Structural Reliability Assessment Considering the Uncertainties of Distribution Parameters

Abstract

In conventional structural reliability evaluation, the probability distributions of the basic random variables are generally assumed to be known and their distribution parameters are usually assumed to be certain. However, since the probability distributions are estimated from statistical data of limited sample size, their distribution parameters or types may change as the amount of statistical data increases. If the parameter uncertainties are considered in structural reliability evaluation, the probability of failure and the corresponding reliability index become random variables, which are referred as the conditional failure probability and the corresponding conditional reliability index, respectively. Therefore, it is necessary to determine not only the mean but also the quantile or even the probability distribution of the conditional failure probability or conditional reliability index. Since the determination of the probability distribution of which is the focus of this study. For this purpose, the first four moments (i.e., mean, standard deviation, skewness and kurtosis) of the conditional reliability index are firstly computed by a point-estimate method based on bivariate dimensionreduction integration. The probability distribution of the conditional reliability index is then approximated by a four-parameter cubic normal distribution, in which four parameters in the probability distribution are directly defined in terms of its first four moments. Finally, an explicit formula for the quantile of the conditional failure probability is obtained by using the probability distribution of the corresponding conditional reliability index. The efficiency and accuracy of the proposed methodology for structural reliability assessment considering the uncertainties of distribution parameters are demonstrated through a numerical example, where Monte-Carlo simulations are utilized for comparison.