×

Partially-coupled nonlinear parameter optimization algorithm for a class of multivariate hybrid models. (English) Zbl 1510.93338

Summary: A key to the analysis and design of a dynamic system is to establish a suitable mathematical model of the system. This paper investigates the parameter optimization problem of a class of radial basis function-based multivariate hybrid models. Taking into account the high dimensions of the models and different forms of the parameters, the original identification model is separated into several regressive sub-identification models according to the characteristics of model outputs. Some auxiliary models are constructed to solve the unmeasurable noise terms in the information matrices. For the purpose of eliminating the redundant computation and to deal with the associate terms caused by the model decomposition, inspired by the coupling concept, a partially-coupled nonlinear parameter optimization algorithm is proposed for the multivariate hybrid models. Through the computational efficiency analysis and numerical simulation verification, it is shown that the proposed algorithm has low computational complexity and high parameter estimation accuracy.

MSC:

93E12 Identification in stochastic control theory
93C10 Nonlinear systems in control theory
93E10 Estimation and detection in stochastic control theory
62J02 General nonlinear regression
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ji, Y.; Kang, Z.; Liu, X. M., The data filtering based multiple-stage Levenberg-Marquardt algorithm for hammerstein nonlinear systems, Int. J. Robust Nonlinear Control, 31, 15, 7007-7025 (2021)
[2] Ding, F.; Xu, L.; Zhu, Q. M., Performance analysis of the generalised projection identification for time-varying systems, IET Control Theory Appl., 10, 18, 2506-2514 (2016)
[3] Chen, G. Y.; Gan, M.; Chen, C. L.P.; Li, H. X., Basis function matrix-based flexible coefficient autoregressive models: a framework for time series and nonlinear system modeling, IEEE Trans. Cybern., 51, 2, 614-623 (2021)
[4] Sersour, L.; Djamah, T.; Bettayeb, M., Nonlinear system identification of fractional wiener models, Nonlinear Dyn., 94, 4, 1493-1505 (2018)
[5] Ji, Y.; Kang, Z., Three-stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems, Int. J. Robust Nonlinear Control, 31, 3, 871-987 (2021) · Zbl 1525.93438
[6] Wang, J. W.; Ji, Y.; Zhang, C., Iterative parameter and order identification for fractional-order nonlinear finite impulse response systems using the key term separation, Int. J. Adapt. Control Signal Process., 35, 8, 1562-1577 (2021)
[7] Volna, E.; Jarusek, R.; Kotyrba, M.; Zacek, J., Training set fuzzification based on histogram to increase the performance of a neural network, Appl. Math. Comput., 398, 125994 (2021) · Zbl 1508.68301
[8] Zhang, G. P., Time series forecasting using a hybrid ARIMA and neural network model, Neurocomputing, 50, 159-175 (2003) · Zbl 1006.68828
[9] Babu, C. N.; Reddy, B. E., A moving-average filter based hybrid ARIMA-ANN model for forecasting time series data, Appl. Soft Comput., 23, 27-38 (2014)
[10] Panigrahi, S.; Behera, H. S., A hybrid ETS ANN model for time series forecasting, Eng. Appl. Artif. Intell., 66, 49-59 (2017)
[11] Xu, W. Q.; Peng, H.; Zeng, X. Y.; Zhou, F.; Tian, X. Y.; Peng, X. Y., Deep belief network-based AR model for nonlinear time series forecasting, Appl. Soft Comput., 77, 605-621 (2019)
[12] Shi, Z. Y.; Tamura, Y.; Ozaki, T., Nonlinear time series modelling with the radial basis function-based state-dependent autoregressive model, Int. J. Syst. Sci., 30, 7, 717-727 (1999) · Zbl 1113.62351
[13] Gan, M.; Li, H. X.; Peng, H., A variable projection approach for efficient estimation of RBF-ARX model, IEEE Trans. Cybern., 45, 3, 476-485 (2015)
[14] Ding, F.; Liu, G.; Liu, X. P., Parameter estimation with scarce measurements, Automatica, 47, 8, 1646-1655 (2011) · Zbl 1232.62043
[15] Article number: 1687814017730003
[16] Ayala, H. V.H.; Habineza, D.; Rakotondrabe, M.; Coelho, L. D., Nonlinear black-box system identification through coevolutionary algorithms and radial basis function artificial neural networks, Appl. Soft Comput., 87, 105990 (2020)
[17] Peng, H.; Ozaki, T.; Haggan-Ozaki, V.; Toyoda, Y., A parameter optimization method for radial basis function type models, IEEE Trans. Neural Netw., 14, 2, 432-438 (2003)
[18] Zeng, X. Y.; Peng, H.; Zhou, F., A regularized SNPOM for stable parameter estimation of RBF-AR(X) model, IEEE Trans. Neural Netw. Learn. Syst., 29, 4, 779-791 (2018)
[19] Gan, M.; Guan, Y.; Chen, G. Y.; Chen, C. L.P., Recursive variable projection algorithm for a class of separable nonlinear models, IEEE Trans. Neural Netw. Learn. Syst. (2021)
[20] Gan, M.; Chen, G. Y.; Chen, L.; Chen, C. L.P., Term selection for a class of separable nonlinear models, IEEE Trans. Neural Netw. Learn. Syst., 31, 2, 445-451 (2020)
[21] Zhou, Y. H., Modeling nonlinear processes using the radial basis function-based state-dependent autoregressive models, IEEE Signal Process. Lett., 27, 1600-1604 (2020)
[22] Kothari, K.; Mehta, U., Fractional-order two-input two-output process identification based on haar operational matrix, Int. J. Syst. Sci., 52, 7, 1373-1385 (2020) · Zbl 1483.93085
[23] Ding, F.; Liu, Y. J.; Bao, B., Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems, Proc. Inst. Mech. Eng., Part I, 226, 1, 43-55 (2012)
[24] Liu, X. M.; Fan, Y. M., Maximum likelihood extended gradient-based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable-gain nonlinearity, Int. J. Robust Nonlinear Control, 31, 9, 4017-4036 (2021) · Zbl 1526.93264
[25] Xu, L.; Chen, L.; Xiong, W. L., Parameter estimation and controller design for dynamic systems from the step responses based on the newton iteration, Nonlinear Dyn., 79, 3, 2155-2163 (2015)
[26] Xu, L., The damping iterative parameter identification method for dynamical systems based on the sine signal measurement, Signal Process., 120, 660-667 (2016)
[27] Li, M. H.; Liu, X. M., The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique, Signal Process., 147, 23-34 (2018)
[28] Li, M. H.; Liu, X. M., Iterative parameter estimation methods for dual-rate sampled-data bilinear systems by means of the data filtering technique, IET Control Theory Appl., 15, 9, 1230-1245 (2021)
[29] Ding, F.; Chen, H. B., A hierarchical least squares identification algorithm for hammerstein nonlinear systems using the key term separation, J. Frankl. Inst., 355, 8, 3737-3752 (2018) · Zbl 1390.93818
[30] Xu, L.; Xiong, W. L.; Alsaedi, A., Hierarchical parameter estimation for the frequency response based on the dynamical window data, Int. J. Control Autom. Syst., 16, 4, 1756-1764 (2018)
[31] Li, M. H.; Liu, X. M., Maximum likelihood hierarchical least squares-based iterative identification for dual-rate stochastic systems, Int. J. Adapt. Control Signal Process., 35, 2, 240-261 (2021)
[32] Wang, L. J.; Ji, Y.; Yang, H. L., Decomposition-based multiinnovation gradient identification algorithms for a special bilinear system based on its input-output representation, Int. J. Robust Nonlinear Control, 30, 9, 3607-3623 (2020) · Zbl 1466.93172
[33] Wang, L. J.; Ji, Y.; Wan, L. J.; Bu, N., Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise, J. Frankl. Inst., 356, 16, 10102-10122 (2019) · Zbl 1423.93371
[34] Ji, Y.; Zhang, C.; Kang, Z.; Yu, T., Parameter estimation for block-oriented nonlinear systems using the key term separation, Int. J. Robust Nonlinear Control, 30, 9, 3727-3752 (2020) · Zbl 1466.93161
[35] Ding, F., Coupled-least-squares identification for multivariable systems, IET Control Theory Appl., 7, 1, 68-79 (2013)
[36] Li, M. H.; Liu, X. M., The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle, Int. J. Adapt. Control Signal Process., 33, 7, 1189-1211 (2019) · Zbl 1425.93284
[37] Ding, F.; Xu, L.; Alsaadi, F. E., Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique, IET Control Theory Appl., 12, 7, 892-899 (2018)
[38] Priestley, M. B., State dependent models: a general approach to nonlinear time series analysis, J. Time Ser. Anal., 1, 1, 57-71 (1980) · Zbl 0496.62076
[39] Konishi, S.; Kitagawa, G., Information Criteria and Statistical Modeling (2008), Springer: Springer Berlin · Zbl 1172.62003
[40] Mao, K. Z., RBF neural network center selection based on fisher ratio class separability measure, IEEE Trans. Neural Netw., 13, 5, 1211-1217 (2002)
[41] Feng, R. B.; Leung, C. S.; Constantinides, A. G., LCA based RBF training algorithm for the concurrent fault situation, Neurocomputing, 191, 341-351 (2016)
[42] Ding, F.; Wang, F. F., Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique, IET Control Theory Appl., 11, 3, 390-400 (2017)
[43] Xu, L.; Song, G. L., A recursive parameter estimation algorithm for modeling signals with multi-frequencies, Circuits Syst. Signal Process., 39, 8, 4198-4224 (2020) · Zbl 1452.94026
[44] Ji, Y.; Kang, Z.; Zhang, C., Two-stage gradient-based recursive estimation for nonlinear models by using the data filtering, Int. J. Control Autom. Syst., 19, 8, 2706-2715 (2021)
[45] Fan, Y. M.; Liu, X. M., Two-stage auxiliary model gradient-based iterative algorithm for the input nonlinear controlled autoregressive system with variable-gain nonlinearity, Int. J. Robust Nonlinear Control, 30, 14, 5492-5509 (2020) · Zbl 1465.93041
[46] Xu, L., Separable multi-innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems, Int. J. Adapt. Control Signal Process., 34, 7, 937-954 (2020) · Zbl 1469.93111
[47] Xu, L.; Chen, F. Y.; Hayat, T., Hierarchical recursive signal modeling for multi-frequency signals based on discrete measured data, Int. J. Adapt. Control Signal Process., 35, 5, 676-693 (2021)
[48] Li, M. H.; Liu, X. M., Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique, Int. J. Control Autom. Syst., 18, 6, 1581-1592 (2020)
[49] Wang, D. Q.; Zhang, S.; Gan, M.; Qiu, J. L., A novel EM identification method for hammerstein systems with missing output data, IEEE Trans. Ind. Inf., 16, 4, 2500-2508 (2020)
[50] Wang, D. Q.; Fan, Q. H.; Ma, Y., An interactive maximum likelihood estimation method for multivariable hammerstein systems, J. Frankl. Inst., 357, 17, 12986-13005 (2020) · Zbl 1454.93285
[51] Wang, D. Q.; Yan, Y. R.; Liu, Y. J.; Ding, J. H., Model recovery for hammerstein systems using the hierarchical orthogonal matching pursuit method, J. Comput. Appl. Math., 345, 135-145 (2019) · Zbl 1398.93349
[52] Wang, D. Q.; Li, L. W.; Ji, Y.; Yan, Y. R., Model recovery for hammerstein systems using the auxiliary model based orthogonal matching pursuit method, Appl. Math. Model., 54, 537-550 (2018) · Zbl 1480.93431
[53] Xu, L., Hierarchical newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses, Int. J. Syst. Sci., 50, 1, 141-151 (2019) · Zbl 1482.93661
[54] Ding, J. L.; Zhang, W. H., Finite-time adaptive control for nonlinear systems with uncertain parameters based on the command filters, Int. J. Adapt. Control Signal Process., 35, 9, 1754-1767 (2021)
[55] Ma, P.; Wang, L., Filtering-based recursive least squares estimation approaches for multivariate equation-error systems by using the multiinnovation theory, Int. J. Adapt. Control Signal Process., 35, 9, 1898-1915 (2021)
[56] Mao, Y. W.; Liu, S.; Liu, J. F., Robust economic model predictive control of nonlinear networked control systems with communication delays, Int. J. Adapt. Control Signal Process., 34, 5, 614-637 (2020) · Zbl 1467.93095
[57] Article number: 109663 · Zbl 1478.93081
[58] Article number: 109034 · Zbl 1447.93350
[59] Chen, J.; Shen, Q. Y.; Ma, J. X.; Liu, Y. J., Stochastic average gradient algorithm for multirate FIR models with varying time delays using self-organizing maps, Int. J. Adapt. Control Signal Process., 34, 7, 955-970 (2020) · Zbl 1469.93108
[60] Xiong, W.; Jia, X.; Yang, D.; Ai, M.; Li, L.; Wang, S., DP-linknet: a convolutional network for historical document image binarization, KSII Trans. Internet Inf. Syst., 15, 5, 1778-1797 (2021)
[61] Article number: 13
[62] Article number: 102570
[63] Wang, G. H.; Zhang, T. L.; Dai, Y. Y.; Lin, J. S.; Chen, L., A serial-parallel self-attention network joint with multi-scale dilated convolution, IEEE Access, 9, 5, 71909-71919 (2021)
[64] Article number: 106134
[65] Article number: 1596
[66] Article number: 1058
[67] Pan, J.; Jiang, X.; Wan, X. K.; Ding, W., A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems, Int. J. Control Autom. Syst., 15, 3, 1189-1197 (2017)
[68] Pan, J.; Ma, H.; Zhang, X., Recursive coupled projection algorithms for multivariable output-error-like systems with coloured noises, IET Signal Proc., 14, 7, 455-466 (2020)
[69] Ma, H.; Zhang, X.; Liu, Q. Y., Partiallly-coupled gradient-based iterative algorithms for multivariable output-error-like systems with autoregressive moving average noises, IET Control Theory Appl., 14, 17, 2613-2627 (2020)
[70] Ma, H.; Pan, J., Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems, IET Control Theory Appl., 13, 18, 3040-3051 (2019)
[71] Han, H. G.; Liu, H. X.; Li, J. M.; Qiao, J. F., Cooperative fuzzy-neural control for wastewater treatment process, IEEE Trans. Ind. Inf., 17, 9, 5971-5981 (2021)
[72] Han, H. G.; Liu, Z.; Liu, H. X.; Qiao, J. F., Knowledge-data-driven model predictive control for a class of nonlinear systems, IEEE Trans. Syst. Man Cybern., 51, 7, 4492-4504 (2021)
[73] Han, H. G.; Zhang, L.; Liu, H. X.; Yang, C. L.; Qiao, J. F., Intelligent optimal control system with flexible objective functions and its applications in wastewater treatment process, IEEE Trans. Syst. Man Cybern., 51, 6, 3464-3476 (2021)
[74] Bu, N.; Pang, J. X.; Deng, M., Robust fault tolerant tracking control for the multi-joint manipulator based on operator theory, J. Frankl. Inst., 357, 5, 2696-2714 (2020) · Zbl 1451.93068
[75] Pan, J.; Li, W.; Zhang, H. P., Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control, Int. J. Control Autom. Syst., 16, 6, 2878-2887 (2018)
[76] Cao, Y.; Ma, L. C.; Xiao, S., Standard analysis for transfer delay in CTCS-3, Chin. J. Electron., 26, 5, 1057-1063 (2017)
[77] Cao, Y.; Wen, J. K.; Ma, L. C., Tracking and collision avoidance of virtual coupling train control system, Alexandria Eng. J., 60, 2, 2115-2125 (2021)
[78] Cao, Y.; Wen, J. K.; Ma, L. C., Tracking and collision avoidance of virtual coupling train control system, Future Gener. Comput. Syst., 120, 76-90 (2021)
[79] Su, S.; Wang, X. K.; Cao, Y.; Yin, J. T., An energy-efficient train operation approach by integrating the metro timetabling and eco-driving, IEEE Trans. Intell. Transp. Syst., 21, 10, 4252-4268 (2020)
[80] Su, S.; Tang, T.; Xun, J.; Cao, F.; Wang, Y. H., Design of running grades for energy-efficient train regulation: a case study for Beijing Yizhuang line, IEEE Intell. Transp. Syst. Mag., 13, 2, 189-200 (2021)
[81] Cao, Y.; Wang, Z.; Liu, F.; Li, P.; Xie, G., Bio-inspired speed curve optimization and sliding mode tracking control for subway trains, IEEE Trans. Veh. Technol., 68, 7, 6331-6342 (2019)
[82] Cao, Y.; Sun, Y. K.; Xie, G.; Wen, T., Fault diagnosis of train plug door based on a hybrid criterion for IMFs selection and fractional wavelet package energy entropy, IEEE Trans. Veh. Technol., 68, 8, 7544-7551 (2019)
[83] Zhao, Z. Y.; Wang, X. Y.; Yao, P.; Bai, Y. T., A health performance evaluation method of multirotors under wind turbulence, Nonlinear Dyn., 102, 3, 1701-1715 (2020)
[84] Golub, G. H.; Loan, C. F.V., Matrix Computations (1996), Johns Hopkins University Press: Johns Hopkins University Press Baltimore, MD · Zbl 0865.65009
[85] Article number: 149
[86] Lin, J.; Li, Y.; Yang, G. C., FPGAN: face de-identification method with generative adversarial networks for social robots, Neural Netw., 133, 132-147 (2021)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.