Constructive neural networks and their application to ship multidisciplinary design optimization

This paper presents a neural network-based response surface method for reducing the cost of computer-intensive optimizations for applications in ship design. In the approach, complex or costly analyses are replaced by a neural network, which is used to instantaneously estimate the value of the function(s) of interest. The cost of the optimization is shifted to the generation of (smaller) data sets used for training the network. The focus of the paper is on the use and analysis of constructive networks, as opposed to networks of fixed size, for treating problems with a large number of variables, say around 30. The advantages offered by constructive networks are emphasized, leading to the selection and discussion of the cascade correlation algorithm. This topology allows for efficient neural network determination when dealing with function representation over large design spaces without requiring prior experience from the user. During training, the network grows until the error on a small set (validation set), different from that used in the training itself (training set), starts increasing. The method is validated for a mathematical function for dimensions ranging from 5 to 30, and the importance of analyzing the error on a set other than the training set is emphasized. The approach is then applied to the automated computational fluid dynamics-based shape optimization of a fast ship configuration known as the twin H-body. The classical approach yields a design improvement of 26%, whereas the neural network-based method allows reaching a 34% improvement at one fifth of the cost of the former. Based on the analysis of the results, areas for future improvements and research are outlined. The results demonstrate the potential of the method in saving valuable development cycle time and increasing the performance of future ship designs.