Research On Time-variant Reliability Methods For Structures With Interval Process Parameters Based On Extreme Value Analysis

Uncertainties exist widely in practical engineering and have effects that not allowed to ignore on the function of the structure,and therefore should be fully considered in the structure safety assessment and optimization design.Structural reliability analysis can quantify the reliability degree of the structure on the basis of taking uncertainty into account and lay foundation for product safety design.In the initial stage of the development of structural reliability analysis,people mainly pay attention to the reliability evaluation under the influence of random time-invariant factors,ignoring the influence of dynamic uncertainty.However,in engineering problems,the uncertainty of structural parameters or loads often changes with time,so the traditional reliability analysis method for dealing with time-invariant problems is difficult to apply.The time-variant reliability analysis methods can consider the effect of dynamic uncertainty on structural safety and have wider applicability.The timevariant reliability analysis methods consequently have been paid more and more attention and got developed.The existing time-variant reliability analysis methods mainly describe the dynamic uncertainty of parameters or loads through random processes,and need sufficient sample data to construct the accurate probability distributions of parameters at any instant.However,under the limitation of actual test conditions or test cost,sufficient sample information is often hard to obtain,and the analysis results of time-variant reliability method based on stochastic process are often lack of sufficient credibility due to the introduction o f subjective assumptions.In view of the above problems,the following studies are carried out in this thesis:(1)The interval process model is applied to structural time-variant reliability analysis and used to describe the dynamic uncertainties of structural parameters.Based on extreme value analysis,the time-variant reliability problem is then transformed into a static reliability problem.A structural time-variant reliability method based on extreme value analysis is therefore developed.Firstly,based on the truncated interval Karhunen-Loève(K-L)expansion and the extreme value analysis,the structural reliability analysis for time-variant problems is transferred into a time-invariant reliability analysis for a structure whose performance function is the extreme value response of the original one with a given design lifetime.Secondly,a new definition of non-probabilistic structural reliability index is developed to measure the safety degree of a structure.Finally,the upper and lower bounds of the extreme value response under the given design lifetime are estimated using the efficient global optimization(EGO)approach,which then is used to the evaluate the structural reliability index.(2)Based on the truncated interval K-L expansion,the interval process is expressed as the superposition of deterministic time functions with coefficients as standard interval variables,and the reliability index based on multi-ellipsoidal convex model is used to represent the safety degree of the structure.An efficient structural time-variant reliability method is therefore developed.First,the use of interval process avoids the obtainment of accurate probability distribution information,thus improving the applicability of structural time-variant reliability method under the condition of insufficient sample information.Second,based on the truncated interval K-L expansion and the extreme value analysis,the structural reliability analysis for time-variant problems is transferred into a time-invariant reliability analysis for a structure whose performance function is the extreme value response of the original one with a given design lifetime,which accomplishes the transformation from time-variant reliability analysis to static reliability analysis.Final,based on the multi-ellipsoidal convex model and its corresponding non-probabilistic reliability index,the effect of time-variant and static uncertainty is considered and the time-variant reliability index of the structure is calculated.