基于时域算法并考虑大幅值初始状态的桥梁高阶模态识别研究

Modal parameters are most fundamental structural dynamic parameters. It’s very important and meaningful to accurately and completely identify modal parameters for bridge model updating, damage detection and vibration control. Modal parameter identification based on ambient excitation (also called operational modal analysis, OMA) does not need special excitation devices and can yields accurate results, therefore, OMA has been extensively applied. However, due to the frequency band of ambient loads is quite narrow, the bridge structure cannot be fully excited. Thus, only lower modes can be extracted. The higher modes, which are more sensitive to structural local damages, are very difficult to identify. Through considering the large amplitude initial conditions of bridge structure induced by vehicle loads, which have wider frequency band and larger excitation density than ambient loads, this study aims to identify the higher modes of bridge structure using the well-developed time domain algorithms. In this study, it is planned to theoretically derive the formulations for modal parameters identification considering larger amplitude initial conditions. The amplitude of the initial conditions can be reasonably determined by numerical analysis. A reinforced concrete frame bridge is designed for laboratory modal test to check whether the higher modes can be extracted or not. Meanwhile, based on theory derivation and numerical analysis, the modal tests for two real bridges will be accomplished. The method of higher modes identification of bridge structure considering large amplitude initial conditions can be illustrated and summarized. The study could partially solve the problem of the identification of higher modes in OMA, and provide more accurate and complete modal parameters for structural local damage identification and finite element model updating.

模态参数是结构最基本的动力参数，准确、完备地识别模态参数对桥梁模型修正、损伤识别和振动控制都有着十分重要的意义。基于环境激励的模态参数识别（工作模态识别）无需专门激励设备且识别结果准确，因此得到广泛应用；但由于环境荷载频带窄，对桥梁激励程度有限，只能识别桥梁低阶模态，而对局部损伤较为敏感的高阶模态难以识别。本项目通过考虑频带更宽、强度更大的车辆荷载引起的桥梁大幅值初始状态，结合成熟的时域算法识别高阶模态；项目拟开展大幅值初始状态下模态参数识别公式的理论推导，并通过数值模拟合理界定初始幅值大小；拟设计一座钢筋混凝土框架桥进行室内模态试验，考察框架桥高阶模态识别情况。同时，依托理论研究和数值分析完成两座实桥模态试验，验证总结考虑大幅值初始状态桥梁高阶模态识别方法。研究成果可以一定程度解决目前桥梁工作模态分析中高阶模态难以识别的问题，为结构局部损伤识别、模型修正提供更为准确和完备的动力参数。

准确、完备地识别结构模态参数是进行模型修正和结构损伤识别的基础。本项目针对桥梁结构工作模态中高阶模态难以识别的问题，基于时域工作模态识别算法，系统地研究了引入宽频带高强度的车辆荷载激励的桥梁高阶模态识别方法；推导了考虑结构初始激励后的时域工作模态识别理论，揭示了初始状态参数对高阶模态参数识别精度的影响规律，完善了桥梁结构工作模态识别方法，提高了试验模态的完备性。基于不确定度量化理论，提出了试验模态参数不确定性量化方法，可评价试验模态参数的准确性。研究成果具体介绍如下。（一）通过引入宽频带高强度车辆荷载，拓宽了环境激励的频带，从而使得桥梁部分高阶模态得以激振。发展了基于时域法且考虑车辆激励后的桥梁初始状态的桥梁工作模态识别算法，揭示了桥梁初始状态参数对高阶模态识别的影响规律，并基于数值模拟合理的界定了初始状态幅值大小和激励时长。通过试验表明，考虑车辆荷载可识别桥梁部分高阶模态，提高试验模态参数的完备性和准确性。（二）识别的高阶模态被进一步用于修正桥梁有限元模型，修正结果表明高阶模态参数对结构局部损伤更为敏感。基于不确定度量化理论，分别从整体和局部两个维度量化了试验模态参数（高阶模态）的不确定度，为评价试验模态参数的精度提供了依据，并据此建立了模型修正参数选择方法和单目标函数响应残差权重系数计算方法，完善了桥梁结构有限元模型修正方法。