Gaussian Process Model Identification Using Artificial Bee Colony Algorithm and Its Application to Modeling of Power Systems
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:67275", author = "Tomohiro Hachino and Hitoshi Takata and Shigeru Nakayama and Ichiro Iimura and Seiji Fukushima and Yasutaka Igarashi", title = "Gaussian Process Model Identification Using Artificial Bee Colony Algorithm and Its Application to Modeling of Power Systems", 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.", volume = "8", number = "2", pages = "441-6", }
