Propagation of uncertain structural properties described by imprecise Probability Density Functions via response surface method

The present study addresses the analysis of structures with uncertain properties modelled as random variables characterized by imprecise Probability Density Functions (PDFs), namely PDFs with interval basic parameters (mean-value, variance, etc.). Due to imprecision in the probabilistic model, the statistics of the response and the failure probability are described by interval quantities. An efficient procedure for evaluating the bounds of such quantities is developed. The proposed method stems from the application of a ratio of polynomial response surface (Impollonia and Sofi, 2003; Sofi and Romeo, 2018) in conjunction with the classical probabilistic analysis and the so-called Improved Interval Analysis via Extra Unitary Interval (IIA via EUI) (Muscolino and Sofi, 2012). Interval response statistics are derived as approximate explicit functions of the interval parameters describing imprecise probabilities. The range of the interval failure probability is estimated in terms of the interval reliability index once the bounds of the interval mean-value and variance of the response are evaluated. Numerical results concerning a frame structure and a grid structure with uncertain Young's moduli characterized by imprecise PDFs are presented. The accuracy of the proposed method along with the influence of randomness and imprecision of the input parameters on response statistics and reliability assessment are investigated.