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Volume 13
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Mathematical Modeling of Signals for Weight Control of Vehicles Using Seismic Sensors

by
Nikita V. Martyushev
1,*,
Boris V. Malozyomov
2,
Anton Y. Demin
1,
Alexander V. Pogrebnoy
1,
Egor A. Efremenkov
3,
Denis V. Valuev
4 and
Aleksandr E. Boltrushevich
1
1
Department of Information Technology, Tomsk Polytechnic University, 634050 Tomsk, Russia
2
Department of Electrotechnical Complexes, Novosibirsk State Technical University, 630073 Novosibirsk, Russia
3
Department of Mechanical Engineering, Tomsk Polytechnic University, 634050 Tomsk, Russia
4
Yurga Technological Institute (Branch), Tomsk Polytechnic University, 652055 Yurga, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(13), 2083; https://doi.org/10.3390/math13132083
Submission received: 27 May 2025 / Revised: 20 June 2025 / Accepted: 23 June 2025 / Published: 24 June 2025
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)
Versions Notes

Abstract

The article presents a new method of passive dynamic weighing of vehicles based on the registration of seismic signals that occur when wheels pass through strips specially applied to the road surface. Signal processing is carried out using spectral methods, including fast Fourier transform, consistent filtering, and regularization methods for solving inverse problems. Special attention is paid to the use of linear-frequency-modulated signals, which make it possible to distinguish the responses of individual axes even when superimposed. Field tests were carried out on a real section of the road, during which signals from vehicles of various classes were recorded using eight geophones. The average error in determining the speed of 1.2 km/h and the weight of 8.7% was experimentally achieved, while the correct determination of the number of axles was 96.5%. The results confirm the high accuracy and sustainability of the proposed approach with minimal implementation costs. It is shown that this system can be scaled up for use in intelligent transport systems and applied in real traffic conditions without the need to intervene in the design of the roadway.
Keywords: passive seismic system; dynamic weighing; vehicles; geophones; spectral analysis; Tikhonov regularization; linear-frequency modulation; intelligent transport systems passive seismic system; dynamic weighing; vehicles; geophones; spectral analysis; Tikhonov regularization; linear-frequency modulation; intelligent transport systems

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MDPI and ACS Style

Martyushev, N.V.; Malozyomov, B.V.; Demin, A.Y.; Pogrebnoy, A.V.; Efremenkov, E.A.; Valuev, D.V.; Boltrushevich, A.E. Mathematical Modeling of Signals for Weight Control of Vehicles Using Seismic Sensors. Mathematics 2025, 13, 2083. https://doi.org/10.3390/math13132083

AMA Style

Martyushev NV, Malozyomov BV, Demin AY, Pogrebnoy AV, Efremenkov EA, Valuev DV, Boltrushevich AE. Mathematical Modeling of Signals for Weight Control of Vehicles Using Seismic Sensors. Mathematics. 2025; 13(13):2083. https://doi.org/10.3390/math13132083

Chicago/Turabian Style

Martyushev, Nikita V., Boris V. Malozyomov, Anton Y. Demin, Alexander V. Pogrebnoy, Egor A. Efremenkov, Denis V. Valuev, and Aleksandr E. Boltrushevich. 2025. "Mathematical Modeling of Signals for Weight Control of Vehicles Using Seismic Sensors" Mathematics 13, no. 13: 2083. https://doi.org/10.3390/math13132083

APA Style

Martyushev, N. V., Malozyomov, B. V., Demin, A. Y., Pogrebnoy, A. V., Efremenkov, E. A., Valuev, D. V., & Boltrushevich, A. E. (2025). Mathematical Modeling of Signals for Weight Control of Vehicles Using Seismic Sensors. Mathematics, 13(13), 2083. https://doi.org/10.3390/math13132083

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