## 2 RBFNN Approximation Method  
### RBFNN Meta-Model in Design Approximation  
RBFNN is originally developed to fit irregular topographic contours of geographical data [8]. RBFNN is originally generated by the same methodology but classified by various types of the basis functions. The accuracy of RBFNN model mainly depends on the applied basis function type for a given set of training and testing data. The most commonly used basis functions are linear, cubic, thin-plate spline, Gaussian, multiquadric, and inverse multiquadric functions [9]. In the research literature on RBFNN, it is applied to approximate global surfaces smoothly interpolating a given scattered data points [10]. As concerns optimization, RBFNN is used to solve global optimum problems where the objective function is nonlinear and nonconvex [11]. The approximate quality of RBFNN is compared with other meta-methods such as response surface methodology (RSM), Kriging and so on [12; 13]. RBFNN model is enhanced by adding extra terms to a regular RBFNN model to increase its flexibility, based on which an optimal model could be searched for [14]. RBFNN approximation is extended using leave-one-out cross validation algorithm that can be applied in the setting of iterated moving least squares approximation and for RBF pseudo-spectral methods for the solution of partial differential equations [15]. Structure design studies that utilize meta-models have been conducted in various industrial fields. Structural analysis was performed using finite element method to review the initial design of structural safety of passive type deck support frame which was developed for the float-over installation of offshore plant, and an approximate optimization was performed using various meta-models to obtain the most efficient optimum design results [16]. Reliability analysis was performed by applying the general Monte Carlo simulation (MCS) and the Sobol sequence method, which is one of the quasi-MCS methods, to derive an efficient reliability evaluation method to ensure the structural design safety of automatic salt collector, and then the probability of reliability based on the sampling method and the accuracy of the Kriging metamodeling were compared [17]. To verify the suitability of the sensitivity analysis results of structural members and the exploration of design of experiments (DOE)-based automatic ocean salt collector improvement cases, meta-modeling using the response surface method was conducted for each DOE technique, and the meta-model accuracy generated from each DOE technique was examined [18]. A novel and cheap technique was developed for finding robust optimal solutions, called confidence-based robust multi-objective optimization, using a Pareto dominance operator to differentiate search agents of meta-heuristics based on both levels of robustness and confidence [19]. An optimum design of investigated an optimal design plan to minimize design risks by applying the constraint-feasible moving least-squares method, which is a conservative approximation model. A new RBDO process was identified to ensure the constraint feasibility in the moving least squares method, and devised constraint feasibility test to quantitatively realize the feasibility of approximate constraint functions [20]. As such, many references have reported various studies related to approximate design optimization using the RBFNN, but the role of the learning parameters including the SSP in the RBFNN application has barely been identified. Previous studies on the SSP were also mostly theoretical studies or application studies to signal processing and image approximation [15; 21; 22]. Based on the aeroelastic analysis, the design enhancement of wing structure was carried out by targeting an optimal wing structure able to withstand flight loads, and simultaneously with stiffness and inertia distributions leading to a configuration free from flutter within the flight envelope [24].