Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.
Surrogate models are commonly used for approximation of large computationally expensive vehicle crash simulation to facilitate rapid design space exploration and optimization. Unfortunately, the optimum design based on surrogates may turn out to be infeasible after running finite element crash simulation due to the surrogate errors. To meet this challenge, conservative strategy of surrogate modeling through compensating fitting errors was used for reliability based design optimization of vehicle structures for crashworthiness and weight reduction. The critical crash responses were constructed by unbiased kriging models, and conservative surrogates were obtained via adding safety margin to estimate the crash responses conservatively. The benefits of using conservative surrogates for reliability based design optimization were investigated in the context of constraint feasibility of the optimum designs through a mathematical example and a case study on vehicle crashworthiness design. The results demonstrate that optimization based on conservative surrogate helps to achieve the feasible optimum design, showing more attractive for reliability based design optimization in engineering applications.
