Structural optimization using MATLAB partial differential equation toolbox and radial basis function based response surface models.

摘要

As a decision making tool, optimization has become an inseparable part of the modern design process. However, in spite of the advances in computer capacity and speed, the computational time for some complex problems is too high to use conventional solution approach. In order to reduce the computational effort and the cost associated with such type of problems, approximation methods such as response surface methodology (RSM) along with design of experiments (DOE) are used in engineering design optimization. The main idea involves replacing the expensive simulation model during the design and optimization process with a simplified mathematical approximation of the original problem. This method is applicable where the calculation of the design sensitivity information is difficult or impossible to compute, and also in the cases with noisy functions, where the sensitivity information is not reliable. Although a variety of optimization techniques are already in use, researchers are working to figure out more efficient and improvised techniques for design optimization.;In this research, an efficient and simple structural optimization method based on response surface methodology and design of experiments has been developed and implemented using MATLAB for solving computationally expensive design optimization problems. Four different radial basis function models known as Multiquadric Interpolation, Multiquadric Regularization, Gauss Interpolation, and Gauss Regularization were utilized for constructing the response surface models and three different low discrepancy sequencing methods known as Halton sequence, Faure sequence, and Sobol sequence were used to generate the design of experiments. MATLAB Partial Differential Equation Toolbox was used for finite element model development and determining the true response of the design problems. Several design optimization problems have been solved using the proposed optimization scheme. The results thus obtained have been compared to that attained by solving the same problems using MATLAB optimization function fmincon. The comparison of the results demonstrates the effectiveness and applicability of the proposed optimization scheme.