Stochastic response analysis techniques for “unconventionally modeled” engineering dynamical systems

有效而严格地处理工程系统中的不确定性是提供研究其行为和评估其可靠性的解决方案框架的关键因素。在结构/机械系统随机动力学领域，与不确定性量化相关的主要挑战之一涉及“非常规”系统建模。这相当于需要以更有效的方式建模系统控制方程，考虑其非线性/滞后行为，以及激励的进化特征。此外，建模者还应考虑采用分数阶演算更好地对系统特性进行建模，并考虑采用基于多体系统的技术来促进复杂系统的建模。此外，考虑到随机动力学领域的另一个主要挑战，即不确定性的有效传播，当代系统建模需要发展分析方法，以绕过频繁计算昂贵的基于MCS的方案。为了解决上述挑战，并针对有效的随机响应分析，本提案的研究目标构成了一项开创性的努力，以适应和扩展随机振动理论工具，以直接的方式处理“非常规建模”动力系统。该项目的学术影响将是广泛和多方面的，因为它位于工程随机动力学和应用/计算数学的交叉点。具体而言，从基础研究的角度来看，将开发一种有效的框架，用于进行“非常规建模”动力系统的联合时频响应分析。这将由一个框架来补充进行随机响应分析类系统赋予分数阶导数项。从应用研究和应用的角度来看，该方法将对各种动力系统的分析和设计产生重大影响，并将有助于许多新兴技术，如纳米力学和振动能量收集。此外，考虑到分数阶微积分建模在众多新兴技术中的广泛使用，处理具有分数阶导数元素的系统变得尤为重要。总体而言，拟议的跨学科项目将有助于不同的研究领域，如（线性/非线性）随机（结构/多体）动力学，以及求解（近似）线性和非线性随机微分方程系统的计算方法。

The efficient and rigorous handling of uncertainties in engineering systems constitutes a key element in providing with solution frameworks to study their behavior and assess their reliability. One of the main challenges associated with uncertainty quantification in the field of stochastic dynamics of structural/mechanical systems relates to “unconventional” system modeling. This equivalently translates to the need for modeling the system governing equations in a more efficient manner, taking into account its nonlinear/hysteretic behavior, as well as the evolutionary characteristics of the excitations. In addition, the modeler should also consider employing fractional calculus to better model the system characteristics, and multi-body system-based techniques to facilitate the complex system modeling. Moreover, considering another main challenge in the field of stochastic dynamics, namely the efficient propagation of uncertainties, contemporary system modeling necessitates the development of analytical methods, to bypass the frequently computational expensive MCS based schemes.Directing attention to addressing the above challenges and also aiming at an efficient stochastic response analysis, the research objective of this proposal constitutes a groundbreaking effort to adapt and extend random vibration theoretical tools for treating in a straightforward manner “unconventionally modeled” dynamical systems.The academic impact of the project will be broad and multifaceted, since it lies in the intersection of engineering stochastic dynamics and applied/computational mathematics. Specifically, from a fundamental research point of view, an efficient framework for conducting joint time-frequency response analyses of “unconventionally modeled” dynamical systems will be developed. This will be complemented by a framework for conducting stochastic response analyses for classes of systems endowed with fractional derivative terms. From an applied research and applications point of view, the methodology will have a major impact on the analysis and design of diverse dynamical systems, and will contribute to a number of emerging technologies such as in nano-mechanics and vibration energy harvesting. Further, treating systems endowed with fractional derivative elements becomes especially important, considering the extensive use of fractional calculus modeling in a plethora of emerging technologies.Overall, the proposed cross-disciplinary project will contribute to diverse research fields, such as (linear/nonlinear) stochastic (structural/multibody) dynamics, and computational methods for solving (approximately) linear and nonlinear systems of stochastic differential equations.