Chen, H., Zeng, Y. and Li, Y. orcid.org/0000-0001-7907-5176 (2021) Machine learning models for the secondary Bjerknes force between two insonated bubbles. Acta Mechanica Sinica, 37 (1). pp. 35-46. ISSN 0567-7718
Abstract
The secondary Bjerknes force plays a significant role in the evolution of bubble clusters. However, due to the complex dependence of the force on multiple parameters, it is highly non-trivial to include its effects in the simulations of bubble clusters. In this paper, machine learning is used to develop a data-driven model for the secondary Bjerknes force between two insonated bubbles as a function of the equilibrium radii of the bubbles, the distance between the bubbles, the amplitude and the center frequency of the ultrasound wave. The sign of the force may change with the phase difference between the oscillating bubbles. Meanwhile, the magnitude of the force varies over several orders of magnitude, which poses a serious challenge for the usual machine learning models. To overcome this difficulty, the magnitudes and the signs of the force are separated and modelled separately. A nonlinear regression is obtained with a feed-forward network model for the logarithm of the magnitude, whereas the sign is modelled by a support-vector machine model. The principle, the practical aspects related to the training and validation of the machine models are introduced. The predictions from the models are checked against the values computed from the Keller–Miksis equations. The results show that the models are extremely efficient while providing accurate estimate of the force. The models make it computationally feasible for the future simulations of the bubble clusters to include the effects of the secondary Bjerknes force.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecomm ons.org/licenses/by/4.0/. |
Keywords: | Bubble clusters; Secondary Bjerknes force; Machine learning; Neural networks; Support-vector machine; Numerical simulations |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 25 Jan 2024 10:26 |
Last Modified: | 25 Jan 2024 10:26 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s10409-020-01028-0 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:207831 |