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In structural reliability analysis, the input variables are often nonnormal and correlated. A procedure for efficient normal transformation, i.e., transforming dependent nonnormal random variables into independent standard normal ones, is often required. In general, Rosenblatt transformation is available to realize the normal transformation when the joint probability density function (PDF) of basic random variables is available and Nataf transformation can be used when the marginal PDFs and correlation coefficients are known. However, the joint PDF and marginal PDFs of some random variables are often unknown in practice, and the probabilistic characteristics of these variables are easier to be expressed using the statistical moments and correlation matrix. It is in this regard that the objective of the present paper is to develop a methodology for normal transformation including correlated random variables with unknown joint PDF and marginal PDFs. Based on the third-moment transformation technique for transforming independent nonnormal random variables into independent standard normal ones, the third-moment transformation is further developed for transforming the correlated variables including unknown joint PDF and marginal PDFs into independent standard normal variables. A first-order reliability method for structural reliability analysis including correlated random variables with unknown joint PDF and marginal PDFs is developed based on the proposed transformation. Using the proposed method, the normal transformation and reliability analysis can also be achieved for correlated nonnormal random variables with knowledge of only the statistical moments and correlation matrix. The simplicity and efficiency of the proposed method is further demonstrated through several numerical examples. [ABSTRACT FROM AUTHOR]

Estimation of statistical moments of performance functions is one of the main topics in structural reliability analysis by moment methods. It is possible to apply the well-developed multiple-dimensional cubature formulas to assess such statistical moments. In this paper, a new criterion is proposed to fulfill the aim. Several efficient cubature formulas are firstly revisited. Then, a new criterion is proposed to select "the best" cubature formula that gives the most accurate statistical moments of performance functions. This criterion is established based on the marginal moments of input random variables. The cubature formula that provides the smallest difference between the estimated values and the exact values of marginal moments is determined as the adopted one for statistical moments of performance functions. Several numerical examples are presented to illustrate the effectiveness of the proposed criterion, in which Monte Carlo simulations are employed for comparison. [ABSTRACT FROM AUTHOR]

In the second-order reliability method (SORM), the failure probability is generally estimated based on parabolic approximation of the performance function. In the present paper, the first four moments (i.e., the mean, standard deviation, skewness, and kurtosis) of the second-order approximation of performance functions are obtained using the definition of the probability moment. Based on the recently developed fourth-moment standardization function, an explicit second-order fourth-moment reliability index is proposed for the estimation of failure probability corresponding to both the simple and general parabolic approximations. The simplicity and accuracy of the secondorder fourth-moment reliability index is demonstrated using numerical examples. It can be concluded that the proposed method is applicable to the second-order approximation of performance functions with strong nonnormality and is accurate enough to improve the existing SORM in structural reliability analysis with minimal additional computational effort. [ABSTRACT FROM AUTHOR]