Adaptive Bayesian grid-free 3D acoustic source imaging for nose landing gear using No-U-Turn sampler

Conventional on-grid and off-grid methods for 3D acoustic source localization suffer from the curse of dimensionality, while existing grid-free approaches often lack adaptive sampling control and exhibit low efficiency. To address these limitations, an adaptive Bayesian grid-free 3D localization method based on the No-U-Turn Sampler (GF-NUTS) is proposed. Built upon the Bayesian inference framework grounded in equivalent source theory, the proposed method introduces the No-U-Turn Sampler to sample posterior distributions of source positions. This enables efficient exploration of high-dimensional parameter spaces via adaptive step size and step count control through binary tree recursion and dual averaging. Source strengths and noise variance are estimated through fixed-point iteration and projection-based inference, respectively. Finally, a potential-energy-based Bayesian Information Criterion is formulated for adaptive source enumeration. Simulation and experiments involving spatially distributed sources confirm that GF-NUTS outperforms existing on-grid, off-grid, and other grid-free methods in terms of localization accuracy, convergence reliability, and computational efficiency. Finally, the method is integrated with Proper Orthogonal Decomposition to identify and analyze aerodynamic noise sources in a nose landing gear model, enabling both localization and physical interpretation of narrowband and broadband noise mechanisms.