A method for reducing dimensionality in large design problems with computationally expensive analyses

Dimensionality reduction;Gradient;Aerodynamic shape optimization;Computational fluid dynamics;Principal component analysis;Principal orthogonal decomposition;Over-wing nacelle;Propulsion-airframe integration;Adjoint methods

Berguin, Steven Henri ; Mavris, Dimitri N. Aerospace Engineering Ruffin, Stephen Kennedy, Graeme Lounici, Karim Hahn, Andrew ; Mavris, Dimitri N.

University:Georgia Institute of Technology

Department:Aerospace Engineering

关键词: Dimensionality reduction;    Gradient;    Aerodynamic shape optimization;    Computational fluid dynamics;    Principal component analysis;    Principal orthogonal decomposition;    Over-wing nacelle;    Propulsion-airframe integration;    Adjoint methods;   

Others  :  https://smartech.gatech.edu/bitstream/1853/53504/1/BERGUIN-DISSERTATION-2015.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

Strides in modern computational fluid dynamics and leaps in high-power computing have led to unprecedented capabilities for handling large aerodynamic problem. In particular, the emergence of adjoint design methods has been a break-through in the field of aerodynamic shape optimization. It enables expensive, high-dimensional optimization problems to be tackled efficiently using gradient-based methods in CFD; a task that was previously inconceivable. However, adjoint design methods are intended for gradient-based optimization; the curse of dimensionality is still very much alive when it comes to design space exploration, where gradient-free methods cannot be avoided. This research describes a novel approach for reducing dimensionality in large, computationally expensive design problems to a point where gradient-free methods become possible. This is done using an innovative application of Principal Component Analysis (PCA), where the latter is applied to the gradient distribution of the objective function; something that had not been done before. This yields a linear transformation that maps a high-dimensional problem onto an equivalent low-dimensional subspace. None of the original variables are discarded; they are simply linearly combined into a new set of variables that are fewer in number. The method is tested on a range of analytical functions, a two-dimensional staggered airfoil test problem and a three-dimensional Over-Wing Nacelle (OWN) integration problem. In all cases, the method performed as expected and was found to be cost effective, requiring only a relatively small number of samples to achieve large dimensionality reduction.