地震动具有多维性，如何合理建立多维地震动是复杂工程结构精细化抗震分析的基础。首先，以1766组实测多维强震记录为依据，建议了一类多维地震动的迟滞相干函数模型；其次，研究地震动平动分量在幅值、持时及频谱之间的关系，建立了多维地震动的演变功率谱模型；最后，基于本征正交分解的随机向量过程降维方法，实现了仅用两个基本随机变量即可有效模拟多维地震动过程。数值算例表明，降维方法生成的多维地震动代表性时程具有良好效率，且平动分量的相干性、反应谱以及幅值谱均与实测记录拟合一致，验证了多维地震动降维模型的精确性和工程适用性。同时，采用降维方法生成的多维地震动代表性时程具有赋得概率，并构成一个完备的概率集，可与概率密度演化理论相结合，进而为复杂工程结构抗震可靠性精细化评价提供有效途径。
关键词：多维地震动；实测强震记录；相干函数；演变功率谱；降维模拟
Abstract
Earthquake ground motion has multi-dimensional characteristic, of which the reasonable description is the basis for the refined seismic analysis of complex engineering structures. Firstly, based on 1766 groups of measured multi-dimensional strong motion records, a kind of lagged coherence function model of multi-dimensional ground motion is proposed. Secondly, the relationship among the amplitude, duration and spectrum of three-dimensional ground motion components is studied, and the evolutionary power spectrum model of multi-dimensional ground motion is established. Finally, by introducing the dimension-reduction method based on proper orthogonal decomposition for the random vector process, the simulation of multi-dimensional ground motion is realized using just two elementary random variables. Numerical examples show that the representative time-histories of multi-dimensional ground motion generated by the dimension-reduction method have good efficiency. The coherence, response spectrum and amplitude spectrum of three-dimensional components are consistent with the measured records, which verifies the accuracy and engineering applicability of the dimension-reduction model. Meanwhile, the representative time-histories have assigned probability and can consist a complete probability set. Thus, the dimension-reduction method can be combined with the probability density evolution theory, which provides an effective way for the refined seismic reliability evaluation of complex engineering structures.
Key words: multi-dimensional ground motion; strong motion records; coherence function; evolutionary power spectrum; dimension-reduction
关键词
多维地震动 /
实测强震记录 /
相干函数 /
演变功率谱 /
降维模拟
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Key words
multi-dimensional ground motion /
strong motion records /
coherence function /
evolutionary power spectrum /
dimension-reduction
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