2412.20778
An accurate approach to determining the spatiotemporal vehicle load on bridges based on measured boundary slopes
Alemdar Hasanov, Onur Baysal
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves the Lipschitz continuity of the Fréchet gradient J′ with the explicit constant LG = sqrt((exp(T)−1)/(2 κ0)) · ℓ^2 C0 C1, using (i) forward boundary time-trace bounds (Corollary 1: C1^2 = (5ℓρ0/3)(C_e^2−1)) and (ii) adjoint weighted-energy and endpoint-trace estimates giving C0^2 = 20ℓ C_T/(3 r0^2). The candidate solution reproduces the same two ingredients—framing them as norms of the forward map B and adjoint map A—and composes them to get exactly the same LG. The only omission in the model is to state the measured-output regularity that the paper uses to justify the gradient formula J′(F)=ϕ; otherwise, the proofs are essentially the same.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper rigorously establishes forward and adjoint estimates for a Kelvin–Voigt damped Euler–Bernoulli beam inverse problem and derives an explicit Lipschitz constant for the Fréchet gradient, which underpins monotone and convergent gradient-based algorithms. The argument is correct and the constants are explicit and useful. Minor clarifications would improve readability and implementation.