A SYNTHESIS METHOD FOR REGIONAL-SPECIFIC GROUND MOTIONS TIME HISTORY BASED ON FEATURE EXTRACTION AND SPECTRAL MATCHING OPTIMIZATION
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摘要: 地震的区域构造背景和传播路径有较大差异特征，因而实际观测的地震动具有显著的区域性差异。在结构动力时程分析时，虽然人工合成方法能够提供匹配设计谱的输入地震动，但是其并不能体现出地震动的区域特征。为了模拟考虑目标区域特征且完美匹配目标谱的地震动，该文提出了一种基于智能算法的地震动合成新方法。该方法应用主成分分析算法获取目标区域地震动的区域特征，由最大方差理论提取目标区域的种子地震动，再用基于粒子群算法优化的时域反应谱匹配方法调整种子地震动的反应谱，最终构造出包含区域特征和谱匹配的地震动时程。以四川地区为例验证了该方法的合理性和有效性，合成的地震动在时域和频域上均与该区域实际地震动特征一致。该文提出的方法的优点在于合成的地震动具有显著的区域特征，且与目标谱有更好的匹配效果和更高的匹配效率，可为结构动力反应分析提供考虑区域性差异、具有低不确定性的地震动输入。Abstract: Due to the influence of regional seismic source structures, the actual observed ground motion has significant regional differences. In the current structural dynamic time-history analysis, although the synthetic method can provide the spectra-compatible ground motion input, it cannot reflect the actual ground motion characteristics in the target area. In order to synthesize the ground motion, which contains the characteristics of the target region and is perfectly compatible with the target spectrum, a new method for ground motion synthesis based on intelligent algorithm is proposed. In this method, the principal component analysis algorithm was used to obtain the actual regional ground motion characteristics, the maximum variance theory was used to extract the seeds ground motion in the target area, the response spectrum of seed ground motion was adjusted by time domain response spectrum matching method optimized by particle swarm optimization algorithm, and the spectra-compatible ground motion time history containing regional characteristics was finally constructed. The rationality and effectiveness of this method are verified by taking Sichuan area as an example, and the characteristics of the synthesized ground motion in time domain and frequency domain are consistent with the actual ground motion in this area. The advantage of the proposed method is that the synthesized ground motion has significant regional characteristics, and has better matching effect and higher matching efficiency with the target spectrum, which can provide low uncertainty ground motion input considering regional differences for structural dynamic response analyses.
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图 1 粒子群算法求最优解γ的流程图
Figure 1. Flow chart of particle swarm optimization for solving optimal solution γ
图 4 种子地震动反应谱与目标反应谱
Figure 4. Seed ground motion response spectrum and target response spectrum
图 6 匹配误差随迭代次数增加的变化曲线
Figure 6. The variation curve of matching error with the increase of iteration number
图 9 初始地震动和合成地震动的归一化Arias强度
Figure 9. Normalized Arias intensities for initial and synthetic ground motion
图 10 初始地震动和合成地震动的傅里叶幅值谱
Figure 10. Fourier amplitude spectra of initial and synthetic ground motion
图 11 初始地震动和合成地震动的时频图
Figure 11. Time-frequency diagrams of initial and synthetic ground motion
表 1 误差函数的定义
Table 1. Definition of error function
误差函数 反应谱差值(ERR1) 反应谱差值与目标谱之比(ERR2) 总体平均值(ERRmean) $ERR_{ {\rm{mean} } }^1 = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {|S{a_{\rm c}}({T_i}) - S{a_{\rm t}}({T_i})} |$ $ERR_{ {\rm{mean} } }^2 = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N \left|\dfrac{ {S{a_{\rm c}}({T_i}) - S{a_{\rm t}}({T_i})} }{ {S{a_{\rm t}}({T_i})} } \right|$ 个体最大值(ERRmax) $ERR_{\max }^1 = \max \{ |S{a_{\rm c}}({T_i}) - S{a_{\rm t}}({T_i})|\}$ $ERR_{\max }^2 = \max \left\{ \left|\dfrac{ {S{a_{\rm c}}({T_i}) - S{a_{\rm t}}({T_i})} }{ {S{a_{\rm t}}({T_i})} }\right|\right\}$ 
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表 2 区域地震动信息
Table 2. Regional ground motion information
地震名称 地震时间 北纬/(°) 东经/(°) 震源深度/km 震级/Ms 数目/条 四川雅安余震 2013.4.20 30.389 103.010 12 4.5 1 四川雅安余震 2013.4.20 30.180 102.930 19 4.5 2 四川雅安余震 2013.4.20 30.280 102.930 15 4.8 1 四川雅安余震 2013.4.20 30.250 102.830 16 4.7 2 四川雅安余震 2013.4.20 30.170 102.989 19 4.8 2 四川雅安余震 2013.4.20 30.190 102.949 17 4.6 1 四川雅安余震 2013.4.20 30.280 102.989 15 4.9 3 四川雅安余震 2013.4.20 30.129 102.839 17 4.7 3 四川雅安余震 2013.4.20 30.250 103.010 17 4.7 5 四川雅安余震 2013.4.20 30.239 102.940 15 5.4 4 四川雅安余震 2013.4.21 30.360 103.050 27 5.4 2 四川雅安余震 2013.4.21 30.260 103.000 17 4.9 5 四川雅安余震 2013.4.21 30.340 103.000 17 5.4 3
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