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

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

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

收稿日期:2008-04-30 修回日期:2009-03-20 出版日期:2009-06-28 发布日期:2009-06-28
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)

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)

摘要/Abstract

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

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

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.

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.

参考文献

1 Horacio, G., Abante, R., Luis, C., Jorge, R., “Isomerization of C₈ aromatics over a Pt/Mordenite Catalyst. A statistical model”, Ind. Eng. Chem. Res., 35, 3964-3972(1996).
2 Xu, O.G., Su, H.Y., Jin, X.M., Chu, J., “Kinetic model for hydroisomerization reaction of C₈ aromatics”, J. Chem. Eng. Chin. Uni., 21(3), 429-435(2007).
3 Li, Y.G., Chang, X.D., Zeng, Z.H., “Kinetics study of the isomerization of xylene on HZSM-5 zeolite.1.Kinetics model and reaction mechanism”, Ind. Eng. Chem. Res., 31(1), 187-192(1992).
4 Iliyas, A., Al-Khattaf, S., “Xylene isomerization over USY zeolite in a riser simulator:A comprehensive kinetic model”, Ind. Eng. Chem. Res., 43, 1349-1358(2004).
5 Wu, D.X., Lin, Z.X., “Kinetic modeling of hydroisomerization of C₈ aromatics(I) Modeling and estimation of relative rate constants by the wei-prater method”, J. Chem. Ind. Eng.(China), 3, 257-267(1985).(in Chinese)
6 Wu, D.X., Lin, Z.X., “Kinetic modeling of hydroisomerization of C₈ aromatics(II) Mathematical expression of ray vector and its application”, J. Chem. Ind. Eng.(China), 3, 268-277(1985).(in Chinese)
7 Li, Z.H., Chen, D.Z., Zhuang, L., Hu, S.X., “RBF-MCSR approach as modeling technique for equipment of isomerization of xylene”, J. Chem. Ind. Eng.(China), 6, 627-632(2002).(in Chinese)
8 Yan, X., “Aromatic hydrocarbon isomerization process modeling based on adaptive artificial neural networks”, Control and Instruments in Chemical Industry, 33(5), 6-8(2006).
9 Vapnik, V., Statistical Learning Theory, John Wiley, New York(1998).
10 Vapnik, V., The Nature of statistical Learning Theory, Spring-Verlag, New York(1995).
11 Suykens, J. A.K., Vandewalle, J., “Least squares support vector machine classifiers”, Neural Processing Letters, 9, 293-300(1999).
12 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., 44(7), 2101-2105(2005).
13 Zhang, Y., Su, H.Y., Liu, R.L., Chu, J., “Fuzzy support vector regression model of 4CBA concentration of industrial PTA oxidation process”, Chin. J. Chem. Eng., 13(5), 642-648(2005).
14 Zheng, X., Qian, F., “Application of least squares support vector machine within evidence framework in PTA process”, J. Chem. Ind. Eng.(China), 57(7), 1612-1616(2006).(in Chinese)
15 Li, L., Su, H.Y., Chu, J., “Generalized predictive control with online least squares support vector machines”, Acta Automation Sinica, 33(11), 1182-1188(2007).
16 Suykens, J.A.K., Vandewalle, J., “Multiclass least squares support vector machines”, In:International Joint Conference on Neural Networks, Washington(1999).
17 Ljung, L., System Identification—Theory for the User, Prentice Hall PTR, Sebastopol(1999).

[1]	Anjun Liu, Jie Chen, Meng Guo, Chengmin Chen, Meihong Yang, Chao Yang. The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow[J]. 中国化学工程学报, 2023, 59(7): 51-60.
[2]	Dayang Wang, Ningde Jin, Lusheng Zhai, Yingyu Ren. Quantitative research of the liquid film characteristics in upward vertical gas, oil and water flows[J]. 中国化学工程学报, 2023, 54(2): 67-79.
[3]	Hongliang Qian, Hongzhou Tian, Guoqiang Yang, Gaodong Yang, Lei Li, Feng Zhang, Zheng Zhou, Weihua Huang, Yufu Chen, Zhibing Zhang. Microinterface intensification in hydrogenation and air oxidation processes[J]. 中国化学工程学报, 2022, 50(10): 292-300.
[4]	Anjun Liu, Jie Chen, Moshe Favelukis, Meng Guo, Meihong Yang, Chao Yang, Tao Zhang, Min Wang, Hao-yue Quan. External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow[J]. 中国化学工程学报, 2022, 41(1): 230-245.
[5]	Changjie Lu, Weiqiang Tang, Zijiang Dou, Peng Xie, Xiaofei Xu, Shuangliang Zhao. A reaction density functional theory study of solvent effects on keto-enol tautomerism and isomerization in pyruvic acid[J]. 中国化学工程学报, 2021, 29(3): 10-16.
[6]	Gabriel Khew Mun Hong, Mohd Azlan Hussain, Ahmad Khairi Abdul Wahab. Fuzzy logic controller implementation on a microbial electrolysis cell for biohydrogen production and storage[J]. 中国化学工程学报, 2021, 40(12): 149-159.
[7]	Jionghua Xiang, Litao Zhu, Zhenghong Luo. Application of kinetics and computational fluid dynamics in pinene isomerization[J]. 中国化学工程学报, 2020, 28(8): 2111-2120.
[8]	Lukuan Yang, Wenqi Zhong, Li Sun, Xi Chen, Yingjuan Shao. Dynamic optimization oriented modeling and nonlinear model predictive control of the wet limestone FGD system[J]. 中国化学工程学报, 2020, 28(3): 832-845.
[9]	Pengcheng Hu, Jingwei Zheng, Wei Jiang, Lijuan Zhong, Shufeng Zhou. Isomerization of n-pentane catalyzed by amide-AlCl₃-based ionic liquid analogs with various additives[J]. 中国化学工程学报, 2020, 28(1): 152-157.
[10]	Saba Golshan Shandi, Faramarz Doulati Ardejani, Fereydoun Sharifi. Assessment of Cu (II) removal from an aqueous solution by raw Gundelia tournefortii as a new low-cost biosorbent: Experiments and modelling[J]. 中国化学工程学报, 2019, 27(8): 1945-1955.
[11]	Danlei Chen, Xue Ma, Yiqing Luo, Yingjie Ma, Xigang Yuan. Synthesis of refrigeration system based on generalized disjunctive programming model[J]. Chinese Journal of Chemical Engineering, 2018, 26(8): 1613-1620.
[12]	Tao Yang, Yiqing Luo, Yingjie Ma, Xigang Yuan. Optimal synthesis of compression refrigeration system using a novel MINLP approach[J]. Chinese Journal of Chemical Engineering, 2018, 26(8): 1662-1669.
[13]	Jionghua Xiang, Zhenghong Luo. Study on the pinene isomerization catalyzed by TiM[J]. Chinese Journal of Chemical Engineering, 2018, 26(12): 2537-2541.
[14]	Marjan Farshadi, Cavus Falamaki. Ethylbenzene disproportionation and p-xylene selectivity enhancement in xylene isomerization using high crystallinity desilicated H-ZSM-5[J]. Chinese Journal of Chemical Engineering, 2018, 26(1): 116-126.
[15]	Mohammad Mesbah, Ebrahim Soroush, Mashallah Rezakazemi. Development of a least squares support vector machine model for prediction of natural gas hydrate formation temperature[J]. , 2017, 25(9): 1238-1248.

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

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价