基于參數優化變分模態分解的信號降噪方法

摘" 要： 針對心電信號中肌電干擾噪聲難以去除的問題，提出一種基于參數優化變分模態分解（VMD）的信號降噪方法。通過設計動態邊界策略和反向種群生成方式，對白鯨優化（BWO）算法進行改進；采用改進白鯨優化算法對VMD參數自適應尋優，確定分解層數K與懲罰因子α；對含噪心電信號進行分解，得到k個本征模態函數（IMF）分量，同時采用相關系數法進行有效模態和含噪模態識別；對噪聲主導的模態分量采用小波閾值降噪，并重構信號主導模態與降噪后模態。對仿真信號與含真實肌電干擾的心電信號進行降噪處理，實驗結果表明，所提方法去噪效果優于小波閾值去噪法、EMD法、EMD?小波閾值去噪法，真實含噪的心電信號經該方法去噪后自相關系數可達0.91以上。

關鍵詞： 變分模態分解； 信號降噪； 參數優化； 改進白鯨優化算法； 心電信號； IMF分量； 小波閾值降噪； 肌電干擾

中圖分類號： TN911.7?34" " " " " " " " " " " " " "文獻標識碼： A" " " " " " " " " " " 文章編號： 1004?373X（2025）02?0070?07

Method of signal denoising based on parameter?optimized VMD

HE Yujie1， 2， LI Xin’e1， 2， HE Jun1， 2

（1. State Key Laboratory of Dynamic Measurement Technology， North University of China， Taiyuan 030051， China;

2. School of Electrical and Control Engineering， North University of China， Taiyuan 030051， China）

Abstract： In allusion to the problem of difficult removal of electromyographic interference noise in electrocardiogram （ECG） signals， a method of signal denoising based on parameter?optimized variational mode decomposition （VMD） is proposed. The beluga whale optimization （BWO） algorithm is improved by designing the dynamic boundary strategy and inverse population generation. The improved BWO algorithm is used for the adaptive optimization of the VMD parameters to determine the number of decomposition layers K and the penalty factor α. The noise?containing ECG signal is decomposed to obtain k intrinsic mode function （IMF） components， and the correlation coefficient method is used to identify the effective modes and noise?containing modes. The noise?dominated modal components are noise?reduced by means of the wavelet thresholding， and the dominant modes and noise?reduced modes of the reconstructed signal are reconstructed. The simulation signals and ECG signals with real EMG interference are processed for the denoising. The experimental results show that the proposed method is superior to wavelet threshold denoising method， EMD method and EMD?wavelet threshold denoising method， and the autocorrelation coefficient of real ECG signals with noise can reach more than 0.91 after denoising.

Keywords： variational modal decomposition; signal denoising; parameter optimization; improved beluga optimization algorithm; ECG signal; IMF component; wavelet threshold denoising; electromyogrophic interference

0" 引" 言

心電信號（Electrocardiogram， ECG）是診斷人體心血管疾病最為重要的生理參數之一，對心電信號的處理和分析具有極其重要的實用價值[1]。然而心電信號是一種微弱、非線性、非平穩的生理信號，在采集過程中，易受到被測者肌肉收縮所產生的肌電噪聲的干擾。肌電干擾信號頻帶較寬，頻率[2]通常為5～500 Hz，極易與心電信號發生頻譜混疊，因此成為心電信號去噪領域的難點問題。

心電信號肌電干擾的去除，目前常用的去噪方法有：小波閾值去噪法、經驗模態分解（Empirical Mode Decomposition， EMD）、變分模態分解（Variational Mode Decomposition， VMD）等。……