Combining multivariate adaptive regression splines with a response surface methodology for simulation-based design optimization.

摘要

Design optimization is an iterative process involving the modification of specified design variables in an effort to improve the cost, weight or capabilities of a structure while meeting all engineering requirements. The process can be supported by building and testing physical prototypes, using computer simulation, or both. When designing large, complex or costly structures, physical prototypes are not always an option. For such cases, finite element models (FEM) are an efficient alternative. Finite element analysis is a process by which computerized mathematical models are used to evaluate the reaction of a physical component or assembly to its environment. FEM apply integral and differential calculus equations to measure the relationship between load and deflection of the elements when force, heat, or vibration is applied. Due to the computational expense of finite element analysis, researchers continue to look for ways to reduce the number of model evaluations necessary to identify an exact, or approximate the global, optimal solution.; This dissertation develops the use of multivariate adaptive regression splines (MARS) with the successive response surface methodology (SRSM), referred to as MARS/RSM, and a space-filling design of experiments to approximate the highly nonlinear response surface normally associated with structural design. MARS uses piecewise continuous linear approximations to fit the response surface, allowing variables to act locally rather than globally, potentially reducing the number of variables to be tested in areas where the optimum is thought to exist through the MARS approximation. SRSM is used to change the size and location of the test region based on the proximity and degree of oscillation of the best response from successive batch samples.; The MARS/RSM procedure is applied to seven common optimization test functions to demonstrate its model fitting properties as compared to neural networks and generalized additive models, as well as its optimization properties compared to simulated annealing and genetic algorithms. Additionally, two finite element vehicle impact example problems are solved and compared to the results achieved using LS-OPT meta-modeling optimization techniques. Finally, MARS/RSM is used to identify the best design for a novel automobile hood with the objective of reducing the head injury criterion (HIC).