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

Yelbek Bakhitovich Utepov, Shyngys Zharassov, Farit Abdushkurov

2026

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DOI 10.3390/eng7090439
Data confidence 70 medium
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Abstract

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.