Modeling and optimization of response surfaces using an Artificial Neural Networks

In a world where new products are developed using computer simulations, and where every aspect can be measured, and refined with extreme precision, most optimisation algorithms still rely on the existence of a clearly defined function to optimize. In reality however this function is often defined through a FEM-calculation, which may require hours to evaluate each individual point. In order to save time, only a small discrete set of points can be evaluated and are then used to construct a mathematical model, or response surface, of the data. Actual optimisation of the problem can then be done on this model instead. This project focuses on using an artificial neural network (ANN) to construct such a model. The objective is to build a generalised software tool that can take a set of data, construct a response surface, and find the optimal point on it. The tool must also be able to do this with high accuracy and within reasonable time. Because the method requires many mathematical formulations, the tool was written in MATLAB. The structure of the ANN used is limited to feed-forward networks with two hidden layers, where the number of hidden neurons ischosen such that overfitting is avoided. The training of the ANN uses backpropagation and the results are evaluated using the response surface of a quadratic regression model (QRM) for comparison. Testing of the final product shows that the ANN is in most cases able to outperform the QRM, and sometimes with several orders of magnitude. It is also clear that the ANN is more versatile than the QRM when it comes to modelling non-symmetric functions. When the number of input parameters increases, the difference becomes less distinct. However the ANN has the advantage that its adaptability can be easily improved upon if the data set is increased. The applicability of the tool developed in this project is immediate. It can be used as it is to help R&D-staff with their work. The tool does require some experience to be used fluently, and it still has potential for further improvements. It does however illustrate once again that advanced mathematical concepts can be translated into industry-useful aids