Non-Normal Dependent Vectors in Structural Safety

TLDR

Determining failure probability or reliability index is traditionally performed in a space of independent standard normal variables. The study develops a general probability distribution transformation that reduces complex structural reliability problems involving non‑normal, dependent uncertainty vectors to the standard first‑order reliability framework and proposes an algorithm for computing reliability measures. The transformation relies on the joint cumulative distribution function or conditional distributions of the original vector, incorporates detailed technique steps, and introduces approximations for the safe domain shape to enable efficient probability evaluation, often via numerical inversion of distribution functions. Basic properties of the transformation are discussed and its potential applications are illustrated through several examples.

Abstract

A general probability distribution transformation is developed with which complex structural reliability problems involving non-normal, dependent uncertainty vectors can be reduced to the standard case of first-order-reliability, i.e. the problem of determining the failure probability or the reliability index isn the space of independent, standard normal variates. The method requires the knowledge of the joint cumulative distribution function or a certain set of conditional distribution functions of the original vector. Some basic properties of the transformation are discussed. Details of the transformation technique are given. Approximations must be introduced for the shape of the safe domain such that its probability content can easily be evaluated which may involve numerical inversion of distribution functions. A suitable algorithm for computing reliability measures is proposed. The field of potential applications is indicated by a number of examples.