Statistical approximations for multidisciplinary design optimization: The problem of size

Despite the steady increase of computing power and speed, the complexity of many of today's engineering analysis codes seems to keep pace with computing advances, Furthermore, the design and development of complex systems typically requires the integration of multiple disciplines and the resolution of multiple conflicting objectives. A departure from the traditional parametric design analysis and single-objective optimization approaches is necessary for the effective solution of multidisciplinary, multiobjective complex design problems that rely on computer analyses. Statistical design of experiments and response surface modeling have been used extensively to create inexpensive-to-run approximations of expensive-to-run computer analyses and combat the problem of size associated with large, multidisciplinary design problems. However, these statistical approaches also break down because of the curse of dimensionality, wherein the number of design variables becomes too targe to build accurate response surfaces efficiently. Speculations have been offered in the literature regarding the manageable problem size when these approaches are employed. In this paper, the limitations of these approaches are investigated and demonstrated explicitly by pushing the limits in a Large-scale design problem. The design of a high-speed civil transport aircraft wing is used to illustrate 1) the use of these statistical techniques to facilitate multidisciplinary design optimization and 2) the resulting curse of dimensionality associated with large variable design problems. Our current research efforts in system partitioning and hierarchical modeling, and kriging tan alternative statistical approximation technique) are discussed as remedies for the problem of size.