Unified probabilistic and interval analysis of structures with hybrid uncertainties

Abstract

In modern engineering analysis and design, it is well recognized that fluctuations exist in the material properties, geometric characteristics and externally applied loadings. These uncertainties, which are either resulted from the variation of system parameters or the lack of knowledge or information, can significantly affect the performance of engineering systems. Recently, the study in hybrid uncertainty analysis is gaining increasingly popularity duo to the advantage in evaluating the effect of various types of uncertainties in a unified approach. Despite of the availability, the existing methods are developed with strengths in particular engineering applications. Thus, there is a continuous demand on enhancing the reliability, accuracy, computational efficiency and robustness of hybrid uncertainty analysis. This dissertation aims at providing a series of uncertainty analysis approaches for engineering structures with both random and interval uncertain parameters, which can be applied to investigation on various engineering problems. Firstly, the uncertain linear static analysis of discrete structures with hybrid random and interval variables is investigated by using a novel perturbation-based mathematical programming approach. For the structures with non-random and spatially variant uncertainties, a novel interval field concept is adopted to model such uncertainties. Then, the natural frequencies of structures with both random and interval fields are studied for the first time by using the extended unified interval stochastic sampling (X-UISS) method. Finally, a brand-new dynamic reliability analysis through an advanced machine learning algorithm, namely the extended support vector regression (X-SVR), is proposed. Various numerical examples, including both academic-sized and engineering motivated, have been elaborately selected for demonstrating the accuracy, efficiency and applicability of the proposed methods. The computational schemes developed in this dissertation offer new yet efficient strategies for analysing the performance of engineering systems with various uncertain system parameters. Since that the proposed methods are all based on finite element analysis, either intrusively or non-intrusively, it is possible to integrate the introduced approaches with the finite element software. Thus, the methods developed in this research project have the potential to be applied in practical engineering analysis and design.