全非平稳地震动随机场的时-频域混合降维模拟

Time-frequency domain hybrid dimension-reduction simulation for fully non-stationary stochastic ground motion field

  • 摘要: 本研究在过滤白噪声模型的基础上进行了扩展,提出了一种全非平稳地震动随机场的时-频域混合降维建模方法,有效突破了传统模型仅能模拟地震动过程而无法刻画地震动场的局限性。具体地,针对过滤白噪声模型中脉冲响应函数难以直接体现地震动随机场空间相干性的问题,通过引入本征正交分解-降维模拟方法,实现了具有空间相干性的白噪声随机向量过程频域表达。应用地震动随机场不同作用点处的脉冲响应函数和调制函数对相应的白噪声分量过程滤波调幅,实现了全非平稳地震动随机场的时-频域高效降维表达。数值算例分别从均值、标准差、自/互相关函数以及反应谱、相干函数等方面验证了全非平稳地震动随机场时-频域混合降维模型的精确性和工程适用性。

     

    Abstract: This study extends the filtered white noise model by proposing a time-frequency hybrid dimensionality reduction model for fully nonstationary seismic ground motion random fields, thereby overcoming the limitation of simulating only ground motion processes without capturing spatially distributed ground motion fields. Specifically, to address the difficulty in directly representing the spatial coherence of seismic random fields within the impulse response function of the filtered white noise model, a proper orthogonal decomposition (POD)-based dimensionality reduction simulation method is introduced. This approach enables a frequency-domain representation of spatially coherent white noise random vector processes. By applying the impulse response functions and modulation functions corresponding to different locations within the seismic random field to filter and modulate the respective white noise components, an efficient time–frequency hybrid dimensionality reduction representation of fully nonstationary seismic random fields is achieved. Numerical examples validate the accuracy and engineering applicability of the proposed model by comparing mean values, standard deviations, auto-/cross-correlation functions, as well as response spectra and coherence functions.

     

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