There is an expert system of electric transformer's diagnostics. This system can substitutes an expert and to choose the right decision in technical service and repairmen an electric transformer of railway electric substations. The article analyzes the modern methods of diagnostics and control the remaning life of electric transformer of railway electric substation. This analysis shows that all methods of diagnostics can determines the defect when it appeared. The task to create automated neural system for prediction the defect in the future. It is proposed to use expert system with the recurrent neural network, because it has ability to predict the time series.

Keywords: Electric railways, electric transformer, railway electric substation, diagnostics of operating condition, prediction

The article offers a general gradient methods for all-adaptive method. With the help of an experimental environment was developed by a comparative analysis of gradient methods of finding the minimum. As a result of experiments, it was found that the adaptive method for approaching to a minimum minimal number of iterations. Thus encouraged to use this method in the optimization of the error function, artificial neural network training. 
Keywords: neural networks, gradient methods, teaching methods, analysis of optimization techniques.

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