梁式桥监测中的应变—位移转换技术及裂缝损伤识别方法研究
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摘要
桥梁是道路交通的咽喉，桥梁的通行能力直接决定着整个道路的通行能力。施工质量、材料老化以及交通荷载的增长等因素可能会导致桥梁的使用状态退化或不满足交通荷载增长的需求。在这种情况下，如果不对桥梁进行有效的监测，准确掌握桥梁的使用状态信息，很可能会导致桥塌车毁的交通事故，对人民的生命和财产造成极大地伤害。因此，桥梁监测是一项十分有意义的工作。
所谓桥梁监测就是采用预埋等方式在桥梁结构中布置一些监测仪器，实时采集桥梁的不同响应，根据响应对桥梁结构的使用状态进行判定。桥梁的监测参数一般包括位移、应变、变位、温度、动力响应等，而其中位移是一个容易精确测量的重要参数。并且位移可以同桥梁的刚度建立内在联系，因此桥梁结构的位移监测备受人们的青睐。当桥梁跨越江、河、山涧等障碍物，或跨越城市道路时，由于不能布设固定支架，传统的接触式位移测量方法存在无法安装的困难，并且位移测量装置存在人为损坏的风险。而采用可以固定于桥梁上的静力位移测试设备（例如静力水准仪等），又不能实时采集桥梁的动态位移信息。面对这种困境，如何实时获得桥梁结构的位移信息是一个十分有意义的研究课题。
对于梁式桥而言，桥梁结构的应变与位移存在一定的内在联系，通过应变的实时监测数据来获取位移信息是可行的。对于混凝土梁式桥，实测应变中包含了混凝土的徐变、收缩、温度、恒载以及活载等引起的应变。如果想要获得活载引起的桥梁结构位移响应，则需要实测到活载引起的桥梁应变。在混凝土梁式桥的监测中，实测应变包含了徐变、荷载等多种因素引起的应变。因此，如何从监测应变中对各种因素引起的应变进行分离是十分必要的。
裂缝是混凝土梁式桥最为典型的病害之一，裂缝对桥梁结构的耐久性、强度和稳定性都存在一定的影响。因此，准确的掌握裂缝信息，从而采取适当的维修和加固措施对于确保桥梁的安全通行是十分必要的。引起混凝土梁式桥出现裂缝的因素很多，例如荷载、温度变化、收缩、地基础变形、钢筋锈蚀、冻胀、施工材料质量以及施工工艺质量等都会引起裂缝。混凝土梁式桥中的裂缝一般存在两个特点：（1）隐蔽性，包括裂缝早起的隐蔽性和出现在隐蔽部位的裂缝隐蔽性；（2）数量多，对于使用一段时间的老桥，裂缝数量可能会很多。如果采用传统的无损检测方法，则势必要浪费大量的人力和物力，并且难以发现隐蔽部位的裂缝病害。研究表明，桥梁结构的动力参数对裂缝存在一定的敏感性。如何通过动力参数的变化来准确的识别出裂缝损伤是桥梁工程领域一个十分重要的研究方向。
本文依托863国家高科技研究发展计划项目“季节冻土区大范围道路灾害参数监测与辨识预警系统研究（2009AA11Z104）”，针对梁式桥监测中的应变-位移转换技术及裂缝损伤识别方法进行研究，主要开展了以下研究工作：
1、从位移和应变的基本定义出发，通过建立二者的内在联系，来形成基于应变计的梁式桥位移动态测量方法。本方法无需任何位移测量仪器，只利用已有的应变数据，便能实时地分析出桥梁位移，并能形成位移的动力响应。分别对简支梁和连续梁进行了数值模拟分析，模拟分析结果表明，采用本文方法形成的简支梁和连续梁位移静力响应和动力响应精度均较高，在应变数值混有1%随机误差的情况下位移的静力响应和动力响应的误差小于5%。
2、对徐变机理、徐变理论和徐变预测模式进行深入研究的基础上，采用有限元方法与递归方法相结合，形成了基于有限元方法的徐变效应分离两层次递归算法，该算法可以实现徐变效应引起的应变和外荷载引起应变的分离。以长春市东风大街立交桥为工程依托，对本文提出的徐变效应分离算法进行了验证。实践结果表明，本文提出的徐变效应分离算法是可行的和有效的。
3、对基于伯努利梁模型及基于有限元方法的带裂缝工作的简支梁模态参数理论分析模型进行了分析。基于理论分析模型计算了多种裂缝损伤工况下简支梁的模态参数，分析了裂缝宽度和裂缝高度等参数对简支梁模态参数的影响规律。并且对比了这两种理论计算模型的特点。
4、以多片简支梁桥为研究对象，采用基于模态柔度差曲率及优化支持向量机的分步识别法（PSO-SVM）实现其损伤位置及程度的识别。该方法首先通过模态柔度差曲率指标实现结构的损伤定位；其次通过粒子群优化支持向量机实现结构的损伤程度识别。以一座五片简支T梁桥的数值模拟结果来说明本文方法的识别精度和有效性。数值模拟结果表明，PSO-SVM可以准确的实现多片简支梁桥的单位置及多位置损伤定位；对裂缝深度的识别精度较高，最大相对误差为4.13%。
Bridge is the key part of road traffic, whose traffic capacity directly determines that ofthe whole road. The construction quality, material ageing and the increase in traffic load allmay lead to the degradation of bridge service state, or even the failure in meeting the needsof traffic load increase. In this case, the effective monitoring of bridge to accurately grasp ofthe bridge service condition is essential to avoid bridge collapse, which does great harm tothe people’s life and property. Thus, bridge monitoring is a meaningful task..
The so called bridge montoring is to set some monitoring devices in the bridge structureby embedment or other method, so as to timely collect the different responses of the bridge,by which the bridge service state is judged. Of all the monitoring parameters, such asdeflection, strain, displacement, tempreture and dynamic response, deflection is an importantparameter easy to be measured accurately. Because the relationship between the deflectionand the bridge stiffness can be easily found, deflection monitoring of the bridge structure isspecially favored by scholrs. When the bridge steps over the rivers,mountains or urban roads,the traditional contacting displacement measurement devices are difficult to be installed andrisk the artificial damage. What’s more, the static displacement measurement devices (suchas hydrostatic level) can not collect the bridge dynamic deflection information. To handle allthe trouble, it’s a meaningful subject to find a method of obtaining the bridge displacementinformation timely.
For beam bridges, there are some inner relationships between the bridge strain anddeflection. So it’s viable to to obtain the deflection information from the timely monitoringstrain data. For the concrete beam bridge, the measured strain data cover the strain arousedby the creep and shrink of the concrete, tempreture, dead load and live load. The obtain ofthe strain caused by live load needs actual measurement. While in the concrete beammontoring, the actual measurement includes the strain caused by creep, load and so on, soit’s necessary to separate the strain caused by different factors.
Crack is one of the most common damage in concrete beam bridges, which has effecton the bridge durability, strength and stability. Therefore, it’s meaningful to grasp the correctcrack information for taking some proper miantenaince and reinforcement measures toensure the bridge safety. Many factors may lead to the concrete cracks, such as the load, tempreture chang, shrink, foundation deformation, steel corrosion, frost heaving, quality ofthe construction material and the construction process. The cracks in the concrete beambridge have the following two features：first is the concealment, including the elusive crackcause and the crack location; second is the great amount, to a bridge in service for a longtime, cracks are in a large number. The traditional nondestructive detection method costs alarge amount of labour power and material resources, and is hard to find out the hiddencracks. Study shows that the bridge dynamic parameters have certain sensitivity to cracks.So how to detect the cracks accurately by dynamic parameters is an important researchdirection in bridge engineering field.
This paper relies on National High Technology Research and Development Program(“863Program”) of China (Project No.2009AA11Z104) and does some work on the thecrack identification method and strain-deflection transferring technology in beam bridgemonitoring, the researches conducted are as follows:
1. Based on the basic definition of the deflection and strain, the relationship isestablished to form the displacement dynamic measurement method for beam bridges bymeans of strain gauge. No displacement measurement devices are needed in this method,and only by the existing strain data can the bridge displacement be analyzed timely to formthe displacement response. Numerical simulation analysis for both the simply-supportedbeam and continuous beam bridge are conducted, and the results show that the proposedmethod in this paper provides a high level precision for displacement static response and thedynamic response of the simply-supported beam and the continuous beam bridge. The errorsof the displacement static and dynamic responses are less than5%with1%random errors instrain.
2. With the deep researches of creep mechanism, creep theory and the creep predictionmodel and the combination of the finite element method and the recursive method, the creeptwo-separative-stage recursive method is formed which can separate the strain caused bycreep and load. The Changchun Dong Feng Street Overpass, as a practical project, verifiesthe propsed separative method of this paper. The results show that, the method is practicableand effective.
3. Analysis is conducted on the Euler-Bernoulli beam model and the finite elementmodel of simply-supported beam with cracks. Based on the theoretical analysis models, thebeam modal parameters under several crack damage working conditions are calculated andthe influence laws of the crack with and the crack hight on the simply-supported modal parameters are analyzed. Then it discusses the features of the two theoretical models.
4. Taking the multi-span simply-supported beam as the study object, the detection ofdamage location and the damage extent are achieved by means of PSO-SVM. This methodfirst uses the change in curvature of flexibility to detect the damage location, then usespaticle optimization-based support vector machine to detect the damage extent. Thenumerical simulation results of a simply-supported beam bridge with five girders show thatthe proposed method is precise and effective. The results also show that PSO-SVM canaccurately identify the damage location of both the single and multiple location damage ofthe multi-girder simply-supported beam with a high level in damage extent identificationwhose maximum relative errors are4.13%
所谓桥梁监测就是采用预埋等方式在桥梁结构中布置一些监测仪器，实时采集桥梁的不同响应，根据响应对桥梁结构的使用状态进行判定。桥梁的监测参数一般包括位移、应变、变位、温度、动力响应等，而其中位移是一个容易精确测量的重要参数。并且位移可以同桥梁的刚度建立内在联系，因此桥梁结构的位移监测备受人们的青睐。当桥梁跨越江、河、山涧等障碍物，或跨越城市道路时，由于不能布设固定支架，传统的接触式位移测量方法存在无法安装的困难，并且位移测量装置存在人为损坏的风险。而采用可以固定于桥梁上的静力位移测试设备（例如静力水准仪等），又不能实时采集桥梁的动态位移信息。面对这种困境，如何实时获得桥梁结构的位移信息是一个十分有意义的研究课题。
对于梁式桥而言，桥梁结构的应变与位移存在一定的内在联系，通过应变的实时监测数据来获取位移信息是可行的。对于混凝土梁式桥，实测应变中包含了混凝土的徐变、收缩、温度、恒载以及活载等引起的应变。如果想要获得活载引起的桥梁结构位移响应，则需要实测到活载引起的桥梁应变。在混凝土梁式桥的监测中，实测应变包含了徐变、荷载等多种因素引起的应变。因此，如何从监测应变中对各种因素引起的应变进行分离是十分必要的。
裂缝是混凝土梁式桥最为典型的病害之一，裂缝对桥梁结构的耐久性、强度和稳定性都存在一定的影响。因此，准确的掌握裂缝信息，从而采取适当的维修和加固措施对于确保桥梁的安全通行是十分必要的。引起混凝土梁式桥出现裂缝的因素很多，例如荷载、温度变化、收缩、地基础变形、钢筋锈蚀、冻胀、施工材料质量以及施工工艺质量等都会引起裂缝。混凝土梁式桥中的裂缝一般存在两个特点：（1）隐蔽性，包括裂缝早起的隐蔽性和出现在隐蔽部位的裂缝隐蔽性；（2）数量多，对于使用一段时间的老桥，裂缝数量可能会很多。如果采用传统的无损检测方法，则势必要浪费大量的人力和物力，并且难以发现隐蔽部位的裂缝病害。研究表明，桥梁结构的动力参数对裂缝存在一定的敏感性。如何通过动力参数的变化来准确的识别出裂缝损伤是桥梁工程领域一个十分重要的研究方向。
本文依托863国家高科技研究发展计划项目“季节冻土区大范围道路灾害参数监测与辨识预警系统研究（2009AA11Z104）”，针对梁式桥监测中的应变-位移转换技术及裂缝损伤识别方法进行研究，主要开展了以下研究工作：
1、从位移和应变的基本定义出发，通过建立二者的内在联系，来形成基于应变计的梁式桥位移动态测量方法。本方法无需任何位移测量仪器，只利用已有的应变数据，便能实时地分析出桥梁位移，并能形成位移的动力响应。分别对简支梁和连续梁进行了数值模拟分析，模拟分析结果表明，采用本文方法形成的简支梁和连续梁位移静力响应和动力响应精度均较高，在应变数值混有1%随机误差的情况下位移的静力响应和动力响应的误差小于5%。
2、对徐变机理、徐变理论和徐变预测模式进行深入研究的基础上，采用有限元方法与递归方法相结合，形成了基于有限元方法的徐变效应分离两层次递归算法，该算法可以实现徐变效应引起的应变和外荷载引起应变的分离。以长春市东风大街立交桥为工程依托，对本文提出的徐变效应分离算法进行了验证。实践结果表明，本文提出的徐变效应分离算法是可行的和有效的。
3、对基于伯努利梁模型及基于有限元方法的带裂缝工作的简支梁模态参数理论分析模型进行了分析。基于理论分析模型计算了多种裂缝损伤工况下简支梁的模态参数，分析了裂缝宽度和裂缝高度等参数对简支梁模态参数的影响规律。并且对比了这两种理论计算模型的特点。
4、以多片简支梁桥为研究对象，采用基于模态柔度差曲率及优化支持向量机的分步识别法（PSO-SVM）实现其损伤位置及程度的识别。该方法首先通过模态柔度差曲率指标实现结构的损伤定位；其次通过粒子群优化支持向量机实现结构的损伤程度识别。以一座五片简支T梁桥的数值模拟结果来说明本文方法的识别精度和有效性。数值模拟结果表明，PSO-SVM可以准确的实现多片简支梁桥的单位置及多位置损伤定位；对裂缝深度的识别精度较高，最大相对误差为4.13%。
Bridge is the key part of road traffic, whose traffic capacity directly determines that ofthe whole road. The construction quality, material ageing and the increase in traffic load allmay lead to the degradation of bridge service state, or even the failure in meeting the needsof traffic load increase. In this case, the effective monitoring of bridge to accurately grasp ofthe bridge service condition is essential to avoid bridge collapse, which does great harm tothe people’s life and property. Thus, bridge monitoring is a meaningful task..
The so called bridge montoring is to set some monitoring devices in the bridge structureby embedment or other method, so as to timely collect the different responses of the bridge,by which the bridge service state is judged. Of all the monitoring parameters, such asdeflection, strain, displacement, tempreture and dynamic response, deflection is an importantparameter easy to be measured accurately. Because the relationship between the deflectionand the bridge stiffness can be easily found, deflection monitoring of the bridge structure isspecially favored by scholrs. When the bridge steps over the rivers,mountains or urban roads,the traditional contacting displacement measurement devices are difficult to be installed andrisk the artificial damage. What’s more, the static displacement measurement devices (suchas hydrostatic level) can not collect the bridge dynamic deflection information. To handle allthe trouble, it’s a meaningful subject to find a method of obtaining the bridge displacementinformation timely.
For beam bridges, there are some inner relationships between the bridge strain anddeflection. So it’s viable to to obtain the deflection information from the timely monitoringstrain data. For the concrete beam bridge, the measured strain data cover the strain arousedby the creep and shrink of the concrete, tempreture, dead load and live load. The obtain ofthe strain caused by live load needs actual measurement. While in the concrete beammontoring, the actual measurement includes the strain caused by creep, load and so on, soit’s necessary to separate the strain caused by different factors.
Crack is one of the most common damage in concrete beam bridges, which has effecton the bridge durability, strength and stability. Therefore, it’s meaningful to grasp the correctcrack information for taking some proper miantenaince and reinforcement measures toensure the bridge safety. Many factors may lead to the concrete cracks, such as the load, tempreture chang, shrink, foundation deformation, steel corrosion, frost heaving, quality ofthe construction material and the construction process. The cracks in the concrete beambridge have the following two features：first is the concealment, including the elusive crackcause and the crack location; second is the great amount, to a bridge in service for a longtime, cracks are in a large number. The traditional nondestructive detection method costs alarge amount of labour power and material resources, and is hard to find out the hiddencracks. Study shows that the bridge dynamic parameters have certain sensitivity to cracks.So how to detect the cracks accurately by dynamic parameters is an important researchdirection in bridge engineering field.
This paper relies on National High Technology Research and Development Program(“863Program”) of China (Project No.2009AA11Z104) and does some work on the thecrack identification method and strain-deflection transferring technology in beam bridgemonitoring, the researches conducted are as follows:
1. Based on the basic definition of the deflection and strain, the relationship isestablished to form the displacement dynamic measurement method for beam bridges bymeans of strain gauge. No displacement measurement devices are needed in this method,and only by the existing strain data can the bridge displacement be analyzed timely to formthe displacement response. Numerical simulation analysis for both the simply-supportedbeam and continuous beam bridge are conducted, and the results show that the proposedmethod in this paper provides a high level precision for displacement static response and thedynamic response of the simply-supported beam and the continuous beam bridge. The errorsof the displacement static and dynamic responses are less than5%with1%random errors instrain.
2. With the deep researches of creep mechanism, creep theory and the creep predictionmodel and the combination of the finite element method and the recursive method, the creeptwo-separative-stage recursive method is formed which can separate the strain caused bycreep and load. The Changchun Dong Feng Street Overpass, as a practical project, verifiesthe propsed separative method of this paper. The results show that, the method is practicableand effective.
3. Analysis is conducted on the Euler-Bernoulli beam model and the finite elementmodel of simply-supported beam with cracks. Based on the theoretical analysis models, thebeam modal parameters under several crack damage working conditions are calculated andthe influence laws of the crack with and the crack hight on the simply-supported modal parameters are analyzed. Then it discusses the features of the two theoretical models.
4. Taking the multi-span simply-supported beam as the study object, the detection ofdamage location and the damage extent are achieved by means of PSO-SVM. This methodfirst uses the change in curvature of flexibility to detect the damage location, then usespaticle optimization-based support vector machine to detect the damage extent. Thenumerical simulation results of a simply-supported beam bridge with five girders show thatthe proposed method is precise and effective. The results also show that PSO-SVM canaccurately identify the damage location of both the single and multiple location damage ofthe multi-girder simply-supported beam with a high level in damage extent identificationwhose maximum relative errors are4.13%
引文
[1]钱寅泉,张学亮,袁桂芳.中小跨径桥梁挠度测试方法比较[J].中外公路,2012,(2):89-32.
[2]郭飞,彭俊英.基于光纤布拉格光栅的桥梁检测[J].公路交通科技(应用技术版),2012,(1):127-130.
[3]飞张，伟刚，梁龙彬．光纤光栅与电阻应变片应变测量的对比分析[J]．传感技术学报，2001，6(3):200-204．
[4]周智，田石柱，欧进萍．光纤传感器在土木工程中的应用[J]．建筑结构，2002，32(5):65-66．
[5] Moyo P, Brownjohn J MW, Suresh R, et al. Development of f-iber Bragg grating sensorsfor monitoring civil infrastructure[J]. Engineering Structures,2005,27(12):1828-1834.
[6] Catbas F Necati. Structural healthmonitoring and reliability estimation:Long span trussbridge application with environmental monitoring data[J]. Engineering Structures,2008,30(9):2347-2359.
[7]贺志勇,盛飞.大跨度桥梁的变形监测及其精度分析[J].华南理工大学学报(自然科学版),2001,29(8):86-89.
[8]聂让.全站仪与高等级公路测量[M].北京:人民交通出版社,1997.
[9]姜晨光,刘华,刘桂芳,黄家兴.自动电子全站仪桥梁三维动态变形实时监测系统[J].铁路航测,2003,(2):38-40.
[10] Shunichi Nakamura. GPS measurement of wind-induced suspension bridgegirderdisplacements[J]. Journal of Structural Engineering,2000,10:1413-1419.
[11]许晓辉，朱桂新，陈旭东，王迎军.GPS桥梁三维位移自动监测系统的实现[J].华中科技大学学报，2003,9:37-39.
[12]张启伟，袁万城，范立础.大型桥梁结构安全监测的研究现状与发展[J].同济大学学报,1997,25:76-81.
[13]袁万城，崔飞，张启伟.桥梁健康监测与状态评估的研究现状与发展[J].同济大学学报,1999.27(2):184-188.
[14] Lau, C. K.，Wong, K. Y. and Ho, K. S., The Wind and Structural HealthMonitoring System (WASHMS) for the three Long-span Cable-supported Bridges inHong Kong, IABSE, International Association for Bridge and Structural Engineering,15th Congress, June16-20,1996, Copenhagen.
[15]钱帅杰,王存堂,唐立平,等.新型全方位电子水平仪的设计及误差分析[J].传感技术学报,2006,19(2):353-360.
[16]李佳列,颜国正,丁国清.一种新型数字式水平仪:原理与实现[J].传感技术学报,2001(3):191-195.
[17]郭永东.静力水准在桥梁施工竖向位移监控中的应用[J].山西建筑,2002,29(20):86-89.
[18]戴加东,王艳玲,伟洪.静力水准自动化监测系统在某工程中的应用[J].工程勘察,2009,(5):80-84
[19]何小元等.远距离、高精度二维动态位移测量[J].实验力学,1996,11(4):468-472.
[20]于承新等.数字摄影与计算机技术在实时监测结构变形中的应用[J].济南大学学报(自然科学版),2001,15(3):232-234.
[21]罗洪斌,赵文光,文银平.CCD图像监测系统应用于桥梁结构检测[J].华中科技大学学报(城市科学版),2006,23(10):91-93+96.
[22] STANTON JF, EBERHARD MO, BARR PJ. A weighted-stretched-wire system formonitoring deflections[J]. Engineering Structures,2003,25:347-357.
[23] ZHU Y, FU Y, CHEN W, et al. Online deflection monitoring system for dafosicable-stayed bridge[J]. Journal of Intelligent Material Systems and Structures,2006,17(8-9):701-707.
[24]余加勇，朱建军，邹峥嵘，张坤[J].大跨径桥梁挠度测量新方法研究[J].湖南大学学报(自然科学版)，2007，34(10):31-34.
[25]谢浩元.基于无线倾角传感器的桥梁挠度测量研究[D].大连：大连理工大学.2010.
[26]〔苏〕A.E.谢依金,等著.胡春芝,等译.水泥混凝土的结构与性能[M].北京：中国建筑工业出版社，1984.
[27]杜拱辰.现代预应力混凝土结构[M].北京：中国建筑工业出版社，1988.
[28]Paul ACker，Franz-losef Ulm. Creep and shrinkage of concrete: physical origin andpractical measurements[J].Nuclear Engineering and Design，2001(203):143-158.
[29]Z.PBaZant，Delayed thermal dilation of cement Paste and concrete due to masstransport[J]，Nuclear Engng.Design，1970(14):308-318.
[30]SongH-w，SongY-C.， Byum K-J.，etal. Modification of Creep-Prediction Equation ofConcrete utilizing Short-term CreeP Tests，Transaetion[R]， SMIRT16， WashingtonDC， August2001:l-7.
[31]Z.P.Baznat，S.Baweja. Justification and Refinements of Model B3for Concrete CreePand Shrinkgae[J].Materials and Surtcutres，1995，(28):438-495.
[32]Meyerson， R. Compressive Mixtures,Master of Science Creep of PrestressedConcrete Mixtures with and without Thesis in Civil Enginering， Virginal Tech，2001.
[33]Wassim Naguib,Amir Mirmiran. Creep Analysis of Axially Loaded Fiber ReinforcedPolymer-Confined Concrete Columns,Journal of Engineering Mechanics，2003:1308-1319.
[34] N.J，Garder， J.W.Zhao. Creep and Shrinkage Revisited[J]. ACI Materials Journal，1993，90(3):236-246.
[35] N.J.Garder，M.J.Loekman. Design Provisions for Drying Shrinkage and Creep ofNormal Strength-Concrete[J]. ACI Materials Journal，2001，98(2):159-167.
[36]龚洛书，惠满印，杨蓓.砼收缩与徐变的实用数学表达式「J」.建筑结构学报，1988(5):37-42。
[37]向小斌.大跨径连续刚构梁桥混凝土徐变试验研究[D].武汉：武汉理工大学，2007.
[38]丁文胜,吕志涛,孟少平,刘钊.混凝土收缩徐变预测模型的分析比较[J].桥梁建设,2004,(6):13-16.
[39]余志武,薛凯,丁发兴.灰色神经网络在混凝土结构徐变预测中的应用[J].铁道科学与工程学报,2009,6(2):12-16.
[40]潘立本,张苏俊.混凝土收缩与徐变的试验研究[J].河海大学学报,1997,25(5):84-89.
[41]陈志华,肖星荣.基于短期试验的高性能混凝土长期徐变预测[J].华东公路,2007,166(4):94-96.
[42]王辉,钱春香.基于苏通大桥混凝土短期试验结果的徐变预测模型修正[J].桥梁建设,2010,(2):32-36.
[43]刑铁雷.连续刚构桥静动力分析及混凝土应力测试试验[D].成都：西南交通大学，2008.
[44]汪剑,方志.大跨预应力混凝土箱梁桥收缩徐变效应测试与分析[J].土木工程学报,2008,41(1):70-81.
[45]刘宁,刘光廷.混凝土结构的随机温度及随机徐变应力[J].力学进展,1998,28(1):58-70.
[46]李洋波,李翔,黄达海.混凝土徐变度反演分析方法[J].三峡大学学报(自然科学版),2005,27(2):134-136.
[47]高政国,赵国藩.混凝土徐变分析的双功能函数表达[J].建筑材料学报,2001,4(3):250-254.
[48]张子明,周红军,殷波.基于等效时间的混凝土徐变[J].河海大学学报(自然科学版),2005,33(2):173-176.
[49]陈忠,张研,周红军.基于等效时间的混凝土徐变模型[J].河海大学学报(自然科学版),2011,39(3):302-305.
[50]陈松,柯敏勇,刘海祥,洪晓林.基于多孔介质理论的混凝土徐变力学行为的有限元分析[J].固体力学学报,2009,30(5):522-526.
[51]黄耀英,郑宏,周宜红.考虑拉压异性徐变的混凝土温度应力研究[J].武汉理工大学学报,2011,33(3):87-92.
[52]文永奎,陈政清.考虑预应力损失的混凝土梁徐变计算方法[J].中国铁道科学,2005,26(3):36-41.
[53]余报楚,张哲,李生勇,吴立之.一种混凝土桥梁徐变的有效计算方法[J].哈尔滨工业大学学报,2006,38(6):994-996.
[54]孙璨，傅学怡.应用徐变恢复效应建立的应变全量递推方法[J].哈尔滨工业大学学报,2010,42(4):562-567.
[55]方志,李艳,吴鹏扬.先简支后连续混凝土桥梁徐变影响的参数分析[J].桥梁建设,2003,(4):19-22.
[56]王俊,刘立新,尚世宇.预应力度对预应力混凝土梁徐变曲率影响试验研究[J].土木工程学报,2010,43(8):37-43.
[57]李建斌,石现峰.预应力混凝土连续梁桥的收缩徐变分析[J].石家庄铁道学院学报,2003,16(2):15-18.
[58]薛伟辰,胡于明,王巍.预应力混凝土梁徐变性能试验[J].中国公路学报,2008,21(4):61-66.
[59]M.-H. H. Shen, C. Pierre. Natural Modes of Bernoulli-Euler Beams with SymmetricCracks[J]. Journal of Sound and Vibration,1990,138(l):115-134.
[60]Y. Narkis. Identification of Crack Location in Vibrating Simply Supported Beams[J].Journal of Sound and Vibration,1994,(172):549–558.
[61]M.H.H.Shen, C.Pierre. Free vibration of beam with a single-edged crack[J]. Journal ofSound and Vibration,1994,170(2):237-259.
[62]E. I. Shifrin, R. Ruotolo. Natural Frequencies of a Beam with an Arbitrary Number ofCracks[J]. Journal of Sound and Vibration,1999,222(3):409–423.
[63]S. H. S. Carneiro. Comments on the Free Vibrations of Beams with a Single-EdgeCrack[J]. Journal of Sound and Vibration,2001,244(4):729-737.
[64]唐小兵,陈定方,沈成武.结构裂纹位置识别的模态分析[J].武汉理工大学学报,2001,23(5):71-74.
[65]N. T. Khiem, T. V. Lien. A Simplified Method for Natural Frequency Analysis of aMultiple Cracked Beam[J]. Journal of Sound and Vibration,2001,245(4):737-751.
[66]J. K. Sinha, M.I.Friswell,S. Edward. Simplified Models for the Location of Cracks inBeam Structures Using Measured Vibration Data[J]. Journal of Sound and Vibration,2002,251(1):13-38.
[67]H. P. Lin, S.C.Chang, J. D. Wu. Beam Vibrations with an Arbitrary Number ofCracks[J].Journal of Sound and Vibration,2002,258(5):987–999.
[68]王术新,姜哲.裂缝悬臂梁的振动特性及其裂缝参数识别[J]. Journal of Sound andVibration,2003,22(3):83-86.
[69]D.P. Patil, S.K. Maiti. Detection of multiple cracks using frequency measurements[J].Engineering Fracture Mechanics,2003,70:1553–1572.
[70]D.J. Gormana, Luigi Garibaldi. Accurate analytical type solutions for free vibrationfrequencies and mode shapes of multi-span bridge decks the span-by-span approach[J].Journal of Sound and Vibration,2006,290:321–336.
[71]陈长征，罗跃纲，白秉三，唐忠.结构损伤检测与智能诊断[M].北京：科学出版社，2001.
[72]张玲玲，马建劭.服役结构可靠性的模糊评判法及其应用[J].土木工程学报，2001，35（5）：20-23.
[73]邹大力.基于计算智能的结构损伤识别研究[D].大连理工大学博士学位论文，2005.
[74]秦权.桥梁结构的健康监测[J].中国公路学报，2000，13（2）：37-42.
[75]袁万城，崔飞，张启伟.桥梁健康监测与状态评估的现状与发展[J].同济大学学报，1999，27（2）：184-188.
[76]陈长征，罗跃纲，白秉三，唐忠.结构损伤检测与智能诊断[M].北京：科学出版社，2001.
[77]邹大力.基于计算智能的结构损伤识别研究[D].大连理工大学博士学位论文，2005.
[78] Doebling S W. Damage detection and health monitoring of structural and mechanicalsystems from changes in their vibration characteristics: a literature review[R]. LosAlamous National Laboratory Report.1996.
[79]童兆页.论计算智能及其应用[J].计算机研究与发展，1997,34（增刊）：1-4.
[80]何振亚.神经智能[M].长沙：湖南科学技术出版社，1997.
[81]钱敏平.龚光鲁.从数学角度看计算智能[J].科学通报，1999，（16）.
[82]周春光.梁艳春.计算智能.吉林大学出版社[M].2001.
[83]丁雯静.基于柔度矩阵和神经网络的损伤识别方法研究[D].西安：西北工业大学，硕士学位论文，2007.
[84]王兴林.基于径向基网络的损伤识别[D].南京：南京航空航天大学，硕士学位论文，2006.
[85] Cawley P，Adams R D. The location of defects in structures from measurements ofnatural frequencies[J]. Journal of strain analysis.1979，4(2)：49-57.
[86] GeorgeH，ReneBT. Modal analysis for damage detection in structures. Journal ofStructural Engineering，ASCE，1991，117(10):3042一3061.
[87] Robert Y. Liang, Fred K. Choy, Jialou Hu. Detection of cracks in beam structures usingmeasurements of natural frequencies [J], Journal of the Franklin Institute,1991,328(4):505-518.
[88] Friswell M I, Penny JET，Wilson DA. Using vibration data and statistical measures tolocate damage in structures. The International Journal of Analytical and ExperimentalModal Analysis，1994，9(4):239一254.
[89]高芳清，金建明，高淑英.基于模态分析的结构损伤检测方法研究[J]，西南交通大学学报，1998，33（1）：108-113.
[90] S. Hassiotis. Identification of damage using natural frequencies and Markovparameters[J], Journal of Computers and Structures,2000,74:365-373.
[91] Salawu,O S. Detection of Structural damage through changes in frequency: a review.Engineering Structures.1997.19(9):718一723.
[92]钟军军，董聪，夏开全.基于频率及振型参数的结构损伤识别方法[J]，华中科技大学学报(城市科学版)，2009，26（4）：1-9.
[93] Allemang, R.J., Brown, D.L.,1982. A correlation coefficient for modal vectoranalysis[C]. Proc.1st Int. Modal Anal. Conf.1,110–116.
[94] Lieven, N.A.J., Ewins, D.J.,1988. Spatial correlation of mode shapes the coordinatemodal assurance criterion (COMAC)[C]. Proc.6th Int. Modal Anal. Conf.1,690–695.
[95] West, W. M. illustration of the use of modal assurance criterion to detect structuralchanges in an orbiter test specimen[C]. Proceedings of the air force Conference onAircraft Structural Integrity，USA，1984:l-6.
[96] Fox C H J. The location of defects in structures: A comparison of the use of naturalFrequency and mode shape data[C], Proc of the10th IMAC,1992:522-528.
[97] Pandey A K，Biswas M，Samman M M. Damage detection from changes in curvaturemode shapes. Journal of Sound and Vibration.1991.145(2):32l-332.
[98] SalawU O S, Willimas C. Damage location using vibration model shapes.Proceedings of the12thInternational Modal Analysis Conefronce.1994:933-939.
[99] Z. Y. SHI, S. S. LAW. Structural damage localization from modal strain energychange[J], Journal of Sound and Vibration,1998,218(5):825-844.
[100]张勇，静行，袁海庆.基于曲率模态变化率指标的结构损伤识别[J]，华中科技大学学报(城市科学版)，2010,27（2）：82-86.
[101]赵玲，李爱群.基于单元应变能变化率的结构损伤识别方法[J]，东南大学学报(自然科学版)，2007，37（6）：1052-1056.
[102] Z. Zhang, A. E. Aktan. Application of Modal Flexibility and Its Derivatives inStructural Identification[J], Res Nondestr Eval,1998,10:43-61.
[103] ZhaoJ，DewolfJ. Sensitivity study for vibration parameters used in damage detection.Journal of Structural Engineering，1999，125(4):410-416.
[104]LuQ，RenG，ZhaoY. Multiple damage location with flexibility curvature and relativefrequency change for beam structure.Journal of Sound and Vibration，2002，253:1101-1114.
[105] Pandey A.K, Biswas M. Damage detection in structures using changes in flexibility [J].Journal of Sound and Vibration.1994;169:3–17.
[106] Lin C S. Location of modeling errors using modal test data. AIAA Journal，1990，28(9):1650-1654.
[107]赵媛，陆秋海.简支梁桥多位置损伤的检测方法[J].清华大学学报(自然科学版).2002,42(4):434-438.
[108]曹晖，Michael I F.基于模态柔度曲率的损伤检测方法.工程力学，2006，23(4):33-38.
[109] Z. Zhang, A. E. Aktan. Application of Modal Flexibility and Its Derivatives inStructural Identification[J], Res Nondestr Eval,1998,10:43-61.
[110] Hillary B, Ewins DJ. The use of strain gauges in force determination and frequencyresponse function measurements[A]. Proc. Of2nd IMAC(1984):627-634.
[111]李德葆，张元润，罗京.动态应变、应力场分析模态方法[C]，第六届模态分析与试验学术交流会议论文集，1991.
[112]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.
[113]瞿伟廉，陈伟.多层及高层框架结构地震损伤诊断的神经网络方法[J].地震工程与工程振动,2002,22(1):43-48.
[114]邓焱，严普强.梁及桥梁应变模态与损伤测量的新方法[J]，清华大学学报(自然科学版)，2000，40(11):123-127.
[2]郭飞,彭俊英.基于光纤布拉格光栅的桥梁检测[J].公路交通科技(应用技术版),2012,(1):127-130.
[3]飞张，伟刚，梁龙彬．光纤光栅与电阻应变片应变测量的对比分析[J]．传感技术学报，2001，6(3):200-204．
[4]周智，田石柱，欧进萍．光纤传感器在土木工程中的应用[J]．建筑结构，2002，32(5):65-66．
[5] Moyo P, Brownjohn J MW, Suresh R, et al. Development of f-iber Bragg grating sensorsfor monitoring civil infrastructure[J]. Engineering Structures,2005,27(12):1828-1834.
[6] Catbas F Necati. Structural healthmonitoring and reliability estimation:Long span trussbridge application with environmental monitoring data[J]. Engineering Structures,2008,30(9):2347-2359.
[7]贺志勇,盛飞.大跨度桥梁的变形监测及其精度分析[J].华南理工大学学报(自然科学版),2001,29(8):86-89.
[8]聂让.全站仪与高等级公路测量[M].北京:人民交通出版社,1997.
[9]姜晨光,刘华,刘桂芳,黄家兴.自动电子全站仪桥梁三维动态变形实时监测系统[J].铁路航测,2003,(2):38-40.
[10] Shunichi Nakamura. GPS measurement of wind-induced suspension bridgegirderdisplacements[J]. Journal of Structural Engineering,2000,10:1413-1419.
[11]许晓辉，朱桂新，陈旭东，王迎军.GPS桥梁三维位移自动监测系统的实现[J].华中科技大学学报，2003,9:37-39.
[12]张启伟，袁万城，范立础.大型桥梁结构安全监测的研究现状与发展[J].同济大学学报,1997,25:76-81.
[13]袁万城，崔飞，张启伟.桥梁健康监测与状态评估的研究现状与发展[J].同济大学学报,1999.27(2):184-188.
[14] Lau, C. K.，Wong, K. Y. and Ho, K. S., The Wind and Structural HealthMonitoring System (WASHMS) for the three Long-span Cable-supported Bridges inHong Kong, IABSE, International Association for Bridge and Structural Engineering,15th Congress, June16-20,1996, Copenhagen.
[15]钱帅杰,王存堂,唐立平,等.新型全方位电子水平仪的设计及误差分析[J].传感技术学报,2006,19(2):353-360.
[16]李佳列,颜国正,丁国清.一种新型数字式水平仪:原理与实现[J].传感技术学报,2001(3):191-195.
[17]郭永东.静力水准在桥梁施工竖向位移监控中的应用[J].山西建筑,2002,29(20):86-89.
[18]戴加东,王艳玲,伟洪.静力水准自动化监测系统在某工程中的应用[J].工程勘察,2009,(5):80-84
[19]何小元等.远距离、高精度二维动态位移测量[J].实验力学,1996,11(4):468-472.
[20]于承新等.数字摄影与计算机技术在实时监测结构变形中的应用[J].济南大学学报(自然科学版),2001,15(3):232-234.
[21]罗洪斌,赵文光,文银平.CCD图像监测系统应用于桥梁结构检测[J].华中科技大学学报(城市科学版),2006,23(10):91-93+96.
[22] STANTON JF, EBERHARD MO, BARR PJ. A weighted-stretched-wire system formonitoring deflections[J]. Engineering Structures,2003,25:347-357.
[23] ZHU Y, FU Y, CHEN W, et al. Online deflection monitoring system for dafosicable-stayed bridge[J]. Journal of Intelligent Material Systems and Structures,2006,17(8-9):701-707.
[24]余加勇，朱建军，邹峥嵘，张坤[J].大跨径桥梁挠度测量新方法研究[J].湖南大学学报(自然科学版)，2007，34(10):31-34.
[25]谢浩元.基于无线倾角传感器的桥梁挠度测量研究[D].大连：大连理工大学.2010.
[26]〔苏〕A.E.谢依金,等著.胡春芝,等译.水泥混凝土的结构与性能[M].北京：中国建筑工业出版社，1984.
[27]杜拱辰.现代预应力混凝土结构[M].北京：中国建筑工业出版社，1988.
[28]Paul ACker，Franz-losef Ulm. Creep and shrinkage of concrete: physical origin andpractical measurements[J].Nuclear Engineering and Design，2001(203):143-158.
[29]Z.PBaZant，Delayed thermal dilation of cement Paste and concrete due to masstransport[J]，Nuclear Engng.Design，1970(14):308-318.
[30]SongH-w，SongY-C.， Byum K-J.，etal. Modification of Creep-Prediction Equation ofConcrete utilizing Short-term CreeP Tests，Transaetion[R]， SMIRT16， WashingtonDC， August2001:l-7.
[31]Z.P.Baznat，S.Baweja. Justification and Refinements of Model B3for Concrete CreePand Shrinkgae[J].Materials and Surtcutres，1995，(28):438-495.
[32]Meyerson， R. Compressive Mixtures,Master of Science Creep of PrestressedConcrete Mixtures with and without Thesis in Civil Enginering， Virginal Tech，2001.
[33]Wassim Naguib,Amir Mirmiran. Creep Analysis of Axially Loaded Fiber ReinforcedPolymer-Confined Concrete Columns,Journal of Engineering Mechanics，2003:1308-1319.
[34] N.J，Garder， J.W.Zhao. Creep and Shrinkage Revisited[J]. ACI Materials Journal，1993，90(3):236-246.
[35] N.J.Garder，M.J.Loekman. Design Provisions for Drying Shrinkage and Creep ofNormal Strength-Concrete[J]. ACI Materials Journal，2001，98(2):159-167.
[36]龚洛书，惠满印，杨蓓.砼收缩与徐变的实用数学表达式「J」.建筑结构学报，1988(5):37-42。
[37]向小斌.大跨径连续刚构梁桥混凝土徐变试验研究[D].武汉：武汉理工大学，2007.
[38]丁文胜,吕志涛,孟少平,刘钊.混凝土收缩徐变预测模型的分析比较[J].桥梁建设,2004,(6):13-16.
[39]余志武,薛凯,丁发兴.灰色神经网络在混凝土结构徐变预测中的应用[J].铁道科学与工程学报,2009,6(2):12-16.
[40]潘立本,张苏俊.混凝土收缩与徐变的试验研究[J].河海大学学报,1997,25(5):84-89.
[41]陈志华,肖星荣.基于短期试验的高性能混凝土长期徐变预测[J].华东公路,2007,166(4):94-96.
[42]王辉,钱春香.基于苏通大桥混凝土短期试验结果的徐变预测模型修正[J].桥梁建设,2010,(2):32-36.
[43]刑铁雷.连续刚构桥静动力分析及混凝土应力测试试验[D].成都：西南交通大学，2008.
[44]汪剑,方志.大跨预应力混凝土箱梁桥收缩徐变效应测试与分析[J].土木工程学报,2008,41(1):70-81.
[45]刘宁,刘光廷.混凝土结构的随机温度及随机徐变应力[J].力学进展,1998,28(1):58-70.
[46]李洋波,李翔,黄达海.混凝土徐变度反演分析方法[J].三峡大学学报(自然科学版),2005,27(2):134-136.
[47]高政国,赵国藩.混凝土徐变分析的双功能函数表达[J].建筑材料学报,2001,4(3):250-254.
[48]张子明,周红军,殷波.基于等效时间的混凝土徐变[J].河海大学学报(自然科学版),2005,33(2):173-176.
[49]陈忠,张研,周红军.基于等效时间的混凝土徐变模型[J].河海大学学报(自然科学版),2011,39(3):302-305.
[50]陈松,柯敏勇,刘海祥,洪晓林.基于多孔介质理论的混凝土徐变力学行为的有限元分析[J].固体力学学报,2009,30(5):522-526.
[51]黄耀英,郑宏,周宜红.考虑拉压异性徐变的混凝土温度应力研究[J].武汉理工大学学报,2011,33(3):87-92.
[52]文永奎,陈政清.考虑预应力损失的混凝土梁徐变计算方法[J].中国铁道科学,2005,26(3):36-41.
[53]余报楚,张哲,李生勇,吴立之.一种混凝土桥梁徐变的有效计算方法[J].哈尔滨工业大学学报,2006,38(6):994-996.
[54]孙璨，傅学怡.应用徐变恢复效应建立的应变全量递推方法[J].哈尔滨工业大学学报,2010,42(4):562-567.
[55]方志,李艳,吴鹏扬.先简支后连续混凝土桥梁徐变影响的参数分析[J].桥梁建设,2003,(4):19-22.
[56]王俊,刘立新,尚世宇.预应力度对预应力混凝土梁徐变曲率影响试验研究[J].土木工程学报,2010,43(8):37-43.
[57]李建斌,石现峰.预应力混凝土连续梁桥的收缩徐变分析[J].石家庄铁道学院学报,2003,16(2):15-18.
[58]薛伟辰,胡于明,王巍.预应力混凝土梁徐变性能试验[J].中国公路学报,2008,21(4):61-66.
[59]M.-H. H. Shen, C. Pierre. Natural Modes of Bernoulli-Euler Beams with SymmetricCracks[J]. Journal of Sound and Vibration,1990,138(l):115-134.
[60]Y. Narkis. Identification of Crack Location in Vibrating Simply Supported Beams[J].Journal of Sound and Vibration,1994,(172):549–558.
[61]M.H.H.Shen, C.Pierre. Free vibration of beam with a single-edged crack[J]. Journal ofSound and Vibration,1994,170(2):237-259.
[62]E. I. Shifrin, R. Ruotolo. Natural Frequencies of a Beam with an Arbitrary Number ofCracks[J]. Journal of Sound and Vibration,1999,222(3):409–423.
[63]S. H. S. Carneiro. Comments on the Free Vibrations of Beams with a Single-EdgeCrack[J]. Journal of Sound and Vibration,2001,244(4):729-737.
[64]唐小兵,陈定方,沈成武.结构裂纹位置识别的模态分析[J].武汉理工大学学报,2001,23(5):71-74.
[65]N. T. Khiem, T. V. Lien. A Simplified Method for Natural Frequency Analysis of aMultiple Cracked Beam[J]. Journal of Sound and Vibration,2001,245(4):737-751.
[66]J. K. Sinha, M.I.Friswell,S. Edward. Simplified Models for the Location of Cracks inBeam Structures Using Measured Vibration Data[J]. Journal of Sound and Vibration,2002,251(1):13-38.
[67]H. P. Lin, S.C.Chang, J. D. Wu. Beam Vibrations with an Arbitrary Number ofCracks[J].Journal of Sound and Vibration,2002,258(5):987–999.
[68]王术新,姜哲.裂缝悬臂梁的振动特性及其裂缝参数识别[J]. Journal of Sound andVibration,2003,22(3):83-86.
[69]D.P. Patil, S.K. Maiti. Detection of multiple cracks using frequency measurements[J].Engineering Fracture Mechanics,2003,70:1553–1572.
[70]D.J. Gormana, Luigi Garibaldi. Accurate analytical type solutions for free vibrationfrequencies and mode shapes of multi-span bridge decks the span-by-span approach[J].Journal of Sound and Vibration,2006,290:321–336.
[71]陈长征，罗跃纲，白秉三，唐忠.结构损伤检测与智能诊断[M].北京：科学出版社，2001.
[72]张玲玲，马建劭.服役结构可靠性的模糊评判法及其应用[J].土木工程学报，2001，35（5）：20-23.
[73]邹大力.基于计算智能的结构损伤识别研究[D].大连理工大学博士学位论文，2005.
[74]秦权.桥梁结构的健康监测[J].中国公路学报，2000，13（2）：37-42.
[75]袁万城，崔飞，张启伟.桥梁健康监测与状态评估的现状与发展[J].同济大学学报，1999，27（2）：184-188.
[76]陈长征，罗跃纲，白秉三，唐忠.结构损伤检测与智能诊断[M].北京：科学出版社，2001.
[77]邹大力.基于计算智能的结构损伤识别研究[D].大连理工大学博士学位论文，2005.
[78] Doebling S W. Damage detection and health monitoring of structural and mechanicalsystems from changes in their vibration characteristics: a literature review[R]. LosAlamous National Laboratory Report.1996.
[79]童兆页.论计算智能及其应用[J].计算机研究与发展，1997,34（增刊）：1-4.
[80]何振亚.神经智能[M].长沙：湖南科学技术出版社，1997.
[81]钱敏平.龚光鲁.从数学角度看计算智能[J].科学通报，1999，（16）.
[82]周春光.梁艳春.计算智能.吉林大学出版社[M].2001.
[83]丁雯静.基于柔度矩阵和神经网络的损伤识别方法研究[D].西安：西北工业大学，硕士学位论文，2007.
[84]王兴林.基于径向基网络的损伤识别[D].南京：南京航空航天大学，硕士学位论文，2006.
[85] Cawley P，Adams R D. The location of defects in structures from measurements ofnatural frequencies[J]. Journal of strain analysis.1979，4(2)：49-57.
[86] GeorgeH，ReneBT. Modal analysis for damage detection in structures. Journal ofStructural Engineering，ASCE，1991，117(10):3042一3061.
[87] Robert Y. Liang, Fred K. Choy, Jialou Hu. Detection of cracks in beam structures usingmeasurements of natural frequencies [J], Journal of the Franklin Institute,1991,328(4):505-518.
[88] Friswell M I, Penny JET，Wilson DA. Using vibration data and statistical measures tolocate damage in structures. The International Journal of Analytical and ExperimentalModal Analysis，1994，9(4):239一254.
[89]高芳清，金建明，高淑英.基于模态分析的结构损伤检测方法研究[J]，西南交通大学学报，1998，33（1）：108-113.
[90] S. Hassiotis. Identification of damage using natural frequencies and Markovparameters[J], Journal of Computers and Structures,2000,74:365-373.
[91] Salawu,O S. Detection of Structural damage through changes in frequency: a review.Engineering Structures.1997.19(9):718一723.
[92]钟军军，董聪，夏开全.基于频率及振型参数的结构损伤识别方法[J]，华中科技大学学报(城市科学版)，2009，26（4）：1-9.
[93] Allemang, R.J., Brown, D.L.,1982. A correlation coefficient for modal vectoranalysis[C]. Proc.1st Int. Modal Anal. Conf.1,110–116.
[94] Lieven, N.A.J., Ewins, D.J.,1988. Spatial correlation of mode shapes the coordinatemodal assurance criterion (COMAC)[C]. Proc.6th Int. Modal Anal. Conf.1,690–695.
[95] West, W. M. illustration of the use of modal assurance criterion to detect structuralchanges in an orbiter test specimen[C]. Proceedings of the air force Conference onAircraft Structural Integrity，USA，1984:l-6.
[96] Fox C H J. The location of defects in structures: A comparison of the use of naturalFrequency and mode shape data[C], Proc of the10th IMAC,1992:522-528.
[97] Pandey A K，Biswas M，Samman M M. Damage detection from changes in curvaturemode shapes. Journal of Sound and Vibration.1991.145(2):32l-332.
[98] SalawU O S, Willimas C. Damage location using vibration model shapes.Proceedings of the12thInternational Modal Analysis Conefronce.1994:933-939.
[99] Z. Y. SHI, S. S. LAW. Structural damage localization from modal strain energychange[J], Journal of Sound and Vibration,1998,218(5):825-844.
[100]张勇，静行，袁海庆.基于曲率模态变化率指标的结构损伤识别[J]，华中科技大学学报(城市科学版)，2010,27（2）：82-86.
[101]赵玲，李爱群.基于单元应变能变化率的结构损伤识别方法[J]，东南大学学报(自然科学版)，2007，37（6）：1052-1056.
[102] Z. Zhang, A. E. Aktan. Application of Modal Flexibility and Its Derivatives inStructural Identification[J], Res Nondestr Eval,1998,10:43-61.
[103] ZhaoJ，DewolfJ. Sensitivity study for vibration parameters used in damage detection.Journal of Structural Engineering，1999，125(4):410-416.
[104]LuQ，RenG，ZhaoY. Multiple damage location with flexibility curvature and relativefrequency change for beam structure.Journal of Sound and Vibration，2002，253:1101-1114.
[105] Pandey A.K, Biswas M. Damage detection in structures using changes in flexibility [J].Journal of Sound and Vibration.1994;169:3–17.
[106] Lin C S. Location of modeling errors using modal test data. AIAA Journal，1990，28(9):1650-1654.
[107]赵媛，陆秋海.简支梁桥多位置损伤的检测方法[J].清华大学学报(自然科学版).2002,42(4):434-438.
[108]曹晖，Michael I F.基于模态柔度曲率的损伤检测方法.工程力学，2006，23(4):33-38.
[109] Z. Zhang, A. E. Aktan. Application of Modal Flexibility and Its Derivatives inStructural Identification[J], Res Nondestr Eval,1998,10:43-61.
[110] Hillary B, Ewins DJ. The use of strain gauges in force determination and frequencyresponse function measurements[A]. Proc. Of2nd IMAC(1984):627-634.
[111]李德葆，张元润，罗京.动态应变、应力场分析模态方法[C]，第六届模态分析与试验学术交流会议论文集，1991.
[112]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.
[113]瞿伟廉，陈伟.多层及高层框架结构地震损伤诊断的神经网络方法[J].地震工程与工程振动,2002,22(1):43-48.
[114]邓焱，严普强.梁及桥梁应变模态与损伤测量的新方法[J]，清华大学学报(自然科学版)，2000，40(11):123-127.
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