Simulation of multivariate ergodic stochastic processes using adaptive spectral sampling and non-uniform fast Fourier transform

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL
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引用次数: 0

Abstract

The simulation of multivariate ergodic stochastic processes is critical for structural dynamic analysis and reliability evaluation. Although the traditional spectral representation method (SRM) has a wide application in many areas, it is highly inefficient in simulating stochastic processes with many simulation points or long durations due to the significant computational cost associated with matrix factorizations concerning frequency. To address the encountered challenge, this paper presents an efficient approach for simulating ergodic stochastic processes with limited frequencies. Central to this approach is a fusion of the adaptive spectral sampling and the non-uniform fast Fourier transform (NUFFT) techniques. The adaptive spectral sampling of the envelope spectrum enables the determination of limited non-equispaced frequencies, which are randomly sampled according to a uniform distribution. Thus, the Cholesky decomposition is only required at limited specific frequencies, which dramatically reduces the computational cost of matrix factorizations. Since the randomly sampled frequencies are not equispaced, utilizing FFT to accelerate the summation of trigonometric functions becomes impractical. Then, the NUFFT that adapts the non-equispaced sampling points is employed instead to expedite this process with the non-uniform increment approximated through reduced interpolation. By taking the wind field simulation of a long-span suspension bridge as an example, a parametric analysis is conducted to investigate the effect of random frequencies on the simulation error of the developed approach and the convergence of spectra. Finally, the developed approach is further validated by focusing on the spectra and probabilistic density functions of the simulated wind samples, and the simulation performance is compared with that of the traditional approach. The analytical results demonstrate the efficiency and accuracy of the developed approach in simulating ergodic stochastic processes.

利用自适应频谱采样和非均匀快速傅立叶变换模拟多元遍历随机过程
多变量遍历随机过程的模拟对于结构动态分析和可靠性评估至关重要。虽然传统的频谱表示法(SRM)在许多领域都有广泛应用,但由于与频率相关的矩阵因式分解需要大量计算成本,因此在模拟模拟点多或持续时间长的随机过程时效率很低。为了解决所遇到的难题,本文提出了一种模拟有限频率的遍历随机过程的高效方法。这种方法的核心是融合自适应频谱采样和非均匀快速傅里叶变换(NUFFT)技术。包络谱的自适应频谱采样可以确定有限的非匀速频率,这些频率是根据均匀分布随机采样的。因此,只需要在有限的特定频率上进行乔利斯基分解,从而大大降低了矩阵因式分解的计算成本。由于随机采样频率不是等距的,利用 FFT 加速三角函数求和变得不切实际。因此,采用了对非等距采样点进行调整的 NUFFT 来加速这一过程,通过减少插值来近似非均匀增量。以大跨度悬索桥的风场模拟为例,进行了参数分析,研究了随机频率对所开发方法的模拟误差和频谱收敛性的影响。最后,通过关注模拟风样本的频谱和概率密度函数,进一步验证了所开发的方法,并将模拟性能与传统方法进行了比较。分析结果证明了所开发的方法在模拟遍历随机过程中的效率和准确性。
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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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