Sparse representations and compressive sampling for enhancing the computational efficiency of the Wiener path integral technique
Sparse representations and compressive sampling for enhancing the computational efficiency of the Wiener path integral technique
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DOI：
10.1016/j.ymssp.2018.03.056
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发表时间：
2018-10
影响因子：
8.4
通讯作者：
Apostolos F. Psaros;I. Kougioumtzoglou;Ioannis Petromichelakis
中科院分区：
文献类型：
--
作者：
Apostolos F. Psaros;I. Kougioumtzoglou;Ioannis Petromichelakis
利用稀疏表示领域的最新进展，提高了用于确定多种动力系统随机响应的Wiener路径积分（WPI）技术的计算效率。具体而言，利用适当的基础展开系统联合响应概率密度函数（PDF）。其次，基于WPI技术的定位能力，只有很少的PDF点是确定的。此外，压缩抽样程序结合群稀疏性概念和适当的优化算法被用于有效地确定系统响应PDF扩展的系数。结果表明，本文开发的增强使该技术能够轻松地处理相对高维的随机系统。考虑了两个说明性的数值例子。第一个是指具有双峰响应PDF的单自由度Duffing振荡器。在第二个例子中，确定了一个10自由度非线性结构系统在随机激励下的20变量联合响应转换PDF。与相关的蒙特卡罗模拟数据的比较证明了增强WPI技术的准确性。
The computational efficiency of the Wiener path integral (WPI) technique for determining the stochastic response of diverse dynamical systems is enhanced by exploiting recent developments in the area of sparse representations. Specifically, an appropriate basis for expanding the system joint response probability density function (PDF) is utilized. Next, only very few PDF points are determined based on the localization capabilities of the WPI technique. Further, compressive sampling procedures in conjunction with group sparsity concepts and appropriate optimization algorithms are employed for efficiently determining the coefficients of the system response PDF expansion. It is shown that the herein developed enhancement renders the technique capable of treating readily relatively high-dimensional stochastic systems. Two illustrative numerical examples are considered. The first refers to a single-degree-of-freedom Duffing oscillator exhibiting a bimodal response PDF. In the second example, the 20-variate joint response transition PDF of a 10-degree-of-freedom nonlinear structural system under stochastic excitation is determined. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the enhanced WPI technique.