分形理论在土木工程领域中的应用
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摘要
为了进一步拓展分形理论在土木工程中的应用,首先回顾了分形理论的发展历程、基本概念、基本原理及分形维数;然后就其在国内外的土木工程材料、岩土工程、地震工程、结构损伤检测领域中的应用现状进行了总结和述评,并对分形理论与神经网络及数据融合相结合用于钢管混凝土拱桥的损伤识别研究进展进行了介绍;最后对今后的发展前景进行了展望。研究表明:分形理论在土木工程特别是将它与其他技术融合进行损伤检测是切实可行的、有效的。
In this paper,in order to expand the application of fractal theory,the history,concepts,principles of fractal theory are reviewed firstly;then a summary and overview are given to the application of fractal theory in civil engineering materials,geotechnical engineering,earthquake engineering and structural damage detection throughout the world;and the study on fractal theory integrating with neural network and data fusion applied to damage identification is introduced.The prospect and trend are forecasted finally.The study shows that the application of fractal theory in civil engineering,especially the fractal theory integrating with other techniques applied to damage detection for a concrete-filled steel tubular arch bridge,is feasible and efficient.
In this paper,in order to expand the application of fractal theory,the history,concepts,principles of fractal theory are reviewed firstly;then a summary and overview are given to the application of fractal theory in civil engineering materials,geotechnical engineering,earthquake engineering and structural damage detection throughout the world;and the study on fractal theory integrating with neural network and data fusion applied to damage identification is introduced.The prospect and trend are forecasted finally.The study shows that the application of fractal theory in civil engineering,especially the fractal theory integrating with other techniques applied to damage detection for a concrete-filled steel tubular arch bridge,is feasible and efficient.
引文
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[11]Avadh Ram,Roy P N S.Fractal dimensions of blocks using a box-counting technique for the2001Bhuj earthquake,Gujarat,India[J].Pure and Applied Geophysics.2005,162(3):531―548.
[12]Dimitriu,P P.Multifractal analysis of the Arnea,Greece seismicity with potential implications for earthquake prediction[J].Natural Hazards,2000,21:277―295.
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[18]韩小俊,施泽进.利用分形维拾取地震波初至的一种改进算法[J].石油地球物理勘探,2002,37(1):60―63.Han Xiaojun,Shi Zejin.An improved algorithm for picking up seismic first arrivals by using fractal dimension[J].Oil Geophysical Prospecting,2002,37(1):60―63.(in Chinese)
[19]王步宇.基于分形的结构损伤检测方法[J].振动与冲击,2005,24(2):87―88,110.Wang Buyu.Detection of structural damang using fractal dmension technique[J].Journal of Vibration and Shock,2005,24(2):87―88,110.(in Chinese)
[20]王步宇.结构损伤的分形神经网络检测方法[J].振动、测试与诊断,2005,25(4):260―262,315.Wang Buyu.Structural damage detection based on fractal neural network[J].Journal of Vibration,Measure&Diagnosis,2005,25(4):260―262,315.(in Chinese)
[21]王步宇.结构损伤的小波分形神经网络检测[J].应用力学学报,2007,24(1):58―62.Wang Buyu.Wavelet fractal neural network method for structural damage detection[J].Chinese Journal of Applied Mechanics,2007,24(1):58―62.(in Chinese)
[22]苏莹.基于分形理论与神经网络的数据融合损伤识别方法[D].沈阳:沈阳建筑大学,2009.Su Ying.Data-fusion damage identification method based on fractral theorty and probabilistic neural network[D].Shenyang:Shenyang Jianzhu University,2009.(in Chinese)
[23]张英堂,任国全,李国璋.柴油机振动信号分形特征诊断的改进算法[J].内燃机学报,2006,24(5):459―464.Zhang Yingtang,Ren Guoquan,Li Guozhang.Improved algorthm of diesel engine diagnosis based on fractal dimension of vibration signals[J].Transactions of CSICE,2006,24(5):459―464.(in Chinese)
[24]何宇漾,黄福权.分形在齿轮磨损监测中的应用[J].机械工程师,2006(12):41―42.He Yuyang,Huang Fuquan.Application of fractal theoryon gear wear monitor[J].Mechanical Eneineer,2006(12):41―42.(in Chinese)
[25]苑宇,马孝江.局域波时频域多重分形在故障诊断中的应用[J].振动与冲击,2007,26(5):60―63,153.Yuan Yu,Ma Xiaojiang.Fault diagnosis using multifracals in local wave time-frequency domain[J].Journal of Vibration and Shock,2007,26(5):60―63,153.(in Chinese)
[2]谢和平,薛秀谦.分形应用中的数学基础与方法[M].北京:科学出版社,1998.Xie Heping,Xue Xiuqian.Matmatic foundation and method in the application of fractal analysis[M].Beijing:Science Press,1998.(in Chinese)
[3]曹茂森,任青文.钢筋混凝土结构损伤检测的分形特征因子[J].土木工程学报,2005,38(12):59―64.Cao Maosen,Ren Qingwen.Damage detection of reinforced concrete structures based on fractal characteristic factor[J].China Civil Engineering Journal,2005,38(12):59―64.(in Chinese)
[4]Mechtcherine V,Müler H S.Fractological investigation on the fracture in concrete[C]//de Borst R.Fracture Mechanics of Concrete and Concrete Structures.France:Balkema Publishers,2001:81―88.
[5]Carpinteri A,Chiaia B.Three-dimensional fractal analysis of concrete fracture at the meso-level[J].Theoretical and Applied Fracture Mechanics,1999,31:163―172.
[6]Lis Z,Litewka A.Theoretical model of creep fracture under triaxial state of stess[J].Nucl Engng Des,1993,144(3):497―508.
[7]杨明,梁大开,万鹏飞.多重分形的智能材料损伤诊断应用[J].兵器材料科学与工程,2004,27(2):19―22.Yang Ming,Liang Dakai,Wang Pengfei.Application of multi-fractal on diagnosis of smart materials and structures[J].Ordnance Material Science and Engineering,2004,27(2):19―22.(in Chinese)
[8]杨明,梁大开,万鹏飞.基于分形理论的智能材料结构的损伤诊断[J].压电与声光,2004,26(2):146―148.Yang Ming,Liang Dakai,Wang Pengfei.The diagnose of smart materials and structure based on the fractal theory[J].Piezoelectrics&Acoustooptics,2004,26(2):146―148.(in Chinese)
[9]刘艳章,盛建龙,葛修润.基于岩体结构面分布分形维的岩体质量评价[J].岩土力学,2007,28(5):971―975.Liu Yanzhang,Sheng Jianlong,Ge Xiurun.Evaluation of rock mass quality based on fractal dimension of rock mass discontinuity distribution[J].Rock and Soil Mechanics,2007,28(5):971―975.(in Chinese)
[10]胡海浪.岩体工程中分形理论应用初探[J].灾害与防治工程,2007,62(1):19―24.Hu Hailang.Primary exploration based on application of fracta theory to rock mass engineering[J].Disaster and Control Engineering,2007,62(1):19―24.(in Chinese)
[11]Avadh Ram,Roy P N S.Fractal dimensions of blocks using a box-counting technique for the2001Bhuj earthquake,Gujarat,India[J].Pure and Applied Geophysics.2005,162(3):531―548.
[12]Dimitriu,P P.Multifractal analysis of the Arnea,Greece seismicity with potential implications for earthquake prediction[J].Natural Hazards,2000,21:277―295.
[13]Kossobokov V G,Keilis-Borok V I.Implications of a statistical physics approach for earthquake hazard assessment and forecasting[J].Pure and Applied Geophysics,2000,157(11-12):2323―2349.
[14]Kiyashchenko D,Smirnova N.Seismic hazard precursory evolution:fractal and multifractal aspects[J].Physics and Chemistry of the Earth,2004(29):367―378.
[15]徐志斌,高峰.地震预测中的岩石分形统计强度的应用研究[J].武汉理工大学学报,2005,27(12):61―63.Xu Zhibin,Gao Feng.Application study on earthquake forecast with rock fractal statistical strength[J].Journal of Wuhan University of Technology,2005,27(12):61―63.(in Chinese)
[16]李福中,邢国栋.初至波层析反演静校正方法研究[J].石油地球物理勘探,2000,35(6):710―718.Li Fuzhong,Xing Guodong.Study on first break tomographic inversion method for static corrections[J].Oil Geophysical Prospecting,2000,35(6):710―718.(in Chinese)
[17]常旭,刘伊克.地震记录的广义分维及其应用[J].地球物理学报,2002,45(6):839―846.Chang Xu,Liu Yike.The generalized fractal dimension of seismic records and its applications[J].Chinese Journal of Geophysics,2002,45(6):839―846.(in Chinese)
[18]韩小俊,施泽进.利用分形维拾取地震波初至的一种改进算法[J].石油地球物理勘探,2002,37(1):60―63.Han Xiaojun,Shi Zejin.An improved algorithm for picking up seismic first arrivals by using fractal dimension[J].Oil Geophysical Prospecting,2002,37(1):60―63.(in Chinese)
[19]王步宇.基于分形的结构损伤检测方法[J].振动与冲击,2005,24(2):87―88,110.Wang Buyu.Detection of structural damang using fractal dmension technique[J].Journal of Vibration and Shock,2005,24(2):87―88,110.(in Chinese)
[20]王步宇.结构损伤的分形神经网络检测方法[J].振动、测试与诊断,2005,25(4):260―262,315.Wang Buyu.Structural damage detection based on fractal neural network[J].Journal of Vibration,Measure&Diagnosis,2005,25(4):260―262,315.(in Chinese)
[21]王步宇.结构损伤的小波分形神经网络检测[J].应用力学学报,2007,24(1):58―62.Wang Buyu.Wavelet fractal neural network method for structural damage detection[J].Chinese Journal of Applied Mechanics,2007,24(1):58―62.(in Chinese)
[22]苏莹.基于分形理论与神经网络的数据融合损伤识别方法[D].沈阳:沈阳建筑大学,2009.Su Ying.Data-fusion damage identification method based on fractral theorty and probabilistic neural network[D].Shenyang:Shenyang Jianzhu University,2009.(in Chinese)
[23]张英堂,任国全,李国璋.柴油机振动信号分形特征诊断的改进算法[J].内燃机学报,2006,24(5):459―464.Zhang Yingtang,Ren Guoquan,Li Guozhang.Improved algorthm of diesel engine diagnosis based on fractal dimension of vibration signals[J].Transactions of CSICE,2006,24(5):459―464.(in Chinese)
[24]何宇漾,黄福权.分形在齿轮磨损监测中的应用[J].机械工程师,2006(12):41―42.He Yuyang,Huang Fuquan.Application of fractal theoryon gear wear monitor[J].Mechanical Eneineer,2006(12):41―42.(in Chinese)
[25]苑宇,马孝江.局域波时频域多重分形在故障诊断中的应用[J].振动与冲击,2007,26(5):60―63,153.Yuan Yu,Ma Xiaojiang.Fault diagnosis using multifracals in local wave time-frequency domain[J].Journal of Vibration and Shock,2007,26(5):60―63,153.(in Chinese)
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