地震动谱分析中的统计概率问题研究

On the statistical probability issues of ground motion spectral analysis

概率统计是地震工程学中经常遇到的一类数学问题,它是人们进行谱分析并认识地震动特性的重要工具。因此,对于概率论基本理论问题的理解是准确把握地震动特性的前提。作者在对地震动反应谱进行统计分析的过程中,发现传统的对于统计结果及其对应保证概率的认识尚存在一些不足,为了进一步阐释地震动的谱统计概率及相关问题,以芦山强地震动为数据基础,首先通过假设检验考察了地震动规准反应谱的统计谱值在不同周期段内所服从的最优概率分布模型。认为规准化反应谱的统计谱值较好地服从对数正态分布,又结合卡普太因的"比例效应"理论对对数正态分布的成因做了理论推导。发现平均规准谱与对数正态分布50%的保证概率,以及平均加一倍标准差谱与对数正态分布84.1%的保证率谱并非对应,原因在于平均规准谱及平均加一倍标准差谱是关于对数标准差的函数。最后选取平均规准谱作为基准谱曲线,计算并得到了对数正态分布情况下具有不同保证概率的反应谱与基准谱的换算关系,为地震动谱分析中统计结果保证概率的认识,以及不同保证概率设计谱的建立提供了概率理论依据。

Probability and statistics is a class of mathematical problems which is often encountered in earthquake engineering,and it is an important tool for people to perform the spectral analysis and the understanding of ground motion characteristics. Therefore,the fundamental theory of probability problem understanding is the prerequisite to accurately grasp the ground motion characteristics. The author on the ground motion response spectrum in the process of statistical analysis,found that the traditional understanding of statistical results and the corresponding guarantee probability is still some deficiencies,to further explain the spectrum of ground motion statistical probability and related problems,based on the data of Lushan earthquake strong ground motion,first by the hypothesis test to investigate the statistical seismic standard spectral values in different period in obedience to optimal probability distribution model. Think standard response spectral values better statistical lognormal distribution,and combined with ＂scale effect＂the origin of logarithmic normal distribution is derived. Found that the mean standard response spectrum with the lognormal guaranteed probability of 50%,and the mean plus one standard deviation response spectrum with doubled lognormal guaranteed probability of 84. 1% do not correspond,the reason is that the mean response spectrum and the mean plus one standard deviation spectrum is a function of the logarithmic standard deviation. Finally,select the mean response spectrum as a reference spectrum curve,calculation and get the conversionrelation between different guarantee probability response spectra and the reference spectrum,which for seismic spectral analysis of statistical guarantee probability,as well as the establishment of the different design guarantee probability spectra provides the probability theory.