基于改进LHS模式的可靠性设计优化

RELIABILITY-BASED DESIGN OPTIMIZATION BASED ON ADVANCING LHS PATTERN

在设计优化中,确定性优化由于没有考虑输入量的不确定性,其优化结果可能不可靠(不安全),因此基于可靠性的设计优化(reliability-based design optimization,RBDO)得到关注。然而可靠性设计优化计算量大,尤其对于高维问题。基于此,提出一种新方法——改进拉丁超立方体取样(Latin hypercube sampling,LHS)方法,该方法可利用先前迭代步骤已用的取样点,从而降低计算量。其中可靠性指数通过基于漫射近似(diffuse approximation,DA)的一阶可靠性方法(first-order reliability method,FORM)计算得到。最后用两个数学实例验证该方法可以极大地降低RBDO问题的计算量。

Deterministic design optimization without taking uncertainties into consideration may lead to unreliable results.Reliability-based design optimization（RBDO） is getting a lot of attention recently.However,RBDO is computationally expensive,especial for high dimensions.An advancing Latin hypercube sampling（LHS） is proposed to maximally reuse previously computed points while adding a minimal number of new neighboring points at each step.The reliability index is calculated by first-order reliability method（FORM） based on diffuse approximation（DA）.Finally,two mathematic cases were taken to test the new method.The results show that the method proposed can reduce greatly the number of function evaluations and improve the computational efficiency in the solution of problems in RBDO.