Application of artificial intelligence to predict vibrations in mechanical systems with moving boundaries

Литвинов Владислав Львович

Keywords: software package, moving boundaries, boundary value problems, resonance phenomena, artificial intelligence, machine learning, neural networks, MATLAB, vibrations of one-dimensional objects, parameter optimization, variable-length systems

Abstract: The study of the dynamics of objects with moving boundaries described by one-dimensional boundary value problems is of significant interest for modern engineering and scientific calculations. Of particular relevance is the analysis of the resonant properties of objects capable of causing critical states and structural failure. The article presents the developed software package "TB-ANALYSIS", created in the MATLAB environment for mathematical modeling and analysis of the resonant characteristics of objects with moving boundaries. This package is designed to solve one-dimensional boundary value problems describing the dynamics of objects of variable length. The main objectives of the work are: creating software for studying solutions to boundary value problems and modeling resonance phenomena; testing the effectiveness of the software package; developing an algorithmic description of the functionality. A key feature of the package is the integration of classical numerical methods with modern artificial intelligence algorithms. To solve boundary value problems, three main methods are implemented: an analytical method for replacing variables in a system of functional-difference equations, an asymptotic method, and an approximate method for constructing solutions to integro-differential equations. Intelligent selection of the method is carried out automatically depending on the type of the problem being solved. The system's architecture includes interconnected modules accessible through a single graphical interface. The main modules are designed to investigate solutions to boundary value problems, analyze resonance properties, and control resonance phenomena. To ensure calculation accuracy, a special error estimation procedure is implemented at each step. To demonstrate the system's capabilities, a study was conducted on the transverse vibrations of a variable-length viscoelastic cable resting on an elastic foundation. The results of a comparative analysis confirmed the effectiveness of the numerical methods and the correct operation of the algorithms. The study focuses on the use of artificial intelligence, neural networks, and machine learning to analyze resonance phenomena, predict optimal system parameters, and prevent resonance. The use of deep neural networks and adaptive control increased the accuracy of predictions and the effectiveness of system control. As a result, the neural network can predict resonant frequencies and suggest optimal parameters. Calculations confirmed that the parameters suggested by the artificial intelligence do indeed prevent resonance. A comparative analysis conducted across multiple test cases demonstrated that the developed hybrid approach reduces the resonant frequency prediction error to 2.1% and prevents resonance in 96% of cases, which is 34% more accurate and, on average, 5 times faster than classical methods. The developed software package is an effective tool for studying the dynamics of objects with moving boundaries. The key advantages of the package include: versatility for solving various classes of boundary value problems; intelligent selection of solution methods; a user-friendly interface; and built-in tools for evaluating computational accuracy. Prospects for further development include expanding the class of problems solved and implementing additional numerical methods.

Submission Number: 2