Gaussian Process Model Identification Using Artificial Bee Colony Algorithm and Its Application to Modeling of Power Systems
Authors: Tomohiro Hachino, Hitoshi Takata, Shigeru Nakayama, Ichiro Iimura, Seiji Fukushima, Yasutaka Igarashi
Abstract:
This paper presents a nonparametric identification of continuous-time nonlinear systems by using a Gaussian process (GP) model. The GP prior model is trained by artificial bee colony algorithm. The nonlinear function of the objective system is estimated as the predictive mean function of the GP, and the confidence measure of the estimated nonlinear function is given by the predictive covariance of the GP. The proposed identification method is applied to modeling of a simplified electric power system. Simulation results are shown to demonstrate the effectiveness of the proposed method.
Keywords: Artificial bee colony algorithm, Gaussian process model, identification, nonlinear system, electric power system.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1092860
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[1] C. Z. Jin, K. Wada, K. Hirasawa and J. Murata, Identification of nonlinear continuous systems by using neural network compensator (in Japanese), IEEJ Trans. C, Vol. 114, No. 5, pp. 595–602, 1994.
[2] K. M. Tsang and S. A. Billings, Identification of continuous time nonlinear systems using delayed state variable filters, Int. J. Control, Vol. 60, No. 2, pp. 159–180, 1994.
[3] G. P. Liu and V. Kadirkamanathan, Stable sequential identification of continuous nonlinear dynamical systems by growing radial basis function networks, Int. J. Control, Vol. 65, No. 1, pp. 53–69, 1996.
[4] T. Hachino, I. Karube, Y. Minari and H. Takata, Continuous-time identification of nonlinear systems using radial basis function network model and genetic algorithm, Proc. of the 12th IFAC Symposium on System Identification, Vol. 2, pp. 787–792, 2001.
[5] T. Hachino and H. Takata, Identification of continuous-time nonlinear systems via local linear equations united by automatic choosing function and genetic algorithm, Proc. of the 14th World Congress of International Federation of Automatic Control, pp. 259–264, 1999.
[6] J. Kocijan, A. Girard, B. Banko and R. Murray-Smith, Dynamic systems identification with Gaussian processes, Mathematical and Computer Modelling of Dynamical Systems, Vol. 11, No. 4, pp. 411–424, 2005.
[7] T. Hachino and H. Takata, Identification of continuous-time nonlinear systems by using a Gaussian process model, IEEJ Trans. on Electrical and Electronic Engineering, Vol. 3, No. 6, pp. 620–628, 2008.
[8] A. Girard, C. E. Rasmussen, J. Q. Candela and R. Murray-Smith, Gaussian process priors with uncertain inputs -application to multiple-step ahead time series forecasting”, in Advances in Neural Information Processing Systems, Vol. 15, pp. 542–552, MIT Press, 2003.
[9] T. Hachino and V. Kadirkamanathan, Multiple Gaussian process models for direct time series forecasting, IEEJ Trans. on Electrical and Electronic Engineering, Vol. 6, No. 3, pp. 245–252, 2011.
[10] A. O’Hagan, Curve fitting and optimal design for prediction (with discussion), Journal of the Royal Statistical Society B, Vol. 40, pp. 1–42, 1978.
[11] C. K. I. Williams, Prediction with Gaussian processes: from Linear regression to linear prediction and beyond, in Learning and Inference in Graphical Models, Kluwer Academic Press, pp. 599–621, 1998.
[12] M. Seeger, Gaussian processes for machine learning, International Journal of Neural Systems, Vol. 14, No. 2, pp. 1–38, 2004.
[13] C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning, MIT Press, 2006.
[14] J. M. Wang, D. J. Fleet and A. Hertzmann, Gaussian process dynamical models for human motion, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 30, No. 2, pp. 283–298, 2008.
[15] B. Likar and J. Kocijan, Predictive control of a gas-liquid separation plant based on a Gaussian process model, Computers and Chemical Engineering, Vol. 31, No. 3, pp. 142–152, 2007.
[16] D. Karaboga and B. Basturk, On the performance of artificial bee colony (ABC) algorithm, Applied Soft Computing, Vol. 8, No. 1, pp. 687–697, 2008.
[17] I. Iimura and S. Nakayama, Search performance evaluation of artificial bee colony algorithm on high-dimensional function optimization (in Japanese), Trans. of the ISCIE, Vol. 24, No. 4, pp. 97–99, 2011.
[18] R. von Mises, Mathematical Theory of Probability and Statistics, Academic Press, 1964.
[19] H. Takata, An automatic choosing control for nonlinear systems, Proc. of the 35th IEEE CDC, pp. 3453–3458, 1996.