Structural Reliability Methods Under Aleatory And Epistemic Uncertainties

Theory of structural reliability under uncertainty, which has been a foucs of theindustry and academia, is not only a powerful tool for the protection of structuralsystems reliability, but also a hot research topic in reliability engineering. Structuralreliability theory and methods can deal with various uncertainties which come fromdifferent stages of structures effectively as well as the influence of these uncertainties onstructural reliability. Therefore, the advantages of the structures designed usingstructural reliability theory are high reiliability, less costs, more robustness and excellentperformances. Nowadays, lots of theory and application achievements have beenachieved for structural reliability theory under aleatory uncertainty.Uncertainty widely exists in engineering practices, and it can be respectivelydivided into aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty arisesfrom inherent variation while epistemic uncertainty comes from insufficient data andincomplete information. In order to grasp the essentials of these uncertainties forstructural reliability, structural reliability theory under both aleatory and epistemicuncertainties has gained increasing attention for many scholars. In this dissertation,based on the interval theory, fuzzy sets theory and probability theory, the followingproblems are studied: non-probabilistic reliability model with dependent intervalvariables; structural relialibty analysis under both aleatory and epistemic uncertainties;structural reliability sensitivity analysis under both aleatory and epistemic uncertainties.Therefore, the researches in this dissertation extend the traditional structural theory tobecomming a more mature theory.The contributions of this dissertation are summarized as follows:(1) Non-probabilistic reliability model with dependent interval variables. Becauseof the constraints exist in systems for many interval variables, so they often dependenteach other. The non-probabilistic reliability index model and optimization method withdependent interval variables are proposed. Furthermore, based on the finite differencetheory, non-probabilistic reliability sensitivity model and optimization methods withdependent interval variables are also developed. The dependency of interval variables is taken into account in the developed non-probabilistic reliability model to overcome thedeficiencies of the traditional non-probabilistic model, and the research has extended theexisting interval-based non-probabilistic model.(2) Unified uncertainty analysis based on the mean value first order saddlepointapproximation (MVFOSPA-UUA). Variables and parameters are modeled by randomand interval variables under the case of systems associated with both aleatory andepistemic uncertainties. In order to avoid MPP search and non-normal to normaltransformations, a novel model, named MVFOSPA-UUA, is proposed. Furthermoer, themethod for solving the model is also developed. The low efficiency problem for theexisting methods under both aleatory and epistemic uncertainties is solved. Theaccuracy and high efficiency of the proposed method are domenstrated by simulation.(3) Structural reliability analysis under both random variables and fuzzy numbers.Variables and parameters are modeled by random variables and fuzzy numbers underthe case of systems associated with both aleatory and epistemic uncertainties, and theunified uncertainty analysis model under both random variables and fuzzy numbers isproposed. Two unified uncertainy analysis methods, methods I and II, are developed forsolving the model. This research provides an effective reliability method and theoreticalguidance for structural systems with both random variables and fuzzy numbers.(4) Structural reliability analysis method under mixed variables based on theuniversal generation function. Variables and parameters are respectively modeled byrandom variables, P-Box and interval variables according to the amount of data in thesystem. On this basis, the existing universal generating function is extended, and thestructural reliability analysis model under mixed variables based on the universalgenerating function is estabilished. Furthermore, a solution method is also provided.This research provides a practical method for structural reliability analysis undermultiple variables.(5) Structural reliability sensitivity analysis model under both aleatory andepistemic uncertainities. An appropriate reliability sensitivity modeling is provided forvariables and parameters when both aleatory and epistemic uncertainties exist in thesystem. In order to avoid MPP search and improve accuracy, the weights of samples areconsidered, and the limit-state function is linearized based on the moving least squares.The reliability sensitivity model under both aleatory and epistemic uncertainties and its corresponding soulution method are estabilished, and it overcomes the limitations forthe existing methods which can only calculate reliability sensitivity under aleatoryuncertainty effectively. The proposed mthod is robustness, when compared with theexisting reliability sensitivity methods, which is suitable for the situation of thelimit-state function is an implicit function.