Research on denoising of second harmonic signal in photoacoustic spectroscopy based on SSA-VMD-WTD method

Aiming at the problem that second harmonics generated in gas measurement by photoacoustic spectroscopy (PAS) technology based on photoacoustic effect are susceptible to noise. In this paper, a method based on Sparrow Search Algorithm (SSA) optimized Variational Mode Decomposition (VMD) combined with Wavelet Threshold Denoising (SSA-VMD-WTD) was proposed to identify and suppress the noise. Firstly, the SSA algorithm optimizes the VMD parameters, and then the second harmonic signal with noise is decomposed by VMD. Secondly, the Intrinsic Mode Function (IMF) with a smaller Variance Contribution Rate (VCR) is removed, and the optimal mode function is selected to reconstruct the signal. Finally, the reconstructed signal is denoised by WTD, and the final denoised signal is obtained. The algorithm is applied to process simulated and experimental second harmonic signals separately. In the processing results of the simulated signal, it is observed that compared to three different algorithms, namely wavelet filtering, Savitzky-Golay (S-G) filtering, and complete ensemble empirical mode decomposition with adaptive noise and WTD (CEEMDAN-WTD), the proposed algorithm demonstrates more effective identification and noise suppression in the second harmonic signal. In the processing results of the experimental signal, the correlation coefficient (R2) between gas concentration and the maximum value of the second harmonic signal has been improved from the original value of 0.98144 to 0.99773. With the SSA-VMD-WTD enhancement, the optimized acetylene (C2H2) sensor features precision and stability in real-time measurements and achieves the minimum detection limit (MDL) of 7.82 ppm (1σ). The results indicate that the proposed denoising method can more effectively, stably, and accurately process noisy signals.