含区间参数的不确定性结构直接可靠性设计优化（英文）

Direct reliability-based design optimization of uncertain structures with interval parameters

目的:为提高含区间参数不确定性结构的可靠性,提供一种基于区间模型的不确定性结构的高效可靠性设计优化方法。创新点:1.提出结构性能指标区间可靠度的统一计算公式;2.提出区间可靠度违反度的概念和基于区间可靠度违反度的优于关系准则;3.提出并实现区间可靠性优化模型的高效直接智能求解算法。方法:1.借鉴图表法并克服其局限,给出计算区间可靠度的统一公式(公式2);2.利用Kriging近似模型和内层遗传算法计算结构性能指标在不确定性参数影响下的变化区间,从而计算出区间可靠性优化模型中各结构性能指标的区间可靠度及其违反度;3.基于区间可靠度违反度的优于关系准则,通过外层遗传算法实现各结构设计矢量的直接优劣排序和区间可靠性优化模型的直接智能求解;4.通过典型算例(图3和4、表2)和工程应用实例(图8和9、表7)验证所提方法的有效性和相比间接求解方法的优越性。结论:1.考虑结构性能指标可靠性要求的不确定性结构区间可靠性设计优化模型能够有效反映实际工程中提高不确定结构可靠性的需求;2.引入区间可靠度违反度的概念和基于可靠度违反度的优于关系准则,利用嵌套遗传算法和Kriging近似模型可实现不确定性结构区间可靠性优化模型的直接高效智能求解;3.提出的区间可靠性优化模型直接求解方法能比间接方法获得更优的解。

In order to enhance the reliability of an uncertain structure with interval parameters and reduce its chance of function failure under potentially critical conditions, an interval reliability-based design optimization model is constructed. With the introduction of a unified formula for efficiently computing interval reliability, a new concept of the degree of interval reliability violation（DIRV） and the DIRV-based preferential guidelines are put forward for the direct ranking of various design vectors. A direct interval optimization algorithm integrating a nested genetic algorithm（GA） and the Kriging technique is proposed for solving the interval reliability-based design model, which avoids the complicated model transformation process in indirect ones and yields an interval solution that provides more insights into the optimization problem. The effectiveness of the proposed algorithm is demonstrated by a numeric example. Finally, the proposed direct reliability-based design optimization method is applied to the optimization of a press upper beam with interval uncertain parameters, the results of which demonstrate its feasibility and effectiveness in engineering.