Advanced, Guided Procedure for the Calibration and Generalization of Neural Network-Based Models of Combustion and Knock Indexes

Abstract

In the last few years, the artificial neural networks have been widely used in the field of engine modeling. Some of the main reasons for this are, their compatibility with the real-time systems, higher accuracy, and flexibility if compared to other data-driven approaches. One of the main difficulties of using this approach is the calibration of the network itself. It is very difficult to find in the literature procedures that guide the user to completely define a network. Typically, the very last steps (like the choice of the number of neurons) must be selected by the user on the base of his sensitivity to the problem. This work proposes an automatic calibration procedure for the artificial neural networks, considering all the main hyper-parameters of the network such as the training algorithms, the activation functions, the number of the neurons, the number of epochs, and the number of hidden layers, for modeling various combustion indexes in a modern internal combustion engine. However, the proposed procedure can be applied to the training of any neural network-based model. The automatic calibration procedure outputs a configuration of the network, giving the optimal combination in terms of hyper-parameters. The decision of the optimal configuration of the neural network is based on a self-developed formula, which gives a rank of all the possible hyper-parameter combinations using some statistical parameters obtained comparing the simulated and the experimental values. In the end, the lowest rank is selected as the optimal one as it represents the combination having the lowest error. Following the definition of this rank, high accuracy on the results has been achieved in terms of the root mean square error index, for example, on the combustion phase model, the error is 0.139°CA under steady-state conditions. On the maximum in-cylinder pressure model, the error is 1.682 bar, while the knock model has an error of 0.457 bar for the same test that covers the whole engine operating field.