There are many methods for processing spectral data, such as least squares, artificial neural networks, etc. The core idea of the SVM algorithm is to map data into a high-dimensional space, making it easier for data to be separated in that space. In the spectral calculation process, due to the large amount of spectral data and high dimensionality, this algorithm is more suitable. Meanwhile, the SVM algorithm has strong generalization ability, making it more applicable when the type and concentration of mixed gases are unknown. After comprehensive comparison, it is believed that the SVM algorithm is the most suitable method in this system.

SVM is often applied to solve classification and regression problems, and it is suitable for the separation of multi-component gas. It has high applicability and robustness, and is suitable for multi-component separation situations. Assuming the training data (xi, yi), i = 1, 2, 3, …, n (n represents the number of samples), x _i and y _i belong to R, x _i is the sample input, y _i is the expected output, and its fitting function is f x = ω ⋅ x + b (1)

Among them, ω is the space hyperplane, and b offset.

According to the minimum structural risk criterion [20], it can be optimized as V = min 1 2 ω 2 + C ∑ i = 1 l ξ i + ξ i * (2)

And its parameters comply with: s . t . = y i − ω x i − b ≤ ε + ξ i , − y i + ω x i + b ≤ ε + ξ i * ξ i + ξ i * ≥ 0 i = 1,2 , . . . , l (3)

Among them, C represents the penalty factor, which is used to adjust the degree of punishment for sample error exceeding the limit; ξ represents the relaxation factor; Å represents an insensitive parameter used to reflect the system’s tolerance for errors. max − 1 2 ∑ i , j = 1 l α i − α i * α j − α j * x i ⋅ x j − ∑ i = 1 l α i ε + y i s . t . ∑ α i − α i * = 0 0 ≤ α i , α i * ≤ C i = 1,2 , . . . , l (4)

According to the test condition, the output can be calculated as follows: f x = ∑ i = 1 l α i − α i * x i ⋅ x + 1 N s ∑ S t s − ε − ∑ m ∈ S l α m − α m * x m ⋅ x S (5)

The formula for finding the optimal solution through information exchange between sample individuals is X i j k + 1 = X i j k + V i j k + 1 V i j k + 1 = c 1 r 1 P i j k − X i j k + c 2 r 2 P g j k − X i j k + σ V i j k (6)

Among them, i∈N (N represents the total number of particles), j represents the dimension, and σ represents the inertia weight; D represents the dimension; k. k + 1 represents the current and next iteration algebra, respectively; V _ij represents particle velocity; X _ij represents the particle position; P _ij and P _gj represent the extreme values of individuals and groups, respectively, while c ₁ and c ₂ represent the acceleration factor.

By setting constraints on the spectral characteristics of measured gas, the corresponding particles are mutated, thereby guiding the population to achieve the optimal convergence effect; The second is to improve SVM by setting a dynamic change insensitive region ε (y _i ) in support vector regression calculation, which is to replace ε (y _i ) in the original algorithm. On the basis of this improvement idea, Eq. 4 is replaced and simplified to obtain f x = ∑ i = 1 l α i − α i * x i ⋅ x + 1 N s ∑ S t s − ε y i − ∑ m ∈ S l α m − α m * x m ⋅ x S (7)

The introduction of ε (y _i ) can suppress the effect of over-learning model.The specific process for completing the optimization is shown in Figure 2.

When the incident light intensity I ₀ (λ) and transmitted light intensity I _t (λ), as well as the absorption coefficient and effective length L of the gas chamber, are known or can be calculated [21], the concentration of the measured gas c _CH4 can be expressed as c C H 4 = ln I t ν − I 0 ν α ν L (8)

In the formula, v represents the wavenumber, and it is the reciprocal of the wavelength. α (v) represents the absorption coefficient of light intensity. The light intensity between chamber 1 and 2 is I ₁₂. The light intensity between chamber 2 and 3 is I ₂₃. The light intensity between chamber 1 and 3 is I ₁₃.

With T ₁₃, Eq. 8 is substituted into: c C H 4 = ln ⁡ I 12 λ α ν L   T 13 ≥ T 0 (9)

When T ₁₃ > T ₀, it indicates that the absorption intensity of methane gas at this wavelength is positively correlated with methane concentration, and it is considered as a characteristic absorption wavelength with high contribution rate. When T ₁₃ < T ₀, it indicates that the absorption capacity of methane gas at this wavelength is relatively weak. There is the characteristic absorption, and it is susceptible to interference from other gases. Therefore, this wavelength is not selected during the testing and calculation processing, and zero value will be set for its concentration. The difference in light intensity within this range is calculated, and it can significantly suppress the interference of stray signals on the system.

The underground gas contains a large amount of coal dust, dust, and water vapor. So the measured gases are introduced into a filter for dust and moisture removal treatment, and they introduce into the gas chamber for detection. The testing mainly focuses on CH₄ (0%–10%), C₂H₆ (0%–1%), SO₂ (0%–1%), and CO₂ (0%–1%). A total of 800 sets of sample data were collected for the mixed gas, with 400 sets as the sample data and the rest as the test samples. Perform baseline correction, noise reduction, and normalization on the samples to complete the preprocessing of spectral data. It shows in Figure 3.

In Figure 3, the blue curve represents the relationship between the average relative error and the iteration number when traditional algorithms calculate methane concentration. The red curve represents the relationship between the average relative error and the iteration number when calculating methane concentration using this algorithm. In the first 20 iterations, the error of this algorithm decreased from 3.2 × 10⁻⁷ to 2.4 × 10⁻⁷, while the traditional algorithm remained almost unchanged during this stage. When the number of iterations exceeds 50, the error of this algorithm almost reaches a stationary state, with a value of 4.6 × 10⁻⁸. However, traditional algorithms achieve a stationary state through 100 iterations, with a value of 2.1 × 10⁻⁷. Thus, this algorithm has advantages in Rate of convergence and error.

In order to provide the model with fast and efficient prediction capabilities, independent modeling was conducted for different gas components. For the main detection gas CH₄, the particle swarm dimension was set to 2, with 20 particles per dimension. The optimization iteration was 200 generations, with an inertia weight of 0.9 and a termination value of 0.4, completing the generation by generation calculation. The particle swarm optimization error curve is obtained after optimization according to the above model. As shown in Figure 3, the improved particle swarm optimization algorithm only needs 43 steps to reach the global optimal solution, which has high convergence. The optimization time of the 200 generation is about 4,012 s, c = 58.46, σ = 4.67. By incorporating the optimization results into SVM, the predicted mean square error of the test sample is 4.8 × 10⁻⁸. At the same time, the same set of spectral data was separated and the concentrations of each component were inverted using a back propagation network (due to space limitations, only three typical values within the testing range were selected).

In experiments, the response voltage is tested with CH₄ concentration, and the test curve is shown in Figure 4A. The algorithm is used for proportional calculation, and the function curve between proportional value and CH₄ concentration is shown in Figure 4B.

In Figure 4A, when the response voltage increases, the concentration of CH₄ increases, too. There is a linear relationship between them. Its slope value is −0.0215, with good linearity. The sensor response and concentration change trend are consistent with the analysis results, and the curve is linear. Throughout the entire testing process, the maximum response voltage was 3775.217 mV and the minimum was 3551.060 mV. The fitted linearity is 0.9994, with relative errors less than 5.0%. It can be seen that the system linearity meets the design requirements.

In Figure 4B, it can be seen that the CH₄ concentration is linear with respect to the ratio of first harmonic to second harmonic, and the slope of the fitted polynomial is 8.752, with a linearity of 0.997. The linearity is relatively in the 0%–10.0% range, and it meets requirements. The maximum response voltage in the first harmonic is 4938.25 mV, and the minimum value is 4442.89 mV; The maximum response voltage in the second harmonic is 2694.24 mV, and the minimum value is 226.58 mV. It can be seen that there is a significant difference in the voltage ratio between the first and second harmonics, resulting in a significant improvement in their signal-to-noise ratio. Their relative errors are all less than 1.0%, and the testing stability has been improved.

When there is no methane gas, the second harmonic is not zero, which is caused by factors such as circuit and optical path noise, as well as nonlinearity of wavelength modulation. When calculating the ratio of second harmonic to first harmonic, the second harmonic amplitude value at each non-zero concentration should be subtracted from the second harmonic amplitude value in the absence of methane, and then divided by the first harmonic amplitude at that concentration to obtain a result that is closer to the actual concentration value. From the table, it can be seen that when the concentration of methane gas is 1%, the measurement error is the largest.