Environmental vibration reconstruction induced by shield tunneling based on a transfer function framework

Abstract In shield tunneling construction, on-site vibration monitoring is strongly influenced by background noise. To improve the accuracy of vibration signal estimation, this study proposes a transfer-function-based method for reconstructing environmental vibrations induced by shield tunneling under background noise conditions. The method further evaluates multiple combinations of signal-to-noise ratios ( $$\\:SNR$$ ) and sample sizes ( $$\\:M$$ ), validates the results against existing numerical simulations, and performs a systematic error analysis. The results show that: (1) The method exploits the statistical independence between the excavation source signal and environmental background noise, by constructing an estimated transfer function $$\\:{H}^{*}\\left(k\\right)$$ , signal-noise separation is achieved without requiring prior knowledge of the noise distribution; (2) The reconstruction error exhibits pronounced frequency-domain dependence. Under the 5 Hz excitation considered in this study, the relatively small errors are mainly concentrated within 4–6 Hz around the source frequency. Under $$\\:SNR$$ = 40 dB and $$\\:M$$ = 400, the relative-amplitude error remains below 1% over 0–10 Hz. The maximum instantaneous velocity difference between the reconstructed signal and the numerical simulation result is 1.9%, confirming the reliability of the method in time- and frequency-domain reconstruction; (3) Increasing the sample size ( $$\\:M$$ ) and the signal-to-noise ratio significantly suppresses incoherent noise. When $$\\:M$$ = 100, the absolute error decreases by 84.9% compared with the single-sample estimate; further increasing $$\\:M$$ to 400 leads to a plateau in accuracy improvement. The proposed method provides a theoretical framework for extracting shield-induced vibration signals in complex urban monitoring environments.