Research On The Modelling And Computation Of Time-dependent Reliability Of Structures And The Optimization Design Methods

The state or performance of engineering structures in future service are influenced by a number of factors such as materials,environments and load conditions,which are usually time-dependent and possess uncertain features.Based on probability theory for time-dependent reliability analysis,the performance status of structures can be reasonably evaluated to ensure the safety and reliability of structures in use.In addition to safety,economy is also the core issue of engineering structures.Through the optimization analysis and design of structures,the balance between safety and economy can be achieved.There are still some problems in the current structural time-dependent reliability analysis and optimization design: 1)in terms of time-dependent reliability analysis modeling,it is necessary to consider the combined effect of different degradation mechanisms,establish reasonable and feasible reliability models,and develop effective analysis and calculation methods;2)there are still some problems in the accuracy and efficiency of time-dependent reliability modeling and analysis when using stochastic processes;3)when the time-dependent reliability analysis is combined with optimization design and applied to complex structures,it is necessary to develop simple and efficient modeling and solving methods.This paper aims to study reasonable time-dependent reliability modeling methods,develop efficient time-dependent reliability calculation methods and optimization design algorithms,and apply the time-dependent reliability models and methods to the analysis and optimization design of corroded reinforced concrete structures.The main research contents and results of this paper are as follows:(1)Both of the progressive degradation caused by aging effects and the shock degradation caused by shock loads are considered to establish the degradation model of structures.Aiming at the problems that the distributions of random variables in the model do not have additivity or the distributions are even unknown(only with limited datasets),a phase-type(PH)distribution-based method is proposed to solve the time-dependent reliability of deteriorating structures.Using the Expectation Maximization algorithms,any distributions or datasets can be approximated as PH distributions.Owing to the good properties in convolution of PH distributions,the time-dependent reliability can be evaluated conveniently.The results show that this method can accurately and efficiently calculate the time-dependent reliability of deteriorating structures.(2)In the process of structural deterioration,in addition to progressive degradation and shock degradation,it may also encounter sustained loads with characteristic action time,such as internal pressure,snow loads and wind loads,which will cause additional degradation.A combined degradation model considering the above three kinds of degradation mechanisms is proposed.Among them,Gamma process is used to describe the degradation caused by aging effects,Poisson process is used to describe the effects of shock loads,and the stationary binomial process and Poisson square wave process are used to model the sustained loads.Based on the combined degradation model,the time-dependent reliability of structures is analyzed and solved.(3)An instantaneous response surface(t-IRS)method is proposed to calculate the time-dependent reliability of structures.The method uses the expansion optimal linear estimation to discretize and reconstruct the stochastic processes into linear summation of a series of independent standard normal variables.After that,the time parameter is regarded as a uniformly distributed random variable in a given interval.Then,Latin hypercube sampling is used to construct an instantaneous response surrogate model of the Kriging type.The variables in the model include the original random variables,the variables converted from the random processes,and the time variable.The U learning function is used to update the surrogate model iteratively,until the accuracy requirement is met.Finally,based on the updated instantaneous response surrogate model and Monte Carlo simulation method,the time-dependent reliability is calculated.The results show that the t-IRS method can solve the time-dependent reliability problem accurately and efficiently.(4)The PSO-t-IRS method is proposed for the time-dependent reliability-based design optimization(TRBDO)problem.Firstly,the t-IRS is used to establish the extended instantaneous response surrogate model,i.e.,in addition to the original variables in instantaneous response surrogate model,the design variables are also used as the input variables of the surrogate model.When generating Monte Carlo samples for reliability calculation,the design variables and the time parameter are treated as uniformly distributed random variables.Based on the extended surrogate model,time-dependent reliability can be computed conveniently.With the reliability as the constraint condition,the TRBDO model is built and solved by the particle searm optimization(PSO)algorithm.The results verify the effectiveness of the PSO-t-IRS method.(5)The time-dependent reliability analysis and optimal design of corroded reinforced concrete(RC)beams are studied.At first,considering the influence of time-dependent chloride diffusion coefficient and stochastic process,the time-dependent reliability analysis models based on serviceability limit state and ultimate limit state are established respectively.The PH method and t-IRS method are then used to calculate the time-dependent reliability.And based on this,the TRBDO model of RC beams is established and solved by PSO-t-IRS algorithm,with some valuable results being obtained.