基于区间分析的结构非概率可靠性优化设计

Non-probabilistic reliability-based structural design optimization based on the interval analysis method

将结构体系及其所处复杂环境中的不确定参数描述为区间变量,在区间可靠性分析方法的基础上,发展出一种结构非概率可靠性优化模型,可给出满足一定可靠性要求的优化设计方案.结构非概率可靠性优化过程包含两个层面,外层根据问题特征选用不同的全局寻优能力较强的优化算法,内层根据响应对不确定性量的敏感程度可使用基于Taylor展开的区间分析方法和配点型区间分析方法代替优化过程以评估结构响应的上界和下界.这种优化方式既避免了两层嵌套优化,极大的降低了优化过程的计算量,又可充分利用现有成熟的优化算法,程序的可移植性强.模型中使用改进的两种不同的区间可靠性模型,分别为基于区间能度方法的"1公式模型"和基于图表法的"2公式模型",实用性强.文中的两个数值算例表明了本文所提出方法的有效性.

Using interval variables to describe uncertain parameters in structural systems and their complex environments, a non-probabilistic reliability-based optimization model, which can give optimized design to meet certain reliability requirements, is proposed based on the interval reliability analysis method. Two levels are included in the non-probabilistic reliability optimization process for structures. The outer layer uses different global optimization algorithms according to the characteristics of the specific issues. The inner layer evaluates the upper and the lower bounds of the structural responses using the interval analysis method based on the Taylor expansion or the collocation interval analysis method according to the sensitivities of the responses with respect to the uncertainties. The optimization process which has strong portability, can not only avoid the two nested optimization which reduces the computational efficiency, but also take full advantage of existing mature optimization algorithms. Two different improved practical interval reliability models, which named 1-formula model based on interval possibilistic method and 2-formula chart-based model, are used in the optimization model. Two numerical examples in the paper show the effectiveness of the proposed method.