Fourth-Moment Standardization for Structural Reliability Assessment

In structural reliability analysis, the uncertainties related to resistance and load are generally expressed as random variables that have known cumulative distribution functions. However, in practical applications, the cumulative distribution functions of some random variables may be unknown, and the probabilistic characteristics of these variables may be expressed using only statistical moments. In the present paper, in order to conduct structural reliability analysis without the exclusion of random variables having unknown distributions, the third-order polynomial normal transformation technique using the first four central moments is investigated, and an explicit fourth-moment standardization function is proposed. Using the proposed method, the normal transformation for independent random variables with unknown cumulative distribution functions can be realized without using the Rosenblatt transformation or Nataf transformation. Through the numerical examples presented, the proposed method is found to be sufficiently accurate in its inclusion of the independent random variables which have unknown cumulative distribution functions, in structural reliability analyses with minimal additional computational effort.