小波分析在桥梁健康监测中的应用研究
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摘要
桥梁健康监测是现代传感技术、通信技术和评价体系的结合，其可以实时在线监测桥梁运营过程中结构在环境和荷载作用下的结构响应，由获得的各种监测指标信息来分析桥梁的健康状态，并在结构出现异常时及时预警，为桥梁的管理与养护维修提供科学依据。针对在桥梁健康监测损伤和预警中可能存在和面临的问题，本文以小波变换为基本分析手段，将其应用于桥梁健康监测中，从桥梁结构测试数据去噪、模态参数识别、损伤识别、警情分析等方面进行了较为系统的研究，研究成果具有一定的工程应用价值。
由于各种因素影响，桥梁的实际测试数据中往往包含了噪声信息，对结构损伤识别和状态评估等带来较大的影响，从根本上对测试数据进行噪声控制，降低结构分析中由于数据受到噪声干扰而带来的影响，是一种可行的方法。首先阐述了利用小波模极大值去噪和小波阈值去噪的原理，然后以一简支梁结构某阶模态振型作为一维信号，在不同的噪声水平下分别应用两种去噪方法对信号进行了分解重构，根据对信号去噪后的信噪比SNR和均方根误差RMSE两个指标信息的分析，说明了两种方法均能明显降低模态振型信号的噪声强度，通过对比分析，指出小波阈值去噪方法较小波模极大值去噪方法更为简单高效，是更适合于桥梁健康监测数据降噪的方法。
探讨了应用复Morlet小波变换对结构在环境激励下的模态参数识别方法，对结构动力响应信号进行小波变换，从其小波变换系数的时间-尺度图所含的信息，进一步得到其模和相位，从而实现结构模态参数的识别，并通过对一简支梁在稳态白噪声激励下的数值模拟分析和某桥实际环境振动试验分析，验证了方法的有效性，结果还表明在结构模态参数较为密集的时候，提高复Morlet小波分辨率后进行分析能起到良好的模态解耦效果。
基于模式识别的思想，详细分析并研究了以结构曲率模态小波系数差Dd i作为损伤识别指标的可行性、适用性和噪声鲁棒性。对于简单结构和复杂结构在单一损伤、多损伤模式下进行了不同损伤程度的分析，大量分析结果指出，随着损伤程度的增加，构建损伤识别指标所需的模态阶数也逐渐降低；对于边界处损伤单元，提出以信号扩展的方法对结构曲率模态进行边界延拓，使其可以得到完整的边界处单元损伤识别指标信息；通过对复杂结构多损伤工况的分析，指出由于损伤对于各部位结构特性影响程度不同，采用Dd i损伤识别指标进行整体识别时易出现误判和漏判现象，提出了基于Dd i损伤识别指标的复杂结构分段识别方法，并通过分析验证了分段识别可以在很大程度上避免误判和漏判现象。
结构的较高阶模态的测试识别误差相对较大，对结构弱损伤识别造成一定影响，针对Dd i指标的应用局限性，提出了一种新的可供参考的损伤识别指标，即柔度曲率小波系数差的损伤识别指标C di，通过数值和仿真算例分析指出以C di作为损伤识别指标，在结构振动频率相差较大时，仅需要构建结构的低阶损伤指标，就可以对结构在发生弱损伤时进行识别；对于复杂结构，需要其振动频率相近的前几阶模态来构建损伤识别指标；建立了损伤程度与C di指标的回归关系以用来估计损伤程度；同时分析了该指标的噪声鲁棒性。通过对两种损伤识别指标的分析研究，从损伤程度和结构自身力学特性的角度分析对比了Dd i损伤指标和C di损伤指标的适用性。
根据健康监测系统的功能和目的，结合成本——效益分析，设计并建立了陕西省第一个投入使用的桥梁健康监测系统，详细介绍了该系统的组成及特点；深入探讨了桥梁健康监测的警情分析方法，提出桥梁监测警情分析应由损伤警情分析和运营状态警情分析两部分组成；建立了桥梁监测损伤警情分析模型，并对某特大连续刚构桥进行了信号采集→损伤预警→信号去噪→模态参数识别→损伤识别指标选择→损伤识别六个步骤的全过程研究，验证了提出的损伤警情分析体系的可行性；建立了桥梁运营状态警情分析模型，并根据其思想运用C++语言编制了某特大连续刚构桥挠度和应力预警程序。
研究了基于小波变换对反映桥梁状态的参数指标的监测数据的分析，提出将桥梁某一周期内的应变、挠度作为一维信号，对信号进行离散小波变换，由小波系数包含的信息得到了桥梁结构在监测周期内的总体状态趋势；通过对原信号和其小波系数的分析，对信号进行了重构，结合时间序列的ARIMA模型建立了监测参数指标的预测模型，并成功预测了一特大连续刚构桥某时刻后8期的挠度，对于结构状态参数的预测，可以掌握桥梁结构在未来一段时间内的运营状态信息，在结构运营状态监测预警中有重要的意义。
Bridge health monitoring is a combination of modern sensor technology,communications technology and evaluation system, which can provide real-time onlinemonitoring on the structural response in the environment and under the loads during thebridge operation process, and analyze the health status of bridge according to variousmonitoring indicators obtained, and send out timely warning in case of structural abnormality,to provide a scientific basis for the management and maintenance and repair of the bridge. Forthe existing and potential problems in damage and early warning during the bridge healthmonitoring, wavelet transform was adopted in this paper as the basic analytical tool, andapplied in the bridge health monitoring, thus presenting more systematic study in the bridgestructure test data de-noising, modal parameter identification, damage identification, warningsituation analysis, with research results having a certain of engineering application value.
Due to a variety of factors, the actual bridge test data often contain noise data, whichgreatly affects the structural damage identification and status assessment, therefore,controlling noise from test data fundamentally, to reduce the impact of noise interference ondata in the structural analysis, is a viable approach. Firstly, the principle of de-noising bymeans of wavelet transform modulus maxim and wavelet threshold was expounded, and thena simply supported beam structure modal shape was made as a one-dimensional signal,decomposition and reconstruction was conducted on the signal in these two de-noisingmethods under different noise levels, and according to the de-noised signal-to-noise ratio SNRand root mean square error RMSE these two indicators, it was found that the two methodscould significantly reduce the noise strength of modal shape signal, and through comparativeanalysis, it was pointed out that the wavelet threshold de-noising was more simple andefficient than the wavelet transform modulus maxim de-noising, which is better suited to thede-noising of bridge health monitoring data.
In this paper, it was explored that how the complex Morlet wavelet transform was usedin the modal parameter identification of structure under ambient excitation. Wavelet transformwas conducted in the structural dynamic response signal, and according to the informationcontained in the time-scale diagram of wavelet transform coefficients, its modulus and phasewere further obtained, so as to achieve the identification of structural modal parameters. Thenumerical simulation of a simply supported steam imposed with steady-state white noiseexcitation and an actual environment analysis vibration test were analyzed, to verify the validity of the method, and point out that when the structural modal parameters are moreintensive, to improve the resolution of the Morlet wavelet and then make the analysis canproduce good results.
Based on modal identification, the feasibility and suitability of the wavelet coefficientdifference of structural curvature modalDd ias damage identification index are analyzed andresearched in details. The different damage degrees of simple structure and of complexstructure are analyzed under single damage mode and multi-damage mode. Mass analysisresults indicate that: the modals to structure damage identification index will be graduallyreduced with intensification of damage degree; as for boundary damage element, signalextension method is raised for boundary extension of curvature modal so as to obtain integraldamage identification index information of boundary element; in terms of multi-damage modeof complex structure, the damage has different influences on structure characteristicparameters of different parts, thus, it is easy to cause wrong judgment or leak judgment inoverall identification whenDd idamage identification index is used so that the stageidentification of complex structure based onDd idamage identification index is put forward.In addition, it is verified that the stage identification can avoid wrong judgment and leakjudgment to a large extent in the analysis. The analysis also shows that the noise robustness ofDd iindex will be enhanced after the parameters are processed in wavelet thresholdde-noising method.
The test identification error of high level modal of the structure is relative big, whichmay bring certain influence on damage identification. Given application limitation ofDdiindex, a new damage identification index, namely, damage identification indexC diofflexibility curvature wavelet coefficient difference, is proposed for reference. The analysis onvalue and simulation example indicates that it is only required to form low level damageindex of the structure whenC diis used as damage identification index and structurevibration frequency differs much; for complex structure, the front modals with approximatevibration frequency are required to structure damage identification index; there is good noiserobustness of this index. On the basis of analysis and research on two damage identificationindexes, the selection principle ofDd idamage index andC didamage index are concludedin respect of damage degree and mechanical properties of the structure.
According to analysis on the benefit——cost, purposes and functions of healthmonitoring system, design and establish the first health monitoring system——health monitoring system of one super major bridge, which is the first example put into service, andintroduce its composition and characteristics. Deeply explore warning situation analysismethod of bridge health monitoring and mention that the warning situation analysis consistsof damage warning situation analysis and operation warning situation analysis. The fullprocess analysis of damage warning situation of one super major bridge is conducted and thefeasibility of recommended damage identification system is verified.
Research the monitoring data analysis of parameter index which can reflect bridge statusbased on wavelet transform, take bridge strain and deflection curve as one-dimensional signal,conduct multilevel wavelet decomposition of the signal and obtain general status tendency ofbridge structure in monitoring period through analysis on wavelet coefficient; analyzeeffective information of wavelet coefficient to reconstruct deflection curve signal of one supermajor bridge and combine ARIMA model of time series to build prediction model ofdeflection index so as to know operation status of bridge structure in a future period, which isquite significant for the monitoring and warning of structural operation status.
由于各种因素影响，桥梁的实际测试数据中往往包含了噪声信息，对结构损伤识别和状态评估等带来较大的影响，从根本上对测试数据进行噪声控制，降低结构分析中由于数据受到噪声干扰而带来的影响，是一种可行的方法。首先阐述了利用小波模极大值去噪和小波阈值去噪的原理，然后以一简支梁结构某阶模态振型作为一维信号，在不同的噪声水平下分别应用两种去噪方法对信号进行了分解重构，根据对信号去噪后的信噪比SNR和均方根误差RMSE两个指标信息的分析，说明了两种方法均能明显降低模态振型信号的噪声强度，通过对比分析，指出小波阈值去噪方法较小波模极大值去噪方法更为简单高效，是更适合于桥梁健康监测数据降噪的方法。
探讨了应用复Morlet小波变换对结构在环境激励下的模态参数识别方法，对结构动力响应信号进行小波变换，从其小波变换系数的时间-尺度图所含的信息，进一步得到其模和相位，从而实现结构模态参数的识别，并通过对一简支梁在稳态白噪声激励下的数值模拟分析和某桥实际环境振动试验分析，验证了方法的有效性，结果还表明在结构模态参数较为密集的时候，提高复Morlet小波分辨率后进行分析能起到良好的模态解耦效果。
基于模式识别的思想，详细分析并研究了以结构曲率模态小波系数差Dd i作为损伤识别指标的可行性、适用性和噪声鲁棒性。对于简单结构和复杂结构在单一损伤、多损伤模式下进行了不同损伤程度的分析，大量分析结果指出，随着损伤程度的增加，构建损伤识别指标所需的模态阶数也逐渐降低；对于边界处损伤单元，提出以信号扩展的方法对结构曲率模态进行边界延拓，使其可以得到完整的边界处单元损伤识别指标信息；通过对复杂结构多损伤工况的分析，指出由于损伤对于各部位结构特性影响程度不同，采用Dd i损伤识别指标进行整体识别时易出现误判和漏判现象，提出了基于Dd i损伤识别指标的复杂结构分段识别方法，并通过分析验证了分段识别可以在很大程度上避免误判和漏判现象。
结构的较高阶模态的测试识别误差相对较大，对结构弱损伤识别造成一定影响，针对Dd i指标的应用局限性，提出了一种新的可供参考的损伤识别指标，即柔度曲率小波系数差的损伤识别指标C di，通过数值和仿真算例分析指出以C di作为损伤识别指标，在结构振动频率相差较大时，仅需要构建结构的低阶损伤指标，就可以对结构在发生弱损伤时进行识别；对于复杂结构，需要其振动频率相近的前几阶模态来构建损伤识别指标；建立了损伤程度与C di指标的回归关系以用来估计损伤程度；同时分析了该指标的噪声鲁棒性。通过对两种损伤识别指标的分析研究，从损伤程度和结构自身力学特性的角度分析对比了Dd i损伤指标和C di损伤指标的适用性。
根据健康监测系统的功能和目的，结合成本——效益分析，设计并建立了陕西省第一个投入使用的桥梁健康监测系统，详细介绍了该系统的组成及特点；深入探讨了桥梁健康监测的警情分析方法，提出桥梁监测警情分析应由损伤警情分析和运营状态警情分析两部分组成；建立了桥梁监测损伤警情分析模型，并对某特大连续刚构桥进行了信号采集→损伤预警→信号去噪→模态参数识别→损伤识别指标选择→损伤识别六个步骤的全过程研究，验证了提出的损伤警情分析体系的可行性；建立了桥梁运营状态警情分析模型，并根据其思想运用C++语言编制了某特大连续刚构桥挠度和应力预警程序。
研究了基于小波变换对反映桥梁状态的参数指标的监测数据的分析，提出将桥梁某一周期内的应变、挠度作为一维信号，对信号进行离散小波变换，由小波系数包含的信息得到了桥梁结构在监测周期内的总体状态趋势；通过对原信号和其小波系数的分析，对信号进行了重构，结合时间序列的ARIMA模型建立了监测参数指标的预测模型，并成功预测了一特大连续刚构桥某时刻后8期的挠度，对于结构状态参数的预测，可以掌握桥梁结构在未来一段时间内的运营状态信息，在结构运营状态监测预警中有重要的意义。
Bridge health monitoring is a combination of modern sensor technology,communications technology and evaluation system, which can provide real-time onlinemonitoring on the structural response in the environment and under the loads during thebridge operation process, and analyze the health status of bridge according to variousmonitoring indicators obtained, and send out timely warning in case of structural abnormality,to provide a scientific basis for the management and maintenance and repair of the bridge. Forthe existing and potential problems in damage and early warning during the bridge healthmonitoring, wavelet transform was adopted in this paper as the basic analytical tool, andapplied in the bridge health monitoring, thus presenting more systematic study in the bridgestructure test data de-noising, modal parameter identification, damage identification, warningsituation analysis, with research results having a certain of engineering application value.
Due to a variety of factors, the actual bridge test data often contain noise data, whichgreatly affects the structural damage identification and status assessment, therefore,controlling noise from test data fundamentally, to reduce the impact of noise interference ondata in the structural analysis, is a viable approach. Firstly, the principle of de-noising bymeans of wavelet transform modulus maxim and wavelet threshold was expounded, and thena simply supported beam structure modal shape was made as a one-dimensional signal,decomposition and reconstruction was conducted on the signal in these two de-noisingmethods under different noise levels, and according to the de-noised signal-to-noise ratio SNRand root mean square error RMSE these two indicators, it was found that the two methodscould significantly reduce the noise strength of modal shape signal, and through comparativeanalysis, it was pointed out that the wavelet threshold de-noising was more simple andefficient than the wavelet transform modulus maxim de-noising, which is better suited to thede-noising of bridge health monitoring data.
In this paper, it was explored that how the complex Morlet wavelet transform was usedin the modal parameter identification of structure under ambient excitation. Wavelet transformwas conducted in the structural dynamic response signal, and according to the informationcontained in the time-scale diagram of wavelet transform coefficients, its modulus and phasewere further obtained, so as to achieve the identification of structural modal parameters. Thenumerical simulation of a simply supported steam imposed with steady-state white noiseexcitation and an actual environment analysis vibration test were analyzed, to verify the validity of the method, and point out that when the structural modal parameters are moreintensive, to improve the resolution of the Morlet wavelet and then make the analysis canproduce good results.
Based on modal identification, the feasibility and suitability of the wavelet coefficientdifference of structural curvature modalDd ias damage identification index are analyzed andresearched in details. The different damage degrees of simple structure and of complexstructure are analyzed under single damage mode and multi-damage mode. Mass analysisresults indicate that: the modals to structure damage identification index will be graduallyreduced with intensification of damage degree; as for boundary damage element, signalextension method is raised for boundary extension of curvature modal so as to obtain integraldamage identification index information of boundary element; in terms of multi-damage modeof complex structure, the damage has different influences on structure characteristicparameters of different parts, thus, it is easy to cause wrong judgment or leak judgment inoverall identification whenDd idamage identification index is used so that the stageidentification of complex structure based onDd idamage identification index is put forward.In addition, it is verified that the stage identification can avoid wrong judgment and leakjudgment to a large extent in the analysis. The analysis also shows that the noise robustness ofDd iindex will be enhanced after the parameters are processed in wavelet thresholdde-noising method.
The test identification error of high level modal of the structure is relative big, whichmay bring certain influence on damage identification. Given application limitation ofDdiindex, a new damage identification index, namely, damage identification indexC diofflexibility curvature wavelet coefficient difference, is proposed for reference. The analysis onvalue and simulation example indicates that it is only required to form low level damageindex of the structure whenC diis used as damage identification index and structurevibration frequency differs much; for complex structure, the front modals with approximatevibration frequency are required to structure damage identification index; there is good noiserobustness of this index. On the basis of analysis and research on two damage identificationindexes, the selection principle ofDd idamage index andC didamage index are concludedin respect of damage degree and mechanical properties of the structure.
According to analysis on the benefit——cost, purposes and functions of healthmonitoring system, design and establish the first health monitoring system——health monitoring system of one super major bridge, which is the first example put into service, andintroduce its composition and characteristics. Deeply explore warning situation analysismethod of bridge health monitoring and mention that the warning situation analysis consistsof damage warning situation analysis and operation warning situation analysis. The fullprocess analysis of damage warning situation of one super major bridge is conducted and thefeasibility of recommended damage identification system is verified.
Research the monitoring data analysis of parameter index which can reflect bridge statusbased on wavelet transform, take bridge strain and deflection curve as one-dimensional signal,conduct multilevel wavelet decomposition of the signal and obtain general status tendency ofbridge structure in monitoring period through analysis on wavelet coefficient; analyzeeffective information of wavelet coefficient to reconstruct deflection curve signal of one supermajor bridge and combine ARIMA model of time series to build prediction model ofdeflection index so as to know operation status of bridge structure in a future period, which isquite significant for the monitoring and warning of structural operation status.
引文
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