Efficient Modelling and Simulation of Random Fields

The application of random fields to real-world problems, e.g. for assessing the robustness and reliability of structural components with geometrical or material tolerances, has gained much interest recently. However, the large number of random variables involved inhibits the use of accurate and efficient methods to compute failure probabilities. Several measures to handle the large dimension or to reduce it are presented here. Besides advanced estimation and interpolation techniques, the central part is a concept to choose those random variables, which contribute most significantly to the observed structural response. The procedure utilizes tools from robustness assessment after a relatively small pilot simulation. The random field modelled by this reduced set of variables is then put into a reliability analysis. The method yields a drastic reduction of dimension, still it is suitable for robustness and reliability analyses. This is demonstrated by an application from practice. Computations were performed by the optimization and stochastic software package optiSLang.