Physics-informed acoustic metamaterials design via forward-inverse surrogate modelling for gearbox weak signal detection

Acoustic metamaterials have garnered significant research interest due to their unique wave-manipulation capabilities, with potential applications spanning noise control, subwavelength imaging, and non-destructive testing. However, conventional design paradigms rely on trial-and-error experimentation, biomimetic inspiration, and finite element analysis (FEA). These approaches suffer from three critical limitations, namely prohibitive experimental costs, serendipity-driven biological analogies, and computationally intensive simulation cycles. To address these challenges, this study proposes a surrogate model-driven framework for rapid optimal design and performance prediction of gradient acoustic metamaterials (GAM). Specifically, a bidirectional mapping between structural parameters and frequency response characteristics is established through three key innovations: 1) Systematic construction of parameter domains via rigorous screening of structural and frequency-response descriptors; 2) Implementation of Gaussian process regression to quantify nonlinear relationships between design variables and acoustic performance metrics while generating probabilistic predictions with error bounds; 3) Development of an uncertainty-aware prediction model that simultaneously outputs predicted values and confidence intervals, effectively bypassing computationally expensive FEA iterations. Experimental validation demonstrates exceptional accuracy and computational efficiency. Notably, the dual-output capability enhances engineering decision-making by quantifying design reliability, while maintaining physical interpretability through explicit parameter-performance correlations. This paradigm-shifting approach establishes a data-driven design framework for acoustic metamaterials, with methodological innovations readily generalisable to multifunctional metamaterial systems requiring performance predictability and design interpretability.