Rüdiger Rackwitz

TL;DR: In this paper, an algorithm for the calculation of structural reliability under combined loading is formulated, in which loads or any other actions upon structures are modelled as independent random sequences and the relevant limit state criterion is pointwise approximated by a tangent hyperplane.

TL;DR: Theory and methods of structural reliability are briefly summarized and reviewed, both in original and standard space Some extreme examples demonstrate where and why these methods do not work Importance sampling schemes for updating approximate probability estimates are described Algorithmic problems are addressed Some new fields of potential application are outlined Most urgent is the development of suitable optimization procedures for structures as discussed by the authors.

TL;DR: In this paper, 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 in the space of independent, standard normal variates.

TL;DR: In this paper, second-order expansion is used to approximate the failure surface and some results of the statistical theory of quadratic forms in normal variates are used to calculate improved estimates of the failure probability.

TL;DR: In this paper, several widely used importance sampling methods for the estimation of failure probabilities are compared, and a set of evaluation criteria for the comparison of the methods is chosen, in order to perform a fair comparison the developers of the schemes were asked to solve a number of problems selected in view of the evaluation criteria.