VMD-based theoretical calculation of the acoustic attenuation coefficient and pipeline leak localization

In the current research on pipeline leak localization based on acoustic attenuation characteristics, the calculation of the acoustic attenuation coefficient typically requires the collection of experimental leakage signals, which incurs additional economic and time costs. To address this issue, this paper proposes a theoretical method for calculating the acoustic attenuation coefficient based on Variational Mode Decomposition (VMD): First, a damped pipeline vibration equation is established based on the Timoshenko beam theory, and the frequency response function at different pipeline positions is calculated theoretically. The leakage signal is then decomposed into multiple scales using VMD. The main modal components of the leakage signal are extracted based on their peak frequencies and multiplied by the frequency response function to calculate the vibration response energy at various pipeline positions. Finally, a linear fitting is applied to obtain the theoretical solution for the acoustic attenuation coefficient. A pipeline leak localization experimental platform is constructed, and the theoretical solution for the acoustic attenuation coefficient is substituted into the localization formula for testing. The traditional method exhibits a mean localization error of 1.77%, increasing to a maximum of 2.69% under varying leakage conditions. In contrast, the proposed method achieves a mean error of 1.51%, with a maximum increase to 1.56%. These results demonstrate the superior accuracy and robustness of the theoretical calculation of the acoustic attenuation coefficient and the leakage localization method presented in this study. This study is significant for broadening the application of acoustic attenuation characteristics in leak localization scenarios.