工程地震动激励的高斯性检验

Gaussianity detection of engineering seismic ground motion excitation

摘要

工程结构抗震可靠度分析需要采用随机方法对地震动激励进行模拟。常用的地震动模拟方法是将具有特定幅值和随机相角的三角函数叠加并调幅,这样得到的人工地震动具有高斯性。由于高斯和非高斯输入会对结构可靠度分析产生不可忽略的影响,因此需要检验真实地震动记录是否具有高斯性,依此判断地震动模拟方法是否合理,并为地震动筛选提供定量参考。本文选取1817条峰值加速度大于0.06 g的实测地震动,提取70%能量对应的强震段数据,分别依据J-B检验方法和Mardia检验方法计算一维边缘分布和二维联合分布的偏度、峰度来定量判断地震动是否符合高斯性。一维边缘检验将每一条地震动作为样本独立进行统计,结果表明72.6%的数据是非高斯的。二维联合检验针对不同时刻地震动数据进行统计,结果表明在强震段起始时段内,实测数据二维分布具有高斯性,但中后时段数据的非高斯性明显增强。同时进行了地震动峰度、偏度与震中距、地表30 m下土层剪切波速V_S30的相关性检验。结果表明,地震动强震段的一维边缘分布和二维联合分布都具有非高斯性,软土场地上地震动的非高斯性要强于硬土场地,中远场地震动的非高斯性要强于近场。

Abstract

Seismic reliability analysis of engineering structures requires the use of stochastic methods to simulate seismic excitation. A commonly used seismic simulation method involves superimposing trigonometric functions with specific amplitudes and random phase angles, followed by amplitude modification to obtain artificial seismic motions that exhibit Gaussian characteristics. Since Gaussian and non-Gaussian inputs can have a significant impact on structural reliability analysis, it is necessary to verify whether real seismic records exhibit Gaussianity to determine the rationality of the seismic simulation method and provide a quantitative reference for seismic motion selection. This paper selects 1817 measured seismic motions with peak ground acceleration greater than 0.06 g, extracts data from the strong-motion segment corresponding to 70% of the energy, and uses the J-B test and Mardia test to calculate the skewness and kurtosis of the one-dimensional marginal distribution and the two-dimensional joint distribution to quantitatively determine whether the seismic motions conform to Gaussianity. The one-dimensional marginal test statistically analyzes each seismic motion as independent sample, showing that 72.6% of the data is non-Gaussian. The two-dimensional joint test statistically analyzes the seismic data at different times, showing that the two-dimensional distribution of the measured data exhibits Gaussianity in the initial period of the strong-motion segment, but the non-Gaussianity of the data significantly increases in the middle and later periods. Correlation tests are conducted on ground motion kurtosis, skewness, epicentral distance, and V _S30. The results show that both the one-dimensional marginal distribution and the two-dimensional joint distribution of strong ground motion segments are non-Gaussian. The non-Gaussianity of ground motions is stronger on soft soil sites than on hard soil sites, and the non-Gaussianity of ground motions in mid-to-far fields is stronger than that in near fields.

关键词

地震动 / 强震记录 / 相关性分析 / 非高斯 / 地震动持时

Key words

seismic ground motions / strong motion record / correlation analysis / non-Gaussian / duration of ground motion

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基金资助

国家自然科学基金面上项目(52578252)

河北省自然科学基金面上项目(E2020203103)