Adaptive architecture of polynomial artificial neural network to forecast nonlinear time series

There are two important ways in which artificial neural networks are applied for dynamic system identification: preprocessing the training values, and adapting the architecture of the network. The article describes an adaptive process of the architecture of Polynomial Artificial Neural Network (PANN) using a genetic algorithm (GA) to improve the learning process. The optimal structure is obtained without previous knowledge of the behavior of the system to be identified. Due to the nature of the structure of PANN, it is possible to extract the necessary information of the nonlinear time series in order to minimize the training error. The importance of this work lies on adapting the architecture of PANN and processing the necessary inputs to minimize this error at the same time. The training error is compared with other networks used in the field to forecast chaotic time series.

[1]  Sheng Chen,et al.  Representations of non-linear systems: the NARMAX model , 1989 .

[2]  Stephen A. Billings,et al.  International Journal of Control , 2004 .

[3]  Kishan G. Mehrotra,et al.  Forecasting the behavior of multivariate time series using neural networks , 1992, Neural Networks.

[4]  I. J. Leontaritis,et al.  Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .

[5]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[6]  J. Stark,et al.  Recursive prediction of chaotic time series , 1993 .

[7]  Joydeep Ghosh,et al.  Approximation of multivariate functions using ridge polynomial networks , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.

[8]  W.C. Mead,et al.  Using CNLS-net to predict the Mackey-Glass chaotic time series , 1991, IJCNN-91-Seattle International Joint Conference on Neural Networks.

[9]  Lennart Ljung.  PAC-learning and asymptotic system identification theory , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[10]  Y. Shin.  Modified Bernstein polynomials and their connectionist interpretation , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[11]  C.J.S. deSilva,et al.  A modified probabilistic neural network (PNN) for nonlinear time series analysis , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[12]  John Y. Cheung,et al.  Polynomial and standard higher order neural network , 1993, IEEE International Conference on Neural Networks.

[13]  Dale E. Nelson,et al.  Extrapolation of Mackey-Glass data using Cascade Correlation , 1992, Simul..

[14]  Mark A. Franklin,et al.  A Learning Identification Algorithm and Its Application to an Environmental System , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  P. Kumar,et al.  Learning dynamical systems in a stationary environment , 1998 .

[16]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[17]  Stéphane Canu,et al.  The Wavelet Transform for Time Series Prediction , 1998 .

[18]  A. G. Ivakhnenko,et al.  Polynomial Theory of Complex Systems , 1971, IEEE Trans. Syst. Man Cybern..

[19]  Sheng Chen,et al.  Recursive prediction error parameter estimator for non-linear models , 1989 .

[20]  Vincenzo Piuri,et al.  Experimental neural networks for prediction and identification , 1996 .

[21]  H. G. González-Hernández,et al.  Analysis of the dynamics of an underactuated robot: the forced pendubot , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[22]  Robert J. Marks,et al.  Electric load forecasting using an artificial neural network , 1991 .