Sparse representations and compressive sampling for enhancing the computational efficiency of the Wiener path integral technique

• Published in: Mechanical systems and signal processing Vol. 111; pp. 87 - 101
• Main Authors: Psaros, Apostolos F., Kougioumtzoglou, Ioannis A., Petromichelakis, Ioannis
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01.10.2018; Elsevier BV
• Subjects: Compressive sampling; Computational efficiency; Computer simulation; Computing time; Degrees of freedom; Duffing oscillators; Integrals; Monte Carlo simulation; Nonlinear system; Nonlinear systems; Optimization algorithms; Path integral; Probability density functions; Representations; Sampling; Sparse representations; Sparsity; Stochastic dynamics; Stochastic models; Stochastic systems; Sparse representations; Stochastic dynamics; Compressive sampling; Path integral; Nonlinear system
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2018.03.056

•The computational efficiency of the Wiener path integral technique is enhanced.•Compressive sampling tools and sparse representations are exploited.•The nonlinear system joint response PDF is determined efficiently.•The technique is capable of addressing high-dimensional stochastic systems. 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.