A Study on Learning Parameters in Application of Radial Basis Function Neural Network Model to Rotor Blade Design Approximation

Abstract

Meta-model sre generally applied to approximate multi-objective optimization, reliability analysis, reliability based design optimization, etc., not only in order to improve the efficiencies of numerical calculation and convergence, but also to facilitate the analysis of design sensitivity. The radial basis function neural network (RBFNN) is the meta-model employing hidden layer of radial units and output layer of linear units, and characterized by relatively fast training, generalization and compact type of networks. It is important to minimize some scattered noisy data to approximate the design space to prevent local minima in the gradient based optimization or the reliability analysis using the RBFNN. Since the noisy data must be smoothed out in order for the RBFNN to be applied as the meta-model to any actual structural design problem, the smoothing parameter must be properly determined. This study aims to identify the effect of various learning parameters including the spline smoothing parameter on the RBFNN performance regarding the design approximation. An actual rotor blade design problem was considered to investigate the characteristics of RBFNN approximation with respect to the range of spline smoothing parameter, the number of training data, and the number of hidden layers. In the RBFNN approximation of the rotor blade design, design sensitivity characteristics such as main effects were also evaluated including the performance analysis according to the variation of learning parameters. From the evaluation results of learning parameters in the rotor blade design, it was found that the number of training data had larger influence on the RBFNN meta-model accuracy than the spline smoothing parameter while the number of hidden layers had little effect on the performances of RBFNN meta-model.