On the robustness of a simple domain reduction scheme for simulation‐based optimization

Abstract

This paper evaluates a Successive Response Surface Method (SRSM) specifically developed for simulation-based design optimization, e.g. that of explicit nonlinear dynamics in crashworthiness design. Linear response surfaces are constructed in a subregion of the design space using a design of experiments approach with a D-optimal experimental design. To converge to an optimum, a domain reduction scheme is utilized. The scheme requires only one user-defined parameter, namely the size of the initial subregion. During optimization, the size of this region is adapted using a move reversal criterion to counter oscillation and a move distance criterion to gauge accuracy. To test its robustness, the results using the method are compared to SQP results of a selection of the well-known Hock and Schittkowski problems. Although convergence to a small tolerance is slow when compared to SQP, the SRSM method does remarkably well for these sometimes pathological analytical problems. The second test concerns three engineering problems sampled from the nonlinear structural dynamics field to investigate the method's handling of numerical noise and non-linearity. It is shown that, despite its simplicity, the SRSM method converges stably and is relatively insensitive to its only user-required input parameter.

On design optimization of a composite impact attenuator under dynamic axial crushing

“…In the successive surrogate modeling method, the center of RoI at the (k+1)-th iteration is the optimum x (k)* of the k-th iteration and its size is a fraction of the size of the k-th iteration, calculated using the distance between the optimum and the center of the current RoI. While SRSM has been demonstrated to be able to identify the optimum region for various crashworthiness problems [14][15][16], iterative resampling might be prohibited in practice as crashworthiness simulations are rather expensive computationally. Implementation of Latin hypercube design [17], which is a technique to inherit previous sample points, might help reduce the required number of sample points in subsequent iterations.…”

An investigation of structural optimization in crashworthiness design using a stochastic approach

“…If a combination of all above happens, a combination of all factors will shrink the RoI. All equations to calculate the new RoI follows Stander and Craig [22].…”

“…Schramm et al [15][16][17][18] have applied RSM in a vehicle design context. Stander et al [1,14,20,22] th International LS-DYNA Users Conference were also among the first using RSM in structural optimization and have also developed the optimization package LS-OPT. Sobieszczanski-Sobieski et al [19] have done much work in the field of multidisciplinary optimization using RSM.…”

Parameters Determination of Yoshida Uemori Model Through Optimization Process of Cyclic Tension-Compression Test and V-Bending Springback

“…After the required modifications were performed to the file, it was imported to the Ls-OPT V.5. In the optimization procedure, sequential response surface method (SRSM) (Stander and Craig, 2002) was used as a metamodel-based optimization to determine an approximate optimum point for the design variables. Additionally, the polynomial surface response was used to determine the significance of the parameters and the interactions between the each other was constructed.…”