Study On Time-variant Reliability Method Of Deteriorating Structures And Its Application

Time-variant structural reliability analysis of deteriorating structures has been a challenging problem in the field of structural engineering.This work focuses on three major problems: time-variant component reliability,time-variant all component reliability and time-variant system reliability.To solve these problems,three sets of methods with different range of application are proposed,which are: hybrid method,probability density evolution method(PDEM)and adaptive high-order moment method.As for time-variant component reliability analysis,the hybrid method is proposed and further applied to time-variant area.The main idea of hybrid method can be described as follows.Firstly,a general first order reliability method(FORM)with Nataf transform and difference method is introduced;secondly,the rotational transformation of variables and univariate dimension-reduction approximation of the performance function are exploited;thirdly,each component function of approximation is further approximated by a quadratic polynomial based on the function value and its gradient of most probable point(MPP)and the function value of an additional point;having achieved the approximation of entire performance function,importance sampling method is applied for its reliability.The hybrid method can deal with different kinds of performance function,and it can achieve satisfactory accuracy while the computational cost is only a little higher than FORM.However,the hybrid method is based on search of MPP,and it is required to search the MPP for every component when dealing with timevariant all component reliability,which results in low efficiency.What’s more,when dealing with time-variant system reliability,the situation of multiple MPPs could occur.Therefore,the hybrid method is only suitable for time-variant component reliability,and it is difficult to apply hybrid method to time-vairant all component reliability and timevariant system reliability.Furthermore,PDEM is adopted to deal with ime-vairant all component reliability and time-variant system reliability.As for ime-vairant all component reliability,the PDEM,which is not based on the search of MPP,has significant advantages in efficiency over the methods based on the search of MPP,while the accuracy can maintain a good level.As for time-variant system reliability,it is further categorized into two minor problems: classical time-variant system reliability and general time-variant system reliability,and the single equivalent performance function for two kinds of time-variant system reliability is obtained based on the idea of the complete system failure process and the equivalent extreme value event.Therefore,the problems including combination explosion,correlation failure and system evaluation,which are brought by traditional methods based on failure mode identification,can be avoided.On this basis,two derivartion methods are proposed to obtain the generalized density evolution equation(GDEE),and Dirac sequence method is adopted to solve GDEE,and the time-variant system reliability can be dealt with effectively.However,the PDEM has certain restrictions that the choices of sphere radius,number of selected points and the ρ value in Dirac sequence method are empirical and subjective.To avoid the restrictions of PDEM,the adaptive high-order moment method is further proposed,the main idea can be descibed as follows.By introducing the trivariate dimensional decomposition and delineation of cross terms,the first six moments of performance function can be obained by Gauss-Hermite integration,and saddle-point approximation is adopted to evaluate the reliability.When compared with PDEM,the adaptive high-order moment method can also deal with ime-vairant all component reliability and time-variant system reliability effectively,and it is more objective than PDEM.The rationality of the ideas and the effiveness of the proposed methods discussed above are verified through multiple numerical examples and engineering examples.Finally,after summarizing the researches of this work,the problems for future study are discussed at the end of this work.