基于可靠度指标的小概率失效结构优化  

Small probability failure structure optimization based on reliability index

作　　者：吴佳东 颜东煌 许红胜 陈星烨 吕文舒 WU Jia-dong;YAN Dong-huang;XU Hong-sheng;CHEN Xing-ye;LYU Wen-shu(School of Civil Engineering,Changsha University of Science and Technology,Changsha 410114,Hunan,China;CCCC Water Transportation Planning and Design Institute Co.,Ltd.,Beijing 100020,China)

机构地区：[1]长沙理工大学土木工程学院,湖南长沙410114 [2]中交水运规划设计院有限公司,北京100020

出　　处：《长安大学学报（自然科学版）》2021年第1期50-58,共9页Journal of Chang’an University(Natural Science Edition)

基　　金：国家重点基础研究发展计划(“九七三”计划)项目(2015CB057706);国家自然科学基金项目(51878073,51678068)。

摘　　要：针对实际工程中具有隐式功能函数的小概率失效结构的可靠度计算与优化问题,提出一种适用于小概率结构可靠度计算与结构优化设计的方法。该方法首先采用径向基神经网络构建结构的隐式功能函数;其次,引入自适应随机变量对遗传算法进行改进,遗传算法根据可靠度的几何意义搜索可靠度指标最优解及验算点,以此求解可靠度指标;最后,以引入自适应随机变量的遗传算法为主程序,径向基神经网络构建优化变量与结构可靠度之间的隐式关系供主程序调用,对工程结构进行优化,并以矮寨大桥钢桁架为例进行实例验证。研究结果表明:引入的自适应随机变量明显改善了遗传算法初始种群的质量,加快遗传算法收敛速度;根据可靠度的几何意义,采用引用自适应随机变量的遗传算法搜索钢桁架(小概率失效结构)可靠度的方法与蒙特卡洛法计算结果相对偏差仅为0.33%;引入自适应随机变量的遗传算法收敛速度、计算精度明显提高,证明该方法具有鲁棒性强、计算速度快、适用性强、精度高等优点。通过2个优化模型对钢桁架进行了优化,优化结果表明:设计时应适当增加钢桁架腹杆的面积与截面高度,减小纵横梁的截面面积;在钢桁架可靠度指标一定的前提下,质量较优化前减少14.2%;钢桁架设计质量一定的前提下,可靠度指标由4.8212提高至5.9124。Aiming at the problem of reliability calculation and optimization of small probability failure structures with implicit function in practical engineering, a method was proposed for reliability calculation and optimization design of small probability failure structures. The RBF neural network was firstly adopted to construct the implicit function of the structure, and an adaptive random variable was introduced to improve the genetic algorithm, which was used to search the optimal solution and checking points of the reliability index, according to the geometric meaning of the reliability so as to solve the reliability index. Besides, genetic algorithm with adaptive random variables was employed as the main program, and the RBF neural network was called to construct the implicit relationship between optimization variables and structural reliability for the main program to optimize the structure. Aizhai Bridge steel truss was taken as an example. The results show that the introduction of adaptive random variables obviously improves the quality of the initial population and speeds up the convergence rate of genetic algorithm. In addition, based on the geometric meaning of the reliability, the relative error between the reliability method mentioned above and Monte-Carlo method is only 0.33%. Also, the convergence speed and calculation accuracy of the improved genetic algorithm are obviously improved, which proved that the method has the advantages of strong robustness, fast calculation speed, strong applicability and high precision. At last, two optimization models are used to optimize steel trusses and their results show that the area and section height of steel trusses should be increased, while the section area of vertical and horizontal beams should be reduced appropriately. Moreover, the quality of the steel trusses is reduced by 14.2%, when ensuring the reliability of the structure and the reliability index of steel truss has been improved from 4.821 2 to 5.912 4 under the condition of good quality. 5 tabs, 8 fig

关 键 词：桥梁工程 结构优化 小概率失效 可靠度 RBF神经网络 遗传算法 

分 类 号：U441[建筑科学—桥梁与隧道工程]