Neural network and response surface methodology for rocket engine component optimization

The goal of this work is to compare the performance of response surface methodology (RSM) and two types of neural networks (NN) to aid preliminary design of two rocket engine components. A data set of 45 training points and 20 test points, obtained from a semi-empirical model based on three design variables, is used for a shear coaxial injector element. Data for supersonic turbine design is based on six design variables, 76 training data and 18 test data obtained from simplified aerodynamic analysis. Several RS and NN are first constructed using the training data. The test data are then employed to select the best RS or NN. Quadratic and cubic response surfaces, radial basis neural network (RBNN) and back-propagation neural network (BPNN) are compared. Twolayered RBNN are generated using two different training algorithms, namely, solverbe and solverb. A two-layered BPNN is generated with Tan-Sigmoid transfer function. Various issues related to the training of the neural networks are addressed, including number of neurons, error goals, spread constants, and the accuracy of different models in representing the design space. A search for the optimum design is carried out using a standard, gradient-based optimization algorithm over the response surfaces represented by the polynomials and trained neural networks. Usually a cubic polynomial performs better than the quadratic polynomial but exceptions have been noticed. Among the NN choices, the RBNN designed using solverb yields more consistent performance for both engine components considered. The training of RBNN is easier as it requires linear regression. This coupled with the consistency in performance promise the possibility of it being used as an optimization strategy for engineering design problems.