Process Model
A Selective Moving Window Partial Least Squares Method and
Its Application in Process Modeling
☆
Ouguan Xu
1,
⁎
,YongfengFu
1
,HongyeSu
2
,LijuanLi
3
1
Zhijiang College, Zhejiang University of Technology, Hangzhou 310024, China
2
State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China
3
College of Automation and Electrical Engineering, Nanjing University of Technology, Nanjing 210009, China
abstractarticle info
Article history:
Received 15 May 2013
Received in revised form 14 September 2013
Accepted 16 October 2013
Available online 20 June 2014
Keywords:
SMW-PLS
Hydro-isomerization process
Selective updating strategy
Soft sensor
A selective moving window partial least squares (SMW-PLS) soft sensor was proposed in this paper and applied
to a hydro-isomerization process for on-line estimation of para-xylene (PX) content. Aiming at the high frequen-
cy of model updating in previous recursive PLS methods, a selective updating strategy was developed. The model
adaptation is activated once the prediction error is larger than a preset threshold, or the model is kept unchanged.
As a result, the frequency of model updating is reduced greatly, while the change of prediction accuracy is minor.
The performance of the proposed model is better as compared with that of other PLS-based model. The compro-
mise between prediction accuracy and real-time performance can be obtained by regulating the threshold. The
guidelines to determine the model parameters are illustrated. In summary, the proposed SMW-PLS method
can deal with the slow time-varying processes effectively.
© 2014 Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.
1. Introduction
Partial least squares (PLS) regression has many excellent attributes
such as simple model stru cture, stable and robust per formance, and
fewer training s amples needed [1,2], so it is wi dely used in process
modeling [3,4], process control [5,6], process monitoring and fault diag-
nosis [2,7,8]. However, the PLS model may be locally valid and its perfor-
mance will be degraded due to high le vel noise and disturbance in
samples or time-varying industrial process such as catalytic decaying,
equipment aging, or process drifting [9–13]. Many adaptive PLS models
[9–16] have been proposed to deal with the dynamic behavior of
processes. The basic recursive PLS was first proposed by Helland et al.
[9] and then modified by Qin [10]. A representation was given for the
old data that maintain the information without increasing the dimen-
sionality. The block-wise recursive PLS algorithm developed by Qin
[11] was extended from the basic form with a moving window and a
forgetting factor. The algorithm could adapt the model based on new
data and the old PLS model, a voiding re-modeling the old data. A
fast moving window algorithm [12] was derived to update the kernel
PLS model. The proposed approach adapted the parameters of inferential
model with the dissimilarity between the new and oldest data. The time-
varying characteristics of processes could also be dealt with effectively by
moving window approach [11]. However, the effect of discarded sample
on the model could not be evaluated properly. In this case, a new recur-
sive PLS model was developed by Liu [14] through updating the mean
and variance of the new sample and old ones, so part of historical infor-
mation of the abandoned sample remained. The effective model was ex-
panded to an online dual updating method by Mu et al. [15], integrating
the model updating and the output offset updating. Since the dual
updating strategy takes the advantages of the two methods, it is more ef-
fective in adapting process changes. A similar dual updating scheme was
proposed by Ahmed et al. [16] for the prediction of melt index of a contin-
uous polymerization process. The recursive PLS models are updated re-
peatedly either in block-wise or sample-wise once any new sample(s)
is available, inducing a heavy load on the model manager or computation-
al machine. In order to improve the real-time performance of the model,
the frequency of model updating should be properly controlled. Among
the proposed adaptive PLS models, the frequency of model updating is re-
duced with the dual updating method proposed by Mu et al. [15],since
the model updating is activated at regular intervals. Different from the
strategy proposed by Mu et al. [15], the decision of which updating meth-
od to be performed is based on the prediction error [16]. A novel adaptive
modeling method was proposed by Lee et al. [17]. Depending on the
model performance assessment, partial or complete adaptation is utilized
to remodel the PLS method. The adaptive modeling method shows better
updating performance and lower updating frequency compared to the
block-wise recursive PLS modeling technique.
For the purpose of on-line application, more attentions have been
paid to the real-time performance of the model. In this paper, a selective
modeling strategy is proposed for the moving window PLS to decrease
the model adap tation frequency by a preset threshold. The model
Chinese Journal of Chemical Engineering 22 (2014) 799–804
☆
Supp orted by the National Natural Science Foundation of China (61203133,
61203072), an d the Open Project Program of the State Key Laboratory of Industrial
Control Technology (ICT1214).
⁎ Corresponding author.
E-mail address: ogxu@zjut.edu.cn (O. Xu).
http://dx.doi.org/10.1016/j.cjche.2014.05.012
1004-9541/© 2014 Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.
Contents lists available at ScienceDirect
Chinese Journal of Chemical Engineering
journal homepage: www.elsevier.com/locate/CJCHE