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Identification of Wiener model with internal noise using a cubic spline approximation-Bayesian composite quantile regression algorithm. (English) Zbl 1432.93364

Summary: A cubic spline approximation-Bayesian composite quantile regression algorithm is proposed to estimate parameters and structure of the Wiener model with internal noise. Firstly, an ARX model with a high order is taken to represent the linear block; meanwhile, the nonlinear block (reversibility) is approximated by a cubic spline function. Then, parameters are estimated by using the Bayesian composite quantile regression algorithm. In order to reduce the computational burden, the Markov Chain Monte Carlo algorithm is introduced to calculate the expectation of parameters’ posterior distribution. To determine the structure order, the Final Output Error and the Akaike Information Criterion are used in the nonlinear block and the linear block, respectively. Finally, a numerical simulation and an industrial case verify the effectiveness of the proposed algorithm.

MSC:

93E12 Identification in stochastic control theory
93E10 Estimation and detection in stochastic control theory
65C05 Monte Carlo methods
65D07 Numerical computation using splines
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[1] Salhi, H.; Kamoun, S.; Essounbouli, N.; Hamzaoui, A., Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models, International Journal of Control, 89, 3, 611-622 (2016) · Zbl 1332.93079 · doi:10.1080/00207179.2015.1088964
[2] Hamzaoui, H.; Sheng, C., Modeling of complex-valued Wiener systems using B-spline neural network, Neural Networks, 22, 5, 818-825 (2011)
[3] Li, S.; Ge, Y.; Shi, Y., Enhanced oil recovery for ASP flooding based on biorthogonal spatial-temporal Wiener modeling and iterative dynamic programming, Complexity, 2018, 1-19 (2018) · Zbl 1407.93069 · doi:10.1155/2018/9248161
[4] Tan, Q. Y.; Gao, H. L.; Chen, X., Wiener structure based model identification for an electronic throttle body, Proceedings of the 13th IEEE International Conference on Control & Automation
[5] Xu, X.; Bai, B.; Qian, F., Identification of Wiener model based on improved differential evolution (SADE) algorithm, Journal of System Simulation, 28, 1, 147-153 (2016)
[6] Xu, X.; Wang, F.; Qian, F., Support vector machine and higher-order cumulants based blind identification for non-linear Wiener models, IET Signal Processing, 12, 6, 761-769 (2018) · doi:10.1049/iet-spr.2017.0384
[7] Li, J.; Li, X., Particle swarm optimization iterative identification algorithm and gradient iterative identification algorithm for Wiener systems with colored noise, Complexity, 2018 (2018) · Zbl 1398.93346 · doi:10.1155/2018/7353171
[8] Kazemi, M.; Arefi, M. M., A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems, ISA Transactions, 67, 382-388 (2017) · doi:10.1016/j.isatra.2016.12.002
[9] Guo, J.; Wang, L. Y.; Yin, G.; Zhao, Y.; Zhang, J.-F., Identification of Wiener systems with quantized inputs and binary-valued output observations, Automatica, 78, 280-286 (2017) · Zbl 1357.93101 · doi:10.1016/j.automatica.2016.12.034
[10] Lamia, S.; Djamah, T.; Hammar, K.; Bettayeb, M., Wiener system identification using polynomial nonlinear state space model, Proceedings of the 3rd International Conference on Control, Engineering & Information Technology (CEIT)
[11] Risuleo, R. S.; Lindsten, F.; Hjalmarsson, H., Semi-parametric kernel-based identification of Wiener systems, Proceedings of the 2018 IEEE Conference on Decision and Control (CDC)
[12] Al-Dhaifallah, M., Twin support vector machine method for identification of Wiener models, Mathematical Problems in Engineering, 2015, 2, 1-7 (2015) · Zbl 1395.62287 · doi:10.1155/2015/125868
[13] Lindsten, F.; Schön, T. B.; Jordan, M. I., Bayesian semiparametric Wiener system identification, Automatica, 49, 7, 2053-2063 (2013) · Zbl 1364.93831 · doi:10.1016/j.automatica.2013.03.021
[14] Jing, S.; Pan, T.; Li, Z., Variable knot-based spline approximation recursive Bayesian algorithm for the identification of Wiener systems with process noise, Nonlinear Dynamics, 90, 4, 2293-2303 (2017) · Zbl 1393.93031 · doi:10.1007/s11071-017-3803-8
[15] Li, J.; Xiong, Q.; Feng, L., Correlation analysis method based SISO neuro-fuzzy Wiener model, Journal of Process Control, 58, 73-89 (2017) · doi:10.1016/j.jprocont.2017.08.002
[16] Zhang, B.; Mao, Z., A robust adaptive control method for Wiener nonlinear systems, International Journal of Robust and Nonlinear Control, 27, 3, 434-460 (2017) · Zbl 1355.93097 · doi:10.1002/rnc.3580
[17] Liang, S. L.; Li, X. W.; Wang, J. D., Advanced Remote Sensing: Terrestrial Information Extraction and Applications (2012), Cambridge, MA, USA: Elsevier/Academic Press, Cambridge, MA, USA
[18] Xu, W.; Chen, W.; Liang, Y., Feasibility study on the least square method for fitting non-Gaussian noise data, Physica A: Statistical Mechanics and its Applications, 492, 1917-1930 (2018) · doi:10.1016/j.physa.2017.11.108
[19] Bang, S.; Eo, S.-H.; Jhun, M.; Cho, H. J., Composite kernel quantile regression, Communications in Statistics-Simulation and Computation, 46, 3, 2228-2240 (2015) · Zbl 1364.62088 · doi:10.1080/03610918.2015.1039133
[20] Lim, Y.; Oh, H.-S., Variable selection in quantile regression when the models have autoregressive errors, Journal of the Korean Statistical Society, 43, 4, 513-530 (2014) · Zbl 1304.62097 · doi:10.1016/j.jkss.2014.07.002
[21] Kozubowski, T. J.; Podgórski, K., Asymmetric Laplace distributions, Mathematical Scientist, 25, 1, 37-46 (2000) · Zbl 0961.60026
[22] Bleik, J. M., Fully Bayesian estimation of simultaneous regression quantiles under asymmetric laplace distribution specification, Journal of Probability and Statistics, 2, 1-12 (2019) · Zbl 1431.62165
[23] Yu, K.; Moyeed, R. A., Bayesian quantile regression, Statistics and Probability Letters, 40, 1, 37-40 (2001)
[24] Zou, H.; Yuan, M., Composite quantile regression and the oracle model selection theory, The Annals of Statistics, 36, 3, 1108-1126 (2008) · Zbl 1360.62394 · doi:10.1214/07-aos507
[25] Fan, Y.; Tang, M.; Tian, M., Composite quantile regression for varying-coefficient single-index models, Communications in Statistics-Theory and Methods, 45, 10, 3027-3047 (2016) · Zbl 1342.62059 · doi:10.1080/03610926.2014.894069
[26] Li, W.; Peng, C.; Zhou, X., Application of the ecosystem model and Markov chain Monte Carlo for parameter estimation and productivity prediction, Ecosphere, 6, 12, 1-15 (2015) · doi:10.1890/es15-00034.1
[27] Tian, Y.; Lian, H.; Tian, M., Bayesian composite quantile regression for linear mixed-effects models, Communications in Statistics-Theory and Methods, 46, 15, 7717-7731 (2016) · Zbl 1376.62025 · doi:10.1080/03610926.2016.1161798
[28] Liu, M.; Xiao, Y.; Ding, R., Iterative identification algorithm for Wiener nonlinear systems using the Newton method, Applied Mathematical Modelling, 37, 9, 6584-6591 (2013) · Zbl 1438.93229 · doi:10.1016/j.apm.2013.01.025
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