摘要
针对供水管道泄漏振动信号在分析型字典下进行压缩感知时,信号的重构均方误差较大和不能保留信号中重要泄漏信息的问题,提出了基于变分模态分解(VMD)和K-奇异值分解算法(K-SVD)的供水管道泄漏振动信号压缩感知方法。首先,利用VMD算法将管道泄漏振动信号分解若干个本征模态函数(IMF),并对IMF分量进行互相关性分析;然后,选取最优模态分量,构成最优模态集,再借助K-SVD学习算法训练过完备字典;最后,选择高斯随机矩阵为观测矩阵和重构算法为正交匹配追踪算法(OMP)对管道泄漏振动信号进行压缩感知。实验结果表明,基于VMD-K-SVD稀疏表示构造的过完备字典的压缩感知方法与基于FFT正交基、DCT正交基、K-SVD的压缩感知方法相比,在压缩率为50%~89.5%下重构均方误差更小和互相关系数更高,且在相同压缩率下得到的重构信号的互相关延时估计定位误差的平均值分别降低80.12%、64.2%、61.38%。因此,所提的压缩感知方法具有较好的重构性能和稀疏性。
Aiming at the problems that when compressed sensing of the leakage vibration signals in water-supply pipelines is conducted using an analytical dictionary, the reconstruction mean square error of the signal is relatively large and the important leakage information in the signal cannot be retained, this paper proposes a compressed sensing(CS) method for the leakage vibration signals of water-supply pipelines based on variational mode decomposition(VMD) and K-singular value decomposition(K-SVD) algorithm. Firstly, the VMD algorithm is used to decompose the pipeline leakage vibration signal into several intrinsic mode functions(IMF) and perform cross correlation analysis on the IMF components. Secondly, the optimal mode components are selected to form the optimal mode set, and then the K-SVD learning algorithm is used to train the over-complete dictionary. Finally, Gaussian random matrix is selected as the observation matrix and reconstruction algorithm is the orthogonal matching pursuit(OMP) algorithm, which are used to perform compressed sensing of the pipeline leakage vibration signals. The experiment results show that compared with the CS methods based on FFT orthogonal basis, DCT orthogonal basis and K-SVD, the proposed CS method using over-complete dictionary based on VMD-K-SVD sparse representation has smaller reconstruction mean square error and higher cross-correlation coefficient under the compression rate of 50%~89.5%, meanwhile, the average value of the cross-correlation based time-delay estimation positioning error under the fixed compression rate is reduced by 80.12%, 64.2% and 61.38%, respectively. Therefore, the CS method proposed in this paper has better reconstruction performance and sparsity.
作者
李帅永
毛维培
程振华
韩明秀
夏传强
Li Shuaiyong;Mao Weipei;Cheng Zhenhua;Han Mingxiu;Xia Chuanqiang(Key Laboratory of Industrial Internet of Things&Networked Control,Ministry of Education,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)
出处
《仪器仪表学报》
EI
CAS
CSCD
北大核心
2020年第3期49-60,共12页
Chinese Journal of Scientific Instrument
基金
国家自然科学基金(61703066)
重庆市基础研究与前沿探索项目(cstc2018jcyjAX0536)
重庆市科技重大主题专项(cstc2018jszx-cyztzxX0028)
重庆市研究生科研创新项目(CYS19271)
重庆市技术创新与应用示范项目(cstc2018jscx-msybX0022)资助
关键词
管道泄漏
压缩感知
变分模态分解
K-奇异值分解
过完备字典
pipeline leakage
compressed sensing
variational mode decomposition
K-singular value decomposition
over-complete dictionary
