基于三维仿真与模型参数监测的机械结构局部损伤诊断方法
|
摘要
随着科学技术的进步、现代工业的发展以及人类生活日益增长的需求,现代机械装备与结构正在向大型化、复杂化与自动化方向发展。
机械结构在使用过程中,在承受工作载荷的作用以及各种突发性外在因素影响下可能发生局部损伤。当局部损伤积累到一定程度时,会导致局部或整体结构的失效。对于重要结构,损伤所导致的机械装备与结构的故障停机将造成巨大的经济损失,乃至引发重大的灾难性事故。世界上不乏由于机械损伤导致灾难性事故的实例。对机械结构进行损伤监测与失效预警,将在很大程度上消除事故隐患和避免发生灾难性事故。因此,结构损伤监测与诊断方法的研究具有重要意义。
基于振动的结构损伤检测与诊断技术可实现在线损伤(特别是早期损伤)的定量检测与诊断,从而保证在役设备与结构的运行安全,并为近代预知维修提供可靠信息。因此,近年来这种技术得到迅速发展。其中以模型为基础的方法能够实时、敏感地发现由于结构损伤所造成的结构动态特性的本质变化,并有可能对损伤作定量评估,从而受到国内外研究者的广泛关注。
在基于结构振动特性的损伤检测方法中,常用和有效的一种方法是利用结构定量模型(如模态模型)的参数检测方法,如利用结构固有频率、振型、模态曲率、应变模态、传递函数、模态置信判据(MAC)、坐标模态置信判据(COMAC)等模态参数的变化进行结构损伤检测。本文采用了基于模态模型参数辨识的一种模型损伤检测与诊断方法,解决了将此方法应用于复杂机械结构损伤检测的一系列问题,提出了基于结构易损伤部位及关键位置预测、结构损伤-动力学响应特征.模态参数变化之间关系预分析的少传感器结构损伤检测与诊断方法。提高了这种方法应用于复杂工程结构的可行性。
提出了一种基于实验模态分析数据的有约束的贝叶斯估计有限元模型修改方法,以多段组合的门形框架结构为例,建立了修改后的模态模型。分析了这种框架结构在激振器激励下的动力学响应及引起结构损伤的敏感参数。在此基础上,采用了基于三维动力学仿真的疲劳分析,确定了门形框架结构的易损伤位置。为发生损伤后动力学行为变化的进一步分析提供依据。
从理论上研究了损伤对结构模态频率和振型的影响,讨论了基于频率变化监测结构损伤的可行性。以门形框架结构为例,运用有限元方法,计算了疲劳裂纹以及法兰螺栓松动条件下门形框架结构模态频率的变化。用模态实验验证了有损伤门形框架结构的模态频率漂移特征。通过计算与实验结果比较,研究了归一化的模态频率漂移向量的一致性。
运用频响函数结构综合方法,分析了组合结构的频响函数。讨论了几种特殊连接情况下,组合结构中的子结构的频响函数。结果表明,子结构损伤或刚度变化对结构动力学特征或频响函数的影响是复杂的,其影响取决于子结构间连接状况。对于刚性连接结构来说,组合结构中子结构的频响函数极点与整体结构的频响函数极点相同。通过子结构的频响函数极点选取,可以反映整体结构的模态频率变化。
以基于工作模态分析的在线模态参数辨识为基础,分析了辨识结果的不确定性,改进了辨识算法。提出用可表征损伤特征的主模态对应的互功率谱幅值构建Fisher信息阵。通过逐步消除不敏感传感器直到余下的传感器数目为期望数值为止,得到了传感器优化布置(尽可能少的数量与最佳的配置位置)结果。减少了传感器布置数目、且适合于结构关键部位损伤监测。对有损伤的门形框架结构进行工作模态分析,验证了基于三维仿真与模型参数监测的机械结构局部损伤诊断方法。
With the progress of science and technology, modern industrial development, as well as the growing demand for human life, modern machinery and equipment and the structure is developing towards large scale, complication and automation.
Mechanical structure will be partially damaged during working process, which is caused by long-term load operation or other unexpected external factors. When the damage accumulates to a certain extent, the overall or local structure will lead to a sudden failure, which will cause emergent stop of equipments. This will bring large economic losses and even cause disastrous accidents. There are a lot of instances in the world. Structural damage detection and early warning is helpful to eliminating hidden dangers and avoiding catastrophic incidents. Therefore, research on structural damage monitoring and diagnosis is of great significance.
Structural damage detection and diagnosis technique based on vibration can be used to conduct online damage (especially the early damage) and quantitative detection and diagnosis. With this technique, safe operation of in-service equipment and structure can be ensured, and reliable information can be provided for predictive maintenance. Thus, this technology is developing rapidly in recent years. Among them, model-based approach can be used to find the intrinsic changes of the structural dynamic characteristics real-timely and sensitively. Using this approach, it is possible to achieve quantitative assessment of damage. Structural damage detection and diagnosis technique based on model-based has attracted widespread attention by domestic and foreign researchers.
The main technology of structural the damage detection is the diagnosis method based on structural dynamic characteristics parameters, including modal frequency, modal shape, modal curvature, strain mode, transfer function, MAC(Modal Assurance Criterion), COMAC(Coordinate Modal Assurance Criterion) and so on.
In this paper, quantitative damage detection and diagnosis method based on modal parameters identification is presented, and problems aroused by the key techniques to apply this method on complicated mechanical structure are solved. The proposed method has following characteristics:prediction of the easily damaged local sections and key positions, analysis on relationship between structure damage and dynamic response features and less use of sensors. With these characteristics, the feasibility to apply this method on complex engineering structures is improved.
A constrained Bayesian estimation method is proposed to update finite element model. Using this method, the finite element model of the multi-segment gantry is established. According to this model, the dynamic responses excited by work load and structure damage sensitive parameters are analyzed. On this basis, the easily damaged positions are defined, which provides foundation for dynamic analysis of the damaged structure.
The modal frequencies and modal shapes changes of the damaged structure are theoretically studied and feasibility to monitor structure damage according to modal frequency changes is discussed. For a gantry, with finite element method, modal frequency changes are calculated under the condition of the fatigue crack and the flange bolts loose. To verify the calculated results, modal experiments are carried out. By comparison, the experimental results and the calculated results are consistent.
The substructure's FRFs(Frequency Response Functions) are deduced. And for several composite structures with special connection ways, the substructure's FRFs are discussed. The results show that the impact on the structural dynamics characteristics or FRFs by substructure damage or stiffness change is complex and depends on connection condition of structures. For rigid connection structure, the poles of FRFs of composite structure are the same as the substructures'. The poles of the substructure FRFs can reflect the modal frequencies of composite structure.
The inconsistent identification results using two modal parameter identification methods are analyzed. On this basis, the structure damage identification algorithm is improved. A new method to build the Fisher information matrix is developed, which use cross-power spectrum amplitudes of the modal of damage characteristics as its elements. The sensor layout is optimized through gradual elimination of sensor. Thus the number of sensor can be eliminated without effecting the damage detection of critical part. At last, the experiments are conducted, and the results show that the proposed technology is correct.
机械结构在使用过程中,在承受工作载荷的作用以及各种突发性外在因素影响下可能发生局部损伤。当局部损伤积累到一定程度时,会导致局部或整体结构的失效。对于重要结构,损伤所导致的机械装备与结构的故障停机将造成巨大的经济损失,乃至引发重大的灾难性事故。世界上不乏由于机械损伤导致灾难性事故的实例。对机械结构进行损伤监测与失效预警,将在很大程度上消除事故隐患和避免发生灾难性事故。因此,结构损伤监测与诊断方法的研究具有重要意义。
基于振动的结构损伤检测与诊断技术可实现在线损伤(特别是早期损伤)的定量检测与诊断,从而保证在役设备与结构的运行安全,并为近代预知维修提供可靠信息。因此,近年来这种技术得到迅速发展。其中以模型为基础的方法能够实时、敏感地发现由于结构损伤所造成的结构动态特性的本质变化,并有可能对损伤作定量评估,从而受到国内外研究者的广泛关注。
在基于结构振动特性的损伤检测方法中,常用和有效的一种方法是利用结构定量模型(如模态模型)的参数检测方法,如利用结构固有频率、振型、模态曲率、应变模态、传递函数、模态置信判据(MAC)、坐标模态置信判据(COMAC)等模态参数的变化进行结构损伤检测。本文采用了基于模态模型参数辨识的一种模型损伤检测与诊断方法,解决了将此方法应用于复杂机械结构损伤检测的一系列问题,提出了基于结构易损伤部位及关键位置预测、结构损伤-动力学响应特征.模态参数变化之间关系预分析的少传感器结构损伤检测与诊断方法。提高了这种方法应用于复杂工程结构的可行性。
提出了一种基于实验模态分析数据的有约束的贝叶斯估计有限元模型修改方法,以多段组合的门形框架结构为例,建立了修改后的模态模型。分析了这种框架结构在激振器激励下的动力学响应及引起结构损伤的敏感参数。在此基础上,采用了基于三维动力学仿真的疲劳分析,确定了门形框架结构的易损伤位置。为发生损伤后动力学行为变化的进一步分析提供依据。
从理论上研究了损伤对结构模态频率和振型的影响,讨论了基于频率变化监测结构损伤的可行性。以门形框架结构为例,运用有限元方法,计算了疲劳裂纹以及法兰螺栓松动条件下门形框架结构模态频率的变化。用模态实验验证了有损伤门形框架结构的模态频率漂移特征。通过计算与实验结果比较,研究了归一化的模态频率漂移向量的一致性。
运用频响函数结构综合方法,分析了组合结构的频响函数。讨论了几种特殊连接情况下,组合结构中的子结构的频响函数。结果表明,子结构损伤或刚度变化对结构动力学特征或频响函数的影响是复杂的,其影响取决于子结构间连接状况。对于刚性连接结构来说,组合结构中子结构的频响函数极点与整体结构的频响函数极点相同。通过子结构的频响函数极点选取,可以反映整体结构的模态频率变化。
以基于工作模态分析的在线模态参数辨识为基础,分析了辨识结果的不确定性,改进了辨识算法。提出用可表征损伤特征的主模态对应的互功率谱幅值构建Fisher信息阵。通过逐步消除不敏感传感器直到余下的传感器数目为期望数值为止,得到了传感器优化布置(尽可能少的数量与最佳的配置位置)结果。减少了传感器布置数目、且适合于结构关键部位损伤监测。对有损伤的门形框架结构进行工作模态分析,验证了基于三维仿真与模型参数监测的机械结构局部损伤诊断方法。
With the progress of science and technology, modern industrial development, as well as the growing demand for human life, modern machinery and equipment and the structure is developing towards large scale, complication and automation.
Mechanical structure will be partially damaged during working process, which is caused by long-term load operation or other unexpected external factors. When the damage accumulates to a certain extent, the overall or local structure will lead to a sudden failure, which will cause emergent stop of equipments. This will bring large economic losses and even cause disastrous accidents. There are a lot of instances in the world. Structural damage detection and early warning is helpful to eliminating hidden dangers and avoiding catastrophic incidents. Therefore, research on structural damage monitoring and diagnosis is of great significance.
Structural damage detection and diagnosis technique based on vibration can be used to conduct online damage (especially the early damage) and quantitative detection and diagnosis. With this technique, safe operation of in-service equipment and structure can be ensured, and reliable information can be provided for predictive maintenance. Thus, this technology is developing rapidly in recent years. Among them, model-based approach can be used to find the intrinsic changes of the structural dynamic characteristics real-timely and sensitively. Using this approach, it is possible to achieve quantitative assessment of damage. Structural damage detection and diagnosis technique based on model-based has attracted widespread attention by domestic and foreign researchers.
The main technology of structural the damage detection is the diagnosis method based on structural dynamic characteristics parameters, including modal frequency, modal shape, modal curvature, strain mode, transfer function, MAC(Modal Assurance Criterion), COMAC(Coordinate Modal Assurance Criterion) and so on.
In this paper, quantitative damage detection and diagnosis method based on modal parameters identification is presented, and problems aroused by the key techniques to apply this method on complicated mechanical structure are solved. The proposed method has following characteristics:prediction of the easily damaged local sections and key positions, analysis on relationship between structure damage and dynamic response features and less use of sensors. With these characteristics, the feasibility to apply this method on complex engineering structures is improved.
A constrained Bayesian estimation method is proposed to update finite element model. Using this method, the finite element model of the multi-segment gantry is established. According to this model, the dynamic responses excited by work load and structure damage sensitive parameters are analyzed. On this basis, the easily damaged positions are defined, which provides foundation for dynamic analysis of the damaged structure.
The modal frequencies and modal shapes changes of the damaged structure are theoretically studied and feasibility to monitor structure damage according to modal frequency changes is discussed. For a gantry, with finite element method, modal frequency changes are calculated under the condition of the fatigue crack and the flange bolts loose. To verify the calculated results, modal experiments are carried out. By comparison, the experimental results and the calculated results are consistent.
The substructure's FRFs(Frequency Response Functions) are deduced. And for several composite structures with special connection ways, the substructure's FRFs are discussed. The results show that the impact on the structural dynamics characteristics or FRFs by substructure damage or stiffness change is complex and depends on connection condition of structures. For rigid connection structure, the poles of FRFs of composite structure are the same as the substructures'. The poles of the substructure FRFs can reflect the modal frequencies of composite structure.
The inconsistent identification results using two modal parameter identification methods are analyzed. On this basis, the structure damage identification algorithm is improved. A new method to build the Fisher information matrix is developed, which use cross-power spectrum amplitudes of the modal of damage characteristics as its elements. The sensor layout is optimized through gradual elimination of sensor. Thus the number of sensor can be eliminated without effecting the damage detection of critical part. At last, the experiments are conducted, and the results show that the proposed technology is correct.
引文
[1]郑栋梁,李中付,华宏星卜.结构早期损伤识别技术的现状和发展趋势[J].振动与冲击,2002,21(2)：1-8.
[2]胡自力,熊克,杨红.基于智能材料结构的几种损伤评价方法[J].航空学报,2002,23(1)：1-5.
[3]张德海,朱浮生.结构损伤智能诊断研究进展[J].力学与实践,2003,25(4)：1-6.
[4]RILEM. Draft recommendation of damage classification of concrete [J]. Materials and Structure,1994,27(170):362-369.
[5]欧进萍,关新春.土木工程智能结构体系的研究与发展[J].地震工程与工程振动.1999,19(2)：21-28.
[6]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
[7]Tomaszewska A. Influence of statistical errors on damage detection based on structural flexibility and mode shape curvature[J]. Computers & Structures,2010,88:154-164.
[8]Chandrashekhar M, Ganguli R. Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic[J]. Journal of Sound and Vibration,2009, 326:939-957.
[9]李国强.梁远森振型曲率在板类结构动力检测中的应用[J].振动、测试与诊断2004,24(6)：111-116.
[10]王山山,任青文.基于曲率模态振型的刚架结构损伤检测[J].动力学与控制学报,2005,3(2)：81-86.
[11]Pandey A K, Biswas M. Damage Detection in Structures Using Changes in Flexibility [J]. Journal of Sound and Vibration,1994,169(1):3-17.
[12]Aimin Y, Jean-Claude G Structural damage localization by combining flexibility and stiffness methods[J]. Engineering Structures,2005,27(12):1752-1761.
[13]Reynders E, Roeck G D. A local flexibility method for vibration-based damage localization and quantification[J]. Journal of Sound and Vibration,329(12):2367-2383.
[14]曹 晖,张新亮,李英民.利用模态柔度曲率差识别框架的损伤[J].振动与冲击, 2007,26(6)：116-120.
[15]李永梅,周锡元,高向宇.基于柔度差曲率矩阵的结构损伤识别方法[J].工程力学,2009,26(2)：188-195.
[16]Chen J C, Garba J A. on-orbit damage assessment for large space structures [J]. AJAA, 1988,26(9):1198-1126.
[17]Cornwell P, Doebling S W, Farrar C R. Application of the strain energy damage detection method to plate-like structures [J]. Journal of Sound and Vibration,1999,224(2): 359-374.
[18]Kumar M, Shenoi R A., Cox S J. Experimental validation of modal strain energies based damage identification method for a composite sandwich beam[J]. Composites Science and Technology,2009,69(10):1635-1643.
[19]唐天国,刘浩吾,陈春华等.梁裂缝损伤检测的模态应变能法及试验研究[J].工程力学(增刊),2005,26：39-45.
[20]王树青,王长青,李华军.基于模态应变能的海洋平台损伤定位试验研究[J].振动、测试与诊断,2006,26(4)：282-287.
[21]Salane H J, Baldwin J W, Duffield R C. Dynamics approach for monitoring bridge deterioration[J]. Transportation Research Record,1987,21-28.
[22]Mazurek K F, Dewolf J T. Experimental study of bridge monitoring technique[J]. Journal of Structural Engineering,1990,116(9):2532-2549.
[23]Gassiots S, Jeong G D. Identification of stiffness reduction using natural frequencies [J]. Journal of Engineering Mechanics,1995,121(10):1106-1113.
[24]Biswas M, Pandey A K, Samman, M M. Diagnostic experimental spectral/modal analysis of a highway bridge[J]. The International Journal of Analytical and Experimental Modal Analysis,1990,5(1):33-42.
[25]Hearn G, Testa R B. Modal analysis for damage detection in structures [J]. Journal of Structure Engineering,1989,117(10):3042-3063.
[26]Salawu O S. Detection of structural damage through changes in frequency:a review [J]. Engineering Structures,1997,19(9):718-723.
[27]Capecchi D, Vestroni F. Monitoring of structural systems by using frequency data [J]. Earthquake Engineering and Structure Dynamics,1999,28(5):447-461.
[28]Kim J T, Ryu Y S, Cho H M. ect. Damage identification in beam-type structures: frequency-based method vs. mode-shape-based method [J]. Engineering Structures,2003, 25(1):57-67.
[29]Mazurek D F, Dewolf J T. Experimental study of bridge monitoring technique [J]. Journal of Structure Engineering, ASCE,1990,116 (9):2532-2549.
[30]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.
[31]Abdel W M M, De R G., Peeters B. Parameterization of damage in reinforced concrete structures using modal updating [J]. Journal of Sound and Vibration,1999,228(4): 717-730.
[32]Hajela P, Soeiro F. structural damage detection based on static and modal analysis [J]. AIAA Journal,1990,28(6):1110-1115.
[33]Messina A, Williams E J, Contursi T, Contursi T. Structural damage detection by a sensitivity and statistical based method [J]. Journal of Sound and Vibration,1998,216(5): 791-808.
[34]Pandey A K, Biswas M. Damage diagnosis of truss structures by estimation of flexibility change [J]. Modal Analysis:The international Journal of Analytical and Experimental Modal Analysis,1995,10(2):104-117.
[35]Zhao J, Dewolf J T. Sensitivity study for vibration parameters used in damage detection [J]. Journal of Structural Engineering,1999,125(4):410-416.
[36]Shi Z Y, Law S S, Zhang L M. Structural Damage detection from modal strain energy change [J]. Journal of Enngineering Mechanics,2000,126(12):1216-1223.
[37]Hutry W C. Vibration of structure systems by component mode synthesis [J]. Journal of Structural Engineering,1960,86:51-59.
[38]Hutry W C. Dynamic analysis of structural systems using component modes [J], AIAA Journal,1965,3 (4):678-685.
[39]Gladwell G. M L. Branch mode analysis of vibrating systems [J]. Journal of Sound and Vibration,1964,1:41-59.
[40]Craig R R., Bampton C C. Coupling of substructures for dynamic analysis [J]. AIAA Journal,1968,6(7):1313-1319.
[41]Hou S.N. Review of model synthesis techniques and a new approach [J], Shock and Vibration Bulletin.1969,40(4):25-30.
[42]Hintz R.M. Analytical methods in component modal synthesis [J]. AIAA Journal,1975, 13(8):1007-1016.
[43]Rubin S. Improved component-mode representation for structural dynamic analysis [J]. AIAA Journal,1975,13(8):995-1006.
[44]王永岩.动态子结构方法理论及应用[M].北京：科学出版社,1999：2.
[45]Craig Jr R R, Chang C-J. Free interface methods of substructure coupling for dynamic analysis [J]. AIAAJ,1976,14(11):1633-1635.
[46]Suarez L E, Suarez M P. Improved fixed interface method for modal synthesis [J]. AIAA Journal,1992,30:2952-2958.
[47]Jezequel L, Seito H D. Component modal synthesis method based on hybrid models[J]. J Appl Mech Trans ASME,1994,61:100-108.
[48]Leung A Y T. An accurate method of dynamic sub structuring with simplified computation[J]. Inc J Numer Methods Eng,1979,14:1241-1256.
[49]胡海昌.很多自由度体系的有振动问题.约束模态法[J],航空学报,1980,2：28-36.
[50]Qiu J B, Ying Z G, Williams F W. Exact modal synthesis techniques using residual constraint modes [J]. International Journal for Numerical methods in Engineering,1997, 40:2475-2492.
[51]邱吉宝,谭志勇.确精的混合界面模态综合技术[J].计算力学学报.1997,14：859-864.
[52]Qiu J B, Williams F W, Qiu R X. A exact Substructure method using mixed modes [J]. Journal of Sound and Vibration,2003,66:737-757.
[53]Yun C B, Bahng E Y. Sub structural identification using neural networks [J]. Computers & structures,2000,77(1):41-52.
[54]Yun C B, Lee H J. Sub structural identification for damage estimation of structures [J]. Structural Safety,1997,19(1):121-140.
[55]James G H, Carne T G, Lauffer J P. The Natural Excitation Technique (NExT) for Modal Parameter Extraction from Operating Structures [J]. Modal Analysis:the International Journal of Analytical and Experimental Modal Analysis,1995,10:260-277.
[56]Hermans L, H. Auweraer Van der, Modal testing and analysis of structures under operational conditions:industrial applications[J], Mechanical Systems and Signal Processing,19991,3 (2):193-216.
[57]Brincker R, Zhang L, Andersen P. Modal identification of output-only systems using frequency domain decomposition[J], Smart Materials and Structures,2001,10:441-445.
[58]Luz E, Wallaschek J. Experiment modal analysis using ambient vibration [J]. The International Journal of Analytical and Experiment Modal Analysis,1992,7 (1):29-39.
[59]Desforges M J, Cooper J E, Wright J R. Spectral and modal parameter estimation from output-only measurements [J]. Mechanical System and Signal Processing,1995,9(2): 169-186.
[60]Peeters B, Auweraer H Van der, Guillaume P, Leuridan J. The PolyMAX frequency-domain method:a new standard for modal parameter estimation [J]. Shock and Vibration,2004,11:395-409.
[61]Pintelon R, Schoukens J, Guillaume P. Continuous-time noise modelling from sampled data[J]. IEEE Transactions on Instrumentation and Measurement,2006,55 (6): 2253-2258.
[62]Parlooa E, Cauberghea B, Benedettinib F. etc. Sensitivity-based operational mode shape normalization:Application to a bridge [J]. Mechanical Systems and Signal Processing, 2005,19:43-55.
[63]Parloo E, Verboven P, Guillaume P. etc. Force identification by means of in-operation modal models [J], Journal of Sound and Vibration,2003,262 (1):161-173.
[64]Gao Y, Randall R B. Determination of frequency response functions from response measurements. Part ⅰ:extraction of poles and zeros from response measurements [J], Mechanical Systems and Signal Processing,1996,10 (3):293-317.
[65]Gao Y, Randall R B. Determination of frequency response functions from response measurements. Part ⅱ:regeneration of frequency response functions from poles and zeros[J], Mechanical Systems and Signal Processing,1996,10 (3):319-340.
[66]Mohanty P, Rixen D J. Operational modal analysis in the presence of harmonic excitation[J], Journal of Sound and Vibration,2004,270:93-109.
[67]Mohanty P, Rixen D J. Modified ERA method for operational modal analysis in the presence of harmonic excitations[J], Mechanical Systems and Signal Processing,2006, 20:114-130.
[68]Hansen M H, Thomsen K, Fuglsang P. Two methods for estimating aerobatic damping of operational wind turbine modes from experiments [J], Wind Energy,2006,9:179-191.
[69]Devriendt C, Guillaume P. The use of transmissibility measurements in output-only modal analysis[J], Mechanical Systems and Signal Processing,2007,21 (7):2689-2696.
[70]Devriendt C, Sitter G D, Guillaume P. An operational modal analysis approach based on parametrically identified multivariable transmissibilities [EB/OL]. Mechanical Systems and Signal Processing,2009, doi:10.1016/j.ymssp.2009.02.015
[71]Parloo E, Verboven P, Guillaume P. etc. Autonomous structural health monitoring. Part II: vibration-based in-operation damage assessment[J], Mechanical Systems and Signal Processing,2002,16 (4):659-675.
[72]Parloo E, Verboven P, Guillaume P. etc. Increased reliability of reference-based damage identification techniques by using output-only data[J], Journal of Sound and Vibration, 2004,270 (4-5):813-832.
[73]金新灿,孙守光,邢鸿麟等.环境随机激励下高速客车的工作模态分析[J].铁道学报,2003,25(5)：24-28.
[74]Ghaboussi J, Garrett J H, Wu X. Knowledge-based modeling of material behavior with neural network [J]. Journal of Engineering Mechanics,1991,117(1):132-153.
[75]Levin R I, Lieven N A J. Dynamic finite element model updating using neural network [J]. Journal of Sound and Vibration,1998,210(5):593-607.
[76]Atalla M J, Iman D J. On model updating using neural networks [J]. Mechanics system and Signal Processing,1998,12(1):135-161.
[77]Marwala T, Hunt H E M. Fault identification using finite element models and neural networks [J]. Mechanics system and Signal Processing,1999,13(3):475-490.
[78]Zang C, Imregun M. Structural damage detection using artificial neural networks and measured FRF data reduced via principal component projection [J]. Journal of Sound and Vibration,2001,242(5):813-827.
[79]Masri S F, Slllyth A W, Chassiakos A G. etc. Application of neural networks for detection of changes in nonlinear systems[J]. ASCE Journal of Engineering Mechanics,2000, 126(7):666-676.
[80]Marwala T. Damage identification using committee of natural networks [J]. ASCE Journal of Engineering Mechanics,2000,126(1):43-50.
[81]Weir M K. A method for self-determination of adaptive learning rates in back propagation[J]. Natural Networks,1991,4:371-379.
[82]高赞明,孙宗光,倪一清.基于振动方法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.
[83]刘利锋,郑世杰.基于智能元件和神经网络的复合材料损伤监测[J],测试技术学报2003,17(4)：350-353.
[84]Firswell M I, Penny J E T, Garvey S D. A combined genetic and eager sensitivity algorithm for the location of damage in structures [J]. Computers and Structures,1998, 69(5):547-556.
[85]Chou J H, Ghaboussi J. Genetic algorithm in structural damage detection [J]. Computers and Structures,2001, (79):1335-1353.
[86]易伟建,刘霞.结构损伤诊断的遗传算法研究[J].系统工程理论与实践,2001,(5)：114-118.
[87]程远胜,区达光,谭国焕.基于分级遗传算法的结构损伤识别方法[J].华中科技大学学报(自然科学版),2002,30(8)：73-75.
[88]Sone A. Health monitoring system of structures based on orthogonal wavelet transform [J]. Seismic Engineering, Transactions of ASEM,1995,312:161-167.
[89]吴耀军,陶宝棋.基于小波神经网络的复合材料损伤诊断[J].航空学报,1997,18(2)：252-256.
[90]Hou Z, Noori M, Amand R St. Wavelet-based approach for structural damage detection [J]. Journal of Engineering Mechanics,2000,126(7):677-683.
[91]袁慎芳,陶宝棋.应用小波分析及主动监测技术的复合材料损伤监测[J].材料工程,2001,(2)：43-46.
[92]Amaravadi V, Rao V, Kovai L R. etc. Structural health monitoring using wavelet transforms [J]. Proceedings of SPIE,2001,4327:258-269.
[93]Sun Z, Chang C C. Structural damage assessment based on wavelet packet transform [J]. Journal of Structural Engineering,2002,128(10):1354-1361.
[94]楼日明.基于虚拟样机技术的转盘选矿机运动分析及虚拟建模[D].昆明：昆明理工大学,2006.
[95]唐硕,陈士稽,赵建卫.飞行器设计与试验的虚拟样机技术[J].宇航学报,2000,21增刊(11)：1-6.
[96]赵雯,王维平,朱一凡等.协同虚拟样机技术研究[J].系统仿真学报,2001,13(1)：128-130.
[97]熊光楞,李伯虎,柴旭东.虚拟样机技术[J].系统仿真学报,2001,13(1)：114-117.
[98]许京伟,陈举华,于奎刚.悬臂筛网振动筛虚拟样机技术及其筛分机理[J].山东大学学报(工学版),2004,34(6)：9-12.
[99]袁延章.多点成形设备调形机构的虚拟样机研究[D].长春：吉林大学,2006.
[100]徐建锋.4WS整车虚拟样机机械系统与控制系统祸合仿真研究[D].杭州：浙江工业大学,2006.
[101]高娟.基于虚拟样机技术的三自由度重型摇摆试验台的研究[D].哈尔滨：哈尔滨工业大学,2006.
[102]刘星星.基于虚拟技术的汽车操纵稳定性虚拟实验系统的研制[D].杭州：浙江大学,2006.
[103]张巍.三轴光学跟踪试验转台的动力学仿真研究[D].哈尔滨：哈尔滨工业大学,2006.
[104]Hughes P C. Spacecraft Attitude Dynamics [M]. Wiley New York,1986:146～152.
[105]杨娜,王娜,吴知丰.轻型门式刚架结构及其最优腹板高度的研究[J].哈尔滨建筑大学学报,2001,34(1)：16.
[106]董忠心.工厂化养鸡场装配式鸡舍结构优化的研究[D].北京：中国农业大学,2000.
[107]柳锋,郭兵,陈长兵等.门式刚架的经济尺寸与优化初设计[J].钢结构,2003,18(1)：32-34.
[108]Fleury C, Sander G. Dual Methods for Optimizing Finite Element Flexural Systems[J]. Computer Methods in Applied Mechanics and Engineering,1983,37 (3): 249-275.
[109]Haftka R T. Second Order Sensitivity Derivatives in Structural Optimization[J]. AIAA Journal,1982,20:1765-1766.
[110]吴剑国,龚铭,孙苏洵等.门式刚架轻型房屋钢结构离散变量优化设计[J].建筑结构,2001,31(8)：54-55.
[111]褚云朋,王秀丽.门式刚架构造改进型节点试验研究[J].建筑科学,2009,25(9)：24-29.
[112]卢林枫,顾强,解琦.门式刚架屋面坡度对二阶效应的影响及二阶弯矩计算公式[J].建筑结构,2002,32(2)：26-28.
[113]宗丽杰,赵滇生.半刚性柱脚连接门式钢架的几何非线性分析应用[J].能源技术,2007,(2)：1-4.
[114]王传奇,高轩能,李琨.变截面门式刚架的动力特性[J].华侨大学学报,2009,30(1)：75-79.
[115]郭全,秦健.基于ANSYS的门形架结构设计分析[J].中国水运,2008,(8)：224-225.
[116]熊永华.变截面门式刚架稳定性有限元分析[D].武汉：武汉大学,2004
[117]周莉莉,蹇开林,丁剑平.用小波变换求解门形框架动力响应[J].重庆科技学院学报,2006,8(4)：36-39.
[118]张永昌.MSC.Nastran有限元分析理论基础与应用[M].北京：科学出版社,2004：268.
[119]Clough R W, Penzien J,王光远等(译).结构动力学[M],北京：科学出版社,1981：207-211.
[120]Peeters B, Van D A H, Leuridan J. etc. PolyMAX modal parameter estimation: Challenging automotive and aerospace applications [J]. VDI Berichte,2004, (1825): 1-13+572-573.
[121]周云,易伟建.用PolyMAX方法进行弹性地基板的实验模态分析[J].振动与冲击,2007,26(7)：139-144.
[122]傅志方,华宏星.模态分析理论与应用[M].上海：上海交通大学出版社,2000：252-277
[123]成大先.机械设计手册(常用工程材料)[M].北京：化学工业出版社,2004：12.
[124]张新跃,欧进平.CFRP筋的疲劳性能[J].材料研究学报,2006,20(6)：565-570.
[125]杜建根.工程力学[M].武汉：武汉理工大学出版社,2008：166
[126]周传月,郑红霞,罗慧强等.MSC.Fatigue疲劳分析与应用实例[M].北京：科学出版社,2005：24
[127]Lestari W, Lou H, Hanaqud S. Dynamics of composite structures with multiple delimitations [J]. American Society of Mechanical Engineer, Applied Mechanics Division, AMD,2001,249:319-322.
[128]Lee U, Shin J. A structural damage identification method for plate structures [J]. Engineering Structures,2002,24(9):1177-1188.
[129]陈塑寰.结构摄动分析的矩阵摄动理论[M].北京：科学出版社,1999：11-19
[130]Papadopoulos C A, Dimarogonas A D. Coupled longitudinal and bending vibrations of a rotating shaft with an open crack[J]. Journal of Sound and Vibration,1987,117(1): 81～93.
[131]Sekhar A S. Conditioning monitoring of a rotor system having a slant crack in the shaft [J]. Noise and Vibration Worldwide,1999, (3):23～31.
[132]赵玉成,李舜铭,许庆余.裂纹转子的弯扭耦合振动特性分析[J].应用力学学报,1999,16(1)：60-64
[133]张文.转子动力学理论基础[MI.北京：科学出版社,1990：143-158.
[134]Mayes I W. Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor [J]. ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design,1984,106(2):139～145.
[135]Lee C W. Modeling of a simple rotor with a switching crack and its experimental verification[J]. ASME Journal of Vibration and Acoustics,1992,114(2):217～225.
[136]Jetmundsen B, Bielawa R L, Flannelly W G. Generalized frequency domain substructure synthesis[J]. Journal of the American Helicopter Society,1988,33(1):55-64.
[137]Ren Y, Beards C F. On substructure synthesis with FRF data [J].Journal of Sound and Vibration.1995,185(5):845-866.
[138]Ren Y, Beards C F. Identification of joint properties of structure using FRF data [J]. Journal of Sound and Vibration,1995,186(4):567-587.
[139]Worden K, Burrows A P. Optimal Sensor Placement for Fault Detection [J]. Engineering Structures,2001,23:885-901.
[140]Shi Z Y, Law S S, Zhang L M. Optimum Sensor Placement for Structural Damage Detection [J]. Journal of Engineering Mechanics,2000,126 (11):1173-1179.
[141]Cynthia S, Sditi C. Optimization of piezoelectric sensor location for delamination detection in composite laminates [J]. Engineering Optimization,2006,38(5):511-528.
[142]吴子燕,代凤娟,宋静.损伤检测中的传感器优化布置方法研究[J].西北工业大学学报,2007,25(4)：503-507.
[143]Kammer D C. Sensor Placement for On-Orbit Modal Identification and Corrlelation of Large Space Structures [J]. Journal of Guidance, Control, and Dynamics.1991,14 (2): 251-258.
[144]Kammer D C. Effect of Model Error on Sensor Placement for On-Orbit Modal Identification of Large Space Structures [J]. Journal of Guidance, Control, and Dynamics, 1992,15 (2):334-341.
[2]胡自力,熊克,杨红.基于智能材料结构的几种损伤评价方法[J].航空学报,2002,23(1)：1-5.
[3]张德海,朱浮生.结构损伤智能诊断研究进展[J].力学与实践,2003,25(4)：1-6.
[4]RILEM. Draft recommendation of damage classification of concrete [J]. Materials and Structure,1994,27(170):362-369.
[5]欧进萍,关新春.土木工程智能结构体系的研究与发展[J].地震工程与工程振动.1999,19(2)：21-28.
[6]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
[7]Tomaszewska A. Influence of statistical errors on damage detection based on structural flexibility and mode shape curvature[J]. Computers & Structures,2010,88:154-164.
[8]Chandrashekhar M, Ganguli R. Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic[J]. Journal of Sound and Vibration,2009, 326:939-957.
[9]李国强.梁远森振型曲率在板类结构动力检测中的应用[J].振动、测试与诊断2004,24(6)：111-116.
[10]王山山,任青文.基于曲率模态振型的刚架结构损伤检测[J].动力学与控制学报,2005,3(2)：81-86.
[11]Pandey A K, Biswas M. Damage Detection in Structures Using Changes in Flexibility [J]. Journal of Sound and Vibration,1994,169(1):3-17.
[12]Aimin Y, Jean-Claude G Structural damage localization by combining flexibility and stiffness methods[J]. Engineering Structures,2005,27(12):1752-1761.
[13]Reynders E, Roeck G D. A local flexibility method for vibration-based damage localization and quantification[J]. Journal of Sound and Vibration,329(12):2367-2383.
[14]曹 晖,张新亮,李英民.利用模态柔度曲率差识别框架的损伤[J].振动与冲击, 2007,26(6)：116-120.
[15]李永梅,周锡元,高向宇.基于柔度差曲率矩阵的结构损伤识别方法[J].工程力学,2009,26(2)：188-195.
[16]Chen J C, Garba J A. on-orbit damage assessment for large space structures [J]. AJAA, 1988,26(9):1198-1126.
[17]Cornwell P, Doebling S W, Farrar C R. Application of the strain energy damage detection method to plate-like structures [J]. Journal of Sound and Vibration,1999,224(2): 359-374.
[18]Kumar M, Shenoi R A., Cox S J. Experimental validation of modal strain energies based damage identification method for a composite sandwich beam[J]. Composites Science and Technology,2009,69(10):1635-1643.
[19]唐天国,刘浩吾,陈春华等.梁裂缝损伤检测的模态应变能法及试验研究[J].工程力学(增刊),2005,26：39-45.
[20]王树青,王长青,李华军.基于模态应变能的海洋平台损伤定位试验研究[J].振动、测试与诊断,2006,26(4)：282-287.
[21]Salane H J, Baldwin J W, Duffield R C. Dynamics approach for monitoring bridge deterioration[J]. Transportation Research Record,1987,21-28.
[22]Mazurek K F, Dewolf J T. Experimental study of bridge monitoring technique[J]. Journal of Structural Engineering,1990,116(9):2532-2549.
[23]Gassiots S, Jeong G D. Identification of stiffness reduction using natural frequencies [J]. Journal of Engineering Mechanics,1995,121(10):1106-1113.
[24]Biswas M, Pandey A K, Samman, M M. Diagnostic experimental spectral/modal analysis of a highway bridge[J]. The International Journal of Analytical and Experimental Modal Analysis,1990,5(1):33-42.
[25]Hearn G, Testa R B. Modal analysis for damage detection in structures [J]. Journal of Structure Engineering,1989,117(10):3042-3063.
[26]Salawu O S. Detection of structural damage through changes in frequency:a review [J]. Engineering Structures,1997,19(9):718-723.
[27]Capecchi D, Vestroni F. Monitoring of structural systems by using frequency data [J]. Earthquake Engineering and Structure Dynamics,1999,28(5):447-461.
[28]Kim J T, Ryu Y S, Cho H M. ect. Damage identification in beam-type structures: frequency-based method vs. mode-shape-based method [J]. Engineering Structures,2003, 25(1):57-67.
[29]Mazurek D F, Dewolf J T. Experimental study of bridge monitoring technique [J]. Journal of Structure Engineering, ASCE,1990,116 (9):2532-2549.
[30]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.
[31]Abdel W M M, De R G., Peeters B. Parameterization of damage in reinforced concrete structures using modal updating [J]. Journal of Sound and Vibration,1999,228(4): 717-730.
[32]Hajela P, Soeiro F. structural damage detection based on static and modal analysis [J]. AIAA Journal,1990,28(6):1110-1115.
[33]Messina A, Williams E J, Contursi T, Contursi T. Structural damage detection by a sensitivity and statistical based method [J]. Journal of Sound and Vibration,1998,216(5): 791-808.
[34]Pandey A K, Biswas M. Damage diagnosis of truss structures by estimation of flexibility change [J]. Modal Analysis:The international Journal of Analytical and Experimental Modal Analysis,1995,10(2):104-117.
[35]Zhao J, Dewolf J T. Sensitivity study for vibration parameters used in damage detection [J]. Journal of Structural Engineering,1999,125(4):410-416.
[36]Shi Z Y, Law S S, Zhang L M. Structural Damage detection from modal strain energy change [J]. Journal of Enngineering Mechanics,2000,126(12):1216-1223.
[37]Hutry W C. Vibration of structure systems by component mode synthesis [J]. Journal of Structural Engineering,1960,86:51-59.
[38]Hutry W C. Dynamic analysis of structural systems using component modes [J], AIAA Journal,1965,3 (4):678-685.
[39]Gladwell G. M L. Branch mode analysis of vibrating systems [J]. Journal of Sound and Vibration,1964,1:41-59.
[40]Craig R R., Bampton C C. Coupling of substructures for dynamic analysis [J]. AIAA Journal,1968,6(7):1313-1319.
[41]Hou S.N. Review of model synthesis techniques and a new approach [J], Shock and Vibration Bulletin.1969,40(4):25-30.
[42]Hintz R.M. Analytical methods in component modal synthesis [J]. AIAA Journal,1975, 13(8):1007-1016.
[43]Rubin S. Improved component-mode representation for structural dynamic analysis [J]. AIAA Journal,1975,13(8):995-1006.
[44]王永岩.动态子结构方法理论及应用[M].北京：科学出版社,1999：2.
[45]Craig Jr R R, Chang C-J. Free interface methods of substructure coupling for dynamic analysis [J]. AIAAJ,1976,14(11):1633-1635.
[46]Suarez L E, Suarez M P. Improved fixed interface method for modal synthesis [J]. AIAA Journal,1992,30:2952-2958.
[47]Jezequel L, Seito H D. Component modal synthesis method based on hybrid models[J]. J Appl Mech Trans ASME,1994,61:100-108.
[48]Leung A Y T. An accurate method of dynamic sub structuring with simplified computation[J]. Inc J Numer Methods Eng,1979,14:1241-1256.
[49]胡海昌.很多自由度体系的有振动问题.约束模态法[J],航空学报,1980,2：28-36.
[50]Qiu J B, Ying Z G, Williams F W. Exact modal synthesis techniques using residual constraint modes [J]. International Journal for Numerical methods in Engineering,1997, 40:2475-2492.
[51]邱吉宝,谭志勇.确精的混合界面模态综合技术[J].计算力学学报.1997,14：859-864.
[52]Qiu J B, Williams F W, Qiu R X. A exact Substructure method using mixed modes [J]. Journal of Sound and Vibration,2003,66:737-757.
[53]Yun C B, Bahng E Y. Sub structural identification using neural networks [J]. Computers & structures,2000,77(1):41-52.
[54]Yun C B, Lee H J. Sub structural identification for damage estimation of structures [J]. Structural Safety,1997,19(1):121-140.
[55]James G H, Carne T G, Lauffer J P. The Natural Excitation Technique (NExT) for Modal Parameter Extraction from Operating Structures [J]. Modal Analysis:the International Journal of Analytical and Experimental Modal Analysis,1995,10:260-277.
[56]Hermans L, H. Auweraer Van der, Modal testing and analysis of structures under operational conditions:industrial applications[J], Mechanical Systems and Signal Processing,19991,3 (2):193-216.
[57]Brincker R, Zhang L, Andersen P. Modal identification of output-only systems using frequency domain decomposition[J], Smart Materials and Structures,2001,10:441-445.
[58]Luz E, Wallaschek J. Experiment modal analysis using ambient vibration [J]. The International Journal of Analytical and Experiment Modal Analysis,1992,7 (1):29-39.
[59]Desforges M J, Cooper J E, Wright J R. Spectral and modal parameter estimation from output-only measurements [J]. Mechanical System and Signal Processing,1995,9(2): 169-186.
[60]Peeters B, Auweraer H Van der, Guillaume P, Leuridan J. The PolyMAX frequency-domain method:a new standard for modal parameter estimation [J]. Shock and Vibration,2004,11:395-409.
[61]Pintelon R, Schoukens J, Guillaume P. Continuous-time noise modelling from sampled data[J]. IEEE Transactions on Instrumentation and Measurement,2006,55 (6): 2253-2258.
[62]Parlooa E, Cauberghea B, Benedettinib F. etc. Sensitivity-based operational mode shape normalization:Application to a bridge [J]. Mechanical Systems and Signal Processing, 2005,19:43-55.
[63]Parloo E, Verboven P, Guillaume P. etc. Force identification by means of in-operation modal models [J], Journal of Sound and Vibration,2003,262 (1):161-173.
[64]Gao Y, Randall R B. Determination of frequency response functions from response measurements. Part ⅰ:extraction of poles and zeros from response measurements [J], Mechanical Systems and Signal Processing,1996,10 (3):293-317.
[65]Gao Y, Randall R B. Determination of frequency response functions from response measurements. Part ⅱ:regeneration of frequency response functions from poles and zeros[J], Mechanical Systems and Signal Processing,1996,10 (3):319-340.
[66]Mohanty P, Rixen D J. Operational modal analysis in the presence of harmonic excitation[J], Journal of Sound and Vibration,2004,270:93-109.
[67]Mohanty P, Rixen D J. Modified ERA method for operational modal analysis in the presence of harmonic excitations[J], Mechanical Systems and Signal Processing,2006, 20:114-130.
[68]Hansen M H, Thomsen K, Fuglsang P. Two methods for estimating aerobatic damping of operational wind turbine modes from experiments [J], Wind Energy,2006,9:179-191.
[69]Devriendt C, Guillaume P. The use of transmissibility measurements in output-only modal analysis[J], Mechanical Systems and Signal Processing,2007,21 (7):2689-2696.
[70]Devriendt C, Sitter G D, Guillaume P. An operational modal analysis approach based on parametrically identified multivariable transmissibilities [EB/OL]. Mechanical Systems and Signal Processing,2009, doi:10.1016/j.ymssp.2009.02.015
[71]Parloo E, Verboven P, Guillaume P. etc. Autonomous structural health monitoring. Part II: vibration-based in-operation damage assessment[J], Mechanical Systems and Signal Processing,2002,16 (4):659-675.
[72]Parloo E, Verboven P, Guillaume P. etc. Increased reliability of reference-based damage identification techniques by using output-only data[J], Journal of Sound and Vibration, 2004,270 (4-5):813-832.
[73]金新灿,孙守光,邢鸿麟等.环境随机激励下高速客车的工作模态分析[J].铁道学报,2003,25(5)：24-28.
[74]Ghaboussi J, Garrett J H, Wu X. Knowledge-based modeling of material behavior with neural network [J]. Journal of Engineering Mechanics,1991,117(1):132-153.
[75]Levin R I, Lieven N A J. Dynamic finite element model updating using neural network [J]. Journal of Sound and Vibration,1998,210(5):593-607.
[76]Atalla M J, Iman D J. On model updating using neural networks [J]. Mechanics system and Signal Processing,1998,12(1):135-161.
[77]Marwala T, Hunt H E M. Fault identification using finite element models and neural networks [J]. Mechanics system and Signal Processing,1999,13(3):475-490.
[78]Zang C, Imregun M. Structural damage detection using artificial neural networks and measured FRF data reduced via principal component projection [J]. Journal of Sound and Vibration,2001,242(5):813-827.
[79]Masri S F, Slllyth A W, Chassiakos A G. etc. Application of neural networks for detection of changes in nonlinear systems[J]. ASCE Journal of Engineering Mechanics,2000, 126(7):666-676.
[80]Marwala T. Damage identification using committee of natural networks [J]. ASCE Journal of Engineering Mechanics,2000,126(1):43-50.
[81]Weir M K. A method for self-determination of adaptive learning rates in back propagation[J]. Natural Networks,1991,4:371-379.
[82]高赞明,孙宗光,倪一清.基于振动方法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.
[83]刘利锋,郑世杰.基于智能元件和神经网络的复合材料损伤监测[J],测试技术学报2003,17(4)：350-353.
[84]Firswell M I, Penny J E T, Garvey S D. A combined genetic and eager sensitivity algorithm for the location of damage in structures [J]. Computers and Structures,1998, 69(5):547-556.
[85]Chou J H, Ghaboussi J. Genetic algorithm in structural damage detection [J]. Computers and Structures,2001, (79):1335-1353.
[86]易伟建,刘霞.结构损伤诊断的遗传算法研究[J].系统工程理论与实践,2001,(5)：114-118.
[87]程远胜,区达光,谭国焕.基于分级遗传算法的结构损伤识别方法[J].华中科技大学学报(自然科学版),2002,30(8)：73-75.
[88]Sone A. Health monitoring system of structures based on orthogonal wavelet transform [J]. Seismic Engineering, Transactions of ASEM,1995,312:161-167.
[89]吴耀军,陶宝棋.基于小波神经网络的复合材料损伤诊断[J].航空学报,1997,18(2)：252-256.
[90]Hou Z, Noori M, Amand R St. Wavelet-based approach for structural damage detection [J]. Journal of Engineering Mechanics,2000,126(7):677-683.
[91]袁慎芳,陶宝棋.应用小波分析及主动监测技术的复合材料损伤监测[J].材料工程,2001,(2)：43-46.
[92]Amaravadi V, Rao V, Kovai L R. etc. Structural health monitoring using wavelet transforms [J]. Proceedings of SPIE,2001,4327:258-269.
[93]Sun Z, Chang C C. Structural damage assessment based on wavelet packet transform [J]. Journal of Structural Engineering,2002,128(10):1354-1361.
[94]楼日明.基于虚拟样机技术的转盘选矿机运动分析及虚拟建模[D].昆明：昆明理工大学,2006.
[95]唐硕,陈士稽,赵建卫.飞行器设计与试验的虚拟样机技术[J].宇航学报,2000,21增刊(11)：1-6.
[96]赵雯,王维平,朱一凡等.协同虚拟样机技术研究[J].系统仿真学报,2001,13(1)：128-130.
[97]熊光楞,李伯虎,柴旭东.虚拟样机技术[J].系统仿真学报,2001,13(1)：114-117.
[98]许京伟,陈举华,于奎刚.悬臂筛网振动筛虚拟样机技术及其筛分机理[J].山东大学学报(工学版),2004,34(6)：9-12.
[99]袁延章.多点成形设备调形机构的虚拟样机研究[D].长春：吉林大学,2006.
[100]徐建锋.4WS整车虚拟样机机械系统与控制系统祸合仿真研究[D].杭州：浙江工业大学,2006.
[101]高娟.基于虚拟样机技术的三自由度重型摇摆试验台的研究[D].哈尔滨：哈尔滨工业大学,2006.
[102]刘星星.基于虚拟技术的汽车操纵稳定性虚拟实验系统的研制[D].杭州：浙江大学,2006.
[103]张巍.三轴光学跟踪试验转台的动力学仿真研究[D].哈尔滨：哈尔滨工业大学,2006.
[104]Hughes P C. Spacecraft Attitude Dynamics [M]. Wiley New York,1986:146～152.
[105]杨娜,王娜,吴知丰.轻型门式刚架结构及其最优腹板高度的研究[J].哈尔滨建筑大学学报,2001,34(1)：16.
[106]董忠心.工厂化养鸡场装配式鸡舍结构优化的研究[D].北京：中国农业大学,2000.
[107]柳锋,郭兵,陈长兵等.门式刚架的经济尺寸与优化初设计[J].钢结构,2003,18(1)：32-34.
[108]Fleury C, Sander G. Dual Methods for Optimizing Finite Element Flexural Systems[J]. Computer Methods in Applied Mechanics and Engineering,1983,37 (3): 249-275.
[109]Haftka R T. Second Order Sensitivity Derivatives in Structural Optimization[J]. AIAA Journal,1982,20:1765-1766.
[110]吴剑国,龚铭,孙苏洵等.门式刚架轻型房屋钢结构离散变量优化设计[J].建筑结构,2001,31(8)：54-55.
[111]褚云朋,王秀丽.门式刚架构造改进型节点试验研究[J].建筑科学,2009,25(9)：24-29.
[112]卢林枫,顾强,解琦.门式刚架屋面坡度对二阶效应的影响及二阶弯矩计算公式[J].建筑结构,2002,32(2)：26-28.
[113]宗丽杰,赵滇生.半刚性柱脚连接门式钢架的几何非线性分析应用[J].能源技术,2007,(2)：1-4.
[114]王传奇,高轩能,李琨.变截面门式刚架的动力特性[J].华侨大学学报,2009,30(1)：75-79.
[115]郭全,秦健.基于ANSYS的门形架结构设计分析[J].中国水运,2008,(8)：224-225.
[116]熊永华.变截面门式刚架稳定性有限元分析[D].武汉：武汉大学,2004
[117]周莉莉,蹇开林,丁剑平.用小波变换求解门形框架动力响应[J].重庆科技学院学报,2006,8(4)：36-39.
[118]张永昌.MSC.Nastran有限元分析理论基础与应用[M].北京：科学出版社,2004：268.
[119]Clough R W, Penzien J,王光远等(译).结构动力学[M],北京：科学出版社,1981：207-211.
[120]Peeters B, Van D A H, Leuridan J. etc. PolyMAX modal parameter estimation: Challenging automotive and aerospace applications [J]. VDI Berichte,2004, (1825): 1-13+572-573.
[121]周云,易伟建.用PolyMAX方法进行弹性地基板的实验模态分析[J].振动与冲击,2007,26(7)：139-144.
[122]傅志方,华宏星.模态分析理论与应用[M].上海：上海交通大学出版社,2000：252-277
[123]成大先.机械设计手册(常用工程材料)[M].北京：化学工业出版社,2004：12.
[124]张新跃,欧进平.CFRP筋的疲劳性能[J].材料研究学报,2006,20(6)：565-570.
[125]杜建根.工程力学[M].武汉：武汉理工大学出版社,2008：166
[126]周传月,郑红霞,罗慧强等.MSC.Fatigue疲劳分析与应用实例[M].北京：科学出版社,2005：24
[127]Lestari W, Lou H, Hanaqud S. Dynamics of composite structures with multiple delimitations [J]. American Society of Mechanical Engineer, Applied Mechanics Division, AMD,2001,249:319-322.
[128]Lee U, Shin J. A structural damage identification method for plate structures [J]. Engineering Structures,2002,24(9):1177-1188.
[129]陈塑寰.结构摄动分析的矩阵摄动理论[M].北京：科学出版社,1999：11-19
[130]Papadopoulos C A, Dimarogonas A D. Coupled longitudinal and bending vibrations of a rotating shaft with an open crack[J]. Journal of Sound and Vibration,1987,117(1): 81～93.
[131]Sekhar A S. Conditioning monitoring of a rotor system having a slant crack in the shaft [J]. Noise and Vibration Worldwide,1999, (3):23～31.
[132]赵玉成,李舜铭,许庆余.裂纹转子的弯扭耦合振动特性分析[J].应用力学学报,1999,16(1)：60-64
[133]张文.转子动力学理论基础[MI.北京：科学出版社,1990：143-158.
[134]Mayes I W. Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor [J]. ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design,1984,106(2):139～145.
[135]Lee C W. Modeling of a simple rotor with a switching crack and its experimental verification[J]. ASME Journal of Vibration and Acoustics,1992,114(2):217～225.
[136]Jetmundsen B, Bielawa R L, Flannelly W G. Generalized frequency domain substructure synthesis[J]. Journal of the American Helicopter Society,1988,33(1):55-64.
[137]Ren Y, Beards C F. On substructure synthesis with FRF data [J].Journal of Sound and Vibration.1995,185(5):845-866.
[138]Ren Y, Beards C F. Identification of joint properties of structure using FRF data [J]. Journal of Sound and Vibration,1995,186(4):567-587.
[139]Worden K, Burrows A P. Optimal Sensor Placement for Fault Detection [J]. Engineering Structures,2001,23:885-901.
[140]Shi Z Y, Law S S, Zhang L M. Optimum Sensor Placement for Structural Damage Detection [J]. Journal of Engineering Mechanics,2000,126 (11):1173-1179.
[141]Cynthia S, Sditi C. Optimization of piezoelectric sensor location for delamination detection in composite laminates [J]. Engineering Optimization,2006,38(5):511-528.
[142]吴子燕,代凤娟,宋静.损伤检测中的传感器优化布置方法研究[J].西北工业大学学报,2007,25(4)：503-507.
[143]Kammer D C. Sensor Placement for On-Orbit Modal Identification and Corrlelation of Large Space Structures [J]. Journal of Guidance, Control, and Dynamics.1991,14 (2): 251-258.
[144]Kammer D C. Effect of Model Error on Sensor Placement for On-Orbit Modal Identification of Large Space Structures [J]. Journal of Guidance, Control, and Dynamics, 1992,15 (2):334-341.