具有分数阶导数单元的随机激励非线性结构系统的概率失效分析

IF 11 1区 工程技术 Q1 ENGINEERING, INDUSTRIAL
Marco Behrendt , Vasileios C. Fragkoulis , George D. Pasparakis , Michael Beer
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引用次数: 0

摘要

本文将放宽功率谱密度(PSD)框架应用于具有分数阶导数元素的动力系统的不确定性量化。所提出的方法为基于谱的随机模拟中的不确定性及其传播提供了系统的处理,以确定具有记忆依赖或粘弹性行为的系统的响应。该框架的一个关键优势在于它能够使用非参数概率表示对估计的PSD函数的可变性进行建模,同时明确地考虑在传统的基于PSD的估计中通常被忽视的频域相关性。首先,通过提取离散化PSD估计集合的统计矩,得到一个“松弛”版本的功率谱密度。接下来,使用频率相关的截断正态分布来捕获PSD不确定性。统计兼容实现使用三种不同的采样策略:基于单变量逆累积分布函数的边际概率密度函数有效采样方法,包含交叉频率协方差的多元高斯方法来捕获全局相关结构,以及重建平滑相关PSD轨迹的Ornstein-Uhlenbeck马尔可夫过程模型。通过三个有代表性的案例研究,证明了该方法的有效性。它们是具有分数阶阻尼的Duffing非线性振荡器,具有非线性耦合特性的调谐质量阻尼-干涉器系统,以及随机激励下的非线性振动能量收集器。结果表明,通过考虑PSD的综合概率处理,所提出的框架在谱不确定性下可以提高动力系统的可靠性分析结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Probabilistic failure analysis of stochastically excited nonlinear structural systems with fractional derivative elements
In this paper, the application of the relaxed power spectral density (PSD) framework is developed for quantifying uncertainties in dynamical systems with fractional derivative elements. The proposed methodology offers a systematic treatment of uncertainties in spectrum-based stochastic simulation and their propagation for response determination of systems with memory-dependent or viscoelastic behavior. A key advantage of the framework lies in its ability to model the variability of estimated PSD functions using a non-parametric probabilistic representation, while explicitly accounting for frequency-domain correlations that are typically overlooked in conventional PSD-based estimates. First, a “relaxed” version of the power spectral density is derived by extracting statistical moments across ensembles of discretized PSD estimates. Next, frequency-dependent truncated normal distributions are employed to capture PSD uncertainties. Statistically compatible realizations are generated using three distinct sampling strategies: a single-variable inverse cumulative distribution function-based method for efficient sampling of marginal probability density functions, a multivariate Gaussian approach that incorporates cross-frequency covariance to capture global correlation structure, and an Ornstein–Uhlenbeck Markov process model, which reconstructs smoothly correlated PSD trajectories. The efficiency of the proposed approach is demonstrated by considering three representative case studies. These are a Duffing nonlinear oscillator with fractional damping, a tuned mass-damper-inerter system with nonlinear coupling characteristics, and a nonlinear vibration energy harvester under stochastic excitation. It is shown that by accounting for a comprehensive probabilistic treatment of the PSD, the proposed framework yields enhanced reliability analysis results of dynamical systems under spectral uncertainty.
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来源期刊
Reliability Engineering & System Safety
Reliability Engineering & System Safety 管理科学-工程:工业
CiteScore
15.20
自引率
39.50%
发文量
621
审稿时长
67 days
期刊介绍: Elsevier publishes Reliability Engineering & System Safety in association with the European Safety and Reliability Association and the Safety Engineering and Risk Analysis Division. The international journal is devoted to developing and applying methods to enhance the safety and reliability of complex technological systems, like nuclear power plants, chemical plants, hazardous waste facilities, space systems, offshore and maritime systems, transportation systems, constructed infrastructure, and manufacturing plants. The journal normally publishes only articles that involve the analysis of substantive problems related to the reliability of complex systems or present techniques and/or theoretical results that have a discernable relationship to the solution of such problems. An important aim is to balance academic material and practical applications.
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