was developed by integrating a commercial MPC software and LW-PLS-based soft-sensor. The developed system can be easily implemented to processes using common software and personal computers as shown in the next subsection. In addition, by using LW-PLS-based soft-sensors, the burden of the model maintenance can be reduced since they can cope with changes in process characteristics as well as process nonlinearity. This section explains the details of the configuration of the developed inferential control system and two successful results of applying the system to chemical processes. In these

(7)

N

∑ ωnynl / ∑ ωn n=1

n=1

(8)

where 1N ∈ 9 is a vector of ones. 4. Derive the rth latent variable of X N

tr = X rwr

(9) 12347

dx.doi.org/10.1021/ie303488m | Ind. Eng. Chem. Res. 2013, 52, 12346−12356


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applications, the following form of the similarity ωn is used for the sake of simplicity. ⎛ d ⎞ ωn = exp⎜ − n ⎟ ⎝ σdφ ⎠ dn =

(x n − xq)T (x n − xq)

(17) (18)

Here, σd is a standard deviation of dn (n = 1, 2, ..., N) and φ is a localization parameter. The similarity decreases steeply when φ is small and gradually when φ is large. To cope with nonlinear between input and output variables, φ needs to be small, however, LW-PLS models can be sensitive to noise when φ is too small. 3.1. Configuration of the Inferential Control System. Figure 1 shows the inferential control system configuration

Figure 2. Schematic diagram of the CGL fractionator of the ethylene production process at the SDK Oita plant.

usually analyzed only once a day in a laboratory. The concentration has a soft lower bound constraint and should be kept close to the constraint in order to satisfy the product specification and to reduce operation cost. Equivalently speaking, short-time violations are acceptable. The coil outlet temperature (COT) of the cracking furnace is the main manipulated variable for the aromatics concentration control; the aromatics concentration can be increased by increasing COT. However, higher COT requires higher operation cost. Although a PLS-based soft-sensor and MPC had been implemented to estimate and control the aromatics concentration, the estimation performance was not high enough. Thus, COT had been kept excessively higher than optimal to satisfy the constraint on the aromatics concentration. LW-PLS replaced conventional PLS to enhance the estimation accuracy, decrease COT and lower the operation cost, which is dominated by the energy consumption amount in the cracking furnace. A commercial MPC software package has been implemented in this ethylene production process. The package has various functions for different scales of processes and different purposes. One of the functions of the package is to solve an optimization problem by using a model of the whole ethylene production process. The constraint on the aromatics concentration is taken into account in the optimization problem whereas no MPC controller is implemented in the CGL fractionator itself. Other MPC controllers implemented in other processes in the ethylene production process control each process so that the constraint on the aromatics concentration is satisfied. Eight process variables shown in Figure 2 were selected as input variables of the soft-sensor on the basis of engineers’ process knowledge. In addition, COT measured 4 h before was used as an input variable together with the selected input variables, since it takes about 4 h for materials to reach the CGL fractionator from the cracking furnace. Hence, the total number of input variables is nine. The number of latent variables R and the localization parameter φ were determined by cross validation; R and φ were set to four and 0.5, respectively. When PLS was applied to the aromatics concentration estimation, bias update have been used to reduce estimation error. After LW-PLS was implemented instead of PLS, the 30 newest samples were stored in the database to cope with recent changes in process characteristics. In addition, 395 samples

Figure 1. Configuration of the developed inferential control system in the SDK Oita plant.

developed at the SDK Oita plant, in which soft-sensors, a commercial MPC software, and a distributed control system (DCS) are combined with each other. A DCS accumulates measurements of process variables and returns the control signals to the process. The personal computer 1 (PC 1) for MPC receives the information of process variables including controlled variables (CVs) and disturbance variables (DVs) from the DCS and returns the optimized values of manipulated variables (MVs) to the DCS. In addition, PC 1 transfers values of input variables of the soft-sensors from the database to the Excel platform in PC 2. The soft-sensor programs in PC 2 calculate the output estimates using the data in the Excel platform, and the output estimates are returned to PC 1 and DCS. The soft-sensor programs are coded in MATLAB and compiled into C language using a MATLAB Compiler in order to make them available without MATLAB. The soft-sensor programs and the MPC software can be easily installed in commercial PCs, which can be connected to the DCS. In addition, this inferential control system can be applied to any processes. Thus, the developed system can reduce cost and time for implementation. 3.2. CGL Fractionator of the Ethylene Production Process. A schematic diagram of the cracked gasoline (CGL) fractionator of the ethylene production process at the SDK Oita plant is shown in Figure 2. The concentration of aromatics in the product CGL, which is an important quality variable, is 12348



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Figure 3. Application results of the developed inferential control system integrating MPC and soft-sensors at the ethylene production process in the SDK Oita plant: the aromatics concentration and COT using PLS (from May 1 to June 30, 2011) (left) and LW-PLS (from October 1 to November 30, 2011) (right).

using two towers, a degassing tower and a product tower, as shown in Figure 4. This process has been operated by using a multivariate MPC controller for more than 8 months; CVs, MVs, and DVs are shown in Figure 4 and Table 2. Twelve measurements are set as CVs and are controlled by using three MVs: steam flow rate in the degassing tower, reflux flow rate of the product tower, and a temperature in the product tower. The amount of impurity in the product has a soft upper constraint and should be kept close to the constraint in order to satisfy the product specification and to reduce operation cost. In other words, short-term violations are acceptable. In this process, the control performance has been poor since the amount of impurity has been usually measured only once a day. To solve this problem and minimize the steam flow rates in the degassing tower and the product tower, the developed inferential control system was implemented. Twenty three process variables such as temperature, feed flow rate, differential pressure, and steam flow rate were selected as input variables of the soft-sensor on the basis of engineers’ process knowledge. The number of latent variables R and the localization parameter φ were determined by cross validation; R and φ were set to five and 0.8, respectively. The 30 newest samples and core data which consists of 297 samples obtained from May 1, 2010, to October 31, 2011, were used to construct locally weighted PLS models. The number of newest samples and the core data were selected by trial and error. Figure 5 shows the laboratory measurements of impurity amount yim, the estimates, the constraint, and the steam flow rate in the degassing tower before and after LW-PLS was implemented. All variables are scaled in this figure, and the control results before and after the implementation of LW-PLS are compared. Neither a soft-sensor nor MPC software was applied to this process before the implementation of LW-PLS. In addition, Table 3 shows the standard deviation σ of yim, mean absolute deviation (MAD) of yim from the upper bound, mean of the steam flow rate in the degassing tower F1 and that in the product tower F2, which is used for control of the temperature in the product tower (MV-T1 in Table 2 and Figure 4) in a lower level control loop. Here, σyim, MADyim, and

obtained from June 1, 2010, to May 31, 2011, were selected as core data, which had been always stored in the database to prevent overfitting and cope with nonlinearity and abrupt changes in process characteristics. The use of core data is significantly useful to make JIT soft-sensors robust. The core data was selected by trial and error. Figure 3 shows the laboratory measurements of the aromatics concentration yaroma, the estimates, the soft constraint, and COT, which is the main MV of MPC. All variables are scaled in this figure, and the control results before and after the implementation of LW-PLS are compared. In addition, Table 1 Table 1. Application Results of the Developed Inferential Control System Integrating MPC and Soft-Sensors at the Ethylene Production Process in the SDK Oita Plant: Comparison between PLS-Based Soft-Sensor and LW-PLSBased Soft-Sensor PLS LW-PLS

RMSE [%]

MADyaroma [%]

σyaroma [%]

mean of COT [%]

100 70.4

100 74.1

100 93.3

100 99.6

summarizes root-mean-square errors (RMSE) of prediction, mean absolute deviation (MAD) of yaroma from the lower bound, standard deviation σ of yaroma, and mean of COT. Here, RMSE, MADyaroma, σyaroma, and COT are scaled so that they are 100 when PLS was used, i.e. before the implementation of LWPLS. The unit of COT is Celsius. All indexes in Table 1 were improved by using LW-PLS. About 0.6% operation cost was reduced by using the MPC system combined with the LW-PLS-based soft-sensor. Although some of the laboratory measurements of aromatics concentration are under the lower bound when LW-PLS is applied, this is acceptable since the violation did not continue for a long time. The control system has been stably working for more than a year although only 2 months of the data are shown in Figure 3. 3.3. Purification Section for Acetyl Plant. In the purification section for an acetyl plant, the feed is purified 12349



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Figure 4. Schematic diagram of the purification section for an acetyl plant at the SDK Oita plant.

Table 2. Variables Used in MPC in the Purification Section for Acetyl Planta

a

tag

variable name

CV-P1 CV-P2 CV-T1, 2, 3 CV-T4 CV-T5, 6, 7, 8 CV-F1 CV-F2 MV-F1 MV-F2 MV-T1 DV-T1 DV-T2 DV-F1 DV-F2

differential pressure (DT) differential pressure (PT) temperatures (DT) temperature of the outlet flow from the top (DT) temperatures (PT) feed flow rate into the reflux drum (DT) reflux ratio (PT) steam flow rate (DT) reflux flow rate (PT) temperature (PT) feed temperature (DT) temperature of the reflux flow (DT) feed flow rate (DT) side cut flow rate (PT)

Table 3. Comparison between the Control Results by Using the Conventional Control System and the Developed Inferential Control System Integrating MPC and LW-PLS at the Purification Section for Acetyl Plant in the SDK Oita Plant

conventional system MPC and LW-PLS

MADyim [%]

σyim [%]

mean of F1 [%]

mean of F2 [%]

100 36.1

100 67.5

100 74.6

100 97.2

means of F1 and F2 are scaled so that they are 100 before the implementation of LW-PLS. As shown in Figure 5 and Table 3, the impurity amount has been kept close to the soft upper bound using the MPC system combined with the LW-PLSbased soft-sensor. In addition, σyim, F1, and F2 were reduced by 32.5%, 25.4%, and 2.8%, respectively, and the operation cost was significantly reduced.

DT and PT denote product tower and degassing tower, respectively.

Figure 5. Application results of the conventional control system (from April 9 to May 9, 2012) (left) and the developed inferential control system integrating MPC and LW-PLS (from August 1−31, 2012) (right) at the purification section for acetyl plant in the SDK Oita plant. 12350



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4. REMAINING ISSUES Although two successful applications of the MPC system combined with the LW-PLS-based soft-sensor were described in the last section, the authors faced many problems during development of the system and some of them still remain to be solved to promote industrial application of inferential control, in particular, LW-PLS-based soft-sensors. In this section, the remaining problems revealed mainly from engineers’ points of view and the future research direction are discussed. 4.1. Parameter Tuning. To construct an accurate softsensor, tuning parameters must be properly determined. For example, in the application examples shown in section 3, the number of latent variables R, the localization parameter φ, and the number of newest samples in the database were treated as tuning parameters. In addition, selection of input variables, model structure, and similarity measure are important. To realize robust soft-sensors, core data kept in the database needs to be appropriately determined. These parameters are mostly determined by time-consuming trial and error or cross validation, and it is required to reduce the burden of parameter tuning in order to promote the use of soft-sensors. One of the problems of cross validation is its computational load. To reduce the computational load of cross validation, it is crucial to know about the qualitative meaning of tuning parameters and to limit the search range. For example, the localization parameter φ is a parameter which determines the nonlinearity of the soft-sensor; the soft-sensor can cope with process nonlinearity when φ is small, but overfitting can occur when it is too small. The optimal value of φ depends on the number of samples, strength of process nonlinearity, etc., and the optimal value is usually from 0.1 to 1.5 based on the authors’ experience. Another problem of cross validation is that the evaluation function, which is usually RMSE of cross validation (RMSECV), is not always reliable. Shao31 and Baumann32 showed that using RMSECV derived by leave-one-out cross validation (LOOCV) tends to lead to overfitting. In practical applications, a parameter set which derives the minimum RMSECV is not always selected. Instead, a parameter set is determined by taking account of the trade-off between the robustness and the prediction performance. For example, a lesser number of latent variables is used when RMSECV is not significantly reduced by increasing the number of latent variables. However, such a decision is subjective and depends on engineers’ experience, thus a reliable systematic method for parameter tuning should be developed. 4.2. Input Variable Selection. It is crucial to select appropriate input variables to enhance the estimation accuracy and the reliability of soft-sensors, but the variable selection is one of the most difficult parts concerning soft-sensor development.33 In the application examples shown in this paper, experienced engineers selected the input variables mainly based on their process knowledge. However, it is timeconsuming for the engineers to select the input variables since trial and error is inevitable. In addition, the selected variable might not be optimal. Also, it becomes very difficult even for experienced engineers to properly select input variables when numbers of variables are measured and physical and chemical phenomena are not sufficiently understood. Thus, a systematic input variable selection method is required to improve the estimation performance of soft-sensors and reduce the development period.

In the past, many indexes for selecting a set of input variables were proposed. A well-known index for MLR is the F-value based on the statistical hypothesis test. F=

Vr Ve

(19) N

∑n = 1 (yn̂ − y ̅ )2 Sr Vr = = M M

(20)

N

Ve =

∑ (y ̂ − yn )2 Se = n=1 n N−M−1 N−M−1

(21)

where N is the number of samples and M is that of input variables. ŷn and y ̅ denote the estimate and the mean of the nth output measurement yn, respectively. Other popular indexes include adjusted coefficient of determination R2, Akaike information criterion (AIC),34 Mallow’s Cp,35 and RMSECV.

Vr Vr + Ve

(22)

AIC = 2K − 2ln(L)

(23)

R2 =

Cp =

Sr − N − 2M Sr ,all

(24)

N

∑n = 1 (ycv,̂ n − yn )2

RMSECV =

N

(25)

Here, K is the number of independently adjusted parameters, L is the maximized value of the likelihood function for the estimated model, Sr,all is Sr derived by using all input variables, and ŷcv,n is the estimate of yn in cross validation. These indexes select a set of input variables based on the fitness and the complexity of the corresponding regression model. It is not practical to calculate an index for all combinations of input variables when a large number of variables are measured. To select input variables efficiently, two types of methods are available: one uses optimization techniques to evaluate the goodness of combinations, and the other evaluates the importance of each input variable separately. Among the optimization-based methods there are the stepwise method and the genetic algorithm (GA). The stepwise method repeatedly constructs models by adding or removing a variable with a greedy algorithm. GA is an algorithm that mimics the process of natural evolution. GA has been used to solve input variable selection problems formulated as mixedinteger problems.36,37 The indexes for evaluating each variable include magnitude of regression coefficient, variable influence on the projection (VIP),38 uninformative variable elimination (UVE),39 and others. In this type of approach, input variables are selected if the corresponding indexes are larger than a threshold. The idea of using the magnitude of regression coefficients for input variable selection is simple; variables having larger coefficients are more important. In this direction, an interesting method is least absolute shrinkage and selection operator (Lasso),40 which is MLR with a penalty on the L-1 norm of the regression coefficient vector β as βLasso = arg min y − Xβ β

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2

+λ β

1

(26)



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where λ is a tuning parameter. By penalizing the L-1 norm, unlike ridge regression that penalizes the L-2 norm, Lasso forces some regression coefficients to be zero; consequently, the corresponding input variables can be removed. When only one output is estimated, the regression coefficient vector derived by PLS is represented as βPLS = W(PTW)−1q

(27)

W = [w1, w2 , ..., wR]

(28)

q = [q1 , q2 , ..., qR ]T

(29)

and manual selection by the engineers with industrial operation data of an ethylene fractionator. The NCSC-based variable selection (NCSC-VS) outperformed the others. This result demonstrates the advantage of the groupwise variable selection method over conventional methods. In addition, the computational load can be reduced by grouping input variables. More indexes can be found in the literature.23,43,45,46 Nevertheless, trial and error is unavoidable in practice because different methods can derive the best performance depending on the case,47 and it is not clearly understood how to choose an input variable selection method. Thus it is not enough to propose a new method and evaluate it in particular cases. The reason why a method functions well or not should also be investigated so that an appropriate input variable selection method can be found with less effort, and hence, the burden of soft-sensor development can be reduced. 4.3. Definition of Similarity in JIT Modeling. To construct highly accurate JIT soft-sensors, it is crucial to define the similarity between samples. In the SDK Oita plant, the similarity defined by eqs 17 and 18 have been used because the distance-based similarity is frequently used and the development time is limited; however, the estimation performance could be improved by using another similarity. This section summarizes the similarity proposed so far and discusses the future direction. In JIT modeling methods, local models are constructed by using the similarity in different ways. The simplest model uses the output of the most similar sample to a query sample as the output estimate. The mean or the weighted mean of the output measurements of some of the most similar samples can be used also. Another way is to construct a local linear or nonlinear model f(x) which minimizes the weighted sum of the squared errors E defined as

where wr and qr are the weight vector and the regression coefficient for the rth latent variable, which can be derived by the algorithm explained in section 2 with all the similarity ωn = 1.41 The input variable selection method using βPLS is referred to as PLS-Beta.42 Another index for PLS is VIP.38 The VIP score of the mth variable is defined as

VIPm =

R ⎡ M ∑r = 1 ⎢(qr 2 trTtr) ⎣

2⎤

( ) ⎥⎦ wmr wr

R

∑r = 1 (qr 2 trTtr)

(30)

where wmr is the mth component of the rth weight vector wr. The VIP score is a weighted sum of the contribution of each input variable to latent variables. The contribution (wmr/∥wr∥)2 is weighted by qr2tTr tr, which is the variance of output explained by the rth latent variable tr. Chong and Jun42 applied the stepwise method, PLS-Beta, and VIP to artificial data and compared their performance. VIP and PLS-Beta achieved similar performances and were superior to the stepwise method and Lasso. UVE, proposed by Centner et al.,39 uses regression coefficients and their standard deviation for each input variable derived by LOOCV. UVE of the mth input variable is defined as UVEm =

β̅ m * = σβ * m

N

∑n = 1

N

E=

n=1

(32)

The similarity should be properly defined to develop accurate JIT models because it affects the accuracy significantly. The most frequently used similarity measures are based on the Euclidean distance or the Mahalanobis distance.8,24−29 Many kinds of functions such as Gaussian and tricube are used to define the similarity from the distance, but the selection of the functions does not have much effect on the estimation performance.48 To improve the performance of JIT models, the similarity based on the WED

βnm N

2 N (β − β ̅ ) ∑n = 1 nmN − *1m

∑ ωn(yn − f (x))2

(31)

where βnm is a regression coefficient of the mth input variable when the nth sample is used as a prediction sample in LOOCV and β̅*m is the mean of βnm(n = 1, 2, ..., N). β̅*m expresses the strength of the effect of each input variable on the output, and σβ*m means the variability of the regression coefficient. In other input variable selection methods, groups of input variables are generated and groupwise selection is conducted. For example, when spectrum data is analyzed, interval selection methods such as interval partial least squares (iPLS) can be used to make the groups of the input variables (wavelengths).43 In interval selection methods, neighboring wavelengths are grouped into one group since they are expected to have a similar effect on the output from the viewpoint of spectroscopy. Then, a selection index such as RMSECV or an optimizationbased method is used to select the groups. Fujiwara et al.44 proposed a novel grouping method based on the correlation between input variables. In their method, nearest correlation spectral clustering (NCSC)18,19 is used for variable grouping. They compared the proposed method with conventional methods such as the stepwise method, PLS-Beta, VIP, Lasso,

dn =

(x n − xq)T Θ(x n − xq)

Θ = diag(θ1, θ2 , ..., θM )

(33) (34)

was proposed. Here, θm is a weight for the mth input. Shigemori et al.20 proposed to define the weight θm as the absolute value of the mth input variable’s regression coefficient of an MLR model, and locally weighted MLR models were constructed by using the proposed similarity. The developed system based on the LWR model has been used in a real steel process for more than seven years to estimate the quality of the steel products and optimize the operating conditions, and it has contributed to reducing the operation cost. Kim et al.21 defined θm as the absolute value of the mth input variable’s regression coefficient of an LW-PLS model, which was built without weights, i.e. θm = 1. By using this similarity measure, a new LW20,21

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Figure 6. Importance of the age and the density of samples for database management.

In addition to the distance, Cheng and Chiu17 proposed using the angle between samples to determine the similarity.

PLS model was constructed. The usefulness of the proposed method was confirmed by comparing it to PLS and LW-PLS with the similarity based on the Euclidean distance in a case study, where active pharmaceutical ingredient (API) content in granules for tableting was estimated from near-infrared spectra (NIRS). The method using local models for weighting21 is more complicated than the method using a global model,20 but it is effective at improving the estimation performance for nonlinear processes. In addition, Nakagawa et al.22 proposed another weighting method which uses the property of the output to be estimated. The amounts of residual drug substances after the cleaning of equipment were estimated from the infrared-reflection absorption spectroscopy (IR-RAS) by using LW-PLS and the similarity based on the WED. The weights were defined as the second differential spectra of IR attenuated total reflection (IR-ATR) of the drug substances. Using this similarity improved the estimation performance compared to the conventional method such as LW-PLS with the similarity based on the Euclidean distance and PLS. This result shows that the estimation performance can be improved by using the available process knowledge. The above-mentioned similarity measures use only the information about input variables, but the estimation performance of JIT models can be enhanced by incorporating the information about the output variable. Wang et al.16 proposed a similarity measure which is based not only on the distance dx in the input space but on the distance dy in the output space. The initial output estimate for a query sample is calculated through principal component regression (PCR), and the similarity ωn = λdx , n + (1 − λ)dy , n

⎧ ⎪ λ exp( −d 2) + (1 − λ) (x Tx ≥ 0) n q n ⎪ ⎪ x n Txq ωn = ⎨ ⎪ x n ∥xq∥ ⎪ ⎪0 (otherwise) ⎩

(36)

The usefulness of this similarity was demonstrated by applying it to simulated isothermal and nonisothermal continuous stirred tank reactors (CSTR). Another similarity measure is used in the correlation-based JIT (CoJIT) modeling method proposed by Fujiwara et al.,18 in which several databases are generated from the original database before a query sample is given, and the index J based on Hotelling’s T2 and Q statistics is calculated for each database.

J = λT 2 + (1 − λ)Q

(37)

Then, a PCR model is constructed by using the database whose J is the minimum. CoJIT was applied to the CGL fractionator and RMSE was improved by 28% compared to recursive PLS. As described above, it is crucial to properly define the similarity between samples in order to enhance the estimation accuracy of JIT models. To determine the similarity, the kind of regression function f(x) should also be considered since the best similarity measure may depend on f(x). Kim et al.49 pointed out that the similarity based on the WED was suitable when PLS was used for local modeling, and that the weight θm should correspond to the strength of the nonlinear effect of the mth input on the output around a query sample. Furthermore, the estimation accuracy of JIT models is expected to be further improved by selecting the optimal combination of an input variable method, a similarity measure, and a regression function simultaneously. 4.4. Management of Database. The estimation performance of JIT soft-sensors depends on quality and quantity of samples stored in a database, thus the samples should be carefully selected to enhance the estimation performance. In

(35)

is calculated, where λ is a tuning parameter. Then, a locally weighted PCR model is constructed. The proposed method was compared to PCR, PLS, and a JIT modeling method with the similarity based only on dx through their application to the estimation of the fat concentration in beef samples and the composition of gases. They concluded that the proposed method derived better estimation result with fewer latent variables and was less sensitive to noise than the conventional methods. 12353



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applies a clustering method based on the adaptive-resonancetheory-2 (ART2) or the WED between samples. Then, it checks the number of samples in the cluster whose sample size is the maximum. If the number is less than three, no sample is removed. Otherwise, the oldest sample in the cluster is removed. This method was compared to the moving timewindow method through their applications to photo processes of a fifth-generation thin-film transistor liquid crystal display (TFT-LCD) factory. They recommended the use of the WEDbased method in terms of estimation accuracy and the computational time. This result implies that the processes are NLTV and the density of samples is important to improve the estimation performance. Such characteristics are common in semiconductor processes since replacement and cleaning of equipment are often conducted. As explained above, the age and the density of samples are important indexes for database management. To develop a better database management method, it seems crucial to evaluate the strength of the process nonlinearity to determine the density needed. Kim et al.49 proposed to use the weighted variance of regression coefficients of LW-PLS models to quantify the nonlinearity and properly define the similarity. This method can also be used for database management. 4.5. Assessment and Enhancement of Soft-Sensor Reliability. An important purpose of soft-sensor implementation in industry is to decrease frequency of the off-line laboratory analysis, which requires considerable cost and time. To realize the quality assurance and efficient process operation with less frequent laboratory analysis, the assessment and enhancement of soft-sensor reliability is indispensable. In other words, it is crucial to develop a method that can prevent and detect the performance deterioration of soft-sensors without results of laboratory analysis. To enhance the reliability of soft-sensors, it is required to detect and remove outliers. The Shewhart chart51 and Hample identifier52 are famous and easy-to-use outlier detection tools and are adopted in practice. Multivariate statistical process control (MSPC) is also popular.53,54 Kamohara et al.54 applied the PLS-based MSPC method to the ethylene fractionator at the SDK Oita plant. This method aimed to detect the deterioration of the estimation performance by monitoring Hotelling’s T2 and Q statistics. When either T2 or Q exceeds its control limit, the estimate is judged unreliable since the corresponding sample is different from the samples in a database, i.e. extrapolation is required. Sonoda et al.55 proposed a method which can estimate the output distribution. Their method based on the bootstrap filter and the Bayes’ rule was applied to estimation of the liquid steel temperature in a steel production process. They suggest that the information of the distribution of output can be used for sensitivity analysis, process scheduling, and liquid steel temperature control. In addition, the reliability can be evaluated on the basis of the estimation distribution; reliability is low when the distribution is broad, and high when it is sharp. Kaneko et al.56 proposed a method for predicting the estimation error of soft-sensor based on the distance between a query sample and samples in a database. Two kinds of distance were utilized to predict the estimation error. One is the distance between a query and the nearest sample in a database. The other one is the distance between a query and the average point of all the samples in a database. They have shown that the estimation accuracy tends to be bad when the distance is large by applying the proposed method to a real chemical process.

the application examples in the SDK Oita plant, samples obtained in a year (core data), which have been always stored in the database, and 30 newest samples have been used to construct JIT soft-sensors. The estimation performance of the developed soft-sensors have been kept high so far. However, research works on database management have not been actively conducted and it took long time to select core data and the number of newest samples. This section discusses how to manage the database. In general, the age and the density of samples are important indexes to evaluate the goodness of database, since the estimation performance may deteriorate when the samples in the database are old and sparse. However, the relative importance of these indexes changes according to the nonlinearity and time-variance of processes, and also characteristic of changes in input variables. Figure 6 summarizes the importance of the indexes for different kinds of processes, and the characteristic of changes in input variables. Here, processes are classified into four groups: linear time-invariant (LTIV), linear time-variant (LTV), nonlinear time-invariant (NLTIV), and nonlinear time-variant (NLTV). In addition, changes in input variables are classified into two types: gradual and abrupt. When a process is LTIV, the high estimation performance will be achieved even if samples are old and sparse. When a process is LTV, the estimation performance will be improved by storing newer samples in the database since older samples cannot represent the current input−output relationship. In addition, the improvement becomes more significant as the changes in the input−output relationship becomes slower, or the changes in input variables becomes more gradual. When a process is NLTIV, the density of the samples is dominant; the higher density is required as the nonlinearity becomes stronger. When input variables change gradually, using the newer samples may improve the estimation performance since a query sample can be assumed to be similar to newer samples. When a process is NTLV, both the age and the density of samples are important. In the application examples at the SDK Oita plant, the 30 newest samples have been stored in each database so that the LW-PLS-based soft-sensor can fit the current input−output relationship. In addition, samples obtained in the particular period in the past, which cover the relatively wide range of operating conditions, have been also stored in the database in order to make the soft-sensor robust. Another updating method is the moving time-window method, in which a newly obtained sample is added to the database and the oldest sample is removed from the database. This method has been used successfully in the steel process for more than 7 years.20 In this application, as shown in section 4.3, regression coefficients of a global MLR model were used as weights to determine the similarity used in LWR and the estimation performance was improved. This result suggests that the process nonlinearity is not strong. In addition, the operating conditions are frequently changed to manufacture various products for various customers. Also, the optimal condition for each product changes with time; therefore, laborious table maintenance was required in the past. These results suggest that the process is LTVslow with abrupt input changes. Since the age of samples in the database is important for this process as shown in Figure 6, the moving time-window method is suitable for this application. Wu et al.50 proposed a database management method which takes into account both the age and the density of samples. When a new sample is added to a database, their method 12354



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(3) Baffi, G.; Martin, E. B.; Morris, A. J. Non-linear projection to latent structures revisited (the neural network PLS algorithm). Comput. Chem. Eng. 1999, 23, 1293−1307. (4) Qin, S. J.; McAvovy, T. J. Nonlinear PLS modeling using neural networks. Comput. Chem. Eng. 1992, 16, 379−391. (5) Pérez-Marin, D.; Garrido-Varo, A.; Guerrero, J. E.; GutiérrezEstrada, J. C. Use of artifcial neural networks in near-infrared reflectance spectroscopy calibrations for predicting the inclusion percentages of wheat and sunflower meal in compound feedingstuffs. Appl. Spectrosc. 2006, 60, 1062−1069. (6) Nadadoor, V. R.; Siegler, H.; Shah, S. L.; McCaffrey, W. C.; BenZvi, A. Online sensor for monitoring a microalgal bioreactor system using support vector regression vector regression. Chemom. Intell. Lab. Syst. 2012, 44, 2101−2105. (7) Barman, I.; Kong, C. R.; Dingari, N. C.; Dasari, R. R.; Feld, M. S. Development of robust calibration models using support vector machines for spectroscopic monitoring of blood glucose. Chemom. Intell. Lab. Syst. 2012, 82, 9719−9726. (8) Lee, D. E.; Song, J. H.; Song, S. O.; Yoon, E. S. Weighted support vector machine for quality estimation in the polymerization process. Ind. Eng. Chem. Res. 2005, 44, 2101−2105. (9) Wold, S.; Wold, N. K.; Skagerberg, B. Nonlinear PLS modeling. Chemom. Intell. Lab. Syst. 1989, 7, 53−65. (10) Robertsson, G. Contributions to the problem of approximation of non-linear data with linear PLS in an absorption spectroscopic context. Chemom. Intell. Lab. Syst. 1999, 47, 99−106. (11) Abdel-Rahmana, A. I.; Lim, G. J. A nonlinear partial least squares algorithm using quadratic fuzzy inference system. J. Chemom. 2009, 23, 530−537. (12) Kadlec, P.; Gabrys, B.; Strandt, S. Data-driven soft sensors in the process industry. Comput. Chem. Eng. 2009, 33, 795−814. (13) Chang, S. Y.; Baughman, E. H.; McIntosh, B. C. Implementation of locally weighted regression to maintain calibrations on FT-NIR analyzers for industrial processes. Appl. Spectrosc. 2001, 55, 1199− 1206. (14) Kadlec, P.; Grbić, R.; Gabrys, B. Review of adaptation mechanisms for data-driven soft sensors. Comput. Chem. Eng. 2011, 35, 1−24. (15) Cleveland, W. S. Robust locally weighted regression and smoothing scatterplots. J. Am. Stat. Assoc. 1979, 74, 829−836. (16) Wang, Z. Y.; Isaksson, T.; Kowalski, B. R. New approach for distance measurement in locally weighted regression. Anal. Chem. 1994, 66, 249−260. (17) Cheng, C.; Chiu, M. S. A new data-based methodology for nonlinear process modeling. Chem. Eng. Sci. 2004, 59, 2801−2810. (18) Fujiwara, K.; Kano, M.; Hasebe, S.; Takinami, A. Soft-sensor development using correlation-based just-in-time modeling. AIChE J. 2009, 55, 1754−1765. (19) Fujiwara, K.; Kano, M.; Hasebe, S. Development of correlationbased clustering method and its application to software sensing. Chemom. Intell. Lab. Syst. 2010, 101, 130−138. (20) Shigemori, H.; Kano, M.; Hasebe, S. Optimum quality design system for steel products through locally weighted regression model. J. Proc. Cont. 2011, 21, 293−301. (21) Kim, S.; Kano, M.; Nakagawa, H.; Hasebe, S. Estimation of active pharmaceutical ingredients content using locally weighted partial least squares and statistical wavelength selection. Int. J. Pharm. 2011, 421, 269−274. (22) Nakagawa, H.; Tajima, T.; Kano, M.; Kim, S.; Hasebe, S.; Suzuki, T.; Nakagami, H. Evaluation of infrared-reflection absorption spectroscopy measurement and locally weighted partial least squares for rapid analysis of residual drug substances in cleaning processes. Anal. Chem. 2012, 84, 3820−3826. (23) Kano, M.; Fujiwara, K. Virtual sensing technology in process industries: trends and challenges revealed by recent industrial applications. J. Chem. Eng. Jpn. 2012, DOI: 10.1252/jcej.12we167. (24) Schaal, S.; Atkeson, C. G.; Vijayakumar, S. Scalable techniques from nonparametric statistics for real time robot learning. Appl. Intell. 2002, 17, 49−60.

Combining the above-mentioned methods with inferential control systems can result in reliable process operation. However, only a few implementation results have been reported in the literature. Hence, more research and practice are encouraged.

5. CONCLUSIONS In this research, a practical configuration of an inferential control system was developed, which enabled the integration of a just-in-time (JIT) soft-sensor with commercial model predictive control (MPC) software with less cost and time than before. To cope with changes in process characteristics as well as process nonlinearity and to achieve the high estimation performance, soft-sensors were developed by using locally weighted partial least squares (LW-PLS). The developed inferential control systems have successfully worked for more than a year at the Showa Denko K.K. (SDK) Oita plant in Japan. The operation cost and environmental burden have been significantly reduced. In the cracked gasoline (CGL) fractionator, for example, about 0.6% operation cost was cut successfully by decreasing the coil outlet temperature (COT) of the cracking furnace. In the purification section for an acetyl plant, the operation cost was significantly reduced by keeping the impurity amount in the product close to the upper bound. Furthermore, the implementation of the developed inferential control system has contributed toward reducing the burden of model maintenance, which was recognized as the most serious problem in practice. The inferential control system combining MPC and the LW-PLS-based soft-sensor is now spreading as a standard process control method to other processes of SDK. In addition, this paper discussed the remaining issues revealed from engineers’ points of view through the longterm applications of the developed inferential control system: the parameter tuning, the selection of input variables, the definition of similarity in JIT modeling, the management of database, and the assessment and enhancement of soft-sensor reliability. Soft-sensors have drawn increasing attention not only from the chemical industry but also from other industries such as pharmaceutical, steel, and semiconductor. Thus, active research works on these issues are crucial.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-(0) 75-753-3367. Fax: +81-(0)75-753-3371. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially supported by the Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (C) 24560940.

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Long-Term Industrial Applications of Inferential Control Based on Just

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