Inverse Acoustic Localization of Pile-Driving Noise from Synchronized Multi-Receiver SPL Measurements

Construction noise assessment commonly assumes that the source location is already known, which limits its applicability when active equipment cannot be accessed or precisely surveyed. This study proposes a transparent inverse acoustic model for jointly estimating the location and time-dependent sound pressure level (SPL) of a pile-driving source from synchronized field measurements. Noise was recorded for 5 s at five GNSS-defined receiver positions on a construction site in Astana, Kazakhstan, producing 40 SPL values per receiver at 0.125 s intervals. The model applied spherical geometrical spreading and identified the source position by minimizing the disagreement among the distance-corrected source levels obtained from the receivers. The source was estimated at local coordinates [56.6, 113.8] m, with a Monte Carlo sensitivity analysis indicating a 95% confidence region of approximately 5–8 m under combined receiver-coordinate and SPL-measurement uncertainty. Its reconstructed SPL ranged from 81.6 to 99.9 dB(A) at the 1 m reference distance, while the equivalent source SPL was 90.4 dB(A). The measured impulsive pattern was preserved in the reconstructed source history, with dominant peaks occurring at approximately 1 s intervals. Comparison of measured and predicted receiver levels yielded an overall MAE of 1.3 dB(A) and RMSE of 1.6 dB(A), reflecting internal consistency between measured and reconstructed receiver levels. The as-driven pile position was subsequently surveyed independently, giving a true localization error of 2.3 m for the estimated position, within the 95% confidence region above. Out-of-sample cross-validation and synthetic sweep across the search zone further characterize the method’s identifiability and its expected sensitivity away from the search-zone center.