Leakage problems are common in the water supply pipeline system, which will threaten the health of residents and cause economic losses. Negative pressure wave (NPW) technology calculates the time difference through the inflection point to locate the leak. However, due to the nonlinear and nonstationary characteristics of the pressure signal, it is difficult to obtain an accurate inflection point of the NPW by the traditional method. Therefore, the advantages of applying variational mode decomposition (VMD) in NPW technology are explored. Firstly, the correlation coefficient and permutation entropy (PE) are used for effective intrinsic mode function (IMF) component selection and parameter optimization. Thus, an adaptive denoising method based on VMD (AD-VMD) is presented. Then, to effectively separate the detail features of the NPW, a novel inflection point extraction method based on VMD (IPE-VMD) is proposed. Simulation and experimental results show that AD-VMD can effectively suppress noise interference and conserve the mutation characteristic of the leakage. IPE-VMD can obtain a distinct maximum peak at the inflection point and has good robustness to noise interference. This method can calculate the time difference precisely and stably. In addition, the accuracy of the leak location is verified. The average relative positioning error is 5.13%.

中文翻译：

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VMD在基于负压波的管道泄漏检测中的应用

供水管道系统普遍存在渗漏问题，会威胁居民的身体健康，造成经济损失。负压波 (NPW) 技术通过拐点计算时间差以定位泄漏。然而，由于压力信号的非线性和非平稳特性，传统方法难以获得准确的NPW拐点。因此，探讨了在 NPW 技术中应用变分模式分解 (VMD) 的优势。首先，相关系数和置换熵（PE）用于有效的本征模式函数（IMF）组件选择和参数优化。因此，提出了一种基于VMD（AD-VMD）的自适应去噪方法。然后，为了有效地分离 NPW 的细节特征，提出了一种新的基于VMD的拐点提取方法(IPE-VMD)。仿真和实验结果表明，AD-VMD可以有效抑制噪声干扰，并保持泄漏的突变特性。IPE-VMD 可以在拐点处获得明显的最大峰值，对噪声干扰具有良好的鲁棒性。这种方法可以精确、稳定地计算时差。此外，还验证了泄漏位置的准确性。平均相对定位误差为5.13%。这种方法可以精确、稳定地计算时差。此外，还验证了泄漏位置的准确性。平均相对定位误差为5.13%。这种方法可以精确、稳定地计算时差。此外，还验证了泄漏位置的准确性。平均相对定位误差为5.13%。