JEOS RP ISSN03 | Page 135

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J. Eur. Opt. Society-Rapid Publ. 22, 13( 2026)

Table 1. Inverted kinematic parameters and validation against AIS( Mean ± SD over 10 independent runs).

interference patterns and the hyperbolic nature of the moveouts. To avoid the local minima that are inherent to gradient-based methods in such rugged landscapes, we employed Differential Evolution( DE) [ 10 ], a robust stochastic global optimization algorithm. The vessel state is defined by the parameter vector m =[ v s, h 0, z s, f 0, L s, W s, c ] T, representing the speed, angular offset, source depth, fundamental frequency, vessel length, vessel width, and spreading coefficient, respectively. The search space is bounded by physically constrained limits( e. g., v s 2 [ 1, 20 ] m / s) to ensure the algorithm converges to realistic solutions.

Using a classic DE / rand / 1 / bin strategy, the algorithm evolves a population of candidate vectors over successive generations. A mutant vector v i; g is generated for each target vector m i; g by mixing three random population members:

� v i; g ¼ m r1; g þ F m r2; g � m r3; g; ð3Þ

where F is the differential scaling factor. Binomial crossover is then performed to create a trial vector, which replaces the target vector only if it yields an improvement in the objective function.

To address the lack of absolute amplitude calibration in DAS data( which can vary due to fiber coupling and signal fading), we chose to optimize for structural similarity rather than absolute intensity. We minimize a correlation-based loss function J ðmÞ:

Jðm

Þ ¼ 1 � CovðSðmÞ; RÞ; ð4Þ r S r R

where S( m) is the simulated field generated by the candidate parameters, R is the observed experimental data, and r denotes the standard deviation. This scale-invariant metric ensures the model locks onto geometric features – such as the hyperbolic curvature and interference nulls – independent of the overall signal magnitude.

5 Material and methods

5.1 Data acquisition

The experimental data was acquired using a standard commercial DAS interrogator unit connected to a bottommounted submarine telecommunications cable. The interrogator’ s pulse repetition rate yielded a temporal sampling frequency f s sufficient to capture the acoustic spectrum of vessel noise, while the optical gauge length L g provided a spatial sampling resolution of approximately 9.8 m.

5.2 Signal preprocessing pipeline

Before the optimization process, the raw optical phase data undergoes a rigorous, multi-stage preprocessing pipeline designed to maximize the Signal-to-Noise Ratio( SNR) and ensure statistical consistency with the forward model. Raw DAS data is typically dominated by high-amplitude, low-frequency environmental noise, such as ocean swell and hydrostatic pressure variations(< 1 Hz). To isolate the specific mechanical signature of the vessel, we applied an 8th-order Butterworth bandpass filter with a passband of [ 2, 120 ] Hz. This range was selected to capture the fundamental engine harmonics and propeller blade pass frequencies while effectively rejecting microseisms and highfrequency system noise.

Following filtration, we addressed the computational constraints imposed by the high sampling rates of DAS systems. We performed temporal decimation immediately following the anti-aliasing filter to reduce the computational load of the fitness evaluation function. For datasets with high SNR( Case B), the raw coherent strain was used directly. However, for lower SNR scenarios( Case A), we computed the Hilbert envelope of the signal. This transformation focuses the optimizer on the energy distribution of the acoustic arrival rather than the rapidly oscillating phase carrier, significantly improving convergence stability in noise-limited regimes. Finally, because the correlation-based loss function requires that the simulated and experimental data share comparable statistical properties, we applied a Z-score standardization to the preprocessed data matrix D, subtracting the global mean l D and dividing by the standard deviation r D. To prevent transient artifacts( e. g., system glitches or dropped channels) from skewing the correlation metric, the data was robustly clipped to the 99th percentile. This ensures the optimization surface remains smooth and gradients are driven by the persistent vessel wake geometry.

6 Results

The efficacy of the proposed model was assessed via wavefield reconstruction and validation against independent AIS