基于替代模型的缆索承重桥梁固有频率预测  

Natural frequency prediction of cable supported bridges based on surrogate model

作　　者：马亚飞 付曙雯 何羽 鲁乃唯 王磊 MA Yafei;FU Shuwen;HE Yu;LU Naiwei;WANG Lei(School of Civil Engineering,Changsha University of Science&Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学土木工程学院,湖南长沙410114

出　　处：《铁道科学与工程学报》2023年第7期2594-2603,共10页Journal of Railway Science and Engineering

基　　金：国家重点研发计划项目(2019YFC1511000);国家自然科学基金资助项目(52078055);湖南省教育厅资助科研项目(20A003)。

摘　　要：大跨缆索承重桥梁空间组成复杂,影响参数多,结构动力分析具有显著不确定性。提出一种基于支持向量机的结构固有频率预测方法,采用遗传算法和交叉验证算法进行超参数寻优,实现了复杂高维结构参数与动力响应间的非线性映射建模。以南溪长江大桥为背景,采用ANSYS三维建模对悬索桥进行模态分析,选用拉丁超立方试验抽取样本数据保证结果的全面性,考虑参数敏感性和样本量对模型预测精度和效率的影响,利用MATLAB函数实现固有频率的回归预测。研究结果表明:遗传支持向量机替代模型样本量达350组时,均方误差值为7.8482×10^(−4)基本收敛;样本量在50~1000组范围内,经遗传算法参数寻优的预测误差随样本量增加的变化趋势与交叉验证算法较一致,但遗传算法精度更高;在350组样本量下,遗传算法单次寻优耗时仅为交叉验证算法的37.06%。准确预测基频后,进一步预测了南溪长江大桥第3阶、第5阶和第7阶固有频率,预测结果的均方误差和平均绝对误差均小于0.005,满足精度要求。研究成果可为复杂结构动力分析和安全状态评估提供一种精确高效的分析方法。The complex spatial composition and numerous influencing parameters will result in huge uncertainties in the mechanism dynamic analysis of long-span cable supported bridges.This paper proposed a natural frequency prediction method based on support vector machine.Genetic algorithm and cross-validation algorithm were used to optimize hyper-parameters,and the nonlinear mapping relationship between complex high-dimensional structural parameters and dynamic responses was obtained.A three-dimensional model of the Nanxi Yangtze River Bridge was established using ANSYS to perform modal analysis of suspension bridge.Latin hypercube sampling method was selected to ensure the comprehensiveness of the sample results,and the effects of parameter sensitivity and sample size on the model prediction accuracy and efficiency were also included.MATLAB function was used to realize the regression prediction of natural frequency.The results show that the mean square error value is 7.8482×10^(-4) and converges when the sample size of the Genetic Algorithm Support Vector Machine alternative model reaches 350 groups.With the increase of the sample size,the variation trend of the prediction error optimized by genetic algorithm parameter optimization is consistent with that of the crossvalidation algorithm,but the genetic algorithm has a higher precision when the sample size is in the range of 50~1000 groups.With a sample size of 350,the single optimization time of genetic algorithm is only 37.06%of that of the cross-validation algorithm.After accurately predicting the fundamental frequency,the natural frequencies of the 3rd,5th and 7th orders of the Nanxi Yangtze River Bridge are also given.The mean square error and the mean absolute error of the prediction results are less than 0.005,which meets the accuracy requirement.The results can provide an accurate and efficient theoretical method for the dynamic analysis and safety assessment of complex structures.

关 键 词：桥梁固有频率 有限元分析 支持向量机 遗传算法 替代模型 

分 类 号：U446[建筑科学—桥梁与隧道工程]