Sains Malaysiana 47(3)(2018): 635–643

http://dx.doi.org/10.17576/jsm-2018-4703-25

Parallel Based Support Vector Regression for Empirical Modeling of Nonlinear Chemical Process Systems

(Regresi Vektor Sokongan Berdasarkan Selari untuk Pemodelan Empirikal Sistem Proses Kimia Nonlinear)

HASLINDA ZABIRI*, RAMASAMY MARAPPAGOUNDER & NASSER M. RAMLI

Chemical Engineering Department, Universiti Teknologi PETRONAS, 32610 Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia

Diserahkan: 7 Mac 2017/Diterima: 26 September 2017

ABSTRACT

In this paper, a support vector regression (SVR) using radial basis function (RBF) kernel is proposed using an integrated parallel linear-and-nonlinear model framework for empirical modeling of nonlinear chemical process systems. Utilizing linear orthonormal basis filters (OBF) model to represent the linear structure, the developed empirical parallel model is tested for its performance under open-loop conditions in a nonlinear continuous stirred-tank reactor simulation case study as well as a highly nonlinear cascaded tank benchmark system. A comparative study between SVR and the parallel OBF-SVR models is then investigated. The results showed that the proposed parallel OBF-SVR model retained the same modelling efficiency as that of the SVR, whilst enhancing the generalization properties to out-of-sample data.

Keywords: Empirical modeling; linear and nonlinear models; nonlinear system; OBF; SVR

ABSTRAK

Di dalam kertas ini, sebuah regresi vektor sokongan (SVR) yang menggunakan fungsi asas jejarian (RBF) dicadangkan menggunakan sebuah model rangka kerja linear dan tidak linear selari bersepadu untuk pemodelan empirik sistem pemprosesan kimia tidak linear. Dengan menggunakan model penapis asas ortonormal (OBF) untuk mewakili struktur linear, model selari empirik yang terbentuk seterusnya diuji prestasinya di bawah keadaan kitaran-terbuka dalam sebuah kajian kes simulasi reaktor tangki aduk berterusan (CSTR) yang tidak selari dan juga sistem penanda aras tangka sebaran tidak linear tertinggi. Sebuah kajian perbandingan antara model SVR dan juga model OBF-SVR selari kemudiannya dikaji dengan lebih terperinci. Keputusan menunjukkan bahawa model OBF-SVR selari yang dicadang juga telah mengekalkan kecekapan pemodelan yang sama seperti SVR, di samping memperkukuh ciri generalisasi terhadap data luaran sampel.

Kata kunci: Model linear dan tidak linear; OBF; pemodelan empirik; sistem tidak linear; SVR

RUJUKAN

Babuška, R. & Verbruggen, H. 2003. Neuro-fuzzy methods for nonlinear system identification. Annual Reviews in Control 27(1): 73-85.

Beyhan, S. & Alci, M. 2010. Fuzzy functions based Arx model and new fuzzy basis function models for nonlinear system identification. Applied Soft Computing 10(2): 439-444.

Billings, S.A. & Wei, H.L. 2005. A new class of wavelet networks for nonlinear system identification. IEEE Transactions on Neural Networks 16(4): 862-874.

Castillo, F., Marshall, K., Green, J. & Kordon, A. 2003. A methodology for combining symbolic regression and design of experiments to improve empirical model building. Paper Presented at the Genetic and Evolutionary Computation Conference - GECCO. Springer: Berlin/Heidelberg. pp. 212-212.

Cheng, Y. & Hu, J. 2012. Nonlinear system identification based on Svr with quasi-linear kernel. IEEE International Joint Conference on Neural Networks (IJCNN). pp.1-8.

Cherkassky, V. & Ma, Y. 2004. Practical selection of Svm parameters and noise estimation for Svm regression. Neural Networks 17(1): 113-126.

Crone, S.F., Guajardo, J. & Weber, R. 2006. The impact of preprocessing on support vector regression and neural networks in time series prediction. Proceedings of the International Conference on Data Mining, Last Vegas. pp. 37-44.

Himmelblau, D.M. 2008. Accounts of experiences in the application of artificial neural networks in chemical engineering. Industrial & Engineering Chemistry Research 47(16): 5782-5796.

Iplikci, S. 2010. Support vector machines based neuro-fuzzy control of nonlinear systems. Neurocomputing 73(10): 2097-2107.

Kordon, A.K. 2004. Hybrid intelligent systems for industrial data analysis. International Journal of Intelligent Systems 19(4): 367-383.

Lennox, B., Montague, G.A., Frith, A.M., Gent, C. & Bevan, V. 2001. Industrial application of neural networks - an investigation. Journal of Process Control 11(5): 497-507.

Lin, S., Zhang, S., Qiao, J., Liu, H. & Yu, G. 2008. A parameter choosing method of Svr for time series prediction. In Young Computer Scientists, 2008. ICYCS 2008. The 9th International Conference for IEEE. pp. 130-135.

Liu, Y., Wang, H., Yu, J. & Li, P. 2010. Selective recursive kernel learning for online identification of nonlinear systems with Narx form. Journal of Process Control 20(2): 181-194.

Ljung, L. 2010. Perspectives on system identification. Annual Reviews in Control 34(1): 1-12.

Lu, Z. & Sun, J. 2009. Non-Mercer hybrid kernel for linear programming support vector regression in nonlinear systems identification. Applied Soft Computing 9(1): 94-99.

Lu, Z., Sun, J. & Butts, K.R. 2009. Linear programming support vector regression with wavelet kernel: A new approach to nonlinear dynamical systems identification. Mathematics and Computers in Simulation 79(7): 2051-2063.

Mahmoodi, S., Montazeri, A., Poshtan, J., Jahed-Motlagh, M. & Poshtan, M. 2007. Volterra-Laguerre modeling for Nmpc. In Signal Processsing and Its Applications, 2007, ISSPA 2007, 9th International Symposium on IEEE. pp. 1-4.

Nelles, O. 2013. Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models. New York: Springer Science & Business Media.

Nørgård, P.M., Ravn, O., Poulsen, N.K. & Hansen, L.K. 2000. Neural Networks for Modelling and Control of Dynamic Systems-a Practitioner's Handbook. Location: Publisher.

Ratcliffe, S.J. & Shults, J. 2008. Geeqbox: A Matlab toolbox for generalized estimating equations and quasi-least squares. Journal of Statistical Software 25(14): 1-14.

Shirzad, A., Tabesh, M. & Farmani, R. 2014. A comparison between performance of support vector regression and artificial neural network in prediction of pipe burst rate in water distribution networks. KSCE Journal of Civil Engineering 18(4): 941-948.

Smola, A.J. & Schölkopf, B. 2004. A tutorial on support vector regression. Statistics and Computing 14(3): 199-222.

Suganyadevi, M.V. & Babulal, C.K. 2014. Support vector regression model for the prediction of loadability margin of a power system. Applied Soft Computing 24: 304-315.

Tötterman, S. & Toivonen, H.T. 2009. Support vector method for identification of Wiener models. Journal of Process Control 19(7): 1174-1181.

Tufa, L.D., Ramasamy, M. & Shuhaimi, M. 2011. Improved method for development of parsimonious orthonormal basis filter models. Journal of Process Control 21(1): 36-45.

Wang, X., Dong, J., Hang, Y. & Du, Z. 2013. Identif‍ication of nonlinear system via Svr optimized by particle swarm algorithm. Journal of Theoretical & Applied Information Technology 48(2): 967-972.

Wigren, T. 2006. Recursive prediction error identif‍ication and scaling of non-linear state space models using a restricted black box parameterization. Automatica 42(1): 159-168.

Wigren, T. & Schoukens, J. 2013. Three free data sets for development and benchmarking in nonlinear system identification. In IEEE Control Conference (ECC), 2013 European. pp. 2933-2938.

Yao, X.J., Panaye, A., Doucet, J.P., Zhang, R.S., Chen, H.F., Liu, M.C., Hu, Z.D. & Fan, B.T. 2004. Comparative study of Qsar/Qspr correlations using support vector machines, radial basis function neural networks, and multiple linear regression. Journal of Chemical Information and Computer Sciences 44(4): 1257-1266.

Zabiri, H., Ramasamy, M., Tufa, L.D. & Maulud, A. 2013. Integrated Obf-Nn models with enhanced extrapolation capability for nonlinear systems. Journal of Process Control 23(10): 1562-1566.

*Pengarang untuk surat menyurat; email: haslindazabiri@utp.edu.my