High-precision leakage detection in fresh-air ducts: an adaptive wavelet denoising approach with enhanced energy tracking

Abstract Conventional wavelet denoising methods based on hard and soft threshold functions exhibit significant limitations in terms of signal discontinuity and systematic deviation, resulting in compromised signal smoothness and reconstruction fidelity. To address these challenges, this paper proposes a novel wavelet denoising method incorporating three key innovations: (1) An adaptive threshold calculation method is proposed, which is based on all wavelet coefficients across different decomposition levels to achieve cross-scale noise suppression; (2) To overcome the critical drawbacks of traditional threshold functions, a novel continuous nonlinear threshold function is developed. The proposed method simultaneously eliminates the discontinuity associated with hard thresholding and corrects the systematic bias caused by soft thresholding; (3) An adaptive energy detection algorithm is proposed to further improve the time positioning accuracy of the denoised signal. This algorithm autonomously tracks signal energy fluctuations and dynamically optimizes detection thresholds in real-time, achieving unprecedented accuracy in rising edge identification. Finally, the proposed method is evaluated on a real-world fresh-air duct leakage dataset and compared against five baselines. The experimental results demonstrate that the proposed wavelet threshold denoising method outperforms all baseline methods across the established evaluation criteria. Furthermore, the proposed energy detection algorithm achieves a remarkable time positioning error of only 0.0009 s, significantly surpassing the performance of the traditional envelope method. These findings conclusively validate the robustness and practical efficacy of the proposed method for accurate leakage detection in complex multi-source noise environments characteristic of fresh-air duct systems.