We propose an adaptive algorithm that is a Variational Mode Decomposition (VMD) optimized by the particle swarm optimization (PSO) algorithm, named PSO-VMD. The method selects the envelope entropy of the last intrinsic mode function (IMF) in the VMD as the fitness function of the PSO and 1/10 of the maximum value of the correlation coefficient between the IMFs and the standard signal as the threshold of the correlation coefficient. In the processing of simulated and experimental second harmonic signals, a series of standards, including the same correlation coefficient threshold and standard signal, are used to adaptively achieve noise reduction processing. After processing a simulated signal using PSO-VMD, the signal-to-noise ratio (SNR) was improved by 4.03877 dB and the correlation coefficient (R2) between the gas concentration and the second harmonic maximum was improved from 0.97743 to 0.99782. In the processing of an experimental signal, the correlation coefficient (R2) was 0.99733. The mean value and standard deviation of the second harmonic signal of multiple cycles processed by PSO-VMD were improved compared to the unprocessed experimental signal. This demonstrated that the method has the advantage of being reliable and stable.

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We propose to replace the traditional time-frequency domain filtering with feature domain filtering to realize an innovation of filtering algorithm. A feature domain transform filter (FDTF) is composed of the feature domain transform layer based on principal component analysis (PCA) algorithm, the feature domain information extractor based on deep learning and the time domain transform layer. It is established to filter out the noise with the same frequency and phase as the signal and is verified on methane gas. Although FDTF is established based on the simulated data set, the filtering effects of the simulation test set and the experimental data set show that the proposed FDTF outperforms other widely used time-frequency filtering algorithms. The FDTF-assisted methane sensor has good linearity at different concentrations of methane gas. With the FDTF enhancement, the optimized methane sensor performs excellent precision and stability in real-time measurements and achieves the minimum detectable column density of 2.50 ppm• m. This is undoubtedly a successful attempt to move the signal to a new domain for parsing and separation.

The line width of different line shapes is a very important parameter in absorption spectroscopy sensing techniques. Based on the high sensitivity and low noise properties of wavelength modulation spectroscopy, we report a novel line width measurement method. After theoretically proving the relationship between line width, modulation amplitude and the amplitude of the second harmonic at the center frequency, the absorption lines of CH4 near 6046.96 cm−1 and CO2 4989.97 cm−1 were chosen for simulation, and the relative errors of the line width between our method and theoretical data were kept at about 1%. A distributed feedback laser diode operating near 1653 nm with three different concentrations of CH4 was used for experimental validation, and the results were consistent with the numerical simulation. Additionally, since only the peaks of second harmonic need to be measured, the advantages of wavelength modulation can be utilized while reducing the difficulty of data acquisition.

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