Structural Reliability Analysis And Application With Aleatory And Epistemic Uncertainties

There are many uncertainties affecting the safety,durability and applicability of the structure in the real engineering environment,these uncertainties can normally be divided into aleatory uncertainty and epistemic uncertainty,aleatory uncertainty requires the statistical information of variables to be complete,and it can strictly characterize the probability of the structure to achieve the predetermined performance,when the test data is scarce enough to build a precise probability model,epistemic uncertainty can be used to describe the uncertainty of the probability itself.Trade-off can be achieved between structural safety and economic cost by structural reliability analysis utilizing available information.At present,reliability analysis mostly stays at the theoretical level of research,and is committed to developing high-precision and efficient reliability analysis algorithms,but engineering structures have structural complexity and functional diversity,and many reliability algorithms are difficult to generalize into engineering practice.This thesis mainly studies the reliability of two types of uncertain characterization,and proposes efficient and flexible reliability analysis algorithms for structural reliability analysis and application to structural progressive collapse analysis.This thesis focuses on the following:(1)For the problem of precise probability characterized by aleatory uncertainty,a multi-fidelity integral rule for statistical moment and failure probability estimation is proposed.First,the contribution degree analysis developed based on sensitivity analysis is introduced,which is divided into two parts according to the degree of closeness of the relationship between the input variables,based on which the original limit state function can be additively decoupled into two low-dimensional sub-functions,thus alleviating the problem of "dimensional disaster" to a certain extent.For sub-functions composed of closely related variables,the adaptive fifth-order spherical-radial cubature formula that takes into account both precision and flexibility is used to estimate its statistical moments;for the sub-functions composed of variables related to relative evacuation,the efficient mixed-order volume formula composed of three-order and fifth-order radial composition is used to estimate its statistical moments.After obtaining the statistical moments of limit state function,the maximum entropy method can be used to reconstruct the unknown probability distribution of structure,and then obtain the failure probability of the structure to evaluate the reliability of the structure.(2)Introduce the imprecise probability problem characterized by epistemic uncertainty described by the probability-boxes,and combine the proposed active learning Kriging(AK)model with an efficient global optimization algorithm(EGO)to estimate the uncertainty of structural reliability ind ex.Based on the relative entropy theory,with the goal of entropy stability of limit state function information,the relative entropy learning function(REF)is proposed to select the learning samples that affect Kriging stability in the Monte-Carlo sample pool(MCS),to construct the AK-MCS-REF algorithm for efficiently estimating the failure probability of the structure.On this basis,combined with the EGO algorithm,the uncertainty of the structural reliability index due to epistemic uncertainty can be accurately estimated,that is,the AKMCS-REF-EGO algorithm.AK-MCS-REF-EGO is a decoupled imprecise probability analysis algorithm,which takes the distribution parameters as the optimization body,effectively uses the real response values of random samples under different distribution parameters,breaks the traditional double-cycle calculation idea,and the efficiency of calculation can be greatly improved.(3)Taking a plane frame of 4 spans and 8 stories as the research object,this paper expounds the influence of uncertainty on the progressive collapse of structure under accidental load from the Angle of inherent uncertainty and cognitive uncertainty.Multi-fidelity integration rule,AK-MCS-REF and AKMCS-REF-EGO are used to calculate the probability of progressive collapse and the probability interval of remaining damaged structures under different columns removal floors.The overall robustness of the structure is evaluated,and relevant decision-making opinions are provided for the robustness design of engineering structures to enhance the overall safety of the structure referring to outcomes of reliability analysis.