Structural Reliability Analysis with Imprecise Uncertainties

Abstract

Analysis and design involves consideration of many factors which are inherently uncertain. Reliability analysis requires information about the uncertainties in the system, and structural reliability is the probability of a structure performing its purpose adequately for the period of time intended under the operating conditions encountered. Many approaches developed for dealing with the uncertainties demand a mathematical representation of uncertainties on the basis of available information. Probability theory is the most customary technique to describe the uncertainties as random variables characterised by the probability density functions (PDF). However, if the data is inaccurate, ambiguous and incomplete, it is inept to form the PDF, and hence the conventional probabilistic approach becomes inadequate. Therefore, the imprecise parameters should be treated appropriately for improving the reliability of the system. If the information about the uncertainty is insufficient and non-stochastic in nature, the approaches based on interval analysis or fuzzy set theory can be adopted in uncertainty quantification. Hybrid approaches are also available to handle the situations where both the nature of uncertainties namely aleatory and epistemic are uniquely present in the system. In reality, when the aleatory uncertainty is characterised with imprecise parameters, none of the above approaches yields a reliable and optimum design. In such situations, the concepts of probability-box (p-box) can be adopted for characterising the uncertainties. Uncertainty analysis of multi-dimensional and highly nonlinear structures using simulation-based methods is cumbersome, and the hybridity demands the exploration of entire domain of bounds on imprecision. Response surface methods facilitate surrogate models to reduce the effort involved during the simulation. High dimensional model representation (HDMR) is a computationally efficient technique developed for the parameter interaction in physical problems. Therefore, in the present work, HDMR based uncertainty analysis is developed for estimating the structural reliability in the presence of various imprecise uncertainties. The methodology involves characterising the imprecise uncertainties as p-box variables, developing limit state functions using HDMR techniques, and estimating the reliability by interval Monte-Carlo simulations. Furthermore, as the prediction of structural behaviour might diverge due to the presence of various uncertainties, an attempt has been made by studying the systems with hybrid uncertainties from four different sources. The results of the numerical examples are compared with the traditional approaches to demonstrate the efficiency of the methodology.