基于响应面法的斜拉桥动力模型修正方法

A Method for Modifying Dynamic Model of Cable-stayed Bridge Based on Response Surface Method

为建立能够精确反映实际桥梁结构特性的基准有限元模型,提高结构分析和损伤识别的准确性,在斜拉桥健康监测和参数化有限元分析技术的基础上,基于响应面法建立了斜拉桥动力模型修正方法,实现斜拉桥有限元模型修正和健康监测数据的快速分析。提出了基于频率监测的斜拉桥模型修正方法,解决了响应面方程建立,目标函数求解和最优化算法等斜拉桥动力模型修正的关键问题,得出了斜拉桥动力模型修正的一般流程。利用实际监测的动力特征参数构造出适用于斜拉桥模型修正的响应面方程和目标函数,讨论了目标函数中权重系数的相关性及其取值方法,采用最小二乘法求解出待定系数和最优化结果。以东海大桥主航道斜拉桥为研究对象,建立了精细化的初始有限元模型,根据工程经验确定待修正参数,采用中心复合设计法确定响应面的试验工况并得出有限元分析结果。应用最小二乘法回归出响应面方程,进而求解出目标函数的最优解。结果表明:修正后有限元模型计算的振动频率值与实际桥梁结构监测的振动频率值的误差由2.03%~7.95%提高到0.05%~1.27%,其中一阶振动频率几乎与实际监测的振动频率值一致;修正后的有限元模型能够精确模拟实际斜拉桥结构的动力性能,表明该方法对斜拉桥的模型修正具有很好的适应性。

In order to establish a benchmark finite element model that can accurately reflect the actual bridge structural characteristics and improve the accuracy of structural analysis and damage identification,based on the technology of health monitoring and parametric finite element analysis for cable-stayed bridges,a dynamic model modification method for cable-stayed bridges based on response surface method is established to realize fast analysis of cable-stayed bridge finite element model modification and health monitoring data.The method for modifying cable-stayed bridge model based on frequency monitoring is proposed,and the key problems of dynamic model modification of cable-stayed bridge such as establishment of response surface equation,objective function solution and optimization algorithm are solved,and the general procedure of dynamic model modification of cable-stayed bridge is obtained.The response surface equation and objective function suitable for the modification of the cable-stayed bridge model are constructed by using the dynamic characteristic parameters of actual monitoring,the correlation of the weight coefficient in the objective function and its valuing method are discussed,and the undetermined coefficients and optimization result are solved by the least square method.Taking the cable-stayed bridge in the main channel of the Donghai Bridge as the research object,a refined initial finite element model is established,the parameters to be modified are determined according to engineering experience,and the test conditions of the response surface are determined and the finite element analysis result is obtained by the central composite design method.The response surface equation is regressed by using the least squares,and the optimal solution of the objective function is obtained.The result shows that(1) The error between the vibration frequency value calculated by the modified finite element model and the vibration frequency value monitored on the actual bridge structure is increased from 2.03%-7.95% to 0.05%-1.27%,and the first-order vibration frequency is almost consistent with the actual monitored vibration frequency value;(2) the modified finite element model can accurately simulate the dynamic performance of the actual cable-stayed bridge structure,showing that the method has good adaptability to the model modification of the cable-stayed bridge.