Comprehensive Investigation into the Accuracy and Applicability of Monte Carlo Simulations in Stochastic Structural Analysis

摘要

Monte Carlo simulation method has been used extensively in probabilistic analyses of engineering systems and its popularity has been growing. While it is widely accepted that the simulation results are asymptotically accurate when the number of samples increases, certain exceptions do exist. The major objectives of this study are to reveal the conditions of the applicability of Monte Carlo method and to provide new insights into the accuracy of the simulation results in stochastic structural analysis. Firstly, a simple problem of a spring with random axial stiffness subject to a deterministic tension is investigated, using normal and lognormal distributions. Analytical solutions for moments of spring elongation are derived through the explicit integration, and numerical solutions by Monte Carlo simulations with different sample sizes are carried out. This study shows analytically that when a normal distribution is assumed, integrals for calculating the moments do not exist and the first moment has a Cauchy principal value, and numerically that Monte Carlo simulation method may fail to yield convergent results for the non-existent moments. Secondly, parallel and series spring systems with normally distributed and correlated axial stiffness values are considered, and the same findings are made as for the single spring problem. Finally, conclusions are made on the importance of checking integrability before Monte Carlo simulations are conducted in the stochastic analysis and the advantages of lognormal distribution for modelling material parameters. Considering that Monte Carlo simulation method has great potential in engineering applications due to the ever-increasing computer power, the findings are crucial for the stochastic analysis in a variety of engineering fields.