Yuji Kajitani

Self generating radial basis function as neuro-fuzzy model and its application to nonlinear prediction of chaotic time series

The authors propose a self-generating algorithm for radial basis functions to automatically determine the minimal number of basis functions to achieve the specified model error. This model is also regarded as a multilayered neural network or fuzzy model of class C/sup infinity /. The self-generating algorithm consists of two processes: model parameter tuning by the gradient method for a fixed number of rules, and a basis function generation procedure by which a new basis function is generated in such a way that the center is located at the point where maximal inference error takes place in the input space, when the effect of parameter tuning is diminished. A numerical example shows that the algorithm can achieve the specified model error with fewer basis functions than other methods by which only coefficients of the basis functions are tuned. The method is applied to the nonlinear prediction of optical chaotic time series.<<ETX>>

Developing tools and methods for applications incorporating neuro, fuzzy and chaos technology

Abstract In recent years, intelligent industrial systems and consumer electronic products are widely and intensively developed. Fuzzy logic, neural network, and neuro & fuzzy technology which integrates these approaches are now regarded as an effective method to realize such intelligent features. Furthermore, a novel paradigm, “ chaos engineering ”, is now expected to be another key technology for various applications such as nonlinear prediction of time series, diagnosis for complex systems and comfortable home appliances. In this paper, a review of the fuzzy boom in consumer electronics market in Japan is presented, and the research projects, developing tools, and applications by Sanyo Electric Co. Ltd concerning fuzzy logic, neural network, and chaos technology, are described.

Embedding dimension estimation of chaotic time series using self-generating radial basis function network

Abstract In this paper, we apply the self-generating radial basis function network (SGRBF) to the dimension analysis of the nonlinear dynamical systems including chaotic time series. Firstly, we formulate a nonlinear time series identification problem with a nonlinear autoregressive moving average (NARMAX) model. Secondly, we propose an identification algorithm using SGRBF, which is regarded as both a three-layer network or a fuzzy model of class C∞ with Gaussian membership function. We apply this method to the estimation of embedding dimension for chaotic time series, since the embedding dimension plays an essential role for the identification and the prediction of nonlinear dynamical systems including chaos. In this estimation method, identification problems with gradually increasing embedding dimension are solved, and the identified result is used for computing correlation coefficients between the predicted time series and the observed one. We apply this method to the embedding dimension estimation of a Henon map and a chaotic pulsation time series in a fingers capillary vessels.