Mean Value Standard Deviation

Summary 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. Furthermore, the deterministic optimization algorithms tend to push an optimized design towards the boundaries of the design space. This paper reviews theories and methodologies that have been developed to solve optimization problems under uncertainties. In the first part the paper gives an overview over the state of the art in stochastic optimization methods such as robust design and reliability-based design optimization. In addition, global response surface techniques as well as genetic programming in combination with first order reliability methods in reliability-based optimization are discussed. Two numerical examples from structural analysis under static and dynamic loading conditions show the applicability of these concepts. The probabilistic and structural analysis tasks are performed with ANSYS DesignXplorer and OptiSLang software packages