A Reduced-Order Wiener Path Integral Formalism for Determining the Stochastic Response of Nonlinear Systems With Fractional Derivative Elements
A Reduced-Order Wiener Path Integral Formalism for Determining the Stochastic Response of Nonlinear Systems With Fractional Derivative Elements
复制标题
确定具有分数阶微分元的非线性系统随机响应的降阶维纳路径积分形式
DOI：
10.1115/1.4056902
复制
发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Kougioumtzoglou, Ioannis A.
中科院分区：
文献类型：
--
作者：
Mavromatis, Ilias G.;Kougioumtzoglou, Ioannis A.
开发了一种基于维纳路径积分 (WPI) 的技术，用于确定具有分数导数元素的各种非线性系统的随机响应。具体来说，提出了降阶 WPI 公式，它可以被解释为一种无近似降维方法，使相关的计算成本独立于问题的随机维度总数。事实上，本文开发的技术可以直接确定与仅响应向量分量的子集相对应的任何低维联合响应概率密度函数。这是通过在相关变分、函数最小化问题中利用固定和自由边界条件的适当组合来完成的。值得注意的是，降阶 WPI 公式对于仅关注少数特定自由度且其随机响应对于整个系统的设计和优化至关重要的问题特别有利。考虑一个指示性数值示例，该示例涉及具有分数导数元素的随机激励调谐质量阻尼器惰性非线性系统。与相关蒙特卡罗模拟数据的比较证明了该技术的准确性和计算效率。
A technique based on the Wiener path integral (WPI) is developed for determining the stochastic response of diverse nonlinear systems with fractional derivative elements. Specifically, a reduced-order WPI formulation is proposed, which can be construed as an approximation-free dimension reduction approach that renders the associated computational cost independent of the total number of stochastic dimensions of the problem. In fact, the herein developed technique can determine, directly, any lower-dimensional joint response probability density function corresponding to a subset only of the response vector components. This is done by utilizing an appropriate combination of fixed and free boundary conditions in the related variational, functional minimization, problem. Notably, the reduced-order WPI formulation is particularly advantageous for problems where the interest lies in few only specific degrees-of-freedom whose stochastic response is critical for the design and optimization of the overall system. An indicative numerical example is considered pertaining to a stochastically excited tuned mass-damper-inerter nonlinear system with a fractional derivative element. Comparisons with relevant Monte Carlo simulation data demonstrate the accuracy and computational efficiency of the technique.