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.
