含同类构件的多构件结构区间不确定性优化

Interval uncertain optimazation for multi-component structural with the same components

在土木工程领域,工程结构往往为含同类构件的多构件结构。针对该类结构的区间不确定性优化模型无法直接转换为数值模型且计算量巨大的问题,本文提出了一种含同类构件的多构件结构区间不确定性优化方法,该方法结合基于数值转换的二阶区间泰勒展开公式与不确定目标函数与约束的转换方法,将区间不确定性优化模型转换为确定性优化模型,最后通过遗传算法求解。研究结果表明:六杆桁架内力计算误差由0.047~0.08减少到0.001~0.005,计算精度显著提高,在十杆桁架优化中,本文的方法与2层嵌套优化方法结果一致,且其遗传算法迭代时间仅为2层嵌套优化方法的1/30左右,证明对于小不确定性问题,该方法不存在区间扩张与缩减问题,同时计算精度高,计算量小。

In the field of civil engineering,the engineering structure is usually a multi-component structure with the same components.Moreover,the interval model of such structure cannot be directly converted into a numerical model with large amount of computation.Therefore,a method of interval uncertain optimization for multi-component structures with the same components was put forward in this paper.Combining the second-order interval Taylor expansion on the basis of numerical conversion and the transformation method of uncertain objective functions and uncertain constraints,this method transformed the interval uncertainty optimization model into a deterministic optimization model,and then solved the problem by genetic algorithm.The result shows that the computational error of internal forces in six-bar trusses is reduced from 0.047~0.08 to 0.001~0.005 and the computational precision is significantly improved.In the ten-bar truss optimization,the result of the method in this paper are consistent with the result of the nesting optimization method and its iteration time of the genetic algorithm is only about 1/30 of that of the nesting optimization method.The result proves that the interval uncertain optimization method introduced in this paper can effectively avoid interval expansion and reduction with higher computational precision and lower computational complexity for optimization problems with little uncertainty.