Structural Time-dependent Reliability Analysis Methods Based On FORM

Structural reliability is defined as the probability that a structure can complete its assigned task under given conditions and in given time inverval.The definition shows that time is a key factor affecting the structural reliability.In practical engineering,the structure's performance may decrease due to corrosion and abrasion.Besides,the structure is usually subjedted to stochastic time-dependent loads.Those two factors make the structural response vary with time and hence the structural reliability decreases with the increase of time.Traditional static reliability analysis,however,ignores the time factor,leading to an oversimplified reliability model,overoptimistic reliability,and potential safety hazard.Therefore,the time-dependent reliability analysis,which conforms more to reality,obtains more and more attention.Taking into consideration the time-dependent reliability is important to the structural performace in its entire service time.Altough many time-dependent reliability analysis methods have been developed in the last decade,there are still challenges in improving their efficiency,accuracy,applicability and robustness.In ths paper,we focus on developing time-dependent reliability analysis methods.The four works in this paper are based on the widely used First Order Reliability Method(FORM),and the main idea is to convert the time-dependent performance function into an equivalent Gaussian vector or an equivalent Gaussian process.The four works in this paper are as follows:(1)An improved time-dependent reliability analysis method based on process discretization(i TRPD)is developed.First,the time-dependent performance function is discretized into a series of instantaneous performance functions.Then,FORM is used to convert those instantaneous performance functions into an equivalent Gaussian vector.Next,the correlation coefficient matrix of the Gaussian vector is derived with the results of FORM analysis.Finally,the time-dependent reliability is obtained through calculating a high-dimensional Gaussian integration.(2)A time-dependent system reliability analysis method based on PHI2 is proposed.First,difference method based outcrossing rate models for series,parallel and compound sysems are constructed.Then,FORM is used to convert the instantaneous performance functions in the outcrossing rate models into equivalent Gaussian variables,whose correlation coefficient matrix is derived in detail.Next,the outcrossing rate of the system is calculated through high-dimensional Gaussian integrations.Finally,the Markov process model is employed to convert the outcrossing rate into the time-dependent system reliability.(3)An improved time-dependent system reliability analysis method based on process discretization(i TRPDs)is developed.First,the time-dependent performance functions of the system are discretized into a series of instantaneous performance functions.Then,FORM is used to convert those instantaneous performance functions into corresponding equivalent Gaussian vectors.Next,the autocorrelation and cross-correlation coefficient matrixes of those Gaussian vectors are derived with the results of FORM analysis.Finally,the time-dependent system reliability is obtained through calculating multiple highdimensional Gaussian integrations.(4)An efficient method based on equivalent Gaussian process is proposed to evaluate structural average lifetime.First,the adaptive Kring model and FORM are employed to efficiently convert the performance function into an equivalent Gaussian process.Then,the Expansion Optimal Linear Estimation(EOLE)is used to obtain the series expansion of the equivalent Gaussian process.Next,random samples of the equivalent Gaussian process are generated to calculate the time-dependent reliability function.Finally,the structural average lifetime is obtained through numerical integration of the time-dependent reliability function.