Structural Time-Variant Reliability Analysis And Design Optimization

Uncertainties widely exist in practical engineering problems,such as external loads,geometric dimensions,material properties and boundary conditions,which may lead to fluctuation of structural performance or even failure.Conventional structural analysis and design optimization are generally based on deterministic structural parameters and optimization models,which will probably result in mistake in analysis results or unreliable design.For solving such problems,a series of structural reliability analysis methods and reliability based design optimization methods that have great significance to analysis and design of practical engineering structures and systems were developed.However,such methods only take time-invariant uncertainties into consideration,while there are a lot of time-variant or dynamic parameters in engineering problems,such as dynamic loads,varying physical dimension,and deteriorating material strength.Under influence of time-variant parameters,the reliability of structures is generally not a deterministic value,but will decrease gradually in design period,namely the reliability is also time-variant.Without consideration of time-variant factors,the application of the methods mentioned above is limited since the reliability index those methods yield is generally deterministic.In recent decades,time-variant reliability analysis and time-variant reliability based design optimization have become a research focus in this field due to their ability to consider time-variant factors during the process of calculation by introducing stochastic process to describe time-variant uncertainties.However,the research of time-variant reliability analysis methods and time-variant reliability based design optimization is still at early stage and there are still a series of key problems on computational accuracy,computational efficiency,iteration strategy,stability and practical application to be overcome.For this purpose,this dissertation studies structural time-variant analysis problem and timevariant reliability based design optimization problem,expecting to develop systematic methods for structural time-variant analysis and reliability based design optimization.The research contents of this dissertation can be summarized as follows:1.For time-variant reliability analysis problems with single stochastic process,a time-variant reliability analysis method based on the total probability theorem is proposed.This method converts the calculation of time-variant reliability index into a multi-dimensional integral,the integrand of which is the product of joint probability density function of random variables and the probability of single stochastic process crossing a threshold during design period.Therefore,the stochastic process is decoupled from random variables.The improved PHI2 method and dimension reduction integral are adopted for efficiently solving the multi-dimensional integral,which effectively solves the massive computational problem.Finally,the proposed method is applied to a numerical example and an engineering application to verify its effectiveness.2.The proposed method above is only suitable for time-variant reliability analysis problems with single stochastic process.However,when there are multiple stochastic processes or explicit time in the problem,the analysis cannot be conducted because of the difficulties to calculate the probability that a stochastic vector crosses the limit state surface in stochastic process space.Therefore,this dissertation proposes a time-variant reliability method based on linear approximation.By introducing the idea of first reliability method,the limit state surface in stochastic process space is linearly expanded and a hyperplane is obtained to replace the limit state surface.Therefore,the probability of a stochastic process vector crossing the limit state surface is approximately transformed into the probability of a stochastic process vector crossing the hyperplane.Due to the simple mathematical form of hyperplane,the crossing probability can be efficiently calculated so that the proposed method is successfully extended to those problems involving multiple stochastic processes and explicit time.Finally,the proposed method is applied to two numerical examples and an engineering application to verify its effectiveness.3.For structural time-variant reliability based design optimization problem,a general solution framework is developed,providing an effective tool for reliability design of complex structures or systems considering their whole life cycles.In each cycle,the time-variant reliability analysis is frstly carried out at current design point to calculate the time-variant reliability index of each constraint,based on which an equivalent time-invariant reliability based design optimization problem is then constructed.By solving the equivalent problem the design point can be updated.Besides,an iteration mechanism is proposed to ensure the convergence of the whole optimization procedure.Therefore,the time-variant reliability based design optimization problem is decoupled into a series of timevariant reliability analyses and time-invariant reliability based design optimization problems that are alternately solved,which avoids massive time-variant reliability analyses and dramatically promotes the computational efficiency.Finally,the proposed method is applied to four numerical examples and an engineering application to verify its effectiveness.4.A solution method using the equivalent most probable point is proposed for structural timevariant reliability based design optimization problems.The most probable point is widely used in time-invariant reliability based design optimization algorithms.However,the conception of most probable point is no longer in existence in time-variant problems.Consequently,many helpful solution strategies for time-invariant reliability based design optimization problems cannot be extended to time-variant problems directly.This dissertation proposes the conception of equivalent most probable point and applies it to the solution of time-variant reliability based design optimization problems.In each iteration,the equivalent most probable point of each constraint is obtained based on the time-variant reliability analysis results and initial reliability index of the constraint at current design point.With the equivalent most probable point,many existing solution methods of timeinvariant reliability based design optimization can be used to solve the time-variant problems so that the computational efficiency is dramatically promoted.Finally,the proposed method is applied to a numerical examples and an engineering application to verify its effectiveness.