基于可靠性映射函数的结构优化

Structural optimization based on reliability mapping functions

基于可靠性分析理论,构建可靠性映射函数,将基于可靠性的结构优化由双层优化转化为单层优化,提高优化效率,解决基于可靠性结构优化的计算量大、不利用于工程应用的问题。可靠性映射函数具有明确理论依据,能够确保将其应用到基于可靠性的结构优化是可行的。为提高失效概率求解精度,以设计点为基础,提出一种改进响应面方法,并将其用于可靠性映射函数的求解。算例表明,该方法具有较好计算精度,功能函数评估次数明显少于其他方法,计算效率高,能够获得满意的优化结果。

Reliability mapping functions are constructed based on the theory of structural reliability analy- sis,the double-loop for reliability-based structural optimization （RBSO） can be transformed into the single-loop by using reliability mapping functions. The reliability mapping function can solve the problem that RBSO is unfavorable for engineering application because of the large number of calculations. The reliability mapping function has a clear theoretical basis,and can ensure that its application to RBSO is feasible. To improve the evaluation accuracy of failure probability,an improved response surface method （RSM） is proposed based on the design point, and the improved RSM is used to obtain reliability mapping functions. Examples are shown that the proposed method has high accuracy and efficiency,the number of performance function evaluation of the proposed method is less than that of other methods, and can obtain satisfactory optimization results.