**4. Conclusions**

272 Recurrent Neural Networks and Soft Computing

testing data set, with a maximum achieved error of 17.95% and 0.43% for the training and respectively the testing data sets. Figure 24 presents the error distribution for training and

For the NN used to evaluate the argument of the mutual impedances between MP and the other conductors the optimal NN2 architecture is a feed forward NN with two hidden layers: 20 neurons on the first hidden layer and 20 neurons in the second hidden layer. The average error is 0.249% for the training data set and respectively 0.313% for the testing data set, with a maximum achieved error of 6.71% and 1.43% for the training and respectively the testing data sets. Figure 25 presents the error distribution for training and testing problem

After identifying the optimal architecture of the neural networks these two NN were unified in a virtual black box in order to evaluate mutual impedances real and imaginary part. This unification procedure has as secondary unwanted result a change in the final complex mutual impedance evaluation error. Thus the average error become 0.665% for the training data set and respectively 0.407% for the testing data set, with a maximum achieved error of 18.728% and 1.107% for the training and respectively the testing data sets. Figure 26 presents the global evaluation error distribution of complex mutual impedance for both training and

Also, the authors implemented and tested some layer recurrent neural network architectures. But unfortunately because of the large training database with very different output values the training process proved to be very time consuming (more than one hour) and the obtained results had the same accuracy as the previous feed-forward networks.

testing problem geometry data sets.

Fig. 24. Error distribution for Amplitude NN2.

Fig. 25. Error distribution for Argument NN2.

testing problem geometry data sets.

geometry data sets.

In this chapter the authors implement neural networks based artificial intelligence techniques in the study of electromagnetic interference problems (right of way EPL-MP) focusing on finding an easier method to identify the optimal solution.

To solve the differential equation which describes the couplings between EPL and nearby MP usually a finite element method is used. This FEM calculation needs excessive computational time especially if different problem geometries of the same interference problem have to be studied.

In order to reduce computation time the authors proposed two neural networks based artificial intelligence techniques to scale the results from a set of known problem geometries to any new problem geometry. The proposed neural networks were implemented for specific EPL-MP interference problems. The first one evaluates the magnetic vector potential in case of a phase to earth EPL fault and second one determines the self and mutual impedance matrix in case of a three vertical layer earth.

The obtained results with the proposed neural network solutions proved themselves to be very accurate. Thus ad shown neural network based solution to study EPL-MP interference problems could be a very effective one, especially if we take into account the fact that the solutions provided are obtained instantaneously ones they are properly trained.

Also it has been shown that even there is a special requirement to use recurrent neural networks, these NN architectures could provide more accurate solutions than the basic feedforward structures.
