基于AR算法的小波技术在随机场模拟中的应用
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摘要
采用线性滤波器法中的AR法模拟生成了地震动场和风场的时程信号。由于AR算法具有很高的计算效率,但模拟精度却不理想,故引入小波分析中的小波分解方法和小波包分解方法对AR算法模拟的信号进行调整,并对这两种方法改进的效果进行对比。算例分析表明由改进的AR法得到的样本信号频谱与目标谱吻合良好,且发现小波包分解方法调整信号具有比小波分解方法更好的精度。
The time histories signals in earthquake motion field and wind field were simulated with the help of AR (autoregression)method.In view of the deficiency of low accuracy by use of AR method,the signals simulated were modified by wavelet decomposition as well as wavelet packet decomposition methods.The improvement measures were discussed in detail.Several examples show that the simulated spectra by the improved AR method are in good agreement with the corresponding target spectra.Furthermore,the signals modified by the wavelet packet decomposition method are of better precision than those modified by the wavelet decomposition method.
The time histories signals in earthquake motion field and wind field were simulated with the help of AR (autoregression)method.In view of the deficiency of low accuracy by use of AR method,the signals simulated were modified by wavelet decomposition as well as wavelet packet decomposition methods.The improvement measures were discussed in detail.Several examples show that the simulated spectra by the improved AR method are in good agreement with the corresponding target spectra.Furthermore,the signals modified by the wavelet packet decomposition method are of better precision than those modified by the wavelet decomposition method.
引文
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[2]Deodatis G.Simulation of ergodic multivariate stochastic process[J].J Eng Mech ASCE,1996,122(3):778-787.
[3]Cao Y H,Xiang HF,Zhou Y.Simulation of stochastic wind velocity field on long-span bridges[J].J Eng Mech ASCE,2000,126(1):1-6.
[4]李永乐,周述华,强士中.大跨度斜拉桥三维脉动风场模拟[J].土木工程学报,2003,36(10):60-65.
[5]李黎,胡亮,樊剑,等.具有桥塔风效应的桥梁风场数值模拟[J].振动与冲击,2007,26(5):14-18.
[6]王学利,王肇民.高耸结构空间相关风场的模拟研究[J].建筑结构,2000,20(4):45-47.
[7]王修琼,张相庭.混合回归模型及其在高层建筑风响应时域分析中的应用[J].振动与冲击,2000,19(1):5-7.
[8]Owen J S.The application of auto-regressive time series mod-eling for the time frequency analysis of civil engineering struc-tures[J].Engineering Structures,2001,23:521-536.
[9]舒新玲,周岱.风速时程AR模型及其快速实现[J].空间结构,2003,9(4):27-32.
[10]Samaras E,Shinozuka M,Tsurui A.ARMA representation of random process[J].J.Eng Mech,ASCE1985,111(3):449-461.
[11]Naganuma T,Deodatis G,Shinozuka M.ARMA model fortwo-dimensional process[J].Journal of Engineering Mechanics,ASCE1987,113(2):234-251.
[12]胡孔国,陈小兵,岳清瑞.随机地震动模拟的时间序列法及其工程应用[J].世界地震工程,2003,19(1):141-153.
[13]张华,单建.薄膜结构随机风场模拟和耦合风振响应分析[J].工程力学,2006,23(10):19-24.
[14]柳杰,周岱,黄剑伟.大跨空间结构风模拟的改进方法及其小波识别[J].振动与冲击,2006,25(4):21-24.
[15]Kitagawa T,Nomura T.A wavelet-based method to generate artificial wind fluctuation data[J].J.Wind Eng Ind Aero-dyn,2003,90:943-964.
[16]周岱,马骏,吴筑海.空间结构三维风时程模拟及其小波分析[J].工程力学,2006,23(3):88-92.
[17]文建波,周进雄,张陵.设计地震波的小波包多尺度调整[J].振动工程学报,2004,17(3):341-343.
[18]邹立华,刘爱平,杨宏.利用小波重构合成地震波方法及特性研究[J].地震学报,2007,29(6):635-642.
[19]张玲华,郑宝玉.随机信号处理[M].北京:清华大学出版社,2003:51-52,57-58,62-65.
[20]唐向宏,李齐良.时频分析与小波变换[M].北京:科学出版社,2008:118-129,151-172,222-233.
[21]Rossi R,Lazzari M,Vitaliani R.Wind field simulation for structural engineering purpose[J].J.Numer.Meth.Engng2004,61:738-763.
[22]张善文,雷英杰,冯有前.Matlab在时间序列分析中的应用[M].西安:西安电子科技大学出版社,2007:152-154.
[23]白国良,朱丽华.基于现行抗震规范的Kanai-Tajimi模型参数研究[J].世界地震工程,2004,20(3):114-118.
[24]屈铁军,王君杰,王前信.空间变化的地震动功率谱的实用模型[J].地震学报,1996,18(1):55-62.
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