基于动力测试的桥梁损伤识别研究
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摘要
随着交通事业的发展，对梁式桥进行损伤识别研究，有重要的理论意义和实用价值。损伤识别是桥梁健康监测过程中的关键环节。本文通过理论分析、数值模拟和实桥应用，对受损梁桥的频率和曲率模态的变化规律进行了研究，并以动力测试参数为输入信息，基于固有频率、曲率模态、柔度矩阵、频响函数构建梁桥的损伤识别方法体系。论文的主要研究内容如下：
通过对固有频率、曲率模态、柔度矩阵和频响函数等方法在损伤识别应用中的基本理论分析，界定了基于频率、曲率模态、柔度矩阵及频响函数方法进行损伤识别的适用情形。
以Euler-Bernoulli梁理论和结构动力学理论为基础，通过数值模拟分析，引入损伤因子、频率变化率、频率变化率震荡幅度、频率变化率中值、频率变化率比值等概念，从固有频率以及频率变化率、频率变化率比值等方面，研究了梁桥振动频率变化的规律；通过数值模拟分析，探讨了曲率模态和曲率模态差对梁桥损伤的敏感性。
根据最小二乘目标优化方法和图形法，以频率为动力测试参数，采用频率变化率比值及正则化的频率变化率两种频率指纹，对单损伤梁桥的损伤位置进行识别。依据“第i阶模态下，频率变化的平方和损伤因子成线性关系”基本特征，采用频率变化的平方和损伤因子数值模拟折线图的线性插值对损伤程度进行了识别。
通过数值模拟，以位移振型为动力测试参数，对比分析了位移模态差和曲率模态差对梁桥的损伤识别效果，以及测点密度、噪声对曲率模态差损伤识别的影响，并运用曲率模态振型的相对变化量方法对损伤程度做出识别。
以频响函数损伤识别的已有研究成果为基础，通过理论分析，提取了加速度频响函数能量曲率差和加速度频响函数最大值曲率差两种指标。以脉冲激励信号为输入力，输入和输出的加速度时程为动力测试参数，分析了加速度频响函数能量曲率差和加速度频响函数最大值曲率差在提取不同的测点度数目和不同的噪声影响下对梁桥的损伤识别能力。
在结构柔度矩阵理论分析的基础上，根据已有的柔度矩阵对角元素差、模态柔度差、模态柔度改变率、模态柔度曲率差及均匀荷载面曲率差五种指标，提出了修正的柔度曲率指标。通过数值模拟，在模态测试信息不完备即提取不同的自由度数目和模态测试误差即不同的噪声影响的条件下，以频率和位移振型为动力测试参数，分别对基于柔度矩阵指标的损伤识别能力进行了分析，以及对损伤指标和损伤程度的关系进行了研究。
基于固有频率、曲率模态、柔度矩阵及频响函数方法构建了相对完整地梁桥损伤识别方法体系，并编制MATLAB应用程序。以实际桥梁工程为背景，比较分析了均匀荷载面曲率差方法和本文提出的修正的柔度曲率方法进行损伤位置识别的能力，采用本文提出的加速度频响函数能量曲率差及加速度频响函数最大值曲率差方法进行损伤位置识别，以及基于曲率模态振型的相对变化量方法进行损伤程度识别，验证了识别方法体系的可行性和正确性，以便为桥梁健康监测系统的进一步完善应用提供理论与方法支撑。
With the development of the transportation, it is of theoretical significance and practicalvalue to make researches on the bridge structure damage identification (SDI). SDI is a keyproblem of bridge structure health monitoring (SHM). In this dissertation, some issues arestudied based on dynamic testing parameters and through theoretical analysis, numericalsimulation and practical application, which are natural frequency and curvature mode rules ofthe damaged beam bridge, and the bridge SDI methods system based on frequency, curvaturemode, flexibility matrix and frequency response functions. The main works are as follows:
Through theoretical analysis, the bridge SDI methods applicability of the frequencyvariation, curvature mode, flexibility matrix and frequency response function (FRF) aredefined.
Based on Euler-Bernoulli beam and structure dynamics theory, and by means of dynamicfinite element model (FEM) analysis, the natural frequencies are obtained throughcalculations in various kinds of damage states. With the concept of damage factor，frequencychange rate, frequency change rate oscillation amplitude, frequency change rate mid-valueand the ratio of frequency change rate, the thesis researches the rule of beam bridge frequencyresponse from various aspects of natural frequency, frequency change rate and the ratio offrequency change rate characteristics. Through numerical simulation analysis, SDI sensitivityrules with curvature mode and curvature mode difference are obtained.
With the fingerprints of frequency ratio of change rate and normalized rate frequencychange ratio, based on the least square objective optimization method and graphical method,the result of damage position identification of simply supported beam bridge with singledamage is effective. According to the theoretical derivation of frequency change square anddamage factor are linear relation, the linear interpolation of the frequency change square anddamage factor numerical simulation line graph can be used to infer the damage degree ofsimply supported beam bridge with single damage.
Through numerical simulation analysis, the displacement mode and curvature modedifference of SDI results are comparatively analyzed, the effects of measuring points density on SDI of modal curvature difference are studied, and damage degree is identified using therelative change amount of curvature mode shapes.
On the basis of the existing research results of the FRF damage identification, thecurvature difference index of acceleration FRF energy (CEFRF) and the curvature differenceindex of acceleration FRF maximum (CMFRF) are extracted. According to the commonsource of excitation, and taking the pulse excitation signal as the input force, SDI ability withmensuration dots number and noise effects are studied.
A flexibility index of modify modal flexibility curvature(MMFC) is presented throughanalyzing these exiting flexibility-matrix-based indexes of flexibility difference, modalflexibility (MF), modal flexibility Index (MFI), modal flexibility curvature (MFC), andchange in uniform load surface curvature (ULSC). These SDI indexes abilities are studiedthrough numerical simulation in the cases of modal testing with incomplete information andtesting error. And the relations of indexes and damage degrees are also studied.
The methods system based on the frequency variation, curvature mode, flexibility matrix,and FRF are constructed, and the MATLAB application compositions are programmed.Taking Jinshuigou Bridge as the background, damage location identification capability ofULSC and MMFC methods are comparatively analyzed, CEFRF and CMFRF methods areused for damage location identification, and the method of curvature modal relative variationis used for damage degree identification. These methods are verified to be feasible and correct,which can support for the application of bridge SHM system in theory and methods.
通过对固有频率、曲率模态、柔度矩阵和频响函数等方法在损伤识别应用中的基本理论分析，界定了基于频率、曲率模态、柔度矩阵及频响函数方法进行损伤识别的适用情形。
以Euler-Bernoulli梁理论和结构动力学理论为基础，通过数值模拟分析，引入损伤因子、频率变化率、频率变化率震荡幅度、频率变化率中值、频率变化率比值等概念，从固有频率以及频率变化率、频率变化率比值等方面，研究了梁桥振动频率变化的规律；通过数值模拟分析，探讨了曲率模态和曲率模态差对梁桥损伤的敏感性。
根据最小二乘目标优化方法和图形法，以频率为动力测试参数，采用频率变化率比值及正则化的频率变化率两种频率指纹，对单损伤梁桥的损伤位置进行识别。依据“第i阶模态下，频率变化的平方和损伤因子成线性关系”基本特征，采用频率变化的平方和损伤因子数值模拟折线图的线性插值对损伤程度进行了识别。
通过数值模拟，以位移振型为动力测试参数，对比分析了位移模态差和曲率模态差对梁桥的损伤识别效果，以及测点密度、噪声对曲率模态差损伤识别的影响，并运用曲率模态振型的相对变化量方法对损伤程度做出识别。
以频响函数损伤识别的已有研究成果为基础，通过理论分析，提取了加速度频响函数能量曲率差和加速度频响函数最大值曲率差两种指标。以脉冲激励信号为输入力，输入和输出的加速度时程为动力测试参数，分析了加速度频响函数能量曲率差和加速度频响函数最大值曲率差在提取不同的测点度数目和不同的噪声影响下对梁桥的损伤识别能力。
在结构柔度矩阵理论分析的基础上，根据已有的柔度矩阵对角元素差、模态柔度差、模态柔度改变率、模态柔度曲率差及均匀荷载面曲率差五种指标，提出了修正的柔度曲率指标。通过数值模拟，在模态测试信息不完备即提取不同的自由度数目和模态测试误差即不同的噪声影响的条件下，以频率和位移振型为动力测试参数，分别对基于柔度矩阵指标的损伤识别能力进行了分析，以及对损伤指标和损伤程度的关系进行了研究。
基于固有频率、曲率模态、柔度矩阵及频响函数方法构建了相对完整地梁桥损伤识别方法体系，并编制MATLAB应用程序。以实际桥梁工程为背景，比较分析了均匀荷载面曲率差方法和本文提出的修正的柔度曲率方法进行损伤位置识别的能力，采用本文提出的加速度频响函数能量曲率差及加速度频响函数最大值曲率差方法进行损伤位置识别，以及基于曲率模态振型的相对变化量方法进行损伤程度识别，验证了识别方法体系的可行性和正确性，以便为桥梁健康监测系统的进一步完善应用提供理论与方法支撑。
With the development of the transportation, it is of theoretical significance and practicalvalue to make researches on the bridge structure damage identification (SDI). SDI is a keyproblem of bridge structure health monitoring (SHM). In this dissertation, some issues arestudied based on dynamic testing parameters and through theoretical analysis, numericalsimulation and practical application, which are natural frequency and curvature mode rules ofthe damaged beam bridge, and the bridge SDI methods system based on frequency, curvaturemode, flexibility matrix and frequency response functions. The main works are as follows:
Through theoretical analysis, the bridge SDI methods applicability of the frequencyvariation, curvature mode, flexibility matrix and frequency response function (FRF) aredefined.
Based on Euler-Bernoulli beam and structure dynamics theory, and by means of dynamicfinite element model (FEM) analysis, the natural frequencies are obtained throughcalculations in various kinds of damage states. With the concept of damage factor，frequencychange rate, frequency change rate oscillation amplitude, frequency change rate mid-valueand the ratio of frequency change rate, the thesis researches the rule of beam bridge frequencyresponse from various aspects of natural frequency, frequency change rate and the ratio offrequency change rate characteristics. Through numerical simulation analysis, SDI sensitivityrules with curvature mode and curvature mode difference are obtained.
With the fingerprints of frequency ratio of change rate and normalized rate frequencychange ratio, based on the least square objective optimization method and graphical method,the result of damage position identification of simply supported beam bridge with singledamage is effective. According to the theoretical derivation of frequency change square anddamage factor are linear relation, the linear interpolation of the frequency change square anddamage factor numerical simulation line graph can be used to infer the damage degree ofsimply supported beam bridge with single damage.
Through numerical simulation analysis, the displacement mode and curvature modedifference of SDI results are comparatively analyzed, the effects of measuring points density on SDI of modal curvature difference are studied, and damage degree is identified using therelative change amount of curvature mode shapes.
On the basis of the existing research results of the FRF damage identification, thecurvature difference index of acceleration FRF energy (CEFRF) and the curvature differenceindex of acceleration FRF maximum (CMFRF) are extracted. According to the commonsource of excitation, and taking the pulse excitation signal as the input force, SDI ability withmensuration dots number and noise effects are studied.
A flexibility index of modify modal flexibility curvature(MMFC) is presented throughanalyzing these exiting flexibility-matrix-based indexes of flexibility difference, modalflexibility (MF), modal flexibility Index (MFI), modal flexibility curvature (MFC), andchange in uniform load surface curvature (ULSC). These SDI indexes abilities are studiedthrough numerical simulation in the cases of modal testing with incomplete information andtesting error. And the relations of indexes and damage degrees are also studied.
The methods system based on the frequency variation, curvature mode, flexibility matrix,and FRF are constructed, and the MATLAB application compositions are programmed.Taking Jinshuigou Bridge as the background, damage location identification capability ofULSC and MMFC methods are comparatively analyzed, CEFRF and CMFRF methods areused for damage location identification, and the method of curvature modal relative variationis used for damage degree identification. These methods are verified to be feasible and correct,which can support for the application of bridge SHM system in theory and methods.
引文
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