This work proposes a new method for using reduced order models in lieu of high fidelity analysis during the sensitivity analysis step of gradient based design optimization. The method offers a reduction in the computational cost of finite difference based sensitivity analysis in that context.
The method relies on interpolating reduced order models which are based on proper orthogonal decomposition. The interpolation process is performed using radial basis functions and Grassmann manifold projection. It does not require additional high fidelity analyses to interpolate a reduced order model for new points in the design space. The interpolated models are used specifically for points in the finite difference stencil during sensitivity analysis.
The proposed method is applied to an airfoil shape optimization (ASO) problem and a transport wing optimization (TWO) problem. The errors associated with the reduced order models themselves as well as the gradients calculated from them are evaluated. The effects of the method on the overall optimization path, computation times, and function counts are also examined.
The ASO results indicate that the proposed scheme is a viable method for reducing the computational cost of these optimizations. They also indicate that the adaptive step is an effective method of improving interpolated gradient accuracy. The TWO results indicate that the interpolation accuracy can have a strong impact on optimization search direction.
|Advisor:||Rais-Rohani, Masoud, Janus, J. Mark|
|Commitee:||Banicescu, Ioana, Newman, James C., III|
|School:||Mississippi State University|
|School Location:||United States -- Mississippi|
|Source:||DAI-B 75/08(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Aerospace engineering, Computer science|
|Keywords:||Interpolation process, Multidisciplinary optimization, Reduced order models, Sensitivity analysis|
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