大跨度悬索桥的温度影响分析
|
摘要
随着桥梁分析理论、施工技术、材料性能的迅速发展,桥梁跨度越来越大,结构越来越柔,不仅要求精确严密的计算与施工技术,而且对桥梁建成后的安全运营提出了更高的要求。对这些大跨度结构进行健康监测与安全评估具有重要意义。桥梁健康监测是在一段较长的时间内通过传感器对结构的响应进行采集,从响应信号中提取出对结构损伤比较敏感的特征,进而区别无损或异常的结构,达到健康监测的目的。基于结构动力学参数的结构损伤识别方法,采用模拟的信号可取得比较好的识别结果,但应用到实际结构和实测信号当中,往往得不到较好的效果。其主要原因之一是,环境因素对结构损伤特征参数的影响有时会淹没掉因结构真实损伤造成的损伤特征参数的改变。因此,对桥梁进行健康监测不应忽略环境因素的影响,结构实际工作环境因素对损伤特征的影响,已成为结构健康监测领域研究的热点和难点。
本文以贵州坝陵河大桥健康监测实测数据为工程背景,采用理论、分析和实测的方法,分析环境温度变化对大跨度悬索桥结构长期性能的影响,重点研究环境温度对动应变实测数据的影响。论文的主要研究工作和结论包括：
1.根据坝陵河悬索桥长期监测数据,分析了环境温度对主梁挠度、塔的倾角、伸缩缝位移和主缆、吊索索力的影响,得到了悬索桥主塔和主跨跨中截面结构的温度变化情况。结果表明,反映桥梁结构物几何线形变化的数据(挠度、倾角和伸缩缝位移)以及吊索索力与温度都有较明显的相关性。
2.分别采用温度应变片和工作应变片,对坝陵河大桥跨中主桁杆件应变响应进行了长期测试。结果显示应变时程中的温度效应成分表现为趋势形式,其形成时间较长；车辆荷载引起的应变时程曲线表现为脉冲形式,历时很短。在此基础上,提出了采用信号分解的方法对应变时程中的温度效应成分和活载效应成分进行分离：首先根据工作应变片和温度应变片信号的功率分布情况确定了信号分离的截止频率。然后,采用解析模式分解法,根据截止频率将工作片原始应变时程分离为慢变成分和快变成分两部分。结果表明,由温度变化产生的应变时程波动(慢变成分)得到有效分离,该方法不仅能去除温度变化引起的应变片自身的应变,同时温度应力引起的应变亦得到有效剔除。通过雨流计数法对提取出的快变成分进行检验分析,快变成分较好地保留了桥梁动荷载产生的应变信息。
3.通过分解出的快变成分得到测试期间各测点的最大应力幅值,对比可知1月份和4月份测试期内通过坝陵河大桥的车辆最大载重情况差别不大。分解出的慢变成分中剔除变温度引起的应变片自身的应变,余下的应变成分反映了各测点结构温度应力的变化情况。4月测试期日温差较大,导致测点温度应力较1月份有大幅增长,且各测点日温差产生的结构温度应力要大于车辆活载产生的最大应力幅。
4.定义了动应变相关函数,证明了结构在白噪声激励下,应变时程的相关函数幅值向量仅与结构的固有频率、模态振型和阻尼比有关,规范化后的相关函数幅值向量具有较固定的比例形态。采用坝陵河大桥监测实测数据,研究了温度对动应变相关函数的影响,证明了以上结论。
5.提出了基于主成分分析的环境温度影响剔除方法,即对测点原始应变时程进行主成分分析,找出主要反映温度信息的特征子空间,将原始应变时程投影至温度特征子空间后再重构时程数据,得到原始应变时程的温度效应成分,由此来消除温度对应变信号的影响。坝陵河大桥动应变监测数据分析结果表明,第一主成分反映了动应变时程绝大部分的波动信息。通过第一主成分特征向量对实测数据进行重构,得到了应变时程中的温度效应成分。
6.基于实测应变数据的相关函数幅值向量在各时段的比例形态均存在差异,对坝陵河大桥动应变监测数据剔除温度效应成分后,所得到的相关函数幅值向量均呈现出一致的比例线形。结果表明,应变时程中的温度效应成分会导致相关函数幅值向量的比例线形发生改变,因此,若不考虑环境温度对应变时程相关函数幅值向量的影响,易对桥梁结构的健康状况产生误判。
With the rapid development of the structural analysis theory, construction techniques and building materials on bridges, the span is increasing and structure tends to be lightweight. Therefore, not only rigorous calculation and construction technology are required, but also higher standard for security operation of the finished bridge. Health monitoring and safety assessment on the large span structure is of great significance. In order to achieve the aim of health monitoring, the structure responses are collected through sensors in a long period, and damage sensitive features are extracted from response signals, then judge whether the structure is abnormal. When damage detection method based on the structural dynamic parameters is applied to simulant signals, the detection result may be good. However, the method in the application of the actual structure and the measured signal is difficult to obtain good results. The change in operating and environmental condition is one of the important factors. Effect of environmental factors on damage indices sometimes may cover the change of damage indices caused by real structure damage, and health monitoring should not ignore the influence of environmental factors. The environmental effect on damage indices has become a hot and difficult point in the research field.
In the thesis, effect of ambient temperature change on long term performance of large span suspension bridge, especially temperature effect on dynamic strain measured data, were analyzed based on the engineering background of Baling River Bridge in Guizhou. The main tasks and conclusions are as follows:
1. Through the long term measured data of Baling River Bridge, temperature effect on deflection of main girder, inclination of tower, displacement of expansion joints and force of the hanger and the cable strand were analyzed. Temperature changes of tower and structure in middle cross section of main span were understood. The results showed that the data reflecting the change of structural geometric configuration (deflection, inclination and displacement) and hanger force had obvious correlation with temperature.
2. Dynamic strains of the active strain gauges fixed on chord of steel truss at mid span of suspension bridge and inactive strain gauges, that didn't sense strains produced by stress but temperature variation induced strains, were measured for a long time. Temperature effect components of strain history showed trend form that experience in a long time. While the components of dynamic load effect, such as vehicle, presented impulse form that lasted shortly. Signal decomposition method was proposed to separate the information in strain data of the active gauges into temperature effect component and live-load effect component. According to power distribution of signals of the active and inactive strain gauges, the cut-off frequency was obtained for signal decomposition. Then, the measured strain data of active strain gauges were separated into the slow-varying component and fast-varying component by analytical mode decomposition method based on the cut-off frequency. It was shown that strain history fluctuation (slow-varying component) induced by varying temperature was extracted. Through the method, all of the gauges strain and stress-induced strain under temperature variation could be effectively eliminated. Via analysis of fast-varying component using rain-flow counting method, fast-varying component properly retained the strain information produced by dynamic load.
3. Maximum stress amplitudes of measuring points were obtained through the extracted fast-varying component during the test. According to amplitudes, it's concluded that maximum vehicle loads of test period in January and April on Baling River Bridge showed little difference. After eliminating the temperature variation-induced gauge strain from slow-varying component, the remaining component reflected the change of structure temperature stress of measuring points. In April, a larger daily temperature difference leaded to much higher temperature stress of measuring points than January and temperature stress produced by daily temperature difference was greater than maximum stress amplitude induced by vehicle load.
4. Correlation function of dynamic strain was defined. It was verified that under white noise excitation, the correlation function amplitude vector (Vcf) of strain history was only related to the natural frequency, mode shape and damping ratio of structure. After Vcf being normalized, it showed a fixed ratio shape. This conclusion was proved by studying temperature effect on correlation function of dynamic strain based on test data.
5. Based on principal component analysis, a method for eliminating the effect of environmental temperature was proposed. The principal component analysis was applied to the measured strain response, and the feature subspace mainly reflecting the temperature information was obtained. Through projecting the measured strain history into feature subspace of temperature and data reconstruction, temperature effect component was extracted. Then, temperature effect on strain signals could be removed. The analysis results of test data showed that the first principal component indicated most of the volatility of information. Through reconstruction of measured data with eigenvector of the first principal component, the temperature effect components of strain history were effectively extracted.
6. In different time period, the shapes of Vcf based on measured data were distinct. After temperature effect component being eliminated from test data, the shapes of Vcf performed consistent. It was showed that temperature effect component in test data leaded to various shapes of Vcf. Therefore, ignoring the temperature effect on the Vcf of strain history was prone to get the false judgment on the real operation condition of structure.
本文以贵州坝陵河大桥健康监测实测数据为工程背景,采用理论、分析和实测的方法,分析环境温度变化对大跨度悬索桥结构长期性能的影响,重点研究环境温度对动应变实测数据的影响。论文的主要研究工作和结论包括：
1.根据坝陵河悬索桥长期监测数据,分析了环境温度对主梁挠度、塔的倾角、伸缩缝位移和主缆、吊索索力的影响,得到了悬索桥主塔和主跨跨中截面结构的温度变化情况。结果表明,反映桥梁结构物几何线形变化的数据(挠度、倾角和伸缩缝位移)以及吊索索力与温度都有较明显的相关性。
2.分别采用温度应变片和工作应变片,对坝陵河大桥跨中主桁杆件应变响应进行了长期测试。结果显示应变时程中的温度效应成分表现为趋势形式,其形成时间较长；车辆荷载引起的应变时程曲线表现为脉冲形式,历时很短。在此基础上,提出了采用信号分解的方法对应变时程中的温度效应成分和活载效应成分进行分离：首先根据工作应变片和温度应变片信号的功率分布情况确定了信号分离的截止频率。然后,采用解析模式分解法,根据截止频率将工作片原始应变时程分离为慢变成分和快变成分两部分。结果表明,由温度变化产生的应变时程波动(慢变成分)得到有效分离,该方法不仅能去除温度变化引起的应变片自身的应变,同时温度应力引起的应变亦得到有效剔除。通过雨流计数法对提取出的快变成分进行检验分析,快变成分较好地保留了桥梁动荷载产生的应变信息。
3.通过分解出的快变成分得到测试期间各测点的最大应力幅值,对比可知1月份和4月份测试期内通过坝陵河大桥的车辆最大载重情况差别不大。分解出的慢变成分中剔除变温度引起的应变片自身的应变,余下的应变成分反映了各测点结构温度应力的变化情况。4月测试期日温差较大,导致测点温度应力较1月份有大幅增长,且各测点日温差产生的结构温度应力要大于车辆活载产生的最大应力幅。
4.定义了动应变相关函数,证明了结构在白噪声激励下,应变时程的相关函数幅值向量仅与结构的固有频率、模态振型和阻尼比有关,规范化后的相关函数幅值向量具有较固定的比例形态。采用坝陵河大桥监测实测数据,研究了温度对动应变相关函数的影响,证明了以上结论。
5.提出了基于主成分分析的环境温度影响剔除方法,即对测点原始应变时程进行主成分分析,找出主要反映温度信息的特征子空间,将原始应变时程投影至温度特征子空间后再重构时程数据,得到原始应变时程的温度效应成分,由此来消除温度对应变信号的影响。坝陵河大桥动应变监测数据分析结果表明,第一主成分反映了动应变时程绝大部分的波动信息。通过第一主成分特征向量对实测数据进行重构,得到了应变时程中的温度效应成分。
6.基于实测应变数据的相关函数幅值向量在各时段的比例形态均存在差异,对坝陵河大桥动应变监测数据剔除温度效应成分后,所得到的相关函数幅值向量均呈现出一致的比例线形。结果表明,应变时程中的温度效应成分会导致相关函数幅值向量的比例线形发生改变,因此,若不考虑环境温度对应变时程相关函数幅值向量的影响,易对桥梁结构的健康状况产生误判。
With the rapid development of the structural analysis theory, construction techniques and building materials on bridges, the span is increasing and structure tends to be lightweight. Therefore, not only rigorous calculation and construction technology are required, but also higher standard for security operation of the finished bridge. Health monitoring and safety assessment on the large span structure is of great significance. In order to achieve the aim of health monitoring, the structure responses are collected through sensors in a long period, and damage sensitive features are extracted from response signals, then judge whether the structure is abnormal. When damage detection method based on the structural dynamic parameters is applied to simulant signals, the detection result may be good. However, the method in the application of the actual structure and the measured signal is difficult to obtain good results. The change in operating and environmental condition is one of the important factors. Effect of environmental factors on damage indices sometimes may cover the change of damage indices caused by real structure damage, and health monitoring should not ignore the influence of environmental factors. The environmental effect on damage indices has become a hot and difficult point in the research field.
In the thesis, effect of ambient temperature change on long term performance of large span suspension bridge, especially temperature effect on dynamic strain measured data, were analyzed based on the engineering background of Baling River Bridge in Guizhou. The main tasks and conclusions are as follows:
1. Through the long term measured data of Baling River Bridge, temperature effect on deflection of main girder, inclination of tower, displacement of expansion joints and force of the hanger and the cable strand were analyzed. Temperature changes of tower and structure in middle cross section of main span were understood. The results showed that the data reflecting the change of structural geometric configuration (deflection, inclination and displacement) and hanger force had obvious correlation with temperature.
2. Dynamic strains of the active strain gauges fixed on chord of steel truss at mid span of suspension bridge and inactive strain gauges, that didn't sense strains produced by stress but temperature variation induced strains, were measured for a long time. Temperature effect components of strain history showed trend form that experience in a long time. While the components of dynamic load effect, such as vehicle, presented impulse form that lasted shortly. Signal decomposition method was proposed to separate the information in strain data of the active gauges into temperature effect component and live-load effect component. According to power distribution of signals of the active and inactive strain gauges, the cut-off frequency was obtained for signal decomposition. Then, the measured strain data of active strain gauges were separated into the slow-varying component and fast-varying component by analytical mode decomposition method based on the cut-off frequency. It was shown that strain history fluctuation (slow-varying component) induced by varying temperature was extracted. Through the method, all of the gauges strain and stress-induced strain under temperature variation could be effectively eliminated. Via analysis of fast-varying component using rain-flow counting method, fast-varying component properly retained the strain information produced by dynamic load.
3. Maximum stress amplitudes of measuring points were obtained through the extracted fast-varying component during the test. According to amplitudes, it's concluded that maximum vehicle loads of test period in January and April on Baling River Bridge showed little difference. After eliminating the temperature variation-induced gauge strain from slow-varying component, the remaining component reflected the change of structure temperature stress of measuring points. In April, a larger daily temperature difference leaded to much higher temperature stress of measuring points than January and temperature stress produced by daily temperature difference was greater than maximum stress amplitude induced by vehicle load.
4. Correlation function of dynamic strain was defined. It was verified that under white noise excitation, the correlation function amplitude vector (Vcf) of strain history was only related to the natural frequency, mode shape and damping ratio of structure. After Vcf being normalized, it showed a fixed ratio shape. This conclusion was proved by studying temperature effect on correlation function of dynamic strain based on test data.
5. Based on principal component analysis, a method for eliminating the effect of environmental temperature was proposed. The principal component analysis was applied to the measured strain response, and the feature subspace mainly reflecting the temperature information was obtained. Through projecting the measured strain history into feature subspace of temperature and data reconstruction, temperature effect component was extracted. Then, temperature effect on strain signals could be removed. The analysis results of test data showed that the first principal component indicated most of the volatility of information. Through reconstruction of measured data with eigenvector of the first principal component, the temperature effect components of strain history were effectively extracted.
6. In different time period, the shapes of Vcf based on measured data were distinct. After temperature effect component being eliminated from test data, the shapes of Vcf performed consistent. It was showed that temperature effect component in test data leaded to various shapes of Vcf. Therefore, ignoring the temperature effect on the Vcf of strain history was prone to get the false judgment on the real operation condition of structure.
引文
[1]Wang M L, Satpathi D. Damage detection of a model bridge using modal testing. Structural Health Monitoring[C], Current Status and Perspectives, Stanford University, Palo Alto,1997, CA,589-600.
[2]秦权.桥梁结构的健康监测[J].中国公路学报,2000,13(2):37-42.
[3]李亚东.既有桥梁评估初探[J].桥梁建设,1997(3):18-21.
[4]李宏男,高东伟,伊廷华.土木工程结构健康监测系统的研究状况与进展[J].力学进展,2008,38(2):151-166.
[5]Ko J M, Ni Y Q, Chan THT. Dynamic monitoring of structural health in cable-supported bridges[C]//Liu S C. Smart Systems for Bridges, Structures, and Highways. SPIE,1999,3671(161):161-172.
[6]Aktan A E, Catbas F N, Grimmelsman K A, et al. Issues in infrastructure health monitoring for management[J]. Journal of Engineering Mechanics,2000,126(7): 711-724.
[7]Ko J M, Ni Y Q. Technology developments in structural health monitoring of large-scale bridges[J]. Engineering Structures,2005,27(12):1715-1725.
[8]Ou J P and Li H. The art-in-the-art and practice of structural health monitoring for civil infrastructures in China[C]//Ou J P, Li H and Duan Z D. Structural Health Monitoring and Intelligent Infrastructure. London:Taylor & Francis,2006:69-88.
[9]Wang M L, Pran K L. A systematic numerical analysis of the damage index method used for bridge diagnostics[C]. Smart Structures and Materials 2000: Smart Systems for Bridge, Structures, and Highways, Proceedings of SPIE,2000, Vol.3988, Newport Beach, CA,154-164.
[10]杨智春,于哲峰.结构健康监测中的损伤检测技术研究进展[J].力学进展,2004,34(2)：215-222.
[11]Housner G W, Bergman L A, Caughney T K, et al. Structural control:past, present and future[J]. Journal of Engineering Mechanics,1997,123(2):897-971.
[12]Curran P, Tilly G Design and monitoring of the Flintshire Bridge[J]. Structural Engineering International, UK,1999,9(3):225-228.
[13]Andersen E Y, Pedersen L. Structural health monitoring of the Great Belt East Bridge[C], Proceedings of the 3rd Symposium on Strait Crossings, J. Krokeborg, A. A. Balkema, Rotterdam, Netherlands,1994:189-195.
[14]Brincker R, Frandsen J B, Andersen P. Ambient response analysis of the Great Belt Analysis [C]. Proceedings of 18th International Modal Analysis Conference, San Antonio, Texas,2000:26-32.
[15]Cheung M S. Instrumentation and field monitoring of the Confederation Bridge[C]. Proceedings of Workshop on Research and Monitoring of Long Span Bridge, Hong Kong, PRC,26-28 April,2000:109-118.
[16]Catbas F N, Grimmelsman K A, Aktan A E. Structural identification of the Commodore Barry Bridge[C]. Proc., SPIE, Nondestructive Evaluation of Highways, Utilities, and Pipelines IV, Newport Beach, Calif.,2000:84-97.
[17]Barrish R A, Grimmelsman K A, Aktan A E. Instrumented monitoring of the Commodore Barry Bridge[C]. Proc.,5th Int. Symp. on Nondestructive Evaluation and Health Monitoring of Aging Infrastructure, Proc. 2000, SPIE, 3995,98-111.
[18]Honshu-Shikoku Bridge Authority. The Akashi-Kaikyo Bridge-Design and Construction of the World's Longest Bridge[M]. Japan, October,1998.
[19]Chang Bang Yun. Recent R&D activities on structural health monitoring for civil infrastructures in Korea[C]. International Workshop on Advanced Sensors, Structural Health Monitoring, and Smart Structures, Keio University, November 2003:1-10.
[20]Galindez N, Marulanda J, Thomson P, et al. Implementation of a modal identification methodology on the Pereira-Dosquebradas Cable-stayed Bridge [C]. 16th ASCE Engineering Mechanics Conference, July 16-18,2003:1-11.
[21]李宏男,李东升.土木工程结构安全性评估、健康监测及诊断述评[J].地震工程与工程振动,2002,22(3)：82-90.
[22]高赞明,孙宗光,倪一清.基于振动方程的汲水门大桥损伤检测研究[J].地震工程与工程振动,2001,21(4):117-124.
[23]周文松,李惠,欧进萍,等.大型桥梁健康监测系统的数据采集子系统设计方法.公路交通科技,2006,23(3)：83-87.
[24]李爱群,缪长青,李兆霞,等.润扬长江大桥结构健康监测系统研究[J].东南大学学报,2003,33(5)：544-548.
[25]董学武,张宇封,徐宏,等.苏通大桥结构健康监测及安全评价系统简介[J]. 桥梁建设,2006(4):71-73.
[26]何旭辉,陈政清,黄方林,等.南京长江大桥安全监测和状态评估的初步研究[J].振动与冲击,2003,22(1)：75-78.
[27]尹仕健,曹映泓,张海明.湛江海湾大桥健康监测系统及其设计[J].中外公路,2006,26(5)：102-105.
[28]宗周红,任伟新,阮毅.土木工程结构损伤诊断研究进展[J].土木工程学报,2003,36(5)：105-110.
[29]韩大建,谢峻.大跨度桥梁健康监测技术的近期研究进展[J].桥梁建设,2002,(6)：69-73.
[30]Doebling S W, Farrar C R, Prime M B, et al. Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics:a literature review[R]. Los Alamos National Laboratory Report, LA-13070-MS,1996.
[31]Sohn H, Farrar C R, Hemez F M, et al. A Review of Structural Health Monitoring Literature:1996-2001[R]. Los Alamos National Laboratory Report, LA-13976-MS,2002.
[32]Cawley P, Adams R D, The location of defects in structures from measurements of the natural frequencies[J]. Journal of Strain Analysis for Engineering Design. 1979,14(2):49-57.
[33]Hearn G, Testa R B, Modal analysis for damage detection in structures[J]. Journal of Structural Engineering, ASCE,1991,117:3042-3063.
[34]Salawu O S. Detection of structural damage through changes in frequency:a review[J]. Engineering Structures.1997,19(9):718-723.
[35]Cornwell P, Farrar C R, Doebling S W, et al. Environmental variability of modal properties[J]. Experimental techniques,1999,23(6):45-48.
[36]West W M, Illustration of the use of modal assurance criterion to detect structural changes in all orbiter test specimen[C]. Proceedings of the 4th International Modal Analysis Conference,1:1-6.
[37]Srinivasan M G, Kot C A. Effects of damage on the modal parameters of a cylindrical shell [C]. in Proceeding of 10th International Modal Analysis Conference,1992:529-535.
[38]Dong C, Zhang P Q, Feng W Q, et al. The sensitivity study of the modal parameters of a cracked beam[C]. in Proceeding of 12th International Modal Analysis Conference,1994:98-104.
[39]周先雁,沈蒲生.用应变模态对混凝土结构进行损伤识别的研究[J].湖南大学学报,1997,24(5)：69-74.
[40]Ren W X, Roeck G D. Structural damage identification using modal data. Ⅰ: simulation verification[J]. Journal of Structural Engineering, ASCE.2002, 128(1):87-95.
[41]Ren W X, Roeck G D. Structural damage identification using modal data. Ⅱ:test verification[J]. Journal of Structural Engineering, ASCE.2002,128(1):96-104.
[42]Pandey A K, Biswas M, Samman M M. Damage detection from changes in curvature mode shapes[J]. Journal of Sound and Vibration,1991,145(2): 321-332.
[43]Maeck J, Wahab M A, Roeck G D, Damage localization in reinforced concrete beams by dynamic stiffness determination[C], Proceeding of 17th International Modal Analysis Conference,1999,1289-1295.
[44]Maeck J, Roeck G D. Dynamic bending and torsion stiffness derivation from modal curvatures and torsion rates [J], Journal of Sound and Vibration,1999, 225(1):153-170.
[45]Ho Y K, Ewins D J. On structural damage identification with mode shape[C]. Proceedings of COST F3 Conference on System Identification and Structural Health Monitoring. Madrid, Spain.2000:677-686.
[46]Chance J, Tomlinson G R, Worden K. A simplified approach to the numerical and experimental modeling of the dynamics of a cracked beam[C]. Proceedings of the 12th International Modal Analysis Conference. Florida, USA.1994: 778-785.
[47]Pandey A K, Biawas M. Damage detection in structures using changes in flexibility [J]. Journal of Sound and Vibration,1994, (169):3-17.
[48]Pandey A K, Biawas M. Experimental verification of flexibility difference method for locating damage in structures [J]. Journal of Sound and Vibration, 1995,184(2):311-328.
[49]Zhao J, Dewolf J T. Sensitivity study for vibrational parameters used in damage detection[J]. Journal of structural engineering,1999,125(4):410-416.
[50]Raghavendrachar M, Aktan A E. Flexibility by multireference impact testing for bridge diagnostics[J]. Journal of structural engineering,1992,118(8): 2186-2203.
[51]颜王吉,任伟新.基于代数算法的模态柔度灵敏度分析[J].铁道科学与工程学报,2009,6(5)：37-41.
[52]Lu Q, Ren G, Zhao Y. Multiple damage location with flexibility curvature and relative frequency change for beam structures [J]. Journal of Sound and Vibration, 2002,253(5):1101-1114.
[53]Chen J C, Garba J A. On-orbit damage assessment for large space structures [J]. AIAA Journal,1988,26(9):1098-1126.
[54]Stubbs N, Kim J T, Topole K. An efficient and robust algorithm for damage localization in offshore platforms [C]. Proceedings of the ASCE 10th Structure Congress,1992:543-546.
[55]Shi Z Y, Law S S. Structure damage localization from modal strain energy change[J]. Journal of Sound and Vibration,1998,218(5):825-844.
[56]Shi Z Y, Law S S, Zhang L M. Structural damage detection from modal strain energy change[J]. Journal of Engineering Mechanics, ASCE,2000,126(12): 1216-1223.
[57]Kim J T, Ryu Y S, Cho H M, et al. Damage identification in beam type structures: frequency-based method vs mode-shape-based method [J]. Engineering Structures,2003,25(1):57-67.
[58]Li H J, Yang H Z, James Hu S L. Modal strain energy decomposition method for damage localization in 3D frame structures [J]. Journal of Engineering Mechanics,2006,132(9):941-951.
[59]Lee U, Shin J. A frequency response function-based structural damage identification method[J]. Computers and Structures.2002,80(2):117-132.
[60]Maia N M, Silva J M M, Almas E A M, et al. Damage detection in structures: from mode shape to frequency response function methods[J]. Mechanical System and Signal Processing,2003,17(3):489-498.
[61]Park N G, Park Y S. Damage detection using spatially incomplete frequency response functions[J]. Mechanical Systems and Signal Processing,2003, 17(3):519-532.
[62]Maia N M M. Location of damage using curvature of the frequency response functions[C]. Proceedings of 15th IMAC. Florida,1997:942-946.
[63]Sampaio R P C, Maia N M M, Silva J M M. Damage detection using the frequency-response-function curvature method[J]. Journal of Sound and Vibration,1999,226(5):1029-1042.
[64]Mohammad Reza Banan, Yousef Mehdi-pour. Detection and assessment of damage in 2Dstructures using measured modal response [J]. Journal of Sound and Vibration,2007,306(3-5):803-817.
[65]Joyner M L. Comparison of two techniques for implementing the proper orthogonal decomposition method in damage detection problems [J]. Mathematical and Computer Modeling,2004,40(5-6):553-571.
[66]Hwang H Y, Kim C. Damage detection in structures using a few frequency response measurements[J]. Journal of Sound and Vibration,2004,270(1-2): 1-14.
[67]Lee U, Kim S. Identification of multiple directional damages in a thin cylindrical shell[J]. International Journal of Solids and Structures,2006,43(9):2723-2743.
[68]Kim H Y. Vibration-based damage identification using reconstructed FRFS in composite structures[J]. Journal of Sound and Vibration,2003,259(5): 1131-1146.
[69]Lew J S. Using transfer function parameter changes for damage detection of structures[J]. AIAA journal,1995,33(11):2189-2193.
[70]Mark J S. Detecting structural damage using transmittance function [C], Proceedings of 15th IMAC. Florida,1997:638-644.
[71]Wang Z, Lin R M, Lim M K. Structural damage detection using measured FRF data[J]. Computer methods in applied mechanics and engineering,1997, 147(1-2):187-197.
[72]Agneni A, Balis Crema L, Mastroddi F. Damage detection from truncated frequency response function[C]. European COST F3 Conference on System Identification and Structural Health Monitoring, Madrid, Spain,2000:137-146.
[73]Lee G C, Liang Z. Development of a bridge monitoring system [C]. Proceedings of the 2nd International Workshop on Structural Health Monitoring. Stanford: Stanford University,1999:349-358.
[74]Liang Z, Tong M, Lee G C. Complex modes in damped linear dynamic system[J]. The International Journal of Analytical and Experimental Modal Analysis,1992, 7(1):1-20.
[75]宗周红,Huang D Z, Wang T L.钢-混凝土组合桥损伤诊断[J].土木工程学报,2004,37(5)：59-69.
[76]Nair K K, Kiremidjian A S, Law K H. Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure[J]. Journal of Sound and Vibration,2006,291(1-2):349-368.
[77]Zhang H, Mita A. Two-stage damage diagnosis based on the distance between ARMA models and pre-whitening filters[J]. Smart Materials and Structures, 2007,16:1829-1836.
[78]Sohn H, Worden K, Farrar C R. Statistical damage classification under changing environmental and operational conditions[J]. Journal of Intelligent Material Systems and Structures,2002,13:561-574.
[79]Ko J M, Ni Y Q. Technology developments in structural health monitoring of large scale bridges[J]. Engineering Structures,2005,27(12):1715-1725.
[80]任伟新,韩建刚,孙增寿.小波分析在土木工程结构中的应用[M].北京：中国铁道出版社,2006.
[81]孙增寿.基于小波的土木工程结构损伤识别方法研究[D].福州：福州大学,2006.
[82]Wang Q, Deng X M. Damage detection with spatial wavelets[J]. International Journal of Solids and Structures,1999,36:2332-2357.
[83]Hou Z, Noori M, Amand R S. Wavelet-based approach for structural damage detection[J]. Journal of Engineering Mechanics, ASCE,2000,126(7):677-683.
[84]Gentile A, Messina A. On the continuous wavelet transforms applied to discrete vibrational data for detecting open cracks in damage beams [J]. International Journal of Solids and Structures,2003,40:295-315.
[85]Yam L H, Yan Y J, Jiang J S. Vibration-based damage detection for composite structures using wavelet transform and neural network identification[J]. Composite Structures,2003,60:403-412.
[86]Han J G, Ren W X, Sun Z S. Wavelet packet based damage identification of beam structures[J]. International Journal of Solids and Structures,2005,42: 6610-6627.
[87]Zhu X Q, Law S S. Wavelet-based crack identification of bridge beam from operational deflection time history[J]. International Journal of Solids and Structures,2006,43(7-8):2299-2317.
[88]Mizuno Y, Monroig E, Fujino Y. Wavelet decomposition-based approach for fast damage detection of civil structures [J]. Journal of Infrastructure Systems, ASCE, 2008,14(1):27-32.
[89]Rezaei D, Taheri F. Experimental validation of a novel structural damage detection method based on empirical mode decomposition[J]. Smart Materials and Structures,2009,18:1-14.
[90]Pines D, Salvino L. Structural health monitoring using empirical mode decomposition and the Hilbert phase[J]. Journal of Sound and Vibration,2006, 294(1-2):97-124.
[91]Yang J N, Lei Y, Lin S, et al. Hilbert-Huang based approach for structural damage detection[J]. Journal of Engineering Mechanics,2004,130(1):85-95.
[92]Imregun M, Visser W J. A review of model updating techniques [J]. The Shock and Vibration Digest,1991,23(1):9-20.
[93]Mottershead J E, Friswell M I. Model updating in structural dynamics:a survey[J]. Journal of Sound and Vibration,1993,167(2):347-375.
[94]Friswell M I, Mottershead J E. Finite element model updating in structural dynamics[M]. Kluwer Academic Publishers, Dordrecht, Netherlands,1995.
[95]Hemez F M, Doebling S W. Review and assessment of model updating for nonlinear, transient dynamics [J]. Mechanical Systems and Signal Processing, 2001,15(1):45-74.
[96]Link M. Updating of analytical models-review of numerical procedures and application aspects[M]. Structural Dynamics 2000, edited by D. J. Ewins and D. J. Inman, Research Studies Press Ltd. Baldock, UK,2001.
[97]Mottershead J E, Friswell M I, Ng G H T, et al. Geometric parameters for finite element model updating of joints and constraint[J]. Mechanical System and Signal Processing,1996,10(2):171-182.
[98]Brownjohn J M W, Xia P Q. Dynamic assessment of curved cable-stayed bridge by model updating[J]. Journal of Structural Engineering, ASCE,2001,126(2): 252-260.
[99]Goge D, Link M. Results obtained by minimizing natural frequency and mode shape errors of a beam model[J]. Mechanical Systems and Signal Processing, 2003,17(1):21-27.
[100]Jaishi B, Ren W X. Structural finite element model updating using ambient vibration test results[J]. Journal of Structural Engineering, ASCE,2005,131(4): 617-628.
[101]Jaishi B, Ren W X. Damage detection by finite element model updating using modal flexibility residual[J]. Journal of Sound and Vibration,2006,290(1-2): 369-387.
[102]Jaishi B, Ren W X. Finite element model updating based on eigenvalue and strain energy residual using multiobjective optimization technique [J]. Mechanical Systems and Signal Processing,2007,21(5):2295-2317.
[103]Doebling S W, Farrar C R, Cornwell P J. A computer toolbox for damage identification based on changes in vibration characteristics[C], Structural Health Monitoring, Current Status and Perspective, Stanford University, Palo Alto, CA,1997,241-254.
[104]Lin R M, Ewins D J. Analytical model improvement using frequency response function[J]. Mechanical Systems and Signal Processing,1994,8(4):437-458.
[105]Imregun M, Visser W J, Ewins D J. Finite element model updating using frequency response function data:I. Theory and initial investigation[J]. Mechanical Systems and Signal Processing,1995,9(2):187-202.
[106]Imregun M, Sanliturk K Y, Ewins D J. Finite element model updating using frequency response function data:Ⅱ. Case study on a medium-size finite element model[J]. Mechanical Systems and Signal Processing,1995,9(2): 203-213.
[107]Ratcliffe M J, Lieven N A J. An investigation into the effects of frequency response function estimators on modal updating [J], Mechanical Systems and Signal Processing,1999:13(2):315-334.
[108]Lin R M, Zhu J. Model updating of damage structures using FRF data[J]. Mechanical Systems and Signal Processing,2006,20(8):2200-2218.
[109]Agbabian M S, Masri S F, Miller R F, et al. System identification approach to detection of structural change[J]. ASCE Journal of Engineering Mechanics. 1990,117(2):370-390.
[110]Worden K, Manson G, Fieller N R J. Damage detection using outlier analysis [J]. Journal of Sound and Vibration,2000,229(3):647-667.
[111]Fang S E, Perera R, Huerta M C. Damage localization based on power spectral density analysis[J]. Journal of Key Engineering Materials,2007,347:589-594.
[112]于哲峰,杨智春.基于互相关函数幅值向量的结构损伤定位方法研究[J].振动与冲击,2006,25(3)：77-80.
[113]Farrar C R, Doebling S W, Nix D A. Vibration-based structural damage identification[J]. Philosophical Transactions of the Royal Society,2001,359: 131-149.
[114]陈志为.基于统计模式识别技术的结构异常检测[D].福州：福州大学,2005.
[115]Wood M G Damage analysis of bridge structures using vibrational techniques[D]. Ph.D. thesis, University of Aston, Birmingham, UK,1992.
[116]Moorty S, Roeder C W. Temperature-dependent bridge movements [J]. Journal of Structural Engineering, ASCE,1992,118(4):1090-1105.
[117]Rohrmann R G, Baessler M, Said S, et al. Structural causes of temperature affected modal data of civil structures obtained by long time monitoring [C]. In Proc. XVII Int. Modal Analysis Conference, Kissimmee, FL,1999:1-6.
[118]Helmicki A, Hunt V, Shell M, et al. Multidimensional performance monitoring of a recently constructed steel-stringer bridge [C]. In Proc.2nd Int. Workshop on Structural Health Monitoring, Stanford University, Palo Alto, CA,1999: 408-416.
[119]Doebling S W, Farrar C R. Using statistical analysis to enhance modal-based damage identification[C]. In Proc. DAMAS 97:structural damage assessment using advanced signal processing procedures, University of Sheffield, UK, 1997:199-210.
[120]Farrar C R, Baker W E, Bell T M, et al. Dynamic characterization and damage detection in the 1-40 bridge over the rio grande[R]. LA--12767-MS,1994.
[121]Askegaard V, Mossing P. Long term observation of RC-bridge using changes in natural frequencies [J]. Journal of Nordic concrete research,1988, (7):20-27.
[122]Liu C Y, DeWolf J T. Effect of temperature on modal variability of a curved bridge under ambient loads [J]. Journal of Structural Engineering,2007,133(12): 1742-1751.
[123]Moser P, Moaveni B. Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge[J]. Mechanical Systems and Signal Processing,2011,25(7):2336-2357.
[124]Zhao J, DeWolf J T. Dynamic monitoring of steel girder highway bridge [J]. Journal of Bridge Engineering, ASCE,2002,7(6):350-356.
[125]Xia Y, Hao H, Zanardo G, et al. Long term vibration monitoring of an RC slab: Temperature and humidity effect[J]. Engineering Structures,2006,28:441-452.
[126]孙君,李爱群,丁幼亮,邓扬.润扬大桥悬索桥模态频率-温度的季节相关性研究及其应用[J].工程力学,2009,26(9):50-55.
[127]林友勤.基于随机状态空间模型的结构损伤识别方法研究[D].福州：福州大学,2007.
[128]Sohn H, Dzwonezyk M, Straser E G, et al. An experimental study of temperature effect on modal parameters of the Alamos Canyon Bridge [J]. Earthquake Engineering and Structural Dynamics,1999,28(8):879-897.
[129]Lloyd G M, Wang M L, Singh V. Observed variations of mode frequencies of a prestressed concrete bridge with temperature [C]. In:Tassoulas JL, editor. Proceedings of the 14th Engineering Mechanics Conference. Reston:American Society of Civil Engineers,2000.
[130]Peeters B, Roeck G D. One-year monitoring of the z24-bridge:Environment effects versus damage event[J]. Earthquake engineering and structural dynamics,2001,30(2):149-171.
[131]樊可清,倪一清,高赞明.大跨度桥梁模态频率识别中的温度影响研究[J].中国公路学报,2006,19(2)：67-73.
[132]Ko J M, Chak K K, Wang J Y, et al, Formulation of an uncertainty model relating modal parameters and environmental factors by using long-term monitoring data[C]. in:S.-C. Liu (Ed.). Smart Systems and Nondestructive Evaluation for Civil Infrastructures, vol.5057, SPIE,2003.
[133]张启伟.桥梁健康监测中的损伤特征提取与异常诊断[J].同济大学学报(自然科学版),2003,31(3)：258-262.
[134]Ren W X. A singular value decomposition based truncation algorithm in solving the structural damage equations[J]. Acta Mechanica Solida Sinica,2005,18(2): 181-188.
[135]Ruotolo R, Surace C. Damage Detection Using Singular Value Decomposition[C], In Proceedings of the 2nd International Conference on Structural Damage Assessment using Advanced Signal Processing Procedures (DAMAS 97), Sheffield, England, UK,1997:87-96.
[136]Yan A M, Kerschen G, Boe P D, et al. Structural damage diagnosis under varying environmental conditions-Part Ⅰ:A linear analysis[J], Mechanical Systems and Signal Processing,2005,19(4):847-864.
[137]Magalhaes F, Cunha A, Caetano E. Vibration based structural health monitoring of an arch bridge:From automated OMA to damage detection[J]. Mechanical Systems and Signal Processing,2012,28:212-228.
[138]Bellino A, Fasana A, Garibaldi L, et al. PCA-based detection of damage in time-varying systems [J]. Mechanical Systems and Signal Processing,2010, 24(7):2250-2260.
[139]Manson G Identifying damage sensitive, environmental insensitive features for damage detection[C]. In 3rd Int. Conf. Identification in Engineering Systems, University of Wales Swansea, UK,2002.
[140]Sohn H, Park G, Wait J R, et al. Wavelet-based active sensing for delamination detection in composite structures [J]. Smart Materials and Structures.2004,13: 153-160.
[141]吴佰建,李兆霞,王滢,等.桥梁结构动态应变监测信息的分离与提取[J].东南大学学报(自然科学版),2008,38(5)：767-773.
[142]周毅,孙利民,闵志华.斜拉桥主梁应变监测数据分析[J].振动与冲击,2011,30(4)：230-235.
[143]李舜酩,李香莲.振动信号的现代分析技术与应用[M].北京：国防工业出版社,2008.
[144]Catbas F N, Susoy M, Frangopol D M. Structural health monitoring and reliability estimation:Long span truss bridge application with environmental monitoring data[J]. Engineering Structures,2008,30(9):2347-2359.
[145]Chen G D, Wang Z C. A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely spaced frequency components[J]. Mechanical Systems and Signal Processing,2012,28:258-279.
[146]Bedrosian E. A product theorem for Hilbert transform[C]. Proceedings of the IEEE,1963,51(5):868-869.
[147]Feldman M. A signal decomposition or lowpass filtering with Hilbert transform[J]. Mechanical Systems and Signal Processing,2011,25(8): 3205-3208.
[148]高镇同.疲劳统计学[M].北京：国防工业出版社,1986.
[149]雷家艳,姚谦峰,雷鹰,刘朝.基于随机振动响应互相关函数的结构损伤识别试验分析[J].振动与冲击,2011,30(8)：221-224.
[150]Li X Y, Law S S. Matrix of the covariance of covariance of acceleration responses for damage detection from ambient vibration measurements[J]. Mechanical Systems and Signal Processing,2010,24:945-956.
[151]庄表中,陈乃立.随机振动的理论及实例分析[M].地震出版社,1985.
[152]李德葆,陆海秋.实验模态分析及其应用[M].科学出版社,2001.
[153]Bendat J S, Piersol A G Engineering Application of Correlation and Spectral Analysis[M], Wiley, New York,1993.
[154]Jackson J E. A user's guide to Principal components[M]. New York:John Wiley, 1991
[155]Dong D, McAvoy T J. Nonlinear principal component analysis-Based on principal curves and neural networks[J]. Computers & Chemical Engineering, 1996,20(1):65-78.
[156]Deraemaeker A, Reynders E, Roeck G D, et al. Vibration-based structural health monitoring using output-only measurements under changing environment[J]. Mechanical Systems and Signal Processing,2008,22(1): 34-56.
[2]秦权.桥梁结构的健康监测[J].中国公路学报,2000,13(2):37-42.
[3]李亚东.既有桥梁评估初探[J].桥梁建设,1997(3):18-21.
[4]李宏男,高东伟,伊廷华.土木工程结构健康监测系统的研究状况与进展[J].力学进展,2008,38(2):151-166.
[5]Ko J M, Ni Y Q, Chan THT. Dynamic monitoring of structural health in cable-supported bridges[C]//Liu S C. Smart Systems for Bridges, Structures, and Highways. SPIE,1999,3671(161):161-172.
[6]Aktan A E, Catbas F N, Grimmelsman K A, et al. Issues in infrastructure health monitoring for management[J]. Journal of Engineering Mechanics,2000,126(7): 711-724.
[7]Ko J M, Ni Y Q. Technology developments in structural health monitoring of large-scale bridges[J]. Engineering Structures,2005,27(12):1715-1725.
[8]Ou J P and Li H. The art-in-the-art and practice of structural health monitoring for civil infrastructures in China[C]//Ou J P, Li H and Duan Z D. Structural Health Monitoring and Intelligent Infrastructure. London:Taylor & Francis,2006:69-88.
[9]Wang M L, Pran K L. A systematic numerical analysis of the damage index method used for bridge diagnostics[C]. Smart Structures and Materials 2000: Smart Systems for Bridge, Structures, and Highways, Proceedings of SPIE,2000, Vol.3988, Newport Beach, CA,154-164.
[10]杨智春,于哲峰.结构健康监测中的损伤检测技术研究进展[J].力学进展,2004,34(2)：215-222.
[11]Housner G W, Bergman L A, Caughney T K, et al. Structural control:past, present and future[J]. Journal of Engineering Mechanics,1997,123(2):897-971.
[12]Curran P, Tilly G Design and monitoring of the Flintshire Bridge[J]. Structural Engineering International, UK,1999,9(3):225-228.
[13]Andersen E Y, Pedersen L. Structural health monitoring of the Great Belt East Bridge[C], Proceedings of the 3rd Symposium on Strait Crossings, J. Krokeborg, A. A. Balkema, Rotterdam, Netherlands,1994:189-195.
[14]Brincker R, Frandsen J B, Andersen P. Ambient response analysis of the Great Belt Analysis [C]. Proceedings of 18th International Modal Analysis Conference, San Antonio, Texas,2000:26-32.
[15]Cheung M S. Instrumentation and field monitoring of the Confederation Bridge[C]. Proceedings of Workshop on Research and Monitoring of Long Span Bridge, Hong Kong, PRC,26-28 April,2000:109-118.
[16]Catbas F N, Grimmelsman K A, Aktan A E. Structural identification of the Commodore Barry Bridge[C]. Proc., SPIE, Nondestructive Evaluation of Highways, Utilities, and Pipelines IV, Newport Beach, Calif.,2000:84-97.
[17]Barrish R A, Grimmelsman K A, Aktan A E. Instrumented monitoring of the Commodore Barry Bridge[C]. Proc.,5th Int. Symp. on Nondestructive Evaluation and Health Monitoring of Aging Infrastructure, Proc. 2000, SPIE, 3995,98-111.
[18]Honshu-Shikoku Bridge Authority. The Akashi-Kaikyo Bridge-Design and Construction of the World's Longest Bridge[M]. Japan, October,1998.
[19]Chang Bang Yun. Recent R&D activities on structural health monitoring for civil infrastructures in Korea[C]. International Workshop on Advanced Sensors, Structural Health Monitoring, and Smart Structures, Keio University, November 2003:1-10.
[20]Galindez N, Marulanda J, Thomson P, et al. Implementation of a modal identification methodology on the Pereira-Dosquebradas Cable-stayed Bridge [C]. 16th ASCE Engineering Mechanics Conference, July 16-18,2003:1-11.
[21]李宏男,李东升.土木工程结构安全性评估、健康监测及诊断述评[J].地震工程与工程振动,2002,22(3)：82-90.
[22]高赞明,孙宗光,倪一清.基于振动方程的汲水门大桥损伤检测研究[J].地震工程与工程振动,2001,21(4):117-124.
[23]周文松,李惠,欧进萍,等.大型桥梁健康监测系统的数据采集子系统设计方法.公路交通科技,2006,23(3)：83-87.
[24]李爱群,缪长青,李兆霞,等.润扬长江大桥结构健康监测系统研究[J].东南大学学报,2003,33(5)：544-548.
[25]董学武,张宇封,徐宏,等.苏通大桥结构健康监测及安全评价系统简介[J]. 桥梁建设,2006(4):71-73.
[26]何旭辉,陈政清,黄方林,等.南京长江大桥安全监测和状态评估的初步研究[J].振动与冲击,2003,22(1)：75-78.
[27]尹仕健,曹映泓,张海明.湛江海湾大桥健康监测系统及其设计[J].中外公路,2006,26(5)：102-105.
[28]宗周红,任伟新,阮毅.土木工程结构损伤诊断研究进展[J].土木工程学报,2003,36(5)：105-110.
[29]韩大建,谢峻.大跨度桥梁健康监测技术的近期研究进展[J].桥梁建设,2002,(6)：69-73.
[30]Doebling S W, Farrar C R, Prime M B, et al. Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics:a literature review[R]. Los Alamos National Laboratory Report, LA-13070-MS,1996.
[31]Sohn H, Farrar C R, Hemez F M, et al. A Review of Structural Health Monitoring Literature:1996-2001[R]. Los Alamos National Laboratory Report, LA-13976-MS,2002.
[32]Cawley P, Adams R D, The location of defects in structures from measurements of the natural frequencies[J]. Journal of Strain Analysis for Engineering Design. 1979,14(2):49-57.
[33]Hearn G, Testa R B, Modal analysis for damage detection in structures[J]. Journal of Structural Engineering, ASCE,1991,117:3042-3063.
[34]Salawu O S. Detection of structural damage through changes in frequency:a review[J]. Engineering Structures.1997,19(9):718-723.
[35]Cornwell P, Farrar C R, Doebling S W, et al. Environmental variability of modal properties[J]. Experimental techniques,1999,23(6):45-48.
[36]West W M, Illustration of the use of modal assurance criterion to detect structural changes in all orbiter test specimen[C]. Proceedings of the 4th International Modal Analysis Conference,1:1-6.
[37]Srinivasan M G, Kot C A. Effects of damage on the modal parameters of a cylindrical shell [C]. in Proceeding of 10th International Modal Analysis Conference,1992:529-535.
[38]Dong C, Zhang P Q, Feng W Q, et al. The sensitivity study of the modal parameters of a cracked beam[C]. in Proceeding of 12th International Modal Analysis Conference,1994:98-104.
[39]周先雁,沈蒲生.用应变模态对混凝土结构进行损伤识别的研究[J].湖南大学学报,1997,24(5)：69-74.
[40]Ren W X, Roeck G D. Structural damage identification using modal data. Ⅰ: simulation verification[J]. Journal of Structural Engineering, ASCE.2002, 128(1):87-95.
[41]Ren W X, Roeck G D. Structural damage identification using modal data. Ⅱ:test verification[J]. Journal of Structural Engineering, ASCE.2002,128(1):96-104.
[42]Pandey A K, Biswas M, Samman M M. Damage detection from changes in curvature mode shapes[J]. Journal of Sound and Vibration,1991,145(2): 321-332.
[43]Maeck J, Wahab M A, Roeck G D, Damage localization in reinforced concrete beams by dynamic stiffness determination[C], Proceeding of 17th International Modal Analysis Conference,1999,1289-1295.
[44]Maeck J, Roeck G D. Dynamic bending and torsion stiffness derivation from modal curvatures and torsion rates [J], Journal of Sound and Vibration,1999, 225(1):153-170.
[45]Ho Y K, Ewins D J. On structural damage identification with mode shape[C]. Proceedings of COST F3 Conference on System Identification and Structural Health Monitoring. Madrid, Spain.2000:677-686.
[46]Chance J, Tomlinson G R, Worden K. A simplified approach to the numerical and experimental modeling of the dynamics of a cracked beam[C]. Proceedings of the 12th International Modal Analysis Conference. Florida, USA.1994: 778-785.
[47]Pandey A K, Biawas M. Damage detection in structures using changes in flexibility [J]. Journal of Sound and Vibration,1994, (169):3-17.
[48]Pandey A K, Biawas M. Experimental verification of flexibility difference method for locating damage in structures [J]. Journal of Sound and Vibration, 1995,184(2):311-328.
[49]Zhao J, Dewolf J T. Sensitivity study for vibrational parameters used in damage detection[J]. Journal of structural engineering,1999,125(4):410-416.
[50]Raghavendrachar M, Aktan A E. Flexibility by multireference impact testing for bridge diagnostics[J]. Journal of structural engineering,1992,118(8): 2186-2203.
[51]颜王吉,任伟新.基于代数算法的模态柔度灵敏度分析[J].铁道科学与工程学报,2009,6(5)：37-41.
[52]Lu Q, Ren G, Zhao Y. Multiple damage location with flexibility curvature and relative frequency change for beam structures [J]. Journal of Sound and Vibration, 2002,253(5):1101-1114.
[53]Chen J C, Garba J A. On-orbit damage assessment for large space structures [J]. AIAA Journal,1988,26(9):1098-1126.
[54]Stubbs N, Kim J T, Topole K. An efficient and robust algorithm for damage localization in offshore platforms [C]. Proceedings of the ASCE 10th Structure Congress,1992:543-546.
[55]Shi Z Y, Law S S. Structure damage localization from modal strain energy change[J]. Journal of Sound and Vibration,1998,218(5):825-844.
[56]Shi Z Y, Law S S, Zhang L M. Structural damage detection from modal strain energy change[J]. Journal of Engineering Mechanics, ASCE,2000,126(12): 1216-1223.
[57]Kim J T, Ryu Y S, Cho H M, et al. Damage identification in beam type structures: frequency-based method vs mode-shape-based method [J]. Engineering Structures,2003,25(1):57-67.
[58]Li H J, Yang H Z, James Hu S L. Modal strain energy decomposition method for damage localization in 3D frame structures [J]. Journal of Engineering Mechanics,2006,132(9):941-951.
[59]Lee U, Shin J. A frequency response function-based structural damage identification method[J]. Computers and Structures.2002,80(2):117-132.
[60]Maia N M, Silva J M M, Almas E A M, et al. Damage detection in structures: from mode shape to frequency response function methods[J]. Mechanical System and Signal Processing,2003,17(3):489-498.
[61]Park N G, Park Y S. Damage detection using spatially incomplete frequency response functions[J]. Mechanical Systems and Signal Processing,2003, 17(3):519-532.
[62]Maia N M M. Location of damage using curvature of the frequency response functions[C]. Proceedings of 15th IMAC. Florida,1997:942-946.
[63]Sampaio R P C, Maia N M M, Silva J M M. Damage detection using the frequency-response-function curvature method[J]. Journal of Sound and Vibration,1999,226(5):1029-1042.
[64]Mohammad Reza Banan, Yousef Mehdi-pour. Detection and assessment of damage in 2Dstructures using measured modal response [J]. Journal of Sound and Vibration,2007,306(3-5):803-817.
[65]Joyner M L. Comparison of two techniques for implementing the proper orthogonal decomposition method in damage detection problems [J]. Mathematical and Computer Modeling,2004,40(5-6):553-571.
[66]Hwang H Y, Kim C. Damage detection in structures using a few frequency response measurements[J]. Journal of Sound and Vibration,2004,270(1-2): 1-14.
[67]Lee U, Kim S. Identification of multiple directional damages in a thin cylindrical shell[J]. International Journal of Solids and Structures,2006,43(9):2723-2743.
[68]Kim H Y. Vibration-based damage identification using reconstructed FRFS in composite structures[J]. Journal of Sound and Vibration,2003,259(5): 1131-1146.
[69]Lew J S. Using transfer function parameter changes for damage detection of structures[J]. AIAA journal,1995,33(11):2189-2193.
[70]Mark J S. Detecting structural damage using transmittance function [C], Proceedings of 15th IMAC. Florida,1997:638-644.
[71]Wang Z, Lin R M, Lim M K. Structural damage detection using measured FRF data[J]. Computer methods in applied mechanics and engineering,1997, 147(1-2):187-197.
[72]Agneni A, Balis Crema L, Mastroddi F. Damage detection from truncated frequency response function[C]. European COST F3 Conference on System Identification and Structural Health Monitoring, Madrid, Spain,2000:137-146.
[73]Lee G C, Liang Z. Development of a bridge monitoring system [C]. Proceedings of the 2nd International Workshop on Structural Health Monitoring. Stanford: Stanford University,1999:349-358.
[74]Liang Z, Tong M, Lee G C. Complex modes in damped linear dynamic system[J]. The International Journal of Analytical and Experimental Modal Analysis,1992, 7(1):1-20.
[75]宗周红,Huang D Z, Wang T L.钢-混凝土组合桥损伤诊断[J].土木工程学报,2004,37(5)：59-69.
[76]Nair K K, Kiremidjian A S, Law K H. Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure[J]. Journal of Sound and Vibration,2006,291(1-2):349-368.
[77]Zhang H, Mita A. Two-stage damage diagnosis based on the distance between ARMA models and pre-whitening filters[J]. Smart Materials and Structures, 2007,16:1829-1836.
[78]Sohn H, Worden K, Farrar C R. Statistical damage classification under changing environmental and operational conditions[J]. Journal of Intelligent Material Systems and Structures,2002,13:561-574.
[79]Ko J M, Ni Y Q. Technology developments in structural health monitoring of large scale bridges[J]. Engineering Structures,2005,27(12):1715-1725.
[80]任伟新,韩建刚,孙增寿.小波分析在土木工程结构中的应用[M].北京：中国铁道出版社,2006.
[81]孙增寿.基于小波的土木工程结构损伤识别方法研究[D].福州：福州大学,2006.
[82]Wang Q, Deng X M. Damage detection with spatial wavelets[J]. International Journal of Solids and Structures,1999,36:2332-2357.
[83]Hou Z, Noori M, Amand R S. Wavelet-based approach for structural damage detection[J]. Journal of Engineering Mechanics, ASCE,2000,126(7):677-683.
[84]Gentile A, Messina A. On the continuous wavelet transforms applied to discrete vibrational data for detecting open cracks in damage beams [J]. International Journal of Solids and Structures,2003,40:295-315.
[85]Yam L H, Yan Y J, Jiang J S. Vibration-based damage detection for composite structures using wavelet transform and neural network identification[J]. Composite Structures,2003,60:403-412.
[86]Han J G, Ren W X, Sun Z S. Wavelet packet based damage identification of beam structures[J]. International Journal of Solids and Structures,2005,42: 6610-6627.
[87]Zhu X Q, Law S S. Wavelet-based crack identification of bridge beam from operational deflection time history[J]. International Journal of Solids and Structures,2006,43(7-8):2299-2317.
[88]Mizuno Y, Monroig E, Fujino Y. Wavelet decomposition-based approach for fast damage detection of civil structures [J]. Journal of Infrastructure Systems, ASCE, 2008,14(1):27-32.
[89]Rezaei D, Taheri F. Experimental validation of a novel structural damage detection method based on empirical mode decomposition[J]. Smart Materials and Structures,2009,18:1-14.
[90]Pines D, Salvino L. Structural health monitoring using empirical mode decomposition and the Hilbert phase[J]. Journal of Sound and Vibration,2006, 294(1-2):97-124.
[91]Yang J N, Lei Y, Lin S, et al. Hilbert-Huang based approach for structural damage detection[J]. Journal of Engineering Mechanics,2004,130(1):85-95.
[92]Imregun M, Visser W J. A review of model updating techniques [J]. The Shock and Vibration Digest,1991,23(1):9-20.
[93]Mottershead J E, Friswell M I. Model updating in structural dynamics:a survey[J]. Journal of Sound and Vibration,1993,167(2):347-375.
[94]Friswell M I, Mottershead J E. Finite element model updating in structural dynamics[M]. Kluwer Academic Publishers, Dordrecht, Netherlands,1995.
[95]Hemez F M, Doebling S W. Review and assessment of model updating for nonlinear, transient dynamics [J]. Mechanical Systems and Signal Processing, 2001,15(1):45-74.
[96]Link M. Updating of analytical models-review of numerical procedures and application aspects[M]. Structural Dynamics 2000, edited by D. J. Ewins and D. J. Inman, Research Studies Press Ltd. Baldock, UK,2001.
[97]Mottershead J E, Friswell M I, Ng G H T, et al. Geometric parameters for finite element model updating of joints and constraint[J]. Mechanical System and Signal Processing,1996,10(2):171-182.
[98]Brownjohn J M W, Xia P Q. Dynamic assessment of curved cable-stayed bridge by model updating[J]. Journal of Structural Engineering, ASCE,2001,126(2): 252-260.
[99]Goge D, Link M. Results obtained by minimizing natural frequency and mode shape errors of a beam model[J]. Mechanical Systems and Signal Processing, 2003,17(1):21-27.
[100]Jaishi B, Ren W X. Structural finite element model updating using ambient vibration test results[J]. Journal of Structural Engineering, ASCE,2005,131(4): 617-628.
[101]Jaishi B, Ren W X. Damage detection by finite element model updating using modal flexibility residual[J]. Journal of Sound and Vibration,2006,290(1-2): 369-387.
[102]Jaishi B, Ren W X. Finite element model updating based on eigenvalue and strain energy residual using multiobjective optimization technique [J]. Mechanical Systems and Signal Processing,2007,21(5):2295-2317.
[103]Doebling S W, Farrar C R, Cornwell P J. A computer toolbox for damage identification based on changes in vibration characteristics[C], Structural Health Monitoring, Current Status and Perspective, Stanford University, Palo Alto, CA,1997,241-254.
[104]Lin R M, Ewins D J. Analytical model improvement using frequency response function[J]. Mechanical Systems and Signal Processing,1994,8(4):437-458.
[105]Imregun M, Visser W J, Ewins D J. Finite element model updating using frequency response function data:I. Theory and initial investigation[J]. Mechanical Systems and Signal Processing,1995,9(2):187-202.
[106]Imregun M, Sanliturk K Y, Ewins D J. Finite element model updating using frequency response function data:Ⅱ. Case study on a medium-size finite element model[J]. Mechanical Systems and Signal Processing,1995,9(2): 203-213.
[107]Ratcliffe M J, Lieven N A J. An investigation into the effects of frequency response function estimators on modal updating [J], Mechanical Systems and Signal Processing,1999:13(2):315-334.
[108]Lin R M, Zhu J. Model updating of damage structures using FRF data[J]. Mechanical Systems and Signal Processing,2006,20(8):2200-2218.
[109]Agbabian M S, Masri S F, Miller R F, et al. System identification approach to detection of structural change[J]. ASCE Journal of Engineering Mechanics. 1990,117(2):370-390.
[110]Worden K, Manson G, Fieller N R J. Damage detection using outlier analysis [J]. Journal of Sound and Vibration,2000,229(3):647-667.
[111]Fang S E, Perera R, Huerta M C. Damage localization based on power spectral density analysis[J]. Journal of Key Engineering Materials,2007,347:589-594.
[112]于哲峰,杨智春.基于互相关函数幅值向量的结构损伤定位方法研究[J].振动与冲击,2006,25(3)：77-80.
[113]Farrar C R, Doebling S W, Nix D A. Vibration-based structural damage identification[J]. Philosophical Transactions of the Royal Society,2001,359: 131-149.
[114]陈志为.基于统计模式识别技术的结构异常检测[D].福州：福州大学,2005.
[115]Wood M G Damage analysis of bridge structures using vibrational techniques[D]. Ph.D. thesis, University of Aston, Birmingham, UK,1992.
[116]Moorty S, Roeder C W. Temperature-dependent bridge movements [J]. Journal of Structural Engineering, ASCE,1992,118(4):1090-1105.
[117]Rohrmann R G, Baessler M, Said S, et al. Structural causes of temperature affected modal data of civil structures obtained by long time monitoring [C]. In Proc. XVII Int. Modal Analysis Conference, Kissimmee, FL,1999:1-6.
[118]Helmicki A, Hunt V, Shell M, et al. Multidimensional performance monitoring of a recently constructed steel-stringer bridge [C]. In Proc.2nd Int. Workshop on Structural Health Monitoring, Stanford University, Palo Alto, CA,1999: 408-416.
[119]Doebling S W, Farrar C R. Using statistical analysis to enhance modal-based damage identification[C]. In Proc. DAMAS 97:structural damage assessment using advanced signal processing procedures, University of Sheffield, UK, 1997:199-210.
[120]Farrar C R, Baker W E, Bell T M, et al. Dynamic characterization and damage detection in the 1-40 bridge over the rio grande[R]. LA--12767-MS,1994.
[121]Askegaard V, Mossing P. Long term observation of RC-bridge using changes in natural frequencies [J]. Journal of Nordic concrete research,1988, (7):20-27.
[122]Liu C Y, DeWolf J T. Effect of temperature on modal variability of a curved bridge under ambient loads [J]. Journal of Structural Engineering,2007,133(12): 1742-1751.
[123]Moser P, Moaveni B. Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge[J]. Mechanical Systems and Signal Processing,2011,25(7):2336-2357.
[124]Zhao J, DeWolf J T. Dynamic monitoring of steel girder highway bridge [J]. Journal of Bridge Engineering, ASCE,2002,7(6):350-356.
[125]Xia Y, Hao H, Zanardo G, et al. Long term vibration monitoring of an RC slab: Temperature and humidity effect[J]. Engineering Structures,2006,28:441-452.
[126]孙君,李爱群,丁幼亮,邓扬.润扬大桥悬索桥模态频率-温度的季节相关性研究及其应用[J].工程力学,2009,26(9):50-55.
[127]林友勤.基于随机状态空间模型的结构损伤识别方法研究[D].福州：福州大学,2007.
[128]Sohn H, Dzwonezyk M, Straser E G, et al. An experimental study of temperature effect on modal parameters of the Alamos Canyon Bridge [J]. Earthquake Engineering and Structural Dynamics,1999,28(8):879-897.
[129]Lloyd G M, Wang M L, Singh V. Observed variations of mode frequencies of a prestressed concrete bridge with temperature [C]. In:Tassoulas JL, editor. Proceedings of the 14th Engineering Mechanics Conference. Reston:American Society of Civil Engineers,2000.
[130]Peeters B, Roeck G D. One-year monitoring of the z24-bridge:Environment effects versus damage event[J]. Earthquake engineering and structural dynamics,2001,30(2):149-171.
[131]樊可清,倪一清,高赞明.大跨度桥梁模态频率识别中的温度影响研究[J].中国公路学报,2006,19(2)：67-73.
[132]Ko J M, Chak K K, Wang J Y, et al, Formulation of an uncertainty model relating modal parameters and environmental factors by using long-term monitoring data[C]. in:S.-C. Liu (Ed.). Smart Systems and Nondestructive Evaluation for Civil Infrastructures, vol.5057, SPIE,2003.
[133]张启伟.桥梁健康监测中的损伤特征提取与异常诊断[J].同济大学学报(自然科学版),2003,31(3)：258-262.
[134]Ren W X. A singular value decomposition based truncation algorithm in solving the structural damage equations[J]. Acta Mechanica Solida Sinica,2005,18(2): 181-188.
[135]Ruotolo R, Surace C. Damage Detection Using Singular Value Decomposition[C], In Proceedings of the 2nd International Conference on Structural Damage Assessment using Advanced Signal Processing Procedures (DAMAS 97), Sheffield, England, UK,1997:87-96.
[136]Yan A M, Kerschen G, Boe P D, et al. Structural damage diagnosis under varying environmental conditions-Part Ⅰ:A linear analysis[J], Mechanical Systems and Signal Processing,2005,19(4):847-864.
[137]Magalhaes F, Cunha A, Caetano E. Vibration based structural health monitoring of an arch bridge:From automated OMA to damage detection[J]. Mechanical Systems and Signal Processing,2012,28:212-228.
[138]Bellino A, Fasana A, Garibaldi L, et al. PCA-based detection of damage in time-varying systems [J]. Mechanical Systems and Signal Processing,2010, 24(7):2250-2260.
[139]Manson G Identifying damage sensitive, environmental insensitive features for damage detection[C]. In 3rd Int. Conf. Identification in Engineering Systems, University of Wales Swansea, UK,2002.
[140]Sohn H, Park G, Wait J R, et al. Wavelet-based active sensing for delamination detection in composite structures [J]. Smart Materials and Structures.2004,13: 153-160.
[141]吴佰建,李兆霞,王滢,等.桥梁结构动态应变监测信息的分离与提取[J].东南大学学报(自然科学版),2008,38(5)：767-773.
[142]周毅,孙利民,闵志华.斜拉桥主梁应变监测数据分析[J].振动与冲击,2011,30(4)：230-235.
[143]李舜酩,李香莲.振动信号的现代分析技术与应用[M].北京：国防工业出版社,2008.
[144]Catbas F N, Susoy M, Frangopol D M. Structural health monitoring and reliability estimation:Long span truss bridge application with environmental monitoring data[J]. Engineering Structures,2008,30(9):2347-2359.
[145]Chen G D, Wang Z C. A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely spaced frequency components[J]. Mechanical Systems and Signal Processing,2012,28:258-279.
[146]Bedrosian E. A product theorem for Hilbert transform[C]. Proceedings of the IEEE,1963,51(5):868-869.
[147]Feldman M. A signal decomposition or lowpass filtering with Hilbert transform[J]. Mechanical Systems and Signal Processing,2011,25(8): 3205-3208.
[148]高镇同.疲劳统计学[M].北京：国防工业出版社,1986.
[149]雷家艳,姚谦峰,雷鹰,刘朝.基于随机振动响应互相关函数的结构损伤识别试验分析[J].振动与冲击,2011,30(8)：221-224.
[150]Li X Y, Law S S. Matrix of the covariance of covariance of acceleration responses for damage detection from ambient vibration measurements[J]. Mechanical Systems and Signal Processing,2010,24:945-956.
[151]庄表中,陈乃立.随机振动的理论及实例分析[M].地震出版社,1985.
[152]李德葆,陆海秋.实验模态分析及其应用[M].科学出版社,2001.
[153]Bendat J S, Piersol A G Engineering Application of Correlation and Spectral Analysis[M], Wiley, New York,1993.
[154]Jackson J E. A user's guide to Principal components[M]. New York:John Wiley, 1991
[155]Dong D, McAvoy T J. Nonlinear principal component analysis-Based on principal curves and neural networks[J]. Computers & Chemical Engineering, 1996,20(1):65-78.
[156]Deraemaeker A, Reynders E, Roeck G D, et al. Vibration-based structural health monitoring using output-only measurements under changing environment[J]. Mechanical Systems and Signal Processing,2008,22(1): 34-56.