Currently, the most common approach to simulate stochastic vector processes for structural dynamic reliability analysis is the Spectral Representation Method (SRM), characterized by a superposition of amplitude-modulated trigonometric functions with random phase angles. However, to represent the vector processes completely, the SRM requires the sampling of a large number of independent random variables, that may cause a large amount of computational cost for the time history sample generation and structural reliability calculation. To reduce the number of random variables, this paper presents a method based on the generalized harmonic wavelet (GHW) to simulate fully nonstationary stochastic vector processes. First, the relationship between the GHW coefficients and the evolutionary cross spectrum matrix of the stochastic vector process is derived. Then, based on the inverse GHW transform, a general simulation formula by superposing GHWs is proposed. The corresponding simplified method which requires less independent random variables is also presented. At last, a numerical case study is provided to emphasize the efficiency of the proposed method. The result indicates that, due to the localization of the energy distribution of the GHW in the time–frequency domain, the proposed method could generate the stochastic vector process samples using less components and is more efficient than the SRM. This method has high potential for application in the Monte Carlo simulation of spatially variable seismic ground motions or wind velocities for structural dynamic reliability analysis.

中文翻译：

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基于广义谐波小波的全非平稳随机矢量过程的高效模拟方法


目前，模拟随机矢量过程进行结构动力可靠性分析的最常用方法是谱表示法（SRM），其特点是具有随机相位角的调幅三角函数的叠加。然而，为了完整地表示矢量过程，SRM需要对大量独立随机变量进行采样，这可能会导致时程样本生成和结构可靠性计算产生大量计算成本。为了减少随机变量的数量，提出一种基于广义谐波小波(GHW)的方法来模拟完全非平稳随机向量过程。首先，推导了随机向量过程的GHW系数与演化互谱矩阵之间的关系。然后，基于GHW逆变换，提出了叠加GHW的通用模拟公式。还提出了相应的需要较少独立随机变量的简化方法。最后，提供了一个数值案例研究来强调所提出方法的效率。结果表明，由于 GHW 的能量分布在时频域中的局域化，所提出的方法可以使用更少的组件生成随机矢量过程样本，并且比 SRM 更有效。该方法在空间可变地震地面运动或风速的蒙特卡罗模拟中具有很高的应用潜力，以进行结构动力可靠性分析。