基于实测频率振型的大跨斜拉桥响应面模型修正研究

Response surface model modification of long-span cable-stayed bridges based on measured frequency mode

为了验证基于实测频率和振型的响应面模型修正方法的准确性与可行性,以某大跨斜拉桥为工程背景,分别进行静载试验和环境激励下的模态测试。以竖向前4阶实测频率及振型作为状态变量,选取合理的修正参数,进行中心复合试验设计;采用考虑交互项的响应面模型进行数据拟合,并计算参数R^(2)值的范围,进行精度检验;分析频率及振型的改变率,将修正后模型的挠度与实测挠度进行对比,验证该模型修正的准确性。结果表明:在参数范围内,各响应面模型的R^(2)值均接近于1,拟合精度较高;修正后模型的频率与振型均接近实测值,能准确反映桥梁的动力特性;修正后模型的挠度计算值与实测值最大误差不超过7.98%,满足工程精度要求,能够真实反映大跨斜拉桥的工作状态。研究证明了基于实测频率与振型的响应面模型修正方法对大跨斜拉桥的适用性和可行性,可为实际工程中类似桥梁的模型修正提供参考。

In order to verify the accuracy and feasibility of the response surface model correction method based on the measured frequency and mode shape,the static load test and the modal test under environmental excitation were carried out with a long-span cable-stayed bridge as the engineering background.Using vertically measured frequencies and modes as state variables for the fourth-order forward experiment,appropriate correction parameters were selected to conduct a central composite experimental design.The response surface model considering the interaction term was used for data fitting,and the R^(2) value of the parameter range was calculated for accuracy testing.The change rate of frequency and mode shape was analyzed,and the deflection of the modified model was compared with the measured deflection to verify the accuracy of the model.The results show that in the parameter range,the R^(2) values of each response surface model are close to one,indicating high fitting accuracy.The frequencies and vibration mode of the modified model closely match the measured values,which can accurately reflect the dynamic characteristics of the bridge.The maximum error between the calculated deflection value and the measured value of the modified model is less than 7.98%,which meets the requirements of the engineering accuracy,and it can realistically reflect the working state of the large-span cable-stayed bridge.The study proves the applicability and feasibility of the response surface model correction method based on the measured frequencies and vibration modes for large-span cable-stayed bridges,which can provide a reference for the model correction of similar bridges in practical engineering.