Structural Stochastic Response Analysis And Dynamic Reliability Evaluation Considering Parameter Uncertainties

Stochastic structural response analysis and dynamic reliability evaluation are indispensable and paramount for guaranteeing the safety of civil engineering structures and facilities while encounting catastrophic stochastic excitation.Nevertheless,in classical structural stochastic response analysis and dynamic reliability evaluation,a number of approaches have been proposed by dint of considering that the sources of the uncertainties are correlated with the time-varying stochastic excitations.Specifically,in those approaches,both presumed structural properties parameters(mass,stiffness and damping,etc.)and excitation characteristics parameters(duration,frequency spectrum and spectral intensity,etc.)are usually treated as being determined.However,in real engineering practices,the aforementioned parameters are indeterminate and correlated;under this circumstance,the first second-order maximum statistical values of the structural stochastic response and failure probability are all becoming random variables,namely mean and standard deviation of conditional maximum random response,and conditional failure probability,respectively.Therefore,during the relevant analyzing and modelling process,potential significant error results will occur if those effects are disregarded.Based on above asserts,in this dissertation,under parameter uncertainties condition,the main research route is as follows:“structural stochastic response analysis–total failure probability(mean of conditional failure probability)calculation–quantile and confidence interval assessment of conditional failure probability”.A high-efficient and feasible approach for structural stochastic response analysis and dynamic reliability assessment is proposed.Additionally,the influences yielded by parameter of uncertainties and correlation on structural performance and safety probability are also deeply investigated.The main research contents of this dissertation are summarized as follows:(1)The analysis method of structural stochastic response is proposed considering parameter uncertainties and statistics correlation:firstly,the computational expression about both mean and variance of structural maximum response are deduced respectively;secondly,by adopting the third-order moment transformation of relevant random variable,the statistical correlative parametric variables are transferred to independent ones;thirdly,the mean and variance of structural maximum stochastical response are obtained by using the point estimation method of standard normal space based on univariate reduced-dimension integration;finally,by studying several relevant cases,the accuracy and feasibility of proposed method are validated,and overall calculation procedures are demonstrated,meanwhile,the effects of both parametric uncertainties and correlation on the mean and variance of structural maximum stochastic response are discussed respectively..(2)Based on classical stochastic vibration theory,under uncertain parameter condition,the fast integration method for determining structural total failure probability is proposed:firstly,the problem of dynamic reliability considering parametric uncertainties is transformed to the integral form of P_F=∫_XP_f(X)f(X)d X;secondly,by adopting the point estimation method of standard normal space based on bivariate reduced-dimension integration,the above-mentioned integral form is calculated,this procedure is namely the fast integration method mentioned;then,the total structural failure probability is able to be obtained in one step;and on this basis,the proposed method is extended to solve the correlative random variable case as well.Eventually,by several cases,the overall calculation procedure is demonstrated,and the accuracy and feasibility of proposed method are validated;meanwhile,the effects of both parametric uncertainties and correlation on the dynamic reliability are discussed respectively.(3)The evaluation method of quantile and confidence interval of conditional failure probability are developed considering uncertainties parameter:firstly,based on the higher order moment reliability theory,the mean,variance,skewness and kurtosis coefficient of the conditional reliability index are obtained by applying the point estimation method of standard normal space based on bivariate reduced-dimension integration;and then,the approximated explicit expressions of probability density function for the conditional reliability index is separately derived on account of the three-parameter square normal distribution and four-parameter cubic normal distribution;subsequently,quartile and confidence interval of the conditional failure probability can be evaluated on the basis of obtained expression of probability distribution function;finally,the overall calculation procedure is demonstrated,and the accuracy and feasibility of the proposed method,through several cases,are validated by comparing with the histogram obtained by Monte Carlo simulation.As a result,the structual dynamic reliability assessment system has been established based on total failure probability,quantile and confidence intervel of conditional failure probability aforementioned;(4)Under parameter uncertainties condition,the accuracy,advantage and feasibility of proposed theory system for structural stochastic response analysis and dynamic reliability evaluation are validated by applying several cases with engineering background.Moreover,the effects of the parameter uncertainties and correlation on the stochastic response and the dynamic reliability,in those engineering examples,are also discussed separately.