基于模态分析的输电塔结构优化模型

选取常见的干字型角钢塔，提出一种新型的基于模态分析输电塔结构优化模型。构建参数化输电塔结构有限元模型，采用拉丁超立方抽样方法进行高效抽样，将样本空间进行均匀划分，再对样本空间抽样，规避了Monte Carlo法样本空间低效重复抽样的缺点，有效提高Monte Carlo随机有限元法的运算效率；分别采用线性回归，纯二次回归，交叉回归及完全二次回归公式优化输电塔结构，通过线性回归残差分析，并综合考虑相关系数R2、F值、P值及评估误差E，选用完全二次回归模型构造输电塔随机输入变量与各随机输出变量之间的数学关系；分别采用模拟退火算法与遗传算法对模型进行优化，优化结果表明：两种算法均能实现全局搜索，规避优化过程中局部最小点；遗传算法的优势更为明显，收敛速度快，计算耗时短，并且目标函数的优化结果较模拟退火算法更优；与输电塔原始结构相比，遗传算法和模拟退火算法优化后的输电塔耗材总体积分别降低19.97%和19.96%，较为接近；经遗传算法优化后的输电塔优化结构五阶固有频率与一阶固有频率的差值是原设计的138.1%，模拟退火算法优化后的结果为113.7%，经遗传算法优化后的输电塔优化结构更好。

A Structural Optimization Model for Transmission Tower Based on Modal Analysis

A new type of transmission tower structure optimization model based on modal analysis is proposed. To construct he parametric finite element model of transmission tower structure, the Latin hypercube sampling method is used for efficient sampling, by which the sample space is evenly divided before the sample space is sampled, thereby avoiding the disadvantage of low efficiency repeated sampling of sample space in the Monte Carlo method, and effectively improving the operation efficiency of Monte Carlo random finite element method. The linear regression, pure quadratic regression, cross regression and complete quadratic regression formula are used to optimize the structure of transmission tower. Through the residual analysis of linear regression and the comprehensive consideration of correlation coefficient R2, F, P and evaluation error E, the mathematical relationship between random input variables and random output variables of transmission tower is constructed by using the complete quadratic regression model. The simulated annealing algorithm and genetic algorithm are used to optimize the model respectively. The optimization results show that both algorithms can realize global search and avoid local minimum points in the optimization process. The advantages of genetic algorithm are more obvious, the convergence speed is fast, the calculation time is short, and the optimization result of objective function is better than that of simulated annealing algorithm. Compared with the original structure of transmission tower, the consumable volume of transmission tower optimized by genetic algorithm and simulated annealing algorithm decreased by 19.97% and 19.96% respectively, which are close to each other. The difference between the fifth order and the first order natural frequencies of the optimized transmission tower structure optimized by genetic algorithm is 138.1% of the original design, and that of simulated annealing algorithm is 113.7%. Therefore, the optimized structure of the transmission tower optimized by genetic algorithm outperforms.