基于“函数变量分离+移动最小二乘拟合”桩板墙高效优化算法探索  

Exploration of Efficient Optimization Algorithm for Pile-Slab Wall Based on“Separation of Function Variables+Moving Least Squares Fitting”

作　　者：梅龙月 杨艳 姚洪锡[2,3] 毛国成 陈罗平 马淑霞[1] MEI Longyue;YANG Yan;YAO Hongxi;MAO Guocheng;CHEN Luoping;MA Shuxia(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China;China Railway Siyuan Survey and Design Group Co.,Ltd.,Wuhan 430063,China;School of Civil Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学数学学院,成都611756 [2]中铁第四勘察设计院集团有限公司,武汉430063 [3]西南交通大学土木工程学院,成都610031

出　　处：《铁道标准设计》2025年第3期122-129,共8页Railway Standard Design

基　　金：国家重点研发计划项目(2021YFB2600404);中国铁建股份有限公司科技研究计划项目(2022-A02)。

摘　　要：桩板墙参数优化设计需要利用岩土有限元检算程序,确保设计参数满足受力与变形等工程安全指标的限制条件,并实现造价最优目标,属于多参数、多约束、非线性优化问题。针对桩板墙岩土有限元检算程序计算过程复杂、难以通过解析方法快速获取造价函数求解的问题,提出一种函数变量分离联合移动最小二乘拟合的参数优化算法。首先,对设计参数进行造价敏感性分析,得到造价函数中桩长变量分离的降维解析表达式;其次,对降维表达式的系数函数进行移动最小二乘拟合,得到系数函数值并选取系数较优对应的桩厚与桩间距参数组合;最后,利用岩土有限元检算程序遍历较优参数组合及已分离的桩长参数,比选得到满足安全指标条件下造价最优的桩长、桩厚、桩间距参数。以实际工程案例对算法进行验证,结果表明,本文算法与遍历参数法得到的最优造价相同,但所使用的数据量是遍历法数据量的17%;同时,该算法相较遗传算法收敛性更为稳定,且运行时间从7.33 s降到0.17 s,优化效果更佳,且大幅缩短了搜索时间。The parameter optimization design of pile-slab wall requires the use of geotechnical finite element calculation programs to ensure that the design parameters meet safety constraints,such as stress and deformation,while achieving the optimal cost goal.It is a multi-parameter,multi-constraint,and non-linear optimization problem.In view of the complexity of the calculation process of the geotechnical finite element calculation program for pile-slab wall and the difficulty of quickly obtaining the cost function solution through analytical methods,a parameter optimization algorithm combining separation of function variables and moving least squares fitting was proposed.Firstly,a cost sensitivity analysis of the design parameters was conducted to obtain the reduced-dimensional analytical expression for the separation of pile length variables in the cost function.Next,the moving least squares fitting was performed on the coefficient function of the reduced-dimensional expression to obtain the coefficient function values and select the optimal combination of pile thickness and pile spacing parameters corresponding to the best coefficients.Finally,the geotechnical finite element calculation program was used to evaluate the optimal parameter combinations and the separated pile length parameters.The optimal pile length,pile thickness,and pile spacing parameters that achieved the optimal cost and met the safety indicators constraints were obtained.The algorithm was verified by practical engineering cases The results showed that the optimal cost obtained by this algorithm was the same as that obtained by the traversal parameter method,but the data volume used was 17%of that required by the traversal method.Moreover,the algorithm exhibited more stable convergence compared to the genetic algorithm,with the runtime reduced from 7.33 s to 0.17 s.The optimization effect was improved,and the search time was significantly shortened.

关 键 词：桩板墙 参数优化 敏感性分析 函数变量分离 移动最小二乘法 安全指标 

分 类 号：U213.1[交通运输工程—道路与铁道工程]