中文摘要：

针对传统基于近似模型的稳健设计方法中近似模型预测误差易导致优化解约束失效的问题，综合考虑参数不确定和近似模型预测不确定的影响，建立基于2种不确定因素的稳健设计方法，并通过数学测试案例验证所提方法的优化效果．同时，针对车身轻量化问题进行应用研究，选取非线性程度高、近似模型不确定影响大的耐撞性指标作为稳健约束．结果表明，基于2种不确定因素的稳健方法可以有效保证高维、强非线性问题优化解的可靠性，并在满足碰撞性能指标的前提下，达到车身减重11．06％的轻量化效果，从而验证了所提方法的可行性．

英文摘要：

In traditional metamodel-based robust design methods, the dependency between metamodels and true responses will inevitably introduce so-called metamodel uncertainty in robust design. Previous robust design methods often treat a metamodel as the real model and ignore the influence of metamodel uncertain- ty in robust solutions. It often finds a solution in the infeasible region. So the concept of robust design is extended for both parametric uncertainty and metamodel uncertainty to evaluate the compound effect in system responses. A mathematical example was employed to illustrate the superior performance of the pro- posed robust design method. The method was applied to an autobody lightweight design problem, in which the high-dimensional and high-nonlinear crashworthiness responses are chosen as constraint functions. The results show that the proposed method can reduce the risk of constraint violation due to metamodel uncer- tainty. The robust solution improves the impact performances and reduces the structure weight by 11.06%. It demonstrates the proposed method is an effective tool in autobody robust design.