Sequential learning artificial fuzzy neural networks (SLAFNN) with single hidden layer

In this paper, a sequential orthogonal approach to the building and trainin g of a single hidden layer fuzzy neural network is presented. Sequential le arning artificial neural network model proposed by Zhang and Morris (Neural Networks 11 (1) (1998) 65) is modified to tackle fuzzy inputs and crisp ou tputs and a sequential learning artificial fuzzy neural network model is de veloped and used in this paper. This model can tackle the common problem en countered by conventional fuzzy back propagation neural network in the dete rmination of the network structure in the number of hidden layers and the n umber of hidden neurons in each layer. Non-linear mapping between fuzzy inp ut vectors and crisp output is performed. Left and right (LR) type represen tation is used to reduce the network complexity. A simple defuzzification p rocess is proposed. The procedure starts with a single hidden neuron and se quentially increases in the number of hidden neurons until the model error is sufficiently small. The classical Gram-Schmidt orthogonalization method is used at each step to form a set of orthogonal bases for the space spanne d by output vectors of the hidden neurons. In this approach it is possible to determine the necessary number of hidden neurons required. The fuzzy neu ral network architecture has been trained and tested to civil engineering p roblems such as determination of allowable stress limits for a beam subject ed to lateral loads, earthquake damage and the evaluation of wind pressure predictions. (C) 2002 Elsevier Science B.V. All rights reserved.