Fractional-order filter approximations for efficient stochastic response determination of wind-excited linear structural systems

IF 3 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics Pub Date : 2024-10-01 DOI:10.1016/j.probengmech.2024.103696

Luca Roncallo , Ilias Mavromatis , Ioannis A. Kougioumtzoglou , Federica Tubino

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引用次数: 0

Abstract

A fractional-order filter approximation is developed for a wind turbulence stochastic excitation model. Specifically, the unknown filter parameters are determined by minimizing the error in the frequency domain between the original and the approximate power spectral densities. It is shown that compared to the limiting case of a standard integer-order filter, and for the same number of parameters to be optimized, the determined fractional-order filter with derivative elements of rational order yields enhanced accuracy. Further, the developed filter approximation enables the analytical calculation of stationary response moments of linear structural systems at practically zero computational cost. This is done by employing a complex modal analysis treatment of the filter state-variable equations, and by relying on Cauchy's residue theorem for evaluating analytically the related random vibration integrals. Comparisons with estimates based on Monte Carlo simulation data demonstrate a quite high degree of accuracy.

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用于风激线性结构系统高效随机响应确定的分数阶滤波器近似值

针对风湍流随机激励模型开发了一种分数阶滤波器近似方法。具体来说，未知滤波器参数是通过最小化原始功率谱密度和近似功率谱密度之间的频域误差来确定的。结果表明，与标准整数阶滤波器的极限情况相比，在需要优化的参数数量相同的情况下，所确定的带有有理阶导数元素的分数阶滤波器能获得更高的精度。此外，所开发的滤波器近似方法可以分析计算线性结构系统的静态响应矩，而计算成本几乎为零。这是通过对滤波器状态变量方程进行复杂模态分析处理，并依靠柯西残差定理对相关随机振动积分进行分析评估实现的。与基于蒙特卡罗模拟数据的估算结果进行比较后发现，其精确度相当高。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Probabilistic Engineering Mechanics 工程技术-工程：机械

CiteScore

3.80

自引率

15.40%

发文量

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.