Multi-Fidelity Aerodynamic Optimization Using Treed Meta-Models
Andrea Nelson, Juan Jose Alonso, Thomas H. Pulliam · 25th AIAA Applied Aerodynamics Conference · 2007
The multi-fidelity Treed Meta-Model (TMM) framework developed and applied here creates a tree-based partitioning of an aerodynamic design space and employs indepen-dent Kriging surfaces in each partition to globally model computationally inexpensive low-fidelity analysis data. Using the low-fidelity meta-model to select points for evaluation with a high-fidelity analysis tool, a multi-fidelity global model is created from collocated high and low fidelity data points. A steady-state genetic algorithm is used to construct an optimal partitioning scheme based on the number of points in each partition and the com-bined predictive capabilities of the Kriging surfaces, as measured through cross-validation. The TMM framework mitigates the effects of the “curse of dimensionality ” associated with surrogate modeling of large datasets, allows for parallelization of design space searches, and increases model flexibility by using a number of smaller Kriging surfaces. Uniform incre-mental sampling is incorporated to build the low-fidelity database progressively while the GA optimizes the partitioning scheme using available data. High-fidelity data points are chosen using a Least Angle Regression Scheme (LARS) to approximate the sensitivity of the meta-model to error in the low-fidelity points. The process is demonstrated from low-fidelity meta-model construction to multi-fidelity model optimization. The optimization includes direct searches on the design space using both the low and high-fidelity analysis tools, as well as searches of the low-fidelity and mulit-fidelity meta-models. The results will show not only the ability of the TMM framework to create a sufficiently accurate partitioned low-fidelity surface but also whether the selection of high-fidelity points will create a multi-fidelity model capable of locating a different optimal than the low-fidelity meta-model. I.