VMD与时间-空间分数阶扩散模型联合分段TEM滤波  

Segmented TEM filtering combined with VMD and time-spacefractional-order diffusion model

作　　者：谭超[1] 谭继伟 沈艳军[1] 袁永榜 欧星作 闵薪宇 孙其浩 TAN Chao;TAN Jiwei;SHEN Yanjun;YUAN Yongbang;OU Xingzuo;MIN Xinyu;SUN Qihao(School of Electrical Engineering and New Energy,Three Gorges University,Yichang 443002,P.R.China;CCTEG Chongqing Research Institute,Chongqing 400039,P.R.China)

机构地区：[1]三峡大学电气与新能源学院,湖北宜昌443002 [2]中煤科工集团重庆研究院有限公司,重庆400039

出　　处：《重庆邮电大学学报(自然科学版)》2025年第2期204-214,共11页Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition)

基　　金：国家自然科学基金项目(62273200)。

摘　　要：为滤除瞬变电磁(transient electromagnetic method,TEM)信号中的噪声,提出一种变分模态分解(variational mode decomposition,VMD)与时间-空间分数阶非线性扩散模型(time-space fractional-order diffusion model,TSFDM)的分段滤波方法。针对TEM信号的特点,将采样信号进行动态阈值分段处理;采用VMD对每一段信号自适应分解,保留第一个内涵模态(intrinsic mode function,IMF)分量作为初次滤波数据;分别使用差分离散和使用带位移的Grunwald-Letnikov逼近法来近似求解时间-空间分数阶扩散方程的时间Caputo分数阶导数和空间Riemann-Liouville分数阶导数,建立迭代收敛差分方程,设置平滑算子得到TSFDM滤波器;利用叠加平均法对TSFDM迭代计算得到的二次滤波信号进行拼接得到完整TEM信号。仿真结果表明,使用所提方法后,整体信号质量提高约22 dB,后期信号信噪比提高约38 dB,与原始信号接近;与传统方法相比,所提方法各项评价指标更优;实测TEM信号中衰减特征被保留,有效还原了频域曲线变化趋势。To eliminate noise in transient electromagnetic(TEM)signals,this paper proposes a segmented filtering method based on variational mode decomposition(VMD)and a time-space fractional nonlinear diffusion model(TSFDM).Considering the characteristics of TEM signals,the sampled signal is dynamically segmented using a threshold-based approach.VMD is then applied to each segment for adaptive decomposition,retaining the first intrinsic mode function(IMF1)as the initial filtered data.The time Caputo fractional derivative and spatial Riemann-Liouville fractional derivative in the time-space fractional diffusion equation are approximated using the discrete difference method and the displaced Grunwald-Letnikov approximation method,respectively.An iterative convergence difference equation is established,and a smoothing operator is applied to construct the TSFDM filter.The second-stage filtered signals obtained through TSFDM iterative computation are stitched together using the superposition averaging method to reconstruct the complete TEM signal.Simulation results show that the proposed method improves overall signal quality by approximately 22 dB and enhances the signal-to-noise ratio(SNR)of later-stage signals by approximately 38 dB,bringing it close to the original signal.Compared to traditional methods,the proposed approach achieves superior evaluation metrics.Additionally,the attenuation characteristics of measured TEM signals are preserved,effectively restoring the variation trend of the frequency-domain curve.

关 键 词：瞬变电磁信号(TEM)滤波 变分模态分解 阈值分段 时间-空间分数阶扩散模型(TSFDM) 差分方程 

分 类 号：TN911.7[电子电信—通信与信息系统]