Ryu Katayama

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>>

Chaos engineering in Japan

Since deterministic chaos is not only a profound concept in science but also a ubiquitous phenomenon in real-world nonlinear systems, extending to a variety of temporal and spatial scales, it can be naturally related to applications in science and technology [4]. In fact, it is not difficult to find the buds of such possible applications in historical papers by Van der Pol and Van der Mark [22], Ulam and von Neumann [21], and Kalman [12], although the term deterministic chaos was not used in those days.

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.

Adaptive Equalizer Using Self-Generating Radial Basis Function Network

In digital communication systems, a linear transversal equalizer was applied to signal equalization. But because of the nonlinearity of the equalization problem, it was desirable to incorporate some nonlinearity in the adaptive equalizer structure. We considered the application of the radial basis function RBF network to the adaptive equalizer and compared the performance of the equalizer using an RBF network between the maximum absolute error MAE selection method and the orthogonal least squares OLS method as a learning procedure. By comparing the MAE method with the OLS method, we show that the MAE method can achieve a more efficient performance in terms of bit error rate with fewer basis functions than the OLS method.

Adaptive tree-structured self-generating radial basis function network and its performance evaluation

Abstract Several algorithms have been proposed to identify a large scale system, such as the neuro-fuzzy GMDH, and the fuzzy modeling using a fuzzy neural network, As another approach, Sanger proposed a tree-structured adaptive network. But in Sangers network, it is not clear how to determine the initial disposition of bases and the number of bases in each subtree. We propose a nonlinear modeling method called the adaptive tree-structured self-generating radial basis function network (ATree0RBFN). In ATree-RBFN, we take the maximum absolute error (MAE) selection method in order to improve Sangers model. We combine Sangers tree-structured adaptive network for an overall model structure with the MAE selection method for a subtree identification problem. In ATree-RBFN, the tuning parameters are not only the coefficients but also the centers and widths of bases, and a subtree can be generated under all leaf nodes. Then, the input-outpu data can be divided into the training data set and the checking data set, and an element of inputs in each subtree is selected according to the corresponding error value from the checking data set. We also demonstrate the effectiveness of the proposed method by solving several numerical examples.

Adaptive tree-structured self generating radial basis function

Abstract In this paper, we propose a new identification method called “Adaptive Tree-Structured Self Generating Radial Basis Function(ATree-RBF) ”. In this method, we combine the Sangers tree-structured adaptive network for overall model structure, with the Maximum Absolute Error(MAE) selection method for sub-tree identification problem.

A Solution to Multi-Objective Decision Problem for Distributed Parameter Control System

Abstract This paper concerns a static multi-objective control problem of the distributed parameter system, in which regionally decentralized plural decision-makers carry out control actions based on their own goals. The problem is formulated as minimization of vector functional to generate noninferior controls. Optimality conditions are derived. Moreover, we study a multi-objective decision problem to choose a preference optimal solution from among a set of non-inferior controls. We consider the following two cases; a) there exists a central decision-maker in the upper level (a central decision problem), and b) no central decision-maker exists and a collective decision is made (a collective decision problem). Two-level computational procedures using a constrained simplex method and an interior penalty method are presented for both cases. Gradient method is used for optimizing a system governed by partial differential equations.