| In structural engineering,the parameters of the structural resistance and load effect are generally correlated,stochastic,and time-varying;and the performance function is usually non-stationary and non-Gaussian.The existing time-dependent reliability analysis methods,however,generally only consider the first two moments,which are difficult to be applicable for the reliability assessment with non-stationary and non-Gaussian performance functions involving correlated random variables.This poses challenges to accurately assess the service reliability of structures.Therefore,in this dissertation,a high-order moment time-dependent reliability method is proposed,and its application in the reliability assessment of track slab is also investigated.The main contributions are summarized as follows.(1)A fourth-moment transformation for linear correlated random variables is developed.Using the first four moments and the correlation coefficient matrix of the random vector,the inter-conversion between the correlated nonnormal random vectors and independent standard normal ones is implemented.For all possible combinations of the first four moments and correlation coefficients,the complete mathematical formula of the equivalent correlation coefficient is proposed,and the application regions of the proposed fourth-moment transformation are also investigated.Combined with the existing reliability methods,the structural reliability analysis with linear correlated random variables can be performed,even when the probability distributions of random variables are unknown.(2)The fourth-moment transformation for random variables with nonlinear correlation is proposed.Using the first four moments of the random variables,a robust cubic normal distribution is first proposed to describe the marginal probability distribution of random variables,of which the detailed formulas of the probability density function and the cumulative distribution function are derived.Combined with the vine copula function,the joint probability density function involving nonnormal distribution and nonlinear correlation random vectors is then constructed.With the aid of the Rosenblatt transformation,the transformation between the random vectors involving nonlinear correlation and the independent standard ones is finally realized.(3)A high-order moment method with Box-Cox transformation is proposed.A new criterion is proposed to select the optimal Box-Cox transformation parameter that makes the transformed performance functions approximately normally distributed.This criterion was established based on the minimum distance between the pair of the skewness and kurtosis of the transformed performance function and that of a normal random variable.Then the reliability index and failure probability of the structure are evaluated using the reliability index derived from the three-parameter log-normal distribution.The proposed higher-order moment method is applicable for the cases where the strongly non-normally distributed performance functions and small failure probabilities are involved.(4)Based on the fourth-moment transformation,a high-order moment time-dependent reliability assessment method is proposed.Based on the proposed fourth-moment transformation,the non-stationary non-Gaussian process is first transformed into a standard Gaussian process.Then,based on the two-component parallel system and the joint cumulative distribution function of the correlated bivariate standard normal distribution,the analytical formula of the mean outcrossing rate of the non-stationary non-Gaussian process is derived.The first four moments and the autocorrelation coefficient function of the performance function can be obtained using the point-estimate method combined with the bivariate dimension-reduction method and the integral over time in the time-dependent failure probability formula is calculated using Gauss-Legendre quadrature,which can efficiently estimate the time-dependent failure probability.(5)The time-dependent reliability of the CRTS Ⅱ track slabs track during its service lifetime is systematically investigated.Based on the vehicle-bridge vibration model,the probability distributions of the vertical and transverse train loads are proposed under the consideration of random track irregularity.According to meteorological data and heat transfer analysis,a time-dependent stochastic model of the temperature field for the track slab during the service life is proposed.The time-variant performance functions for all potential safety and serviceability failure modes of CRTS Ⅱ track slab are established.Based on the proposed high-order moment time-dependent reliability method,the reliability of track slab during its service life is investigated.The results of the dissertation lay the theoretical foundation for the structural reliability analysis involving correlated random variables with unknown probability distribution,develop the high-order moment method,promote the development and application of the structural time-dependent reliability method,and have important guiding significance for the scientific formulation of the maintenance strategies for CRTS Ⅱ track slab. |
