Application of polynomial transformation to normality in structural reliability analysis

Polynomial transformations of a nonnormal variate to a normal variate are considered. Use of the polynomial transformations to normality representing some of the well-known distribution types is examined. Approximate solutions based on the polynomial transformation to normality models fitted to the simulated data points with fractile constraints are given to evaluate the probability of failure of a structural system. The approximate solutions do not require any stringent conditions on integrand or domain of integration. The approximation is easy to implement and can be used to reduce the required number of simulation cycles. Numerical examples indicate that using the approximate solutions accurate estimation of the failure probability can be obtained with fewer simulation cycles than the conventional simulation method.