Generation of strongly non-Gaussian stochastic processes by iterative scheme upgrading phase and amplitude contents |
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| Affiliation: | 1. Institute for Infrastructure and Environment, Heriot–Watt University, Edinburgh EH14 4AS, United Kingdom;2. Creative Engineering and Management Services, Deans Centre Peshawar, Pakistan;3. Department of Mechanical and Industrial Engineering, College of Engineering, Sultan Qaboos University, Oman;4. Maxwell Institute for Mathematical Sciences and Department of Mathematics, Heriot–Watt University, Edinburgh, EH14 4AS, United Kingdom;1. Institute of Advanced Manufacturing and Intelligent Technology, Beijing 100124, PR China;2. Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing 100124, PR China;3. Mechanical Industry Key Laboratory of Heavy Machine Tool Digital Design and Testing, Beijing 100124, PR China;1. Department of Computational Mathematics, Oles Honchar Dnipro National University, Gagarin Av., 72, Dnipro 49010, Ukraine;2. Department of Theoretical and Computational Mechanics, Oles Honchar Dnipro National University, Gagarin Av., 72, Dnipro 49010, Ukraine;3. Université Clermont Auvergne, CNRS, SIGMA Clermont (ex- French Institute of Advanced Mechanics), Institut Pascal, Campus de Clermont-Ferrand, 63178 Aubière, France;1. College of Civil Engineering, Fujian University of Technology, No.33 Xuefu South Road, Shangjie University Town, Fuzhou 350118, China;2. College of Civil Engineering, Fuzhou University, No.2 Xueyuan Road, Shangjie University Town, Fuzhou 350116, China;3. Key Laboratory of Underground Engineering, Fujian Province University, No.33 Xuefu South Road, Shangjie University Town, Fuzhou 350118, China;1. Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China;2. Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China;1. College of Science, China Agricultural University, Beijing 100083, China;2. College of Engineering and Computer Science, Australian National University, Canberra, ACT 2601, Australia;3. School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China |
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| Abstract: | Random excitations, such as wind velocity, always exhibit non-Gaussian features. Sample realisations of stochastic processes satisfying given features should be generated, in order to perform the dynamical analysis of structures under stochastic loads based on the Monte Carlo simulation. In this paper, an efficient method is proposed to generate stationary non-Gaussian stochastic processes. It involves an iterative scheme that produces a class of sample processes satisfying the following conditions. (1) The marginal cumulative distribution function of each sample process is perfectly identical to the prescribed one. (2) The ensemble-averaged power spectral density function of these non-Gaussian sample processes is as close to the prescribed target as possible. In this iterative scheme, the underlying processes are generated by means of the spectral representation method that recombines the upgraded power spectral density function with the phase contents of the new non-Gaussian processes in the latest iteration. Numerical examples are provided to demonstrate the capabilities of the proposed approach for four typical non-Gaussian distributions, some of which deviate significantly from the Gaussian distribution. It is found that the estimated power spectral density functions of non-Gaussian processes are close to the target ones, even for the extremely non-Gaussian case. Furthermore, the capability of the proposed method is compared to two other methods. The results show that the proposed method performs well with convergence speed, accuracy, and random errors of power spectral density functions. |
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