Statistical Characteristics Of Responses Research Articles

Hybrid uncertainty analysis of functionally graded plates via multiple-imprecise-random-field modelling of uncertain material properties

This paper presents the mixed probabilistic/non-probabilistic uncertainty problem regarding the hybrid uncertainty propagation on physical model of functionally graded plates through dissimilarly uncertain characterisation of material properties in the presence of the multiple-imprecise-random-field modelling. The spectral stochastic finite element framework is extended to perform mixed uncertainty analysis of functionally graded material whereby the spatial variation of elastic modulus of the plate is uniquely characterised as the multiple-imprecise-random-field modelling more than a purely homogeneous random field. This characterisation has originated in heeding the construction of physical models and the significant influences of separately uncertain characteristics propagated on the physical model through different material ingredients are examined to make physical models more reliable and realistic. Mechanics and mathematics intrusive-formulations are then established to explicitly produce the uncertain-but-bounded statistical characteristics of responses, namely interval mean value, interval standard deviation. Bounded surfaces of statistical moments and bounding distribution functions are vividly depicted for demonstration. The feasibility and effectiveness of the presented work are illustrated via test cases of numerical examples.

Stochastic finite element analysis of structures in the presence of multiple imprecise random field parameters

The research work presents the study on non-deterministic problems in the presence of the multiple imprecise-random-field uncertainties by extending the spectral stochastic finite element framework. The standard random field is expanded to characterize the behaviour of physical model with imprecise randomness more appropriately for real engineering problems based on available sources of uncertainty. The Young’s modulus and body force of structures are considered as imprecise random fields with bounded statistical moments. Mathematical expressions and solution procedure are developed to produce the uncertain-but-bounded statistical characteristics of responses, namely interval mean value, interval standard deviation and bounding distribution functions. The bounding probability density and cumulative distribution of the imprecise random response are then effectively visualized by means of Polynomial Chaos Expansion. The feasibility and effectiveness of the presented method are illustrated by three numerical examples.

Correlation failure analysis of an uncertain hysteretic vibration system

In this paper, a numerical method for correlation sensitivity analysis of a nonlinear random vibration system is presented. Based on the first passage failure model, the probability perturbation method is employed to determine the statistical characteristics of failure modes and the correlation between them. The sensitivity of correlation between failure modes with respect to random parameters characterizing the uncertainty of the hysteretic loop is discussed. In a numerical example, a two-DOF shear structure with uncertain hysteretic restoring force is considered. The statistical characteristics of response, failure modes and the sensitivity of random hysteretic loop parameters are provided, and also compared with a Monte Carlo simulation.