Advanced Reliability Methods for Structural Evaluation

Approximate solutions to the general structural reliability problem, i.e., computing probabilities of complicated functions of random variables, can be obtained efficiently by the fast probability integration (FPI) methods of Rackwitz-Fiessler and Wu. Relative to Monte Carlo, FPI methods have been found by the authors to require only about 1/10 of the computer time for probability levels of about 10⁻³. For lower probabilities, the differences are more dramatic. FPI can also be employed in situations, e.g., finite element analyses when the relationship between variables is defined only by a numerical algorithm. Unfortunately, FPI requires an explicit function. A strategy is presented herein in which a computer routine is run repeatedly k times with selected perturbed values of the variables to obtain k solutions for a response variable Y. An approximating polynomial is fit to the k “data” sets. FPI methods are then employed for this explicit form. Examples are presented of the FPI method applied to an explicit form and applied to a problem in which a polynomial approximation is made for the response variable of interest.