This paper demonstrates the application of correlated Gaussian process based approximations to optimization where multiple levels of analysis are available, using an extension to the geostatistical method of co-kriging . An exchange algorithm is used to choose which points of the search space to sample within each level of analysis. The derivation of the co-kriging equations is presented in an intuitive manner, along with a new variance estimator to account for varying degrees of computational ‘noise’ in the multiple levels of analysis. A multi-fidelity wing optimization is used to demonstrate the methodology.

Surrogate models expedite the search for promising designs by standing in for expensive design evaluations or simulations. They provide a global model of some metric of a design (such as weight, aerodynamic drag, cost, etc.), which can then be optimized efficiently. Engineering Design via Surrogate Modelling is a self-contained guide to surrogate models and their use in engineering design. The fundamentals of building, selecting, validating, searching and refining a surrogate are presented in a manner accessible to novices in the field. Figures are used liberally to explain the key concepts and clearly show the differences between the various techniques, as well as to emphasize the intuitive nature of the conceptual and mathematical reasoning behind them. More advanced and recent concepts are each presented in stand-alone chapters, allowing readers to concentrate on material pertinent to their current design problems, and concepts are clearly demonstrated using simple design problems. This collection of advanced concepts (visualization, constraint handling, coping with noisy data, gradient-enhanced modelling, multi-fidelity analysis and multiple objectives) represents an invaluable reference manual for engineers and researchers active in the area. Engineering Design via Surrogate Modelling is complemented by a suite of MATLAB® codes, allowing readers to apply all the techniques presented to their own design problems. By applying statistical modelling to engineering design, this book bridges the gap between the engineering and statistics communities. It will appeal to postgraduates and researchers across the academic engineering design community as well as to practicing design engineers.The bookprovides an inclusive and practical guide to using surrogates in engineering design; presents the fundamentals of building, selecting, validating, searching and refining a surrogate model; and guides the reader through the practical implementation of a surrogate-based design process using a set of case studies from real engineering design challenges