地震波时变修正Kanai-Tajimi非平稳随机模型的建立
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摘要
利用谐小波变换对实际强震记录的时变谱进行估计,并统计分析了远场3类不同场地上地震波的时变谱特征,分析发现对于硬场地上的远场地震波在时域内平稳段较短,下降段衰减较快,而在频域内则具有较大的中心频率和较宽的频带.利用均匀调制非平稳模型和时变修正Kanai-Tajimi非平稳模型模拟地震波的时变谱,把非线性函数的参数识别问题转化成求解无约束优化问题,利用拟牛顿迭代法求得最优解,得到3类不同场地上这两种模型的参数具体取值以及参数函数集的具体表达式.为了定量地确定模拟模型的精度,定义了误差函数,验证了所提时变谱参数识别方法的精度,给出了与建筑抗震规范相对应的不同场地不同烈度下多遇和罕遇地震的谱强度因子的大小.最后提出了利用求解时变线性微分方程组来合成非平稳地震波的方法.
Time variable spectra of strong ground motion records are estimated based on the harmonic wavelet transform. The characteristic of time variable spectrum of the strong motion records on the sites of three classes are analyzed. It is shown that the records on hard soil site have shorter stationary duration in time domain,and have higher frequency center and wide frequency band in frequency domain. The average time variable spectra of strong motion records are simulated by uniform non-stationary stochastic model and time variable modified Kanai-Tajimi non-stationary stochastic model. The empirical formulas for the time variable spectra of strong motion records on three class soil sites are established by using nonlinear function fitting method. In order to demonstrate the precision of the simulated stochastic model,an error function is defined and the errors are calculated. The time variable spectrum factors corresponding to relevant seismic intensity and soil site class,which are compatible with the seismic code,are given. Finally,the artificial non-stationary ground motion is generated by solving the time variable linear differential equations.
Time variable spectra of strong ground motion records are estimated based on the harmonic wavelet transform. The characteristic of time variable spectrum of the strong motion records on the sites of three classes are analyzed. It is shown that the records on hard soil site have shorter stationary duration in time domain,and have higher frequency center and wide frequency band in frequency domain. The average time variable spectra of strong motion records are simulated by uniform non-stationary stochastic model and time variable modified Kanai-Tajimi non-stationary stochastic model. The empirical formulas for the time variable spectra of strong motion records on three class soil sites are established by using nonlinear function fitting method. In order to demonstrate the precision of the simulated stochastic model,an error function is defined and the errors are calculated. The time variable spectrum factors corresponding to relevant seismic intensity and soil site class,which are compatible with the seismic code,are given. Finally,the artificial non-stationary ground motion is generated by solving the time variable linear differential equations.
引文
白国良,朱丽华.2004.基于现行抗震规范的Kanai-Taji mi模型参数研究[J].世界地震工程,20(3):50-55.
樊剑,刘铁,胡亮.2007.基于现代时频分析技术的地震波时变谱估计[J].振动与冲击,26(1):79-82.
樊剑,吕超,张辉.2008.基于S变换的地震波时频分析及人工调整[J].振动工程学报,21(4):381-386.
樊剑,吕超,张辉.2009.基于离散谐小波变换的地震波时变谱估计及非平稳地震波人工合成[J].地震学报,31(2):215-223.
洪峰,江近仁,李玉亭.1994.地震地面运动的功率谱模型及其参数的确定[J].地震工程与工程振动,14(2):46-52.
李英民,刘立平,赖明.2008.工程地震动随机功率谱模型的分析与改进[J].工程力学,25(3):43-48.
欧进萍,牛荻涛,杜修力.1994.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,11(3):45-53.
薛素铎,王雪生,曹资.2003.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,36(5):5-10.
张治勇,孙柏涛,宋天舒.2000.新抗震规范地震动功率谱模型参数的研究[J].世界地震工程,16(3):33-38.
Clough R W,Penzien J.1993.Dynamics of Structures[M].2nd ed.New York:McGraw-Hill,Inc:608-611.
Spanos P D,Tezcan J,Tratskas P.2005.Stochastic processes evolutionary spectrumesti mation via harmonic wavelets[J].Comput Methods Appl Mech Engrg,194(12):1367-1383.
Spanos P D,Giaralisb A,Politis N P.2007.Ti me-frequency representation of earthquake accelerograms and inelasticstructural response records usingthe adaptive chirplet decomposition and empirical mode decomposition[J].Soil DynEarthq Eng,27(7):675-689.
Wen Y K,Gu Ping.2004.Description and si mulation of non-stationary processes based on Hilbert spectra[J].J EngMech,130(8):942-951.
樊剑,刘铁,胡亮.2007.基于现代时频分析技术的地震波时变谱估计[J].振动与冲击,26(1):79-82.
樊剑,吕超,张辉.2008.基于S变换的地震波时频分析及人工调整[J].振动工程学报,21(4):381-386.
樊剑,吕超,张辉.2009.基于离散谐小波变换的地震波时变谱估计及非平稳地震波人工合成[J].地震学报,31(2):215-223.
洪峰,江近仁,李玉亭.1994.地震地面运动的功率谱模型及其参数的确定[J].地震工程与工程振动,14(2):46-52.
李英民,刘立平,赖明.2008.工程地震动随机功率谱模型的分析与改进[J].工程力学,25(3):43-48.
欧进萍,牛荻涛,杜修力.1994.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,11(3):45-53.
薛素铎,王雪生,曹资.2003.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,36(5):5-10.
张治勇,孙柏涛,宋天舒.2000.新抗震规范地震动功率谱模型参数的研究[J].世界地震工程,16(3):33-38.
Clough R W,Penzien J.1993.Dynamics of Structures[M].2nd ed.New York:McGraw-Hill,Inc:608-611.
Spanos P D,Tezcan J,Tratskas P.2005.Stochastic processes evolutionary spectrumesti mation via harmonic wavelets[J].Comput Methods Appl Mech Engrg,194(12):1367-1383.
Spanos P D,Giaralisb A,Politis N P.2007.Ti me-frequency representation of earthquake accelerograms and inelasticstructural response records usingthe adaptive chirplet decomposition and empirical mode decomposition[J].Soil DynEarthq Eng,27(7):675-689.
Wen Y K,Gu Ping.2004.Description and si mulation of non-stationary processes based on Hilbert spectra[J].J EngMech,130(8):942-951.
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