## 1 Introduction  
The radial basis function neural network (RBFNN) is one of artificial neural network (ANN) methods employing a hidden layer of radial units and an output layer of linear units, and characterized by relatively fast training, generalization and compact type of network [1]. RBFNN has been widely used in surface and/or image constructions that typically consist of bulky size of data in the order of thousands or even millions of points. It also has been known to be suitable for highly nonlinear function approximate problems. The RBFNN has been recognized as useful method in various fields such as pattern recognition, automatic control, signal processing, approximate optimization and so on [2, 3, 4, 5]. Meta-models are 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 RBFNN has been usefully applied as the meta-model in design approximation. A sequential approximate robust design optimization with the RBFNN was proposed to find a robust optimal solution with a small number of function evaluations, not identifying a set of Pareto-optimal solution using multi-objective evolutionary algorithms [6]. To further reduce the computational expense of metamodel-based design optimization, a novel sequential RBF-based optimization method using virtual sample generation was proposed employing the virtual sample generation mechanism to improve the optimization efficiency [7]. However, the role of learning parameters in the RBFNN meta-model was hardly investigated in the design approximation and its application to the optimization or the reliability analysis. The reason for that the role of learning parameters in the RBFNN meta-model was not investigated closely in design approximation is that the review of parameters affecting the accuracy of the meta-model was overlooked due to the extensive numerical calculation process of optimization or reliability analysis. In Section 2.1, the author reviewed several references in which the RBFNN meta-model was utilized for the design optimizations and the reliability analyses, and it was found that the role of learning parameters in the RBFNN meta-model was hardly investigated in the design approximation. In general, the values of parameters in RBFNN meta-model have been applied empirically or adjusted through simple estimation of the accuracy of RBFNN meta-model or comparison with the results of other meta-models. This study aims to identify the effect of various learning parameters such as the spline smoothing parameter (SSP), the number of training data, and the number of hidden layers on the performances of RBFNN meta-model regarding the design approximation of rotor blade. In particular, it is important to minimize the scattered noisy data to approximate a design space to prevent local minimum in gradient based optimization or reliability analysis using the RBFNN meta-model. Since the noisy data must be smoothed out in order for the RBFNN to be applied as the meta-model to an actual structural design problem, the SSP must be properly determined. In case of applying the RBFNN to approximate the design space, how to determine the learning parameters such as the SSP, training data, and hidden layers is important in the structural design application to enhance the performances of the meta-model. An actual rotor blade design problem was considered to investigate the characteristics of RBFNN approximation with respect to the range of SSP, the number of training data, and the number of hidden layers. In the rotor blade design approximation with the RBFNN, design sensitivity characteristics such as main effects were also evaluated including the performance analysis according to the variation of learning parameters.