Asymptotic- and bifurcation-aware scientific machine learning for nonlinear vibration prediction of submerged floating tunnel tethers under hydrodynamic excitation

  • Mohammad Akram orcid

    Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
  • Umar Ishtiaq orcid

    Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan; Software Development Department, Biruni University, 34010 Istanbul, Turkey; Research Center of Applied Mathematics, Khazar University, Baku AZ1096, Azerbaijan
  • Ioan-Lucian Popa

    Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania; Faculty of Mathematics and Computer Science, Transilvania University of Brasov, 500091 Brasov, Romania
Article ID: 4683
DOI: https://doi.org/10.59400/sv4683
Keywords: submerged floating tunnel; nonlinear cable dynamics; parametric resonance; multiple time scales; frequency-response manifold; scientific machine learning

Abstract

Seabed-anchored submerged floating tunnels transmit most of their transverse stiffness to slender pre-tensioned tethers whose vibration governs the fatigue design of the crossing. A reduced-order model represents the tunnel cross-section as a two-degree-of-freedom rigid tube coupled to small-sag tethers, linearizes the Morison drag into an amplitude-dependent equivalent damping, and yields, through the multiple time scales method, closed-form frequency-response equations for an indirectly forced regime, an indirect parametric regime of Mathieu-Duffing type, and a directly forced regime. These closed forms are exact only as the ordering parameter vanishes, they lose accuracy away from resonance, and their parametric coupling is of order unity, which invalidates small-parameter stability charts. We develop a learning framework that lifts these restrictions while staying close to the analysis. A slow-flow-informed network represents the amplitude and phase modulation, so the fast motion is analytic and the reconstruction error stays uniform over the long horizon rather than growing secularly. A bifurcation-aware operator learns the response in structure-preserving polynomial form, from which steady amplitudes follow as companion-matrix eigenvalues, stability from the modulation Jacobian, folds from the amplitude resultant, cusps from elimination theory, and parametric tongues from a certified Floquet computation. We prove asymptotic-consistency, approximation, and uniform-in-time error theorems. Validated against the closed forms and against direct integration of the unreduced oscillator, the framework reproduces the submerged-tether branch closure, charts the order-unity tongues, and returns a differentiable design manifold with analytic sensitivities, reaching a test coefficient of determination of 0.969 at a query cost several orders of magnitude below direct simulation.

Published
2026-09-24
How to Cite
Akram, M., Ishtiaq, U., & Popa, I.-L. (2026). Asymptotic- and bifurcation-aware scientific machine learning for nonlinear vibration prediction of submerged floating tunnel tethers under hydrodynamic excitation. Sound & Vibration, 60(6). https://doi.org/10.59400/sv4683
Issue
Vol. 60 No. 6 (2026): In Progress
Section
Article

Copyright (c) 2026 Mohammad Akram, Umar Ishtiaq, Ioan-Lucian Popa

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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