结构损伤诊断的类柔度方法研究
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摘要
工程结构在使用的过程中，由于载荷的作用将产生不同位置、不同程度的损伤。为了保证结构的安全，需要及时诊断出这些损伤的位置和损伤的大小，以便对结构使用的可靠性进行合理的评估。这是一类典型的“反问题”。本文提出了三种结构损伤诊断的方法。一种是基于类柔度矩阵差值的结构损伤诊断方法。它是利用类柔度矩阵差值作为诊断损伤的敏感因子。这种方法需要知道结构损伤前即完整结构的参数信息。在此方法基础上经过改进，提出了另一种基于类柔度拟合的结构损伤诊断方法。这种方法是用损伤系数作为诊断损伤的敏感因子。它不需要知道结构损伤前即完整结构的参数信息。第三种是基于振型拟合的结构损伤诊断方法。它也是用损伤系数作为诊断损伤的敏感因子。它也不需要知道结构损伤前即完整结构的参数信息。本文详细讨论了这三种方法，并用仿真算例说明了这三种方法的有效性和可行性。并对三种方法进行了比较。最后，将类柔度拟合法、振型拟合法与振型曲率方法和频率响应函数曲率方法进行了对比。
During operation of engineering structure, damages of different degrees and at different parts will appear due to action of the loading. To guarantee the safety of the engineering structure, we need checking out the positions and dimensions of these damages in order to conduct a reasonable estimate of the reliability of structure operation.This is a typical "inverse problem" .This paper put forward three kinds of structural damage detection methods. One is the diagnosis method of structure damage based on the differeance of analogous flexibility matrix,which takes the difference of analogous flexibility matrix as the sensitive factor of diagnosing damages. Parameter information of structure prior to structure damages is needed for method of this kind. Based on this method, another diagnosis method of structure damages that based on analogous flexibility polyfit is put forward.It takes the damage
index as the sensitive factor of diagnosing damages, and it does not need the parameter information of structure prior to structure damage. The third method is the diagnosis method of structure damage based on mode shape polyfit. It also takes the damage index as the sensitive factor of diagnosing damages, and it also does not need the parameter information of structure prior to structure damage. This paper discusses in detail the three methods and explains their efficiency and feasibility by using simulation calculation examples. And meanwhile , it conducts a comparison of the three methods. Finally, the analogous flexibility polyfit method and the mode shape polyfit method are compared with two other relevant methods-the mode shape curvature method and the frequency response function curvature method.
During operation of engineering structure, damages of different degrees and at different parts will appear due to action of the loading. To guarantee the safety of the engineering structure, we need checking out the positions and dimensions of these damages in order to conduct a reasonable estimate of the reliability of structure operation.This is a typical "inverse problem" .This paper put forward three kinds of structural damage detection methods. One is the diagnosis method of structure damage based on the differeance of analogous flexibility matrix,which takes the difference of analogous flexibility matrix as the sensitive factor of diagnosing damages. Parameter information of structure prior to structure damages is needed for method of this kind. Based on this method, another diagnosis method of structure damages that based on analogous flexibility polyfit is put forward.It takes the damage
index as the sensitive factor of diagnosing damages, and it does not need the parameter information of structure prior to structure damage. The third method is the diagnosis method of structure damage based on mode shape polyfit. It also takes the damage index as the sensitive factor of diagnosing damages, and it also does not need the parameter information of structure prior to structure damage. This paper discusses in detail the three methods and explains their efficiency and feasibility by using simulation calculation examples. And meanwhile , it conducts a comparison of the three methods. Finally, the analogous flexibility polyfit method and the mode shape polyfit method are compared with two other relevant methods-the mode shape curvature method and the frequency response function curvature method.
引文
[1] 丁玉兰，石来德。机械设备故障诊断技术。上海：上海科学技术文献出版社，1994
[2] 黄文虎，夏松波，刘瑞岩等。设备故障诊断原理、技术及应用。北京：科学出版社，1996
[3] Bapat A V,Venkatraman N.New approach for the representation of a point support in the analysis of plates.Journal of Sound and Vibration, 1988,120(1): 107-125
[4] 程庆国。我国桥梁工程的成就与展望。见：中国土木工程学会第八届年会论文集。北京：机械工业出版社，1998
[5] 张安华。机电设备状态监测与故障诊断技术。西安：西北工业大学出版社，1995
[6] Ratcliffe C P, Bagaria W J.Vibration technique for locating delamination in a composite beam.AIAA JOURNAL, 1998,36(6):1074-1077
[7] Kerstems J G M.Vibration of complex structures: the modal constraint method. Journal of Sound and Vibration, 1981,76(4):467-480
[8] 钱管良，顾松年，姜节胜。含裂纹梁的动力特性。航空学报，1989，10 (9)：448-454
[9] 汪风泉，郑万泔。试验振动分析。南京：江苏科学技术出版社，1987
[10] 屈梁生，何正嘉。机械故障诊断学。上海：上海科学技术出版社，1986
[11] 钱管良，顾松年，姜节胜。含裂纹梁的动力响应。振动工程学报，1989，2 (3)：78-85
[12] 虞和济。振动诊断的工程应用。北京：冶金工业出版社，1992
[13] 虞和济。故障诊断的基本原理。北京：冶金工业出版社，1989
[14] 钱管良，顾松年，姜节胜。在线振动监测与故障诊断的一种新途径。固体力学学报，1990，11 (3)：217-228
[15] 郭国会，易伟建。基于模态参数进行连续梁损伤诊断的数值研究。振动与冲击，2001，20(1)：72-75
[16] Cawley P, Adams R D.The location of defects in Structures from measurements of the natural frequencies. Journal of Strain Analysis, 1979,14(2):49-57
[17] Hearn G,Testa R B. Modal analysis for damage detection in structures. Journal of Structural Engineering, 1991,117(10):3042-3061
[18] Pandy A K,Biawas M,Samman M M. Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 1991,145(2):321-332
[19] Yuen M M F. A numerical study of the eigenparameters of a damaged cantilever. Journal of Sound and Vibration, 1985,103(3):301-310
[20] 倪振华。振动力学。西安：西安交通大学出版社，1989
[21] 吴淇泰。振动分析。杭州：浙江大学出版社，1989
[22] 程耀东。机械振动学(线性系统)。杭州：浙江大学出版社，1988
[23] 师汉民，湛刚，吴雅。机械振动系统—分析、测试、建模、对策(上册)。武汉：华中理工大学出版社，1992
[24] 于德介，雷慧，程军圣。基于BP神经网络与柔度变化的结构破损诊断。振动工程学报，2001，14 (3)：345-348
[25] 雷慧。结构损伤诊断的神经网络方法研究：[硕士学位论文]。长沙：湖南大学设备故障诊断中心，1999
[26] Pandey A K, Biswas M. Damage diagnosis of truss structures by estimation of flexibility change. Modal Analysis, 1995,10(2): 104-117
[27] Pandey A K, Biswas M. Damage detection in structures using changes in flexibility. Journal of Sound and Vibration, 1994,169(1):3-17
[28] Pandey A K. Experimental verrification of flexibility difference method for locating damage in structures. Journal of Sound and Vibration, 1995, 184(2):311-328
[29] Berman A, Flannelly W G. Theory of incomplete models of dynamic structures. AIAA JOURNAL, 1971,9(8): 1481-1487
[30] 方同，薛璞。振动理论及应用。西安：西北工业大学出版社，1998
[31] 王文亮，杜作润。结构振动与动态子结构方法。上海：复旦大学出版社，1985
[32] 季文美，方同，陈松淇。机械振动。北京：科学出版社，1985
[33] 卢耀祖，周中坚。机械与汽车结构的有限元分析。上海：同济大学出版社，1997
[34] 程耀东。机械振动学(非线性系统。弹性体)。杭州：浙江大学出版社，1990
[35] 陆宁。MATLAB语言即学即会。北京：机械工业出版社，2000
[36] 程卫国，冯峰，王雪梅等。MATLAB5.3精要、编程及高级应用。北京：机械工业出版社，2000
[37] 许波，刘征。MatLab工程数学应用。北京：清华大学出版社，2000
[38] 傅志方，华宏星。模态分析理论与应用。上海：上海交通大学出版社，2000
[39] 大久保信行。机械模态分析。上海：上海交通大学出版社，1985
[40] 李德葆，陆秋海。实验模态分析及其应用。北京：科学出版社，2001
[41] 周传荣，赵淳生。机械振动参数识别及其应用。北京：科学出版社，1989
[42] 徐宜桂，史铁林，杨叔子。基于神经网络的结构动力模型修改和破损诊断研究。振动工程学报，1997，10 (1)：8-12
[43] Ratcliffe C P. Damage detection using a modified laplacian operator on mode shape data. Journal of Sound and Vibration, 1997,204(3):505-517
[44] Sampaio R P C,Maia N M M,Silva J M M. Damage detection using the frequency-response-function curvature method. Journal of Sound and Vibration, 1999,226(5): 1029-1042
[45] Ratcliffe C P. A frequency and curvature based experimental method for locating damage in structures. Journal of Vibration and Acoustics,2000,122(3):324-329
[2] 黄文虎，夏松波，刘瑞岩等。设备故障诊断原理、技术及应用。北京：科学出版社，1996
[3] Bapat A V,Venkatraman N.New approach for the representation of a point support in the analysis of plates.Journal of Sound and Vibration, 1988,120(1): 107-125
[4] 程庆国。我国桥梁工程的成就与展望。见：中国土木工程学会第八届年会论文集。北京：机械工业出版社，1998
[5] 张安华。机电设备状态监测与故障诊断技术。西安：西北工业大学出版社，1995
[6] Ratcliffe C P, Bagaria W J.Vibration technique for locating delamination in a composite beam.AIAA JOURNAL, 1998,36(6):1074-1077
[7] Kerstems J G M.Vibration of complex structures: the modal constraint method. Journal of Sound and Vibration, 1981,76(4):467-480
[8] 钱管良，顾松年，姜节胜。含裂纹梁的动力特性。航空学报，1989，10 (9)：448-454
[9] 汪风泉，郑万泔。试验振动分析。南京：江苏科学技术出版社，1987
[10] 屈梁生，何正嘉。机械故障诊断学。上海：上海科学技术出版社，1986
[11] 钱管良，顾松年，姜节胜。含裂纹梁的动力响应。振动工程学报，1989，2 (3)：78-85
[12] 虞和济。振动诊断的工程应用。北京：冶金工业出版社，1992
[13] 虞和济。故障诊断的基本原理。北京：冶金工业出版社，1989
[14] 钱管良，顾松年，姜节胜。在线振动监测与故障诊断的一种新途径。固体力学学报，1990，11 (3)：217-228
[15] 郭国会，易伟建。基于模态参数进行连续梁损伤诊断的数值研究。振动与冲击，2001，20(1)：72-75
[16] Cawley P, Adams R D.The location of defects in Structures from measurements of the natural frequencies. Journal of Strain Analysis, 1979,14(2):49-57
[17] Hearn G,Testa R B. Modal analysis for damage detection in structures. Journal of Structural Engineering, 1991,117(10):3042-3061
[18] Pandy A K,Biawas M,Samman M M. Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 1991,145(2):321-332
[19] Yuen M M F. A numerical study of the eigenparameters of a damaged cantilever. Journal of Sound and Vibration, 1985,103(3):301-310
[20] 倪振华。振动力学。西安：西安交通大学出版社，1989
[21] 吴淇泰。振动分析。杭州：浙江大学出版社，1989
[22] 程耀东。机械振动学(线性系统)。杭州：浙江大学出版社，1988
[23] 师汉民，湛刚，吴雅。机械振动系统—分析、测试、建模、对策(上册)。武汉：华中理工大学出版社，1992
[24] 于德介，雷慧，程军圣。基于BP神经网络与柔度变化的结构破损诊断。振动工程学报，2001，14 (3)：345-348
[25] 雷慧。结构损伤诊断的神经网络方法研究：[硕士学位论文]。长沙：湖南大学设备故障诊断中心，1999
[26] Pandey A K, Biswas M. Damage diagnosis of truss structures by estimation of flexibility change. Modal Analysis, 1995,10(2): 104-117
[27] Pandey A K, Biswas M. Damage detection in structures using changes in flexibility. Journal of Sound and Vibration, 1994,169(1):3-17
[28] Pandey A K. Experimental verrification of flexibility difference method for locating damage in structures. Journal of Sound and Vibration, 1995, 184(2):311-328
[29] Berman A, Flannelly W G. Theory of incomplete models of dynamic structures. AIAA JOURNAL, 1971,9(8): 1481-1487
[30] 方同，薛璞。振动理论及应用。西安：西北工业大学出版社，1998
[31] 王文亮，杜作润。结构振动与动态子结构方法。上海：复旦大学出版社，1985
[32] 季文美，方同，陈松淇。机械振动。北京：科学出版社，1985
[33] 卢耀祖，周中坚。机械与汽车结构的有限元分析。上海：同济大学出版社，1997
[34] 程耀东。机械振动学(非线性系统。弹性体)。杭州：浙江大学出版社，1990
[35] 陆宁。MATLAB语言即学即会。北京：机械工业出版社，2000
[36] 程卫国，冯峰，王雪梅等。MATLAB5.3精要、编程及高级应用。北京：机械工业出版社，2000
[37] 许波，刘征。MatLab工程数学应用。北京：清华大学出版社，2000
[38] 傅志方，华宏星。模态分析理论与应用。上海：上海交通大学出版社，2000
[39] 大久保信行。机械模态分析。上海：上海交通大学出版社，1985
[40] 李德葆，陆秋海。实验模态分析及其应用。北京：科学出版社，2001
[41] 周传荣，赵淳生。机械振动参数识别及其应用。北京：科学出版社，1989
[42] 徐宜桂，史铁林，杨叔子。基于神经网络的结构动力模型修改和破损诊断研究。振动工程学报，1997，10 (1)：8-12
[43] Ratcliffe C P. Damage detection using a modified laplacian operator on mode shape data. Journal of Sound and Vibration, 1997,204(3):505-517
[44] Sampaio R P C,Maia N M M,Silva J M M. Damage detection using the frequency-response-function curvature method. Journal of Sound and Vibration, 1999,226(5): 1029-1042
[45] Ratcliffe C P. A frequency and curvature based experimental method for locating damage in structures. Journal of Vibration and Acoustics,2000,122(3):324-329