Abstract
In this project a neural network was designed to determine the amount of air that goes into an engine with variable valve lift. The goal of the project is to have a precise calculation of the air charge for the complete range of input signals. For this application the neural network showed to be a good black box modelling method, with high precision (error below 2% RMS) achievable.
For the neural network itself mapping of the inputs to normalized values shows to be beneficial. A good network structure was found in a network with two hidden layers, fifteen neurons in the first, and ten neurons in the second hidden layer. A Tansig activation function is preferable.
As training method the Levenberg Marquardt algorithm is chosen, with early stopping as method to prevent overfitting. A two stage training method was developed and tested to reduce the number of big errors in the network output. By performing the last training steps on absolute third power errors instead of quadratic errors, the amount of errors above 10% could be strongly reduced, with only a small increase in average error. Still an RMS error below 2% showed to be possible.
As final part of the project the principles of neural network training were applied on training a parameter model. Optimal parameters, within given parameter limits, could be found to give a parameterized engine model the same output as a supplied dataset. Purpose was to improve the engine model that was used for generating training data for the neural network. With the achievement of an RMS error below 2%, this non linear regression technique may also be used to develop an engine model that is both simple and precise enough to be implemented in the engine control unit directly, and thus might replace the neural network in some applications. Since such a white box model is in general more preferable than a black box model, this would be a nice topic for further research.
KEYWORDS – Neural networks, Engine management, Simulation, Internal combustion engine, Variable valve lift.