**6. The synthesis (design) of neural networks for modelling purposes**

Neural network modelling is always based on the measurement points which describe the modelled system behaviour. It is well known from the information theory that the observed function should be sampled frequently enough in order to preserve the system information. Practically, this means that the data should be gathered at least 10 times faster than the highest frequency (in temporal or spatial sense) produced by the system (Shannon's

curve of ap proxim ate d pressu re

stab ilit y ba nd wid th

solution (or any other kind of optimization) (Goldberg, 1998).

closest to the middle curve should be taken as best.

of the training stability should be performed.

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Fig. 6. The upper curve represents the band centre line, which is the most probable model for the given data, and the lower curve represents the band width. The points depict the measured data points that were actually used for training. The lower curve represents the width of the training stability band. The band width is the smallest at the measured points

When the band is too wide, more emphasis has to be given to find the training process that gives the best modelling. In this case, genetic algorithms can be used to find the best

Following a very large number of performed experiments it was shown that the middle curve (centre line) (Fig. 6) between the maximal and minimal curve is the most probable curve for the observed modelling problem. The training stability band middle range curve can be used as the best approximation, and the training repetition that produces the model

Some practitioners use the strategy of division of the measured points into two sets: one is used for training purposes and the other for the model evaluation purposes. This is a very straightforward strategy, but it works well only when the number of the measured points is large enough (in accordance with the dynamics of the system–sampling theorem). If this is not the case, all measured points should be used for the training purposes, and an analysis

Neural network modelling is always based on the measurement points which describe the modelled system behaviour. It is well known from the information theory that the observed function should be sampled frequently enough in order to preserve the system information. Practically, this means that the data should be gathered at least 10 times faster than the highest frequency (in temporal or spatial sense) produced by the system (Shannon's

**6. The synthesis (design) of neural networks for modelling purposes** 

*tim e[min]*

**0.00**

used for training.

**1.00**

**2.00**

**3.00**

*pressure/error*

**4.00**

**5.00**

**6.00**

theorem). If the sampled data is too sparse, the results of the modelling (in fact any kind of modelling) will be poor, and the modelling tools can not be blamed for bad results.

The synthesis of a neural network should be performed in several steps:


Usually, one of the modelled parameters is time. In this case, one of the inputs represents the time points when the data samples were taken. Fig. 6 shows the model of degassing a vacuum system where the x axis represents the time in minutes and the y axis represents the total pressure in the vacuum system (in relative numerical values). In this case, the only input to the neural network was time and the target was to predict the pressure in the vacuum chamber.
