Fuzzy-Evolutionary-Kalman Filter And Application In RBF Artificial Neural Network

Artificial neural network(ANN) is a new class of information processing techniques. It has been applied in solving wide varieties of problems, such as discrete pattern classification, function approximation, signal processing, control, or any other application which requires a mapping from an input to an output. The radial basis function (RBF) neural network as a member of the family of artificial neural network has gained more and more attention in pattern classification for its special character. Training a neural network is, in general, a challenging nonlinear optimization problem. In this paper a new training method for RBFs that is based on fuzzy-evolution-Kalman filtering is presented.Kalman filtering training of RBF networks has proven to be much more effective than many other conventional methods. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. However, it powerful capability depends on the precise of the process noise covariance Q and measurement noise covariance R matrices. If the accurate values can be obtained, the performance ability of the Kalman filter falls down quickly. When the accurate values of the process noise covariance Q and measurement noise covariance R can not be available, the conventional method is to adopt the max value in the value range. This paper proposed another available solution to this problem. The method is: first, an evolutionary algorithm is employed which can select the approximate accurate values of the process noise covariance Q and measurement noise covariance R from their value ranges. Then a fuzzy controller is adopted to adjust the parameters Q and R in case that the process noise covariance Q and measurement noise covariance R matrices might cage with each time step or measurement. The new method is applied to the problem of training a RBF network. It is shown that the use of the solution proposed by this paper results in better learning than conventional RBF networks and faster learning than gradient descent.This paper first provides an overview of artificial neural network and radial basis function (RBF) network, introduces several learning algorithms of RBF networks. Section 3 discussed the basic Kalman filter and made some improvement using fuzzy control theory and evolutionary algorithm. Section 4 show how the fuzzy-evolutionary-Kalman filter can optimize the parameters of an RBF. This section also contains simulation result and a comparison of the fuzzy-evolutionary-Kalman filter with the gradient descent method. Then draw a conclusion that the new method can perform a better and faster learning than other methods in training RBF network.