Reduced-Order Computational Modeling of Small UAV Acoustic Signatures and SNR-Based Passive Detection Range Using Harmonic Aeroacoustic Scaling

Abstract

Small unmanned aerial vehicle (UAV) acoustic signatures are relevant to environmental noise assessment, passive monitoring, and preliminary detectability analysis. This study presents a physics-informed reduced-order framework that combines blade-passing frequency (BPF) harmonic synthesis, rotational-speed acoustic scaling, propagation, and signal-to-noise ratio (SNR) threshold crossing. The RPM–OASPL law was calibrated using ten digitized measurements for a four-rotor DJI Phantom II with Original 9450 propellers and validated, without refitting, against eleven Aftermarket 9443 measurements. The fitted exponent was m = 5.285, and the fitted reference level was Lref = 77.01 dB(A) at 5000 RPM and 1 m. A 100,000-realization Monte Carlo analysis that propagated ±100 RPM and ±0.5 dB digitization bounds, together with residual scatter, produced total 95% intervals of 5.01–5.55 for m and 76.58–77.43 dB(A) for Lref. Calibration yielded RMSE = 0.39 dB and R2 = 0.9979; independent-configuration validation yielded MAE = 2.27 dB, RMSE = 2.38 dB, and R2 = 0.9168. At 5000 RPM, nominal free-field threshold-crossing distances were 70.9, 22.4, and 7.1 m for quiet rural, semi-urban, and urban scenarios. Combined statistical 95% screening intervals were 41.3–121.7, 13.0–38.5, and 4.1–12.2 m, respectively. Sensitivity analyses show that β controls harmonic-specific range but not normalized OASPL, while ground interference, band-limited masking, and detector processing can materially change operational range. The framework is therefore a rapid, interpretable screening tool rather than a universal detector performance model.