基于高斯过程的桥梁结构有限元模型修正方法  

A finite element model correction method for bridge structures based on Gaussian process

作　　者：田钦[1] 陈勍苗 郭新耀 姚凯[1,2] TIAN Qin;CHEN Qingmiao;GUO Xinyao;YAO Kai(School of Infrastructure Engineering,Nanchang University,Nanchang 330031,China;China Construction Third Engineering Bureau Company Limited,Wuhan 430075,China)

机构地区：[1]南昌大学工程建设学院,江西南昌330031 [2]中国建筑第三工程局有限公司,湖北武汉430075

出　　处：《南昌大学学报(工科版)》2025年第1期49-55,共7页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金资助项目(52368023,52168023);江西省科技厅面上基金资助项目(20224BAB204059)。

摘　　要：桥梁健康监测是发现桥梁结构损伤的重要手段,而有限元模型修正是桥梁健康监测的重要研究内容。目前,基于有限元法的模型修正技术计算量大,实用性不强,并且工程结构受荷载变化、材料性能劣化的影响,会引起结构参数的不确定性。为提高计算效率和考虑结构参数的不确定性,提出了一种基于高斯过程模型的桥梁结构有限元模型修正方法。以简支梁结构为例,采用Sobol序列采样结构的弹性模量、质量密度,然后将所采样本映射到对应的物理空间,代入有限元模型,计算出模型的前三阶频率,进而建立了高斯代理模型。采用高斯代理模型分析简支梁结构前三阶固有频率,修正了结构的弹性模量和质量密度,并且弹性模量和质量密度的修正值与有限元模型计算值之间的误差很小。证实了高斯过程模型可以替代复杂的有限元模型,达到模型参数修正的目的。Bridge health monitoring is an important means of detecting bridge structural damage,and finite element model modification is an important research content of bridge health monitoring.At present,the model modification technology based on finite element method has a large amount of calculation and is not practical.Moreover,the engineering structure is affected by the load change and the deterioration of material properties,which will cause the uncertainty of structural parameters.To improve the computational efficiency and consider the uncertainty of structural parameters,a finite element model modification method of bridge structure based on Gaussian process model was proposed.Taking a simply supported beam structure as an example,the elastic modulus and mass density of the structure were sampled by Sobol sequence.Then the collected samples were mapped to the corresponding physical space,substituted into the finite element model,and the first three frequencies of the model were calculated.A Gaussian surrogate model was established for the natural frequency of the structure.By analyzing the first three natural frequencies of the simply-supported beam,the elastic modulus and mass density of the structure were corrected.The error between the corrected values of elastic modulus and mass density and the calculated values of the finite element model was very small.This paper proved that the Gaussian process model could replace the complex finite element model to achieve the purpose of model parameter modification.

关 键 词：桥梁结构 不确定性 健康监测 模型修正 高斯过程 

分 类 号：U441[建筑科学—桥梁与隧道工程]