Design Reliability Analysis

A large number of problems in manufacturing processes, production planning, finance and engineering design require an understanding of potential sources of variations and quantification of the effect of variations on product behavior and performance. Traditionally, in engineering problems uncertainties have been formulated only through coarse safety factors. Such methods often lead to overdesigned products. First, this paper gives an overview over the state of the art in reliability analysis methods to describe model uncertainties and to calculate reliability and safety. Different methods exist, but they all have a limited area of application. The aim of the first part is to investigate the applicability of certain methods for specific problems and to give a general indication, which method is appropriate for certain problem classes, implemented in optiSLang . In addition, a new adaptive response surface method is introduced to analyse the design reliability with high accuracy and efficiency. Whereby the surrogate model is based on an improved moving least square approximation combined with an adaptive design of experiment. In order to obtain a fast simulation procedure on the response surface an adaptive importance sampling concept is developed. Several numerical examples show the applicability of this concept for highly nonlinear state and limit state functions and multiple design points and separated unsafe domains. Furthermore, within a structural reliability analysis example a discretization of random fields in combination with a robustness evaluation to identify the relevant random variables is introduced. The so-called nonparametric structural reliabilty analysis is a new method to estimate the safety and reliability of finite element structures in cases where a CAD-based parametrization is not possible or not meaningful. The probabilistic and structural analysis tasks are performed with the optiSLang , SoS and SLang software packages.