Sparrow search algorithm (SSA) - optimized singular value decomposition (SVD) - wavelet denoising (wD) for the determination of methane using wavelength modulation tunable diode laser absorption spectroscopy (TDLAS) with second-harmonic signals

Methane second-harmonic (2f) signals in wavelength-modulation tunable diode laser absorption spectroscopy (WMS-TDLAS) are susceptible to random noise, fringes, and baseline drift. A denoising method combining singular value decomposition (SVD) and wavelet transform (WT), with joint parameter selection by the sparrow search algorithm (SSA), is proposed. Hankel-SVD reconstruction precedes scale-dependent continuous exponential thresholding. A four-component no-reference objective evaluates residual background noise, high-frequency roughness, baseline drift, and peak preservation. At an input signal-to-noise ratio (SNR) of 5 dB, output SNR was 12.387 ± 0.831 dB. The root-mean-square error (RMSE) and normalized cross-correlation coefficient (NCC) were 0.010827 and 0.972482, respectively. In ablation tests, SSA-SVD-WT achieved the highest mean output SNR and NCC and the lowest mean RMSE across the six configurations. On paired inputs, a long short-term memory denoising autoencoder (LSTM-DAE) gave the best waveform recovery, whereas SSA-SVD-WT approached reference-assisted IGWO-VMD-SG at 5 and 10 dB. Using measured CH4 transmittance spectra and an independently calibrated full-waveform template, numerical WMS validation yielded a 6.377 ppm concentration RMSE, a 1.899 ppm mean bias, and R2 = 0.999243 over 100–500 ppm. No clean references or paired training data are needed for parameter selection.