Modeling of Isomerization of C8 Aromatics by Online Least Squares Support Vector Machine

›› 2009, Vol. 17 ›› Issue (3): 437-444.

• PROCESS SYSTEMS ENGINEERING • Previous Articles Next Articles

Modeling of Isomerization of C₈ Aromatics by Online Least Squares Support Vector Machine

LI Lijuan^1,2, SU Hongye², CHU Jian²

1. College of Automation and Electrical Engineering, Nanjing University of Technology, Nanjing 210009, China;
2. State Key Lab. of Industrial Control Technology, Institute of Cyber-systems and Control, Zhejiang University, Hangzhou 310027, China

Received:2008-04-30 Revised:2009-03-20 Online:2009-06-28 Published:2009-06-28
Supported by:
Supported by the National Creative Research Groups Science Foundation of China (60721062);the National Basic Research Program of China (2007CB714000)

Modeling of Isomerization of C₈ Aromatics by Online Least Squares Support Vector Machine

李丽娟^1,2, 苏宏业², 褚建²

1. College of Automation and Electrical Engineering, Nanjing University of Technology, Nanjing 210009, China;
2. State Key Lab. of Industrial Control Technology, Institute of Cyber-systems and Control, Zhejiang University, Hangzhou 310027, China

通讯作者: LI Lijuan,E-mail:ljli@njut.edu.cn
基金资助:
Supported by the National Creative Research Groups Science Foundation of China (60721062);the National Basic Research Program of China (2007CB714000)

Abstract

Abstract: The least squares support vector regression (LS-SVR) is usually used for the modeling of single output system, but it is not well suitable for the actual multi-input-multi-output system. The paper aims at the modeling of multi-output systems by LS-SVR. The multi-output LS-SVR is derived in detail. To avoid the inversion of large matrix, the recursive algorithm of the parameters is given, which makes the online algorithm of LS-SVR practical. Since the computing time increases with the number of training samples, the sparseness is studied based on the projection of online LS-SVR. The residual of projection less than a threshold is omitted, so that a lot of samples are kept out of the training set and the sparseness is obtained. The standard LS-SVR, nonsparse online LS-SVR and sparse online LS-SVR with different threshold are used for modeling the isomerization of C₈ aromatics. The root-mean-square-error (RMSE), number of support vectors and running time of three algorithms are compared and the result indicates that the performance of sparse online LS-SVR is more favorable.

Key words: least squares support vector machine, multi-variable, online, sparseness, isomerization

摘要： The least squares support vector regression (LS-SVR) is usually used for the modeling of single output system, but it is not well suitable for the actual multi-input-multi-output system. The paper aims at the modeling of multi-output systems by LS-SVR. The multi-output LS-SVR is derived in detail. To avoid the inversion of large matrix, the recursive algorithm of the parameters is given, which makes the online algorithm of LS-SVR practical. Since the computing time increases with the number of training samples, the sparseness is studied based on the projection of online LS-SVR. The residual of projection less than a threshold is omitted, so that a lot of samples are kept out of the training set and the sparseness is obtained. The standard LS-SVR, nonsparse online LS-SVR and sparse online LS-SVR with different threshold are used for modeling the isomerization of C₈ aromatics. The root-mean-square-error (RMSE), number of support vectors and running time of three algorithms are compared and the result indicates that the performance of sparse online LS-SVR is more favorable.

关键词: least squares support vector machine, multi-variable, online, sparseness, isomerization

LI Lijuan, SU Hongye, CHU Jian. Modeling of Isomerization of C₈ Aromatics by Online Least Squares Support Vector Machine[J]. , 2009, 17(3): 437-444.

李丽娟, 苏宏业, 褚建. Modeling of Isomerization of C₈ Aromatics by Online Least Squares Support Vector Machine[J]. , 2009, 17(3): 437-444.

References

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Modeling of Isomerization of C₈ Aromatics by Online Least Squares Support Vector Machine

Modeling of Isomerization of C₈ Aromatics by Online Least Squares Support Vector Machine

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