Constructive neural networks for function approximation and their application to CFD shape optimization.

摘要

This research focuses on the development of constructive neural networks (NN) for regression tasks in high dimensional spaces for application to multidisciplinary design/optimization problems. The objective is to reduce the cost of optimization by replacing computer-intensive analyses, such as computational fluid dynamics (CFD) simulations, with a NN-based regression method. The computational cost of the optimization is shifted from direct CFD computations inside the optimization loop to the generation of small(er) datasets used for training the network, and total optimization cost is therefore reduced. The method is general and can be applied to any problem which can benefit from function approximations in a high dimensional space.;A cascade correlation (CC) training algorithm is improved for regression tasks. Improvements include altering the weight initialization, modifying the candidate hidden unit training, and introducing normalized inputs, alternate correlation formulas, "early stopping" and "ensemble averaging.";The generalization characteristics of the modified CC algorithm, i.e. its ability to accurately predict cases not in the training set, are first analyzed on a model problem. This problem, representative of a shape optimization problem, allows for systematic evaluation and refinement of the NN's ability to replace the CFD method. Next, the algorithm is applied to a mathematical function to study the generalization properties of the network when the input space dimension increases from two to thirty. The study shows that "ensemble averaged" network committees and early stopping greatly improve the generalization performance of the modified CC algorithm.;Finally, the NN approach is applied to the design/optimization of an underwater hull configuration using a genetic algorithm search method. Results are compared with those obtained with a classical optimization approach in which the CFD code is directly coupled with the optimizer, and show that the NN approach can produce better designs at substantially lower computational costs. For the 28 design variable example treated, a 34 percent improvement with the NN approach is obtained whereas the classical approach only yields a 26 percent improvement while using four times more CPU time.;Areas of further research are discussed and include investigating other types of network committees as well as modifying the optimizer itself.