Multiple model approach to nonlinear system identification with an uncertain scheduling variable using em algorithm

Journal of Process Control

Volumn 23, Issue 10, 2013, Pages 1480-1496

  Chen, Lei ^a,b   Tulsyan, Aditya ^b   Huang, Biao ^b   Liu, Fei ^a  

^a JIANGNAN UNIVERSITY   (China)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Expectation maximization algorithm; Kalman smoother; Multiple models; Nonlinear process; Particle smoother; System identification

Indexed keywords

CONTINUOUS STIRRED TANK REACTOR; EXPECTATION - MAXIMIZATIONS; EXPECTATION-MAXIMIZATION ALGORITHMS; KALMAN SMOOTHER; MULTIPLE-MODEL APPROACHES; NONLINEAR PROCESS; PARTICLE SMOOTHERS; SIMULTANEOUS IDENTIFICATION;

DYNAMICS; IDENTIFICATION (CONTROL SYSTEMS); NONLINEAR DYNAMICAL SYSTEMS; SCHEDULING; TANKS (CONTAINERS);

ALGORITHMS;

EID: 84887078962     PISSN: 09591524     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jprocont.2013.09.013     Document Type: Article

References (38)

1. R.D. Nowak Nonlinear system identification Circuits, Systems, and Signal Processing 21 1 2002 109 122 (Pubitemid 34414650)
2. X. Hong, R.J. Mitchell, S. Chen, C.J. Harris, K. Li, and G.W. Irwin Model selection approaches for non-linear system identification: a review International Journal of Systems Science 39 10 2008 925 946
3. L. Ljung Prediction error estimation methods Circuits Systems Signal Processing 21 1 2002 11 21 (Pubitemid 34414643)
4. D.W. Marquardt An algorithm for least-squares estimation of nonlinear parameters Journal of the Society for Industrial and Applied Mathematics 11 2 1963 431 441
5. A. Kottas, M.D. Branco, and A.E. Gelfand A nonparametric Bayesian modeling approach for cytogenetic dosimetry Biometrics 58 3 2002 593 600 (Pubitemid 35001477)
6. M.N. Kashani, and S. Shahhosseini A methodology for modeling batch reactors using generalized dynamic neural networks Chemical Engineering Journal 159 1-3 2010 195 202
7. W. Yan, S. Hu, Y. Yang, F. Gao, and T. Chen Bayesian migration of Gaussian process regression for rapid process modeling and optimization Chemical Engineering Journal 166 3 2011 1095 1103
8. Z.M. Darus I, and A.M. Al-Khafaji A Non-parametric modelling of a rectangular flexible plate structure Engineering Applications of Artificial Intelligence 25 1 2012 94 106
9. J.J. Hopfield Neural networks and physical systems with emergent collective computational abilities Proceedings of the National Academy of Sciences of the United States of America 79 1982 2554 2558
10. C.E. Rasmussen, and C.K.I. Williams Gaussian Processes for Machine learning 2006 MIT Press Cambridge, MA, USA
11. A.J. Smola, and B. Schölkopf A tutorial on support vector regression Statistics and Computing 14 3 2004 199 222 (Pubitemid 39063488)
12. R.B. Gopaluni Nonlinear system identification under missing observations: the case of unknown model structure Journal of Process Control 20 3 2010 314 324
13. C. Fritsche, E. Ozkan, and F. Gustafsson Online EM algorithm for jump Markov systems 15th International Conference on Information Fusion Singapore 2012 1941 1946
14. A. Banerjee, Y. Arkun, B. Ogunnaike, and R. Pearson Estimation of nonlinear systems using linear multiple AIChE Journal 43 5 1997 1204 1226 (Pubitemid 127481052)
15. X. Jin, B. Huang, and D.S. Shook Multiple model LPV approach to nonlinear process identification with EM algorithm Journal of Process Control 21 1 2011 182 193
16. Y. Zhu, and Z. Xu A method of LPV model identification for control 17th IFAC World Congress Seoul, Korea, July 6-11 2008 5018 5023
17. Y. Zhao, B. Huang, H. Su, and J. Chu Prediction error method for identification of LPV models Journal of Process Control 22 1 2012 180 193
18. L. Ljung System Identification: Theory for the User 1987 Prentice Hall New Jersey
19. A.P. Dempster, N.M. Laird, and D.B. Rubin Maximum likelihood from incomplete data via the EM algorithm Journal of the Royal Statistical Society, Series B 39 1 1977 1 38
20. G.J. McLachlan, and T. Krishnan The EM Algorithm and Extensions, 2E 2008 John Wiley & Sons, Inc. Hoboken, NJ, USA
21. J. Wu On the convergence properties of the EM algorithm The Annals of Statistics 11 1 1983 95 103
22. A. Doucet, S. Godsill, and C. Andrieu On sequential Monte Carlo sampling methods for Bayesian filtering Statistics and Computing 10 3 2000 197 208
23. E. Cosme, J. Verron, P. Brasseur, J. Blum, and D. Auroux Smoothing problems in a Bayesian framework and their linear Gaussian solutions Monthly Weather Review 140 2 2012 683 695
24. N. Metropolis, and S. Ulam The Monte Carlo method Journal of the American Statistical Association 44 247 1949 335 341
25. M. Briers, A. Doucet, and S. Maskell Smoothing algorithms for state-space models Annals of Institute of Statistical Mathematics 62 1 2010 61 89
26. D. Karlis A cautionary note about the EM algorithm for finite exponential mixtures 2001 Department of Statistics, Athens University of Economics and Business Technical Report No 150
27. Z. Xu, J. Zhao, J. Qian, and Y. Zhu Nonlinear MPC using an identified LPV model Industrial and Engineering Chemistry Research 48 6 2009 3043 3051
28. Y. Zhu, H. Telkamp, J. Wang, and Q. Fu System identification using slow and irregular output samples Journal of Process Control 19 1 2009 58 67
29. J. Huang, G. Ji, Y. Zhu, and P. Van den Bosch Identification of multi-model LPV models with two scheduling variables Journal of Process Control 22 7 2012 1198 1208
30. S. Skogestad Dynamics and control of distillation columns - a tutorial introduction Chemical Engineering Research and Design 75 1997 539 562
31. R.E. Kalman A new approach to linear filtering and prediction problems Transactions of the ASME-Journal of Basic Engineering 82 Series D 1960 35 45
32. S. Särkkä, A. Vehtari, and J. Lampinen Time series prediction by Kalman smoother with cross-validated noise density Proceedings of the IEEE International Joint Conference on Neural Networks Budapest 2004 1653 1657 (Pubitemid 40011706)
33. A. Sage, and J. Melsa Estimation Theory with Applications to Communications and Control 1971 McGraw-Hill Book Company New York
34. M.P. Tarvainen, S.D. Georgiadis, P.O. Ranta-Aho, and P.a. Karjalainen Time-varying analysis of heart rate variability signals with a Kalman smoother algorithm Physiological Measurement 27 3 2006 225 239 (Pubitemid 43208587)
35. G. Poyiadjis, A. Doucet, and S.S. Singh Maximum likelihood parameter estimation in general state-space models using particle methods Proceedings of Joint Statistical Meeting USA 2005
36. M. Klaas, M. Briers, N. Freitas, A. de Doucet, S. Maskell, and D. Lang Fast particle smoothing: if I had a million particles Proceedings of the 23rd International Conference on Machine Learning Pittsburgh 2006
37. R.B. Gopaluni A particle filter approach to identification of nonlinear processes under missing observations The Canadian Journal of Chemical Engineering 86 6 2008 1081 1092
38. R. Douc, O. Cappé, and E. Moulines Comparison of resampling schemes for particle filtering Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis Zagreb, Croatia 2005