# Transfer distortions of acoustic emission signals - power relations between the signal parameters and normalized temporal shapes of avalanches

## TL;DR

This paper investigates power law relationships in acoustic emission signals and shows how transfer distortions affect signal parameters and shapes.

## Contribution

The study introduces a new model showing that transfer distortions cause mechanism-independent changes in acoustic emission signal parameters.

## Key findings

- A power law correlation between rising time and amplitude of acoustic emission signals was confirmed.
- Transfer distortions heavily affect the tail region of normalized temporal avalanche shapes.
- The calculated exponent φAE = 1 aligns well with experimental data across different structural changes.

## Abstract

Power law correlation between the rising time, \documentclass[12pt]{minimal}
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\begin{document}$$\:R$$\end{document}, and amplitude,\documentclass[12pt]{minimal}
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\begin{document}$$\:\:A$$\end{document}, of the detected acoustic emission, AE, signals is investigated in the framework of a driven damped harmonic oscillator model. It is shown, in contrast to the previous model calculation, that \documentclass[12pt]{minimal}
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\begin{document}$$\:R\sim{A}^{1-{\varphi}_{AE}}$$\end{document} holds, similarly to the well-known enigma for acoustic emission; \documentclass[12pt]{minimal}
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\begin{document}$$\:E\sim{A}^{3-{\varphi}_{AE}}\:$$\end{document}as well as \documentclass[12pt]{minimal}
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\begin{document}$$\:S\sim{A}^{2-{\varphi}_{AE}}$$\end{document}, where E and A are the energy and area, and 3 and 2 are the expected exponents from the mean field theory, MFT. The same value \documentclass[12pt]{minimal}
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\begin{document}$$\:{\varphi}_{AE}=1$$\end{document} was obtained for all the above exponents and transfer distortions cause mechanism independent changes. For the experimental value \documentclass[12pt]{minimal}
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\begin{document}$$\:{\varphi}_{exp}={\varphi}_{AE}+{\varphi}_{o}$$\end{document} is fulfilled, where \documentclass[12pt]{minimal}
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\begin{document}$$\:{\varphi}_{o}$$\end{document} is the exponent in the power relation between the amplitude and the rising time of the source function (\documentclass[12pt]{minimal}
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\begin{document}$$\:{\varphi}_{o}=-0.32$$\end{document} beyond the MFT and \documentclass[12pt]{minimal}
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\begin{document}$$\:{\varphi}_{o}=0\:$$\end{document}in MFT). The calculated value of \documentclass[12pt]{minimal}
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\begin{document}$$\:{\varphi}_{AE}=1$$\end{document} is in good agreement with experimental data obtained for different structural changes: \documentclass[12pt]{minimal}
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\begin{document}$$\:{\varphi}_{exp}\:0.8\pm\:0.2$$\end{document}. Universal functions, well scaled together, can be obtained for the temporal avalanche shapes at fixed area normalizing the voltage by \documentclass[12pt]{minimal}
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\begin{document}$$\:A$$\end{document} and the time by \documentclass[12pt]{minimal}
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\begin{document}$$\:R\sim{A}^{1-{\varphi}_{exp}}$$\end{document}. The first part (around the peak) of it is not sensitive to transfer distortions, while the tail region can be heavily distorted.

The online version contains supplementary material available at 10.1038/s41598-025-26238-z.