Near-Infrared Laser Methane Remote Monitoring Based on Template Matching Algorithm of Harmonic Signals

Abstract

Trustworthy technology for the monitoring of fugitive methane emissions is an indispensable component for low−carbon emission reduction and safe production in oil and gas infrastructure. A miniaturization and low-cost methane remote monitoring prototype based on near-infrared laser absorption spectroscopy is developed to retrieve the path−integral concentration by employing the harmonic conjoint analysis method for the backscattered echo signals from a distant non-cooperative target. A distorted harmonic template matching (DHTM) algorithm is proposed based on wavelength modulation spectroscopy with second harmonic normalized via the first harmonic (WMS−2f/1f) method, which suppresses the output concentration fluctuation caused by open path monitoring with non-cooperative target and avoids the issue of false alarms during the detection process without target gas. The reliability of the WMS−2f/1f−DHTM algorithm is verified by calibration and dynamic experiments. The results showed that this algorithm avoids the dilemma of false alarms in the absence of gas compared to the conventional WMS−2f/1f algorithm, while the root mean square error (RMSE) of the concentration inversion with a detection distance of 20 m is reduced by 57.6% compared to direct absorption spectroscopy (DAS) algorithm. And the minimum detection limit of system is 3.79 ppm·m. The methane telemetry sensor with the WMS−2f/1f−DHTM algorithm exhibits substantial application potential in carbon monitoring of oil and gas industry.

1. Introduction

Methane is a short−lived climate pollutant that has a significant impact on climate change in the short term, unlike longer−lived greenhouse gases [1]. The oil and natural gas industrial supply chain represents a major contributor of fugitive methane emissions that cannot be overlooked [2,3]. Most methane emissions in oil and gas systems are from a small number of high−emitting sources, including compressor equipment leaks within the upstream oil/gas station, especially from solution gas in heavy oil production [4]. Due to the stochastic nature of these emissions, frequent monitoring is needed to identify and mitigate emissions from oil and gas infrastructure.

Traditional detection methods such as electrochemical and semiconductor techniques involve direct contact and close-range sensing, necessitating the entry of personnel into the leaking environment to collect gas samples [5,6,7]. This type of detection method not only exposes the personnel to hazardous methane leak environments, compromising their safety, but it also fails to enable precise monitoring of methane concentration levels in oil and gas field stations. In contrast, optical spectroscopy techniques based on open-path have gradually become some of the most promising solutions for highly efficient and sensitive standoff trace gas detection. Researchers have developed differential optical absorption spectroscopy (DOAS) and Fourier transform infrared (FTIR) spectroscopy systems that utilize sunlight, lamps, or LEDs as light sources to simultaneously measure column concentrations of various trace gases [8,9,10,11]. However, broad-spectrum light sources hinder the improvement of spectral resolution, thereby limiting the spectral selectivity or detection resolution. Additionally, the complex structure and bulky size of FTIR and DOAS systems make them inconvenient for mobile measurement. Surface−enhanced Raman spectroscopy (SERS) [12] and coherent anti−Stokes Raman scattering (CARS) [13] and other Raman spectroscopy techniques provide rich molecular vibrational information along with many advantages in terms of ultrahigh sensitivity and exclusive detection. However, these methods are primarily applied for near-field detection or require sample preprocessing, making it challenging to adapt them for remote detection of industrial hazardous gases in daytime outdoor environments and indoor lighting conditions [14]. Recently, remote solar-blind ultraviolet (UV) Raman spectroscopy has been widely used because of its advantages compared to visible or near-infrared approaches [15,16,17]. Their advantages include a strong resonance effect, lack of interference from ambient light, and relative safety for the human eye. Nonetheless, investigating the impact of reducing UV laser path scattering on the detection sensitivity for industrial standoff applications remains a challenge to be broken [18]. A research group at the National Key Laboratory of Science and Technology on Tunable Laser has been focused on the light-induced thermoelastic spectroscopy (LITES) sensor used for trace gas detection, which used a commercially available piezoelectric element quartz−crystal tuning fork (QCTF) to replace traditional photodetectors for collecting detection signals [19,20,21]. The QCTF detector not only has the narrow resonance width to suppress background acoustic noise, but also has no response wavelength limit. Furthermore, compared with the quartz−enhanced photoacoustic spectroscopy (QEPAS) technique, LITES represents a truly non−contact measurement method [22]. Despite the advantages of high sensitivity and low cost, LITES would encounter some challenges when used for non-cooperative target telemetry. It relies on perfect surface reflection to provide sufficient photons for photo-thermal generation and quartz tuning fork excitation, which also limits its expansion to non-cooperative target on−site applications. Methane remote sensing technology based on non-cooperative targets and tunable diode laser absorption spectroscopy (TDLAS) facilitates non-contact and long−distance detection [23,24]. Laser technology eliminates the need for specific optical reflection backgrounds and allows responders to detect gas remotely so that the detection personnel need not carry the gas detector into the combustible gas plume or even enter the “kill box” [25]. Consequently, unmanned real-time monitoring of environmental methane concentrations in oil/gas station can be achieved.

TDLAS technology can be classified into two categories: wavelength modulation spectroscopy (WMS) and direct absorption spectroscopy (DAS) [26]. In comparison to DAS technology, WMS technology has the capability to eliminate low-frequency noise caused by external environmental interference [27]. The core of TDLAS−WMS technology lies in the extraction of the first harmonic and second harmonic signals. In a controlled gas cell environment, high signal-to-noise ratio harmonic signals can be obtained effectively by suppressing system noise. However, in an open-path environment, especially in remote monitoring applications, interference from background light noise and uncontrollable environmental noise can distort the harmonic signal waveform [28,29,30,31]. This distortion becomes more pronounced when the concentration of the trace methane is at low levels. In our previous testing experiments, we discovered that distorted harmonic signals lead to significant nonlinear deviations in the concentration inversion process, rendering existing linear concentration inversion models unsuitable for trace concentration levels [32]. Furthermore, in the absence of methane gas testing, random fluctuations in the background signal can generate amplitude parameters required for wavelength modulation concentration inversion, leading to the concentration indications in zero gas detection that should not appear [33]. However, to the authors’ knowledge, most prior studies of wavelength modulation spectroscopy optimizing method are focused on reducing various types of harmonic signal noise including white noise, 1/f noise, and fringes noise [34,35,36,37]. For distorted harmonic signals that already exist before data preprocessing, denoising tools cannot accurately restore them to the original waveform, but instead generate interference signals that affect normal concentration inversion.

The main contributions of this paper are as follows. A near-infrared remote monitoring system utilizing TDLAS technology is developed by targeting the absorption line at 1653.7 nm to detect fugitive methane emissions. A distorted harmonic template matching algorithm is proposed based on the wavelength modulation spectroscopy with second harmonic normalized by the first harmonic method, which suppresses the output concentration fluctuation caused by open path monitoring with non−cooperative target and avoids the issue of false alarms during the detection process without target gas. A prototype of the methane telemetry sensor system is self−made, and the performance is evaluated in the laboratory to verify the effectiveness of the WMS−2f/1f−DHTM algorithm. During the monitoring experiment period, a methane gas cell with 200 ppm·m concentration is used as an experimental subject to evaluate the dynamic measurement stability and compare it with the other concentration inversion algorithms.

2. Methodology and Experimental Setup

2.1. Concentration Inversion Based on Harmonic Conjoint Analysis

The theory of WMS has been studied and reported extensively, but enough is reproduced here to define terms and allow the reader to understand the details of the sensor design. WMS utilizes modulation of the output wavelength by the light source to convert the information−carrying signal into a high−frequency signal. The instantaneous laser frequency and intensity of a current−tuned tunable diode laser are governed by:

$$v(t)=\overline{v}(t)+a\cos (\mathsf{\omega }t)$$

(1)

$$I_0(t)={\overline{I}}_0(t)+i_1\cos (\mathsf{\omega }t+{\mathsf{\psi }}_1)$$

(2)

where v is modulation frequency of laser;?v is center frequency of the laser; a is modulation depth; ω is sine modulation frequency; I₀ is modulation intensity of laser; ${\overline{I}}_0$ is average intensity of laser at center frequency; i₁ is linear intensity modulation amplitude; and ψ₁ is linear intensity modulation phase shift. The nonlinear intensity modulation terms have been omitted as they tend to be insignificant at the moderate modulation depths used for WMS at or below atmospheric pressures [38].

The TDLAS technology is based on the Beer–Lambert law, which relates the incident laser intensity I₀(t) and transmitted laser intensity for WMS:

$$I_{\mathrm{t}}(t)=[{\overline{I}}_0(t)+i_1\cos (\mathsf{\omega }t+{\mathsf{\psi }}_1)]\exp \left[-k\left(\overline{v}\left(t\right)+a\cos \left(\mathsf{\omega }t\right)\right)L\right]$$

(3)

If the slow−scan time dependence is neglected, the gas spectral absorption coefficient k is even and can be expanded using the Fourier cosine series:

$$-k\left(\overline{v}\left(t\right)+a\cos \left(\mathsf{\omega }t\right)\right)L={\displaystyle \sum _{n=0}^{\infty }{H}_n(\overline{v},a)\cos (n\mathsf{\omega }t)}$$

(4)

$$H_0(\overline{v},a)=-\frac{PXL}{2\mathsf{\pi }}{\displaystyle {\int }_{-\mathsf{\pi }}^{\mathsf{\pi }}{\displaystyle \sum S\cdot \mathsf{\phi }(\overline{v}+a\cos (\mathsf{\omega }t))}}d\mathsf{\omega }t$$

$$H_n(\overline{v},a)=-\frac{PXL}{2\mathsf{\pi }}{\displaystyle {\int }_{-\mathsf{\pi }}^{\mathsf{\pi }}{\displaystyle \sum S\cdot \mathsf{\phi }(\overline{v}+a\cos (\mathsf{\omega }t))}}\cdot \cos (n\mathsf{\omega }t)d\mathsf{\omega }t$$

In Equation (4), H_n is the Fourier series expansion coefficient of absorption coefficient, and for trace gas with low concentration, there is H_n ≪1 (n = 1, 2,…) [39]. The N−th harmonic component can be described as:

$$H_n(\overline{v},a)=-\frac{PSXL}{2\mathsf{\pi }}{\displaystyle {\int }_{-\mathsf{\pi }}^{\mathsf{\pi }}\mathsf{\phi }(\overline{v}+a\cos (\mathsf{\omega }t))d\mathsf{\omega }t}$$

(5)

$$H_n(\overline{v},a)=-\frac{PSXL}{\mathsf{\pi }}{\displaystyle {\int }_{-\mathsf{\pi }}^{\mathsf{\pi }}\mathsf{\phi }(\overline{v}+a\cos (\mathsf{\omega }t))\cos (n\mathsf{\omega }t)d\mathsf{\omega }t}$$

(6)

where X is the volume fraction concentration of measured methane; P is the static pressure; L is the total path length through the absorbing medium; and S is the line strength of transition for methane absorption line. It can be seen from Equation (6) that the amplitude of Fourier coefficient of absorption coefficient is directly proportional to the product of gas concentration and optical path. The first harmonic signal (1f) and second harmonic signal (2f) are extracted from electrical signals by using Fourier transform. The 1f−normalized 2f signal is now described by:

$$S_{2f/1f}=\frac{S_{2f}}{S_{1f}}=\frac{\frac{G{\overline{I}}_0}{2}{H}_2}{\frac{G{\overline{I}}_0}{2}{i}_1}=\frac{H_2}{i_1}=\frac{PXLS}{\mathsf{\pi }{i}_1}{\displaystyle {\int }_{-\mathsf{\pi }}^{\mathsf{\pi }}\mathsf{\phi }}(\overline{v}+a\cos (\mathsf{\omega }t))\cos (2\mathsf{\omega }t)d\mathsf{\omega }t$$

(7)

where G is the optical–electrical gain of the detection system. It can be seen from Equation (7) that the WMS−2f/1f method effectively eliminates the influence of the light intensity fluctuation on the methane remote sensing results. However, the absorption loss can cause distortion of the harmonic signal, which affects the measurement accuracy.

2.2. Template Matching Algorithm for Distorted Harmonic

The template matching method has become increasingly mature in microseismical detection and recognition of radar signals and various biological signals [40,41]. However, it has not been applied in the recognition of distorted harmonic signals in TDLAS gas detection. This is where the innovation of this work lies. The similarity between the measurement signal and the template signal can be determined by calculating their correlation in a specified range. In this study, the normalized correlation coefficient is used to measure the similarity between the measurement signal and the template signal.

Assuming there are two time series signals, denoted as x(t) and y(t), if one of the signals is expanded by a factor of a, then the error energy between the two signals can be calculated as follows [42]:

$${\mathsf{\epsilon }}^2={\displaystyle \sum _{-\infty }^{\infty }{\left[x\left(t\right)-ay\left(t\right)\right]}^2}$$

(8)

In order to compare the similarity between these two signals, it is necessary to minimize the error energy. Therefore, we have the following equation:

$$\frac{d{\mathsf{\epsilon }}^2}{da}=2{\displaystyle \sum _{-\infty }^{\infty }\left[x\left(t\right)-ay\left(t\right)\right]\cdot \left[-y\left(t\right)\right]=0}$$

(9)

By further calculations, we obtain the expressions for a as well as the minimum error energy, which are as follows:

$$a=\frac{{\displaystyle \sum _{-\infty }^{\infty }x\left(t\right)y\left(t\right)}}{{\displaystyle \sum _{-\infty }^{\infty }{y}^2\left(t\right)}}$$

(10)

$${\mathsf{\epsilon }}^2={\displaystyle \sum _{-\infty }^{\infty }{x}^2\left(t\right)}-\frac{{\left[{\displaystyle \sum _{-\infty }^{\infty }x\left(t\right)y\left(t\right)}\right]}^2}{{\displaystyle \sum _{-\infty }^{\infty }{y}^2\left(t\right)}}$$

(11)

To obtain the relative minimum error energy based on the energy of signal x(t), it can be calculated as follows:

$$e_{\min }{}^2=\frac{{\mathsf{\epsilon }}^2}{{\displaystyle \sum _{-\infty }^{\infty }{x}^2\left(t\right)}}=1-\frac{{\left[{\displaystyle \sum _{-\infty }^{\infty }x\left(t\right)y\left(t\right)}\right]}^2}{{\displaystyle \sum _{-\infty }^{\infty }{x}^2\left(t\right)}{\displaystyle \sum _{-\infty }^{\infty }{y}^2\left(t\right)}}$$

(12)

where

$${\mathsf{\rho }}_{xy}^2=\frac{{\left[{\displaystyle \sum _{-\infty }^{\infty }x\left(t\right)y\left(t\right)}\right]}^2}{{\displaystyle \sum _{-\infty }^{\infty }{x}^2\left(t\right)}{\displaystyle \sum _{-\infty }^{\infty }{y}^2\left(t\right)}}$$

(13)

ρ_xy is referred to as the normalized correlation coefficient or coherence coefficient. When one of the time series signals is moved, the coherence coefficient becomes a coherence function, denoted as:

$${\mathsf{\rho }}_{xy}^2(\mathsf{\tau })=\frac{{\left[{\displaystyle \sum _{-\infty }^{\infty }x\left(t\right)y\left(t+\mathsf{\tau }\right)}\right]}^2}{{\displaystyle \sum _{-\infty }^{\infty }{x}^2\left(t\right)}{\displaystyle \sum _{-\infty }^{\infty }{y}^2\left(t\right)}}$$

(14)

The correlation function between x(t) and y(t) is denoted as:

$$r_{xy}(\mathsf{\tau })={\displaystyle \sum _{-\infty }^{\infty }x\left(t\right)y\left(t+\mathsf{\tau }\right)}$$

(15)

The correlation function is, in fact, the coherence function normalized within the range of [–1, 1]. When the time lag τ is 0, the coherence function represents the conventional cross−coherence coefficient [43]. Since the values of the correlation function are dependent on the magnitude of the time series signals, it is difficult to compare the degree of correlation between different sets of signals. On the other hand, the magnitude of the coherence function is independent of the signal values, enabling it to represent both in−phase coherence and time−delay coherence. Therefore, the coherence function is chosen as the criterion for judging template matching.

The computation of traditional correlation functions is achieved through direct convolution, which is computationally intensive, time consuming, and lacks real−time performance [44]. However, the computation of cross−correlation and autocorrelation functions can be obtained using the fast Fourier transform (FFT). Since the coherence function and coherence coefficient are both related to the correlation function, it is possible to utilize FFT to calculate the normalized correlation function and coherence coefficient. In this way, first, the correlation function is computed using FFT, and then the coherence function and coherence coefficient can be obtained from the correlation function, thereby deriving the cross−coherence coefficients. This method significantly reduces the computational workload and improves processing speed.

The template matching method based on waveform−normalized cross−correlation coefficients is utilized for the identification of distorted harmonic signals. The principle of this algorithm is as follows: the measurement signal is analyzed using a template matching algorithm. If its cross−correlation coefficient with the template signal meets the predetermined threshold range, it is identified as a valid harmonic signal; otherwise, it is considered a distorted harmonic signal. The distorted harmonic signals are eliminated from the system’s computational program, and only the valid harmonic signals are used in the WMS−2f/1f method to estimate the methane concentration. During this process, distorted signals generated by environmental noise and fluctuating signals produced under no absorption conditions are not used for concentration inversion. The specific steps involved in the analysis and identification process are as follows:

(a) Template generation: Create a representative template signal that represents the desired harmonic waveform. This template signal will be used as a reference for comparison with the input signal. The flowchart of 1f and 2f template signals generation processing is shown in Figure 1. The self−made methane telemetry sensor system is utilized to measure methane samples with different standard concentrations (e.g., 200 ppm·m, 600 ppm·m, 1400 ppm·m, and 1800 ppm·m). The entire signal collection process uses the experimental platform introduced in Section 3.1. The measurement process is conducted under controlled laboratory conditions, resulting in the acquisition of legible waveform samples for the 1f and 2f signals. The 1f and 2f signals under each concentration condition are obtained by averaging 30 measurements, and we define them as the raw harmonic signals. Normalizing the harmonic signals is essential to compensate for any variations in signal amplitude. This step ensures that the raw signals are adjusted to a consistent scale, making them comparable and eliminating the influence of amplitude fluctuations. Ulteriorly, the normalized raw signals are subjected to a Hanning window function, and the data at both ends of the waveform are set to zero to obtain standard harmonic signals. As shown in Figure 2, the standard harmonic signals from methane of variable concentrations are subjected to average processing to obtain the template signals, including the waveform for the 1f and 2f signals.

(b) Data preparation: The measured signals are collected and preprocessed by the self−made methane telemetry sensor system. The impact of noise and other factors that might distort the measurements to a significant extent has already been minimized through the adaptive wavelet denoising procedure, providing a more reliable foundation for the subsequent cross−correlation calculations. Similarly to step (a), the measurement signals will also undergo normalization and Hanning window processing. These preprocessing steps ensure that the signals are appropriately scaled, synchronized, and have reduced spectral distortions caused by the finite duration of the signals, enhancing the accuracy and robustness of the subsequent computations.

(c) Cross−correlation calculation: The FFT is employed to compute the auto−power spectrum and cross−power spectrum of the measured signal and the template signal. Subsequently, an inverse fast Fourier Transform (IFFT) is applied to obtain the auto−correlation function and cross−correlation function of the measured signal and the template signal. Finally, the cross−correlation function is utilized to obtain the cross−coherence function, which ultimately yields the normalized correlation coefficient. The flowchart for calculating the normalized correlation coefficient is shown in Figure 3.

(d) Signal identification: Compare the cross−correlation coefficient obtained from computing the measured signal with the template signal to a preset threshold (in this work, the threshold is chosen as 0.85). It is worth noting that during the threshold setting process for harmonic signal identification, a high threshold will reduce the recognition rate, while a low threshold will result in lower accuracy. The threshold in this work is determined based on extensive experimental testing and optimization analysis. If the threshold is surpassed, it indicates a successful match between the measured signal and the template signal, and it is determined as a desired waveform for the 1f and 2f signals. Otherwise, classify the input signal as the distorted harmonic pattern.

(e) Concentration inversion: After the template matching process, the selected 1f and 2f measurement signals are considered suitable for further analysis and concentration inversion calculations. Here, the measurement signal refers to the initial signal acquired by the sensing system, which has undergone noise reduction processing but does not include the normalization and windowing processes mentioned in Step (b).

2.3. Methane Telemetry Sensor System Configuration

The self−made methane telemetry sensor system based on TDLAS−WMS technology is shown in Figure 4, which consists of a sophisticated combination of optical, mechanical and electrical components. The choice of the center wavelength of emitted laser depends on the characteristic absorption frequency of the target gas (i.e., methane in this work). According to the selection principle of absorption line that should meet stronger absorption line intensity and minimal interference from other perimeter substances, a TO−39 package distributed feedback (DFB) laser diode (EP1654−DM−TP39, Eblana Photonics Ltd., Dublin, Ireland) is used as the light source. The selected DFB laser diode with a central output wavelength of 1653.7 nm and a typical power of 6.5 mW. The divergent light emitted from DFB laser diode is collimated to a parallel beam through the aspheric lens pre−mounted in Ø12 mm adjustable collimation tube, where the aspheric lens is anti−reflection coated for etalon suppression. A N−BK7 biconvex lens (d = 50 mm, f = 50 mm) is fixed directly below the adjustable collimation tube to receives the backscattering light from the targets. Ultimately, the weak light containing methane concentration information is converged into the TO−49 package InGaAs PIN photodiode (LSIPD−L2, Beijing Lightsensing Technologies Ltd., Beijing, China) and transformed into the original electrical signal for the subsequent circuit processing system. Moreover, the sensor is generally exposed to an ambient background containing stray light that overlaps the response band of photodiode. Therefore, an IR bandpass filter (FB1750−500, Thorlabs Inc., Newton, NJ, USA) placed at the front end of the active area of photodiode to reject other unwanted radiation. The electrical unit is composed of three circuit modules, namely a laser driving and signal generation module, a photoelectric detection and pre−amplification module, and an integrated signal processing module that enables harmonic demodulation, concentration inversion, general packet radio service (GPRS) communication and power supply. The accuracy of TDLAS is particularly susceptible to harmonic signal waveform, and therefore, the template matching algorithm is utilized before each concentration inversion to filtrate the distortion elements in the measured 1f and 2f signal sequence.

3. Results

3.1. Calibration of the Methane Telemetry Sensor System

Differently from traditional TDLAS sensor systems that measure gas concentration using the amplitude of the 2f signal, in this work, the methane laser remote sensing system utilizes the 1f signal to normalize the 2f signal, mitigating the impact of intensity modulation on the optical power signal. As shown in the following Figure 5, the signal receiving experiment of the methane laser telemetry system was performed in the hallway of NEPU Chemical Laboratory building. The laser platform is mounted on a movable tripod, and the non−cooperative target of painted metal plate was on a fixed mount standing at the end of the hallway. The distance measured with a laser rangefinder is 20 m with precision of ±2 mm. To simulate gas leak scenarios in industrial environments, transparent gas cells made of polytetrafluoroethylene (PTFE) are placed in the optical path of the system. The dimensions of the gas cells are 12 × 8 × 10 cm³, resulting in an effective optical path length of 0.08 m. Different concentrations of methane gas samples (0 ppm·m, 600 ppm·m, 1000 ppm·m, 1400 ppm·m, and 1800 ppm·m) are generated using a dynamic gas mixing system, with nitrogen gas serving as the background gas. These methane gas samples were then filled into gas cells for the purposes of calibration experiments. The obtained results at a telemetry distance of 20 m are shown in Figure 6. The correlation coefficient R² is 0.997, indicating a superior linear relationship between the obtained 2f/1f signal and the path−integral concentration. The relative error of concentration inversion of the result at 0~1800 ppm·m is between 0.36% and 14.75%. When positioning gas cells containing varying concentrations, even a slight disparity in the incident angle can lead to inconsistent optical path lengths, resulting in a minor impact on the outcome of linear regression.

3.2. Algorithm Experimental Verification

To the validate the reliability of the WMS−2f/1f algorithm based on distorted harmonic template matching (WMS−2f/1f−DHTM), a dynamic measurement at a detection distance of 20 m and using non−cooperative targets of painted metal plate is conducted, contrasting with DAS and conventional WMS−2f/1f algorithms. The DAS algorithm is provided by a commercial methane laser telemetry instrument (PGLD200, Huayee Technology Co., Ltd., Hefei, China) that employs a calibration method based on fitting the integrated area of absorption peaks, while the WMS algorithm is implemented by shielding the template matching algorithm based on our developed system.

As shown in Figure 7a, continuous data collection of an authenticated 200 ppm·m methane gas is performed by switching the gas cell insertion and removal path to generate a step signal excitation. Starting from 20 s, the gas cell is placed in the optical path, resulting in a rapid increase in measured concentration. After maintaining this state for 20 s, the gas cell is removed, and the condition is eventually returned to the zero−value test state. In the zero−value testing stage, compared to the DAS and WMS−2f/1f−DHTM algorithms, the inversion result obtained by using the WMS−2f/1f algorithm is not zero. This result will lead to incorrect judgments for operators in practical applications. This phenomenon also exists in the research results of Li et al. [33]. The main reason is that the fluctuation of light intensity during the measurement process introduces invalid signals, and the amplitudes of these invalid signals are also blindly used in the concentration inversion step based on the WMS−2f/1f algorithm. The WMS−2f/1f−DHTM algorithm utilizes distorted signal template recognition programs to avoid this phenomenon. Due to the etalon effect of the gas cell, there is a fluctuation phenomenon in the concentration output indication. The concentration inversion RMSE based on the WMS−2f/1f−DHTM algorithm is the minimum in the comparison results, which is 57.6% lower than the DAS algorithm with the maximum RMSE. The measurement error results, as shown in Figure 7b, lead to the conclusion that the concentration inversion obtained through the WMS−2f/1f DHTM algorithm is more consistent with the actual gas concentration and exhibits a smaller error range. Therefore, WMS−2f/1f−DHTM algorithm is a superior sensing performance improvement method to reduce the output fluctuations for the remote gas detection under a non−cooperative target.

Dynamic testing experiments revealed that the WMS−2f/1f−DHTM algorithm exhibited more reliable results than the WMS−2f/1f algorithm in zero−value testing. In order to quantitatively analyze the false alarm resistance performance of the WMS−2f/1f−DHTM algorithm, a mobile scanning detection experiment is designed using a gas cell array. As shown in Figure 8, gas cells filled with methane at different concentrations are arranged in a row, with values of 650, 0, 150, 0 and 480 ppm·m from left to right. The width of each gas cell is 10 cm, and the adjacent two gas cells are tightly attached through opaque partitions. The methane telemetry sensor is mounted on a movable platform on a slide rail, and the sensor scanned the gas cell array at a forward speed of 4 cm/s driven by a stepper motor. The detection distance is set at 5 m for this experiment, and a painted metal plate is also used as a non−cooperative target. The sampling measurement time is set to 0.5 s, and the measurement value of the center position of each gas cell can be obtained using the displacement velocity of movable platform. Under the same experimental procedures and laboratory environment, five sets of testing data are recorded using the WMS−2f/1f−DHTM and WMS−2f/1f algorithms, as shown in

Table 1. Mobile scanning detection results obtained using WMS−2f/1f and WMS−2f/1f−DHTM algorithms.

	Gas Cell 1	Gas Cell 2	Gas Cell 3	Gas Cell 4	Gas Cell 5
	[ppm·m]
Test 1	642.78	0	156.95	0	451.87
	660.53	6.87	161.49	1.25	447.79
Test 2	679.25	0	140.18	0	465.02
	612.43	11.26	141.54	0	468.43
Test 3	690.71	0	156.65	0	508.75
	626.64	0	153.28	5.61	497.32
Test 4	619.77	0	155.57	0	467.47
	699.46	−2.88	162.12	0	526.71
Test 5	634.66	0	147.27	0	495.22
	697.97	1.64	139.77	−4.55	450.96

. The false alarm rate (FAR) refers to the probability at which an algorithm incorrectly identifies an event as present when it is, in fact, absent. Based on the obtained test results, it can be calculated that the WMS−2f/1f−DHTM algorithm consistently achieved an FAR of 0. In contrast, the WMS−2f/1f algorithm exhibited an FAR of 28%. This significant difference highlights the superior false alarm resistance performance of the WMS−2f/1f−DHTM algorithm. The obtained data supports the notion that the WMS−2f/1f−DHTM algorithm is more reliable and dependable in terms of minimizing false alarm detections, making it a preferable choice for applications performing accurate and robust detection of fugitive methane emissions monitoring.

3.3. Detection Limit Analysis

The detection limit of the methane telemetry sensor system with the WMS−2f/1f−DHTM algorithm and the influence of noise on the detection accuracy can be evaluated through Allan deviation analysis. The Allan variance analysis involves calculating the variance of the measured signal as a function of the integration time. The variance provides information about the stability and noise characteristics of the measurement over different time scales. The test data are recorded from continuous measurement of 1500 ppm·m concentration of methane at a detection distance of 20 m. And the Allan deviation as a function of integration time is plotted in Figure 9. The sensitivity of methane is 88.26 ppm·m at the integration time of 0.2 s. As the integration time increases, the behavior of the Allan deviation follows a pattern similar to 1/√τ, suggesting the prevalence of white noise, or random signal, as the dominant noise source during this period. This plot typically exhibits a decreasing trend at short integration times, reaches a minimum, and then increases at longer averaging times. The detection limit is 3.79 ppm·m at the optimal integration time of 100 s. This point indicates the averaging time beyond which the measurement noise dominates the signal and accurate detection becomes challenging. The main cause of this phenomenon is attributed to system drift, which encompasses frequency drift of the DFB (Distributed Feedback) laser diode and temperature drift of the electronic components.

In order to evaluate the measurement frequency of the methane telemetry sensor under the atmospheric turbulent activity, an analysis of the power spectral density related to methane concentration is performed using the Fourier transform method based on the 300 s monitoring data from the methane laser remote sensor. The obtained relation curve between power spectral density and frequency is plotted on a logarithmic coordinate system, as shown in Figure 10. The outdoor monitoring site is located at the test group of Third Daqing Oilfield Production Factory, Daqing City, Heilongjiang, China (46°41′39.3′′ N, 124°59′15.4′′ E). During the testing process, the temperature is 27.6 °C, the air pressure is 100.83 kPa, and the wind speed is 3.27 m/s. The measurement frequency of the sensor system is F_s = 10 Hz, so the cut−off frequency of the power spectral density is F_c = F_s/2 = 5 Hz. The downward slope of methane concentration power spectral density basically satisfies the “Kolmogorov −5/3 law” in the inertial sub region [45], which verifies that the developed prototype is suitable for measuring high−frequency methane emission flux in atmospheric turbulent environments using the gas turbulent diffusion (GTD) model method. It is worth noting that we are currently conducting research on the quantification of methane emission flux in oilfield sites based on the near−field Gaussian plume inversion (NGI) technique. And the significance of this work lies in providing a monitoring equipment foundation with reliable performance.

4. Conclusions

In this work, a telemetry sensor system is developed to monitor fugitive methane emissions based on near−infrared laser absorption spectroscopy technology. In order to untangle the knot of decreased reliability of concentration indication caused by random signal fluctuations, the WMS with second harmonic normalized by the first harmonic method combined with distorted harmonic template matching algorithm are employed to identify the desired weak harmonic signal from a multisource interference background. This self−made methane telemetry sensor system adopts a digital embedded circuit module and a compact single lens optical receiving module, achieving miniaturization and low−cost system integration. And the calibration of the sensor is implemented proactively in the laboratory and the results display a linear correlation coefficient R² of 0.997 between the WMS−2f/1f amplitude and methane path−integral concentration. The reliability of the WMS−2f/1f−DHTM algorithm is verified by a methane gas cell switching measurement experiment between 0 and 200 ppm·m. In the zero−value test state, this algorithm avoids the dilemma of false alarms in the absence of gas compared to the conventional WMS−2f/1f algorithm, while the RMSE of the concentration inversion with a detection distance of 20 m is reduced 57.6% compared to DAS algorithm. Furthermore, the limit of detection reaches a minimum of 3.79 ppm·m with a 64.8 s integration time via Allan deviation analysis. In addition, the WMS−2f/1f−DHTM algorithm demonstrates compatibility across various TDLAS systems utilizing wavelength modulation, facilitating the monitoring of other hazardous or greenhouse gases of interest by simply replacing the laser with different wavelengths. This flexibility enables the system to cater to specific requirements. Consequently, the methane telemetry sensor with the WMS−2f/1f−DHTM algorithm exhibits substantial application potential within the carbon emission monitoring field.