Abstract: Nondestructive testing is one of the most promising methods for monitoring the state of technical objects, since it allows you to diagnose in real time without interrupting the operation of mechanisms. One of the most effective types of nondestructive testing is vibration-based diagnostics. By tracking the vibrations passing through the diagnosed object, you can build diagrams showing its state. It was previously established that the presence of a defect is indicated by the presence of chaotic oscillations, for the detection of which diagrams are used displaying the dependences between the displacement by speed and acceleration. Tracking these values separately is a fairly resource-consuming process, therefore, it is rational to calculate speed and acceleration by differentiation, and it is enough to know only the displacement. It is known that the classical method of differentiation does not provide the accuracy necessary for finding chaotic oscillations. Therefore, for this task, it is advisable to use spectral methods that provide a standard for double arithmetic accuracy. However, these methods are applicable only to periodic functions, and in the case of, for example, systems with damped oscillations, they give an incorrect result. The solution may be the use of the spectral method of differentiation at Chebyshev nodes. The method is based on differentiation using the Fourier transform. The discreteness of the data makes it possible to use the fast Fourier transform, which is a well-developed and repeatedly implemented computer tool. The calculations in the above method are carried out mainly with matrices, as a result of which the MatLab package was chosen for the experiment, which allowed in addition to create an application with a window interface. The purpose of the practical part of this article is to demonstrate the possibility of constructing state diagrams using the spectral method of differentiation at Chebyshev nodes.
Index terms: nondestructive check, vibration-based diagnostics, spectral differentiation, Fourier transform, numerical method


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