Investigation of the Convergence Domain of the Backpropagation Algorithm for Training the Perceptron in Pattern Recognition in the Problems of Technospheric Safety of Transport Systems

The efficiency of the backpropagation algorithm is considered in relation to the problem of training a three-layer perceptron with two input and two output values. To activate perceptron neurons, a logistic function with parameter a was used. The learning process was carried out using many of 10,000 examples and lasted for 100 epochs. Two training modes are considered - deterministic, in which the sequence of training examples in each epoch is the same, and stochastic, when the training examples are randomly reordered before each epoch. Based on the simulation results, the advantages of the deterministic mode over the stochastic mode were not revealed, which makes it possible to recommend deterministic learning for practical use as it is simpler in computational terms. It is shown that the best training quality is achieved when using 8 neurons in the second hidden layer, when the average relative error of the trained perceptron is less than 0.003. With a decrease in the number of hidden neurons, the quality of learning decreases, with an increase, the range of learning parameters narrows, at which the learning process converges to a satisfactory small error, while the likelihood of an imbalance in synaptic weights increases. With the learning rate parameter values of 0.95, the best quality indicators and the minimum duration of their oscillations between epochs were obtained; a higher rate of convergence of the learning process was recorded. The influence of the parameter a on the quality of training is investigated for its values up to 3.375 inclusive. When the size of the second hidden layer is no more than 8 neurons, an increase in a leads to a decrease in the average error of the trained perceptron. In perceptrons with 16 or more hidden neurons, the convergence region of the algorithm shifts towards small a values (no more than 1.125 for 32 neurons).