Abstract The vertical design spectrum plays an important role in seismic design whether of critical or ordinary structures. However, many studies focused on the vertical to horizontal response spectral ratio and less researchers investigated the properties of vertical design spectra directly. In this study, differential evolution and simulated annealing are firstly examined to determine an appropriate method to estimate the characteristic parameters of the vertical design spectra. Then, the properties of the vertical design spectra in Japan are investigated by applying differential evolution to about 10000 KiK-net seismic data. Compared with epicentral distance, the influence of earthquake magnitude is more obvious which shows up as the linear correlation between the corner period and earthquake magnitude. Moreover, we propose a loglog exponential formula which relates the corner period of vertical design spectra to that of horizontal design spectra, and the formula may be used in other regions.

中文翻译：

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通过对 KiK-net 数据应用差分进化研究日本垂直设计谱的特性

摘要 无论是关键结构还是普通结构，竖向设计谱在抗震设计中都起着重要作用。然而，许多研究集中在垂直与水平响应谱比上，而很少有研究人员直接研究垂直设计谱的特性。在这项研究中，首先研究了差分演化和模拟退火，以确定一种合适的方法来估计垂直设计谱的特征参数。然后，通过对大约 10000 个 KiK-net 地震数据应用差分演化来研究日本的垂直设计谱的特性。与震中距相比，地震震级的影响更为明显，表现为拐角周期与震级的线性相关。而且，