Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size

TLDR

Engineering analysis codes grow in complexity at a rate that outpaces computing power, and multidisciplinary design problems require integrating many disciplines and conflicting objectives, making statistical design of experiments and response surface modeling attractive yet limited by the curse of dimensionality. The study aims to investigate and demonstrate the limitations of statistical design of experiments and response surface modeling for multidisciplinary, multiobjective design optimization by pushing these techniques to their limits in a large‑scale problem. The authors illustrate the approach with a high‑speed civil transport aircraft wing, applying statistical techniques to enable multidisciplinary design optimization while exposing the curse of dimensionality, and discuss system partitioning, hierarchical modeling, and kriging as potential remedies.

Abstract

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 singleobjective 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 large 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 (an alternative statistical approximation technique) are discussed as remedies for the problem of size.