Uncertainty Evaluation of Stochastic Structural Response with Correlated Random Variables

It has been realized that the influence of system parameter uncertainties may be very significant, even dominant, in stochastic response evaluation. Nevertheless, in reality, this evaluation process may be difficult to conduct due to these parameter variables (viz. structural property parameters, such as stiffness, damping, and strength, and excitation characteristics parameters, such as frequency content and duration) that are usually correlated with each other. Therefore, this study devotes to develop a method for evaluating stochastic response uncertainty involving correlated system parameter variables. In this method, the evaluation expression for the mean and standard deviation of the maximum response including uncertainty parameter variables are provided first; subsequently, a third-moment pseudo-correlation normal transformation is able to be performed for converting the correlated and non-normal system parameter variables with unknown joint probability density function (PDF) or marginal PDF into the mutually independent standard normal ones; ultimately, a point estimate procedure (PEP) based on univariate dimension reduction integration can be carried out for evaluating the structural stochastic response including uncertainty system parameters. Several numerical examples with an engineering background involving correlated system parameter variables are analyzed and discussed under stochastic excitation, and their results are compared with those yielded by Monte Carlo simulation (MCS) so as to demonstrate the effectiveness of the approach proposed. It indicated that the method proposed, in this study, provides an effective path to deal with uncertainty evaluation of stochastic structural response involving correlated random variables.