多维标度法在地震动空间特性分析中的应用
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摘要
为寻找适于工程应用的空间地震动输入合理性的判定工具,提出了一种将多维标度法(MDS)和动态时间弯曲距离(DTW)相结合揭示空间地震动相关结构的方法。该方法可将多点地震动数据的差异转化在一个低维空间内,从而通过各点地震动在该空间内对应的位置反映空间地震动台阵数据之间的差异。较传统的方法,该方法具有较好的直观性且有利于挖掘地震动数据间的潜在关联,利用该方法在对某次地震的台阵记录以及相应合成人工波的分析中取得了较好的效果。
In order to search for a tool to test whether the earthquakes is reasonable for the design,a method based on multidimensional scaling(MDS) and the dynamic time warping distance(DTW) was proposed,which represents the dissimilarities of earthquake in a low dimensional space in a visualized way and uncovers hidden structure of earthquake.The analysis of record from the seismic array shows that the proposed method can be a powerful tool in detecting the correlation structure of spatial ground motion as well as verifying whether the algorithm is producing properly correlated motions in space.
In order to search for a tool to test whether the earthquakes is reasonable for the design,a method based on multidimensional scaling(MDS) and the dynamic time warping distance(DTW) was proposed,which represents the dissimilarities of earthquake in a low dimensional space in a visualized way and uncovers hidden structure of earthquake.The analysis of record from the seismic array shows that the proposed method can be a powerful tool in detecting the correlation structure of spatial ground motion as well as verifying whether the algorithm is producing properly correlated motions in space.
引文
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[2]Johnson D E.Applied multivariate methods for dataanalysts[M].Belmont,C A:Duxbury Press,1998:7-11.
[3]Shepard R N.The analysis of proximities:multidimensionalscaling with an unknown distance function I[J].Psychometrica,1962,27(2):125-140.
[4]Kruskal J B.Nonmetric multidimensional scaling:anumerical method[J].Psychometrika,1964,29(2):115-129.
[5]Ayer M.An empirical distribution function for samplingwith incomplete information[J].Annals of MathematicalStatistics,1955,26:641-647.
[6]Boissières H P,Vanmarcke E H.Spatial correlation ofearthquake ground motion:non-parametric estimation[J].Soil Dynamics&Earthquake Engineering,1995,14(1):23-31.
[7]Smith S W,Ehrenberg J E,Hernandez E N.Analysis ofthe El Centro differential array for the 1979ImperialValley earthquake[J].Bulletin of the SeismologidSociety of America,1982,72:237-58.
[8]Todorovska M I,Trifunac M D.Amplitudes,polarityand time of peaks of strong ground motion during the1994 Northridge,California Earthquake[J].SoilDynamics and Earthquake Engineering,1997,16(4):235-258.
[9]der Kmreghian A,Neuenhofer A.Response spectrummethod for multi support seismic excitation[J].Earthquake Engineering&Structural Dynamics,1992,21:713-714.
[10]Berndt D J,Clioffrd J.Finding patterns in time series:adynamic programming approach[M].Advances inKnowledge Discovery and Data Mining,AAAI/MITPress,1996:229-248.
[11]Li Y M,Chen H G,Wu Z Q.Dynamic time warpingdistance method for similarity test of multipoint groundmotion field[J].Mathematical Problems in Engineering,2010,1:1-12.
[12]Hao H,Oloveria C S,Penzien J.Multiple-station groundmotion processing and simulation based on SMART-1array data[J].Nuclear Engineering and Design,1989,111:293-310.
[13]屈铁军,王前信.空间相关的多点地震动合成(Ⅰ)——基本公式[J].地震工程与工程振动,1998,18(1):8-15.QU Tiejun,WANG Qianxin.Simulation of spatialcorrelative time histories of multi-point ground motion,Part I:Fundamental formulas[J].Journal ofEarthquake Engineering and Engineering Vibration,1998,18(1):8-15.
[14]董汝博,周晶,冯新.非平稳空间相关多点地震动合成方法研究[J].地震工程与工程振动,2007,27(3):11-14.DONG Rubo,ZHOU Jing,FENG Xin.Simulation ofnon-stationary spatial correlative time histories of multi-point ground motion[J].Journal of EarthquakeEngineering and Engineering Vibration,2007,27(3):11-14.
[15]Vanmarcke E,Fenton G.Conditioned simulation oflocal fields of earthquake ground motion[J].StructuralSafety,1991,10:247-264.
[16]Heredia Z E.On the response of multi-support MDOFsystems to spatially varying earthquake ground motion[D].Princeton:Princeton University,1993.
[17]Harichandran R,Vanmarcke E.Stochastic variation ofearthquake ground motion in space and time[J].Journalof Engineering Mechanics,1986,112:154-174.
[18]Saragoni G R,Hart G C.Simulation of artificialearthquake[J].Earthquake Engineering&StructuralDynamics,1974,2(3):249-267.
[19]屈铁军,王前信.空间相关的多点地震动合成(Ⅱ)——合成实例[J].地震工程与工程振动,1998,18(2):25-32.QU Tiejun,WANG Qianxin.Simulation of spatialcorrelative time histories of multi-point ground motion,PartⅡ:Example of simulation[J].Journal ofEarthquake Engineering and Engineering Vibration,1998,18(2):25-32.
[20]Vanmarcke E H,Heredia Z E,Fenton G A.Conditionalsimulation of spatially correlated earthquake groundmotion[J].Journal of Engineering Mechanics(ASCE),1993,119(11):2333-2352.
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