Propeller signal denoising based on improved principal component analysis algorithm of VMD

For nonlinear and non-stationary signals, traditional principal component analysis (PCA) shows limitations when dealing with highly correlated intrinsic mode functions (IMFs). To address these issues, variational mode decomposition (VMD) is used to process measured propeller sound signals and extract high-precision sound features, by effectively suppressing modal aliasing and endpoint effects. Kernel principal component analysis (KPCA) is introduced to propose an improved algorithm. The proposed method uses adaptive kernel selection and a feature retention strategy to enhance noise reduction performance and feature extraction accuracy. Compared with two other denoising methods, the proposed VMD + optimized KPCA approach reduces parameter dependency and computational complexity. The experimental results show that the improved KPCA algorithm substantially reduces computational time, effectively suppresses noise redundancy, enhances signal clarity, and exhibits superior robustness. The method achieves signal-to-noise ratio (SNR) improvements of up to 3.59 dB and root mean square error (RMSE) reductions of up to 0.32 for both simulated and measured signals. Under identical conditions, the average CPU time required to process every 10k samples is only 25.1 ms, representing reductions of ~29.7% and 15.7% compared with VMD-wavelet (35.7 ms) and VMD–PCA (29.4 ms), respectively.