Structural System Reliability Analysis Under Evidence Theory Using Kriging Model

Its coupling effect may lead to large fluctuations in product performance or structural characteristics,causing structural safety problems,causing economic losses and even threatening personal safety.Therefore,using reasonable and effective theories and methods to measure the reliability of engineering structures and systems is of great significance to ensure the safety performance and reliable operation of products.Generally,the uncertainty can be divided into stochastic uncertainty and cognitive uncertainty.The research of stochastic uncertainty is based on probability theory,and its related analysis methods and engineering applications have been relatively perfect.Cognitive uncertainty cannot be constructed with accurate probability distribution due to lack of data samples.Generally,non-probability theories such as possibility theory,evidence theory,fuzzy theory,interval analysis theory and so on can be used for analysis.Because of its flexible framework,evidence theory can be equivalent to probability theory and other non-probability theories in different situations,and can fuse evidence from different sources,which has attracted extensive attention.With the large-scale complexity of engineering structures,the reliability requirements for nuclear power,large bridges and other structural systems are getting higher and higher.The system is usually composed of multiple components,which are mutually influenced and coupled,and there are multiple failure modes,which greatly increases the difficulty of reliability analysis.Component-level structural analysis is often difficult to reflect the overall complex performance of the structural system,so it is necessary to analyze the entire structural system.At present,some progress has been made in structural system reliability analysis methods,but there are still many problems,such as the "black box" problem of complex structures,the problem of high-dimensional variables,the problem of large-scale computation under cognitive uncertainty,etc.Therefore,this paper will focus on the reliability of structural systems and carry out research under the framework of evidence theory.The main contents of this paper are as follows:(1)Aiming at the "black box" problem of system reliability,a system reliability analysis method based on active learning kriging is proposed.The method only selec ts training points in the common failure domain,establishes an agent model to replace the mathematical model of the complex engineering structure,and then solves the reliability under the evidence variable,which can effectively improve the calculation efficiency while ensuring the accuracy of the structural reliability and the truth-like degree,and provides an efficient calculation method for the reliability problem of the actual complex engineering structure system.The solution of the method is as fol lows: firstly,an initial kriging proxy model is established based on a small number of sample sets;Secondly,selecting the best sample point through active learning,calculating the response value of the sample point,adding this set of data to the initi al sample set and updating the kriging model until the convergence criterion of the learning function is satisfied;Then the joint focal element is sampled by interval Monte Carlo.Secondly,kriging proxy model is used to analyze the extremum of the sampled joint focal elements to determine whether the focal elements belong to safety domain,failure domain or uncertainty domain.Finally,the reliability and plausibility of structural system reliability are calculated.(2)Aiming at the problem of high dimensional structural system,a reliability analysis method of evidence theory system based on improved kriging model is developed.This method can reduce the optimization of hyperparameters when establishing active learning kriging model,thus improving the co mputational efficiency.The specific solution idea is as follows: firstly,the kernel function of kriging model is modified by partial least square method,and super parameters that are not important to the calculation results are ignored according to prin cipal component analysis;Then a new kriging proxy model is established according to the modified kernel function.Finally,the interval Monte Carlo focal element sampling is used to analyze the extreme value of the sampled joint focal elements.Finally,t he reliability and quasi-truth of the structural system reliability are calculated.