{"title":"Simulation of multivariate ergodic stochastic processes using adaptive spectral sampling and non-uniform fast Fourier transform","authors":"","doi":"10.1016/j.probengmech.2024.103669","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probabilistic Engineering Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0266892024000912","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
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.
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.