ON ONE SOLUTION OF THE PROBLEM OF STOCHASTIC LONGITUDINAL OSCILLATIONS OF A VISCOELASTIC ROPE WITH MOVING BOUNDARIES USING ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING METHODS
Keywords: artificial intelligence, neural networks, stochastic oscillations, boundary movement, integro-differential equations, control of resonance phenomena
Abstract: Addresses the problem of stochastic longitudinal oscillations of a viscoelastic rope with moving boundaries. The main focus is on the application of artificial intelligence (AI), neural networks, and machine learning (ML) methods for analyzing resonance phenomena, predicting optimal system parameters, and preventing resonance. A method for constructing solutions to integro-differential equations is proposed, which is extended to a broader class of problems with moving boundaries. The problem of stochastic longitudinal vibrations of a viscoelastic rope with moving boundaries is formulated taking into account the influence of damping forces in the form of a system of stochastic integro-differential equations, which is reduced to the study of a system of stochastic differential equations with random initial conditions. The use of deep neural networks (DNNs), Monte Carlo methods, and adaptive control significantly improves the accuracy of predictions and the efficiency of system control. The neural network is trained on data on the behavior of the system at different frequencies and parameters. In this case, the network predicts resonant frequencies and suggests optimal parameters. The results of the AI are tested on a mathematical model. Calculations confirmed that the parameters proposed by artificial intelligence do prevent resonance.
Submission Number: 50
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