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Abstract
Remote sensing imaging technology is one of the most powerful tools for gas leak monitoring in chemical industrial parks. In the case of leaks, it is necessary to quickly and accurately obtain detailed information of the gas cloud (volume, distribution, diffusion situation and location). This paper proposes a 3-D quantitative reconstruction method for gas clouds. Two scanning Fourier transform infrared (FTIR) remote-sensing imaging systems were used to perform telemetry experiments in a monitored space with a total volume of 314.9 m3, and the released gases were SF6 and CH4. One scanning FTIR remote-sensing imaging system can only measure a 2-D concentration-path-length product (CL) image of a 3-D gas cloud, where each pixel has attitude information of elevation and azimuth. Geometric methods are applied to locate the monitored space and construct a 3-D grid (longitude, latitude, altitude). The optical path length (OPL) sparse matrix of each layer is generated, and the concentration distribution of each layer is reconstructed by the simultaneous algebraic reconstruction technique (SART). The reconstructed results of each layer are stacked into a 3-D gas cloud and displayed on the 3-D Earth software at a set threshold. Three-dimensional leaking gas clouds (CH4, SF6) with geometric information and concentration distribution has been generated through the above processes from measurement, localization to reconstruction and display. On the premise that the gas cloud is completely covered by the field of view of each scanning system, the localization and quantification of the gas cloud is available. Then weighted concentration centers can be calculated from these gas clouds to approximate the leak source. The proposed method effectively extends the online leak monitoring application of the scanning FTIR remote-sensing imaging system.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of society, many large storage tank farms have been built around the world to store toxic, harmful or flammable and explosive chemicals [1,2]. Especially in the energy industry, diesel, gasoline, jet fuel, heavy oil, aromatics and liquefied natural gas are all kept in storage tanks [3,4]. If a storage tank leaks, a series of chain reactions will cause serious damage to the surrounding residents and the environment [5,6]. Regular leak monitoring of storage tanks is one of the most effective ways to prevent hazardous incidents [7,8]. In the case of gas leakage, if the composition, concentration, location, distribution and propagation path of the leaked gas can be quickly found, then this information can be used for early warning, risk assessment and treatment of gas leaks.
Fourier transform infrared (FTIR) remote sensing is a comprehensive detection technology with great application prospects. Due to its advantages of high sensitivity, high resolution, noncontact and real-time measurement, it is widely used in the remote quantitative detection of polluted gases [9]. A scanning FTIR remote-sensing imaging system can obtain a concentration-path-length product (CL) image (2-D) in which a false-color image with CL information of the gas cloud is fused with a visible image of the scene. However, the CL image is the 2-D projection of the 3-D gas cloud [10–12]. From the CL image, only the gas leakage direction can be judged, but the specific leakage position in this direction cannot be determined. In addition, a scanning system can only measure the CL on the optical path and cannot obtain the spatial concentration distribution. Most of the existing problems that cannot be solved by a single measurement system are solved by using a combination of multiple measurement systems from different perspectives [13,14]. Todd [15] reconstructed 2-D/3-D gas concentration distributions by collaborating with multiple open-path FTIR spectroscopy and computer-assisted tomography. Wood [16] reconstructed the 3-D structure of a volcanic plume using several thermal infrared cameras.
Localization and quantification of leaking gas clouds by multiple scanning FTIR remote-sensing imaging systems have been partially studied. Rusch and Harig [17] proposed a method for 3-D reconstruction of gas clouds based on infrared spectroscopy and tomography. They reconstructed the ammonia plume from industrial chimneys by scanning the monitored space simultaneously with two SIGIS 2. The contour, location and apparent propagation direction of the ammonia gas cloud were obtained. Donato [18] performed an advanced 3-D reconstruction of a SO2 gas cloud detected in the atmosphere of the city of Nancy using SIGIS 2. A method combining triple correlation and 3-D interpolation was proposed. The silhouette of the SO2 gas cloud was 3-D reconstructed by one instrument at three different locations at different times. The existing methods described above for 3-D reconstruction of gas clouds can be further extended. In this paper, the elevation of optical paths is considered, each system is equipped with a high-precision nine-axis gyroscope to measure its own attitude. Therefore, it provides a strong support for the establishment of the 3-D grid of the monitored space. The values in the optical path length (OPL) sparse matrix are corrected by the elevation of each optical path, and the reconstruction results can be improved. Furthermore, it is necessary to more accurately find the leak source within the scope of the gas cloud, relying on the concentration information of the gas cloud.
A 3-D concentration reconstruction method of gas clouds based on multiple scanning FTIR remote-sensing imaging systems is proposed. Then telemetry experiments were carried out using SF6 and CH4 as tracer gases. The main purpose of these experiments is to obtain the volume, location, propagation situation and concentration distribution of the released gas cloud and to further determine the leak source on the basis of the 3-D gas cloud. This paper includes the entire process from gas cloud measurement to gas cloud reconstruction. Section 2.2 introduces the measurement process of the 3-D gas cloud including the acquisition of the geometric information of the monitored space and the collection of the spectral data cube. Section 2.3 describes the processing method of the gas cloud CL image. Section 2.4 explains the corner positioning method of the monitored space. Section 2.5 describes the reconstruction methods of 3-D gas clouds: division of the monitored space, generation of the OPL sparse matrix, and monolayer concentration reconstruction based on the simultaneous algebraic reconstruction technique (SART) [19–21]. Section 2.6 describes the application of quantitative gas clouds in leak detection. The main contribution of this paper is the realization of quantitative reconstruction and leak localization of 3-D gas clouds. An online detection method for gas leakage is provided for the normalized monitoring application of the storage tank area.
2. Materials and methods
All steps from measurement to reconstruction are described in Fig. 1 and can be divided into three major parts: the monitored space, the joint measurement of multiple scanning systems, and the 3-D reconstruction of the leaking gas cloud. Among them, the monitored space determines the scanning field of view of each system. In addition, each scanning system has the same structure and function, and is placed in different orientations of the monitored field to collect and analyze the raw data (location, attitude and radiation). The analysis data from each system is then transferred together for 3-D reconstruction.
Fig. 1. Schematic diagram of 3-D gas cloud generation from measurement to reconstruction based on multiple scanning FTIR remote-sensing imaging systems.
2.1 Scanning FTIR remote-sensing imaging system
The scanning FTIR remote-sensing imaging system (Fig. 2) consists of an FTIR interferometer, reflecting telescope, industrial camera, two degree-of-freedom (DOF) pan-tilt platform, global positioning system (GPS), nine-axis gyroscope, interferogram data acquisition and processing system, and desktop computer (DC). The spectral range of the spectrometer is 600–1800 cm−1, maximum spectral resolution is 1 cm−1, and scan rate for collecting 4 cm−1 spectra is 10 scan/s. The reflecting telescope has a maximum detection range of 5 km and a field of view of 7.5 mrad. The 2-DOF pan-tilt platform has an angular resolution of 0.01° and a field of regard of 360°×60°. GPS can obtain the coordinates of the system under the World Geodetic System 1984 (WGS84). A nine-axis gyroscope is used to measure the attitude (elevation and azimuth) of the scanning system. The industrial camera is composed of a CMOS image sensor and a 12-mm-focal-length lens, which can capture clear background images for long distances.
Fig. 2. (a) System connections in test scenario. (b) Scanning FTIR remote-sensing imaging system (product model: AG-FTIR-GS3000).
Two-dimensional projections of 3-D gas clouds are measured by a scanning FTIR remote-sensing imaging system. The system scans and remotely senses the monitored space according to the sampling array preset by the user with an infrared spectrometer. The radiance spectrum of each pixel is collected by the data acquisition and processing system and transmitted to the DC for component identification, quantitative analysis and false color display with CL information. In addition, the geometric information of each pixel (azimuth, elevation) is uploaded to the DC. After one pixel is measured, the scanning system drives the scanning mirror to point to the next pixel and generates a CL image of the gas cloud.
2.2 Three-dimensional gas cloud measurements
Figure 3 shows a working schematic diagram of two scanning FTIR remote-sensing imaging systems. The measurement process is as follows:
- (1) Two scanning FTIR remote-sensing imaging systems are placed in different directions of the monitored space. Then, the longitude and latitude of each instrument are collected.
- (2) The 2-D field of view of each system is set to ensure that the measurement areas overlap as much as possible in the elevation and azimuth intervals.
- (4) The infrared radiation of the pixel is preprocessed, and the transmittance spectrum is calculated online. Next, the transmittance spectrum is processed by the identification algorithm [10,22,23] for extracting the absorption or emission feature of the possible gas. The single-frame CL image of the identified gas is calculated and corrected by the method in Section 2.3.
After the above measurement process, the collected geometric parameters are as follows: (1) The longitude and latitude of system 1 and system 2. (2) Azimuth matrix and elevation matrix in the measurement area of system 1. (3) Azimuth matrix and elevation matrix in the measurement area of system 2. The interferogram cubes measured by system 1 and system 2. The identified components and their online generated gas CL images are equally essential.
2.3 CL image generation of gas clouds
Remote sensing of hazardous gases is based on the analysis of the infrared absorption and radiation characteristics of various molecules in the gas cloud. Figure 5 shows a simplified three-layer radiation transmission model. The infrared radiation received by the unit detector contains the spectral characteristics of the background, threat gas cloud and atmosphere. Radiation transmission theory [24] is used to describe the propagation process of radiation in the atmosphere, where the atmosphere and the threatening gas cloud layer can be regarded as homogeneous layers. Radiation from the background layer such as the sky, ground or a building, passes through the target gas cloud and atmosphere to reach the infrared detector [9–11].
Fig. 5. Three-layer radiation transmission model for passive FTIR remote sensing of polluted gas clouds.
In this model, the radiance ${L_1}(\nu )$ measured by the spectrometer is
If the radiance of the background and the temperature of the gas cloud are known, it is possible to calculate the transmittance. In many cases, it is not possible to measure the background spectrum. To meet the application requirements of online measurement, this paper uses a real-time background extraction method [25] from the measured spectrum. The blackbody radiance spectrum of the gas cloud can be estimated by the brightness temperature in the opaque spectrum of the atmosphere, and the background spectrum can be estimated by the brightness temperature of the transparent spectrum of the atmosphere. After acquiring the transmittance spectrum of the gas cloud, the Beer-Lambert law in Eq. (3) can be used to invert the CL of the target gas:
where CL is the concentration-path-length product, and $\alpha (\nu )$ is the absorption coefficient of gas molecules.Combining FTIR technology and scanning, we can obtain an infrared hyperspectral data cube. We assume that the dimension of the data cube is (m, n, s), where (m, n) is the spatial dimension and s is the spectral dimension. The inversion of the gas CL is performed by an iterative nonlinear least-square algorithm [26], which can be expressed as
2.4 Locate the monitored space
As shown in Fig. 6, it is assumed that system 1 is placed at point A, and system 2 is placed at point B. The angle DAE is the azimuth range of the field of view for system 1. The angle EBF is the azimuth range of the field of view for system 2. E2AE1 is the elevation range of system 1's field of view. Using the sine theorem, each corner of the monitored space can be determined by constructing a triangle. Next, measurement parameters such as latitude, longitude, azimuth and elevation are used to calculate the side length and angle of a triangle [27,28].
If the latitude and longitude of any two points are known (assuming M and N points), the distance between M and N can be calculated by the following formula:
2.5 Three-dimensional gas cloud reconstruction
The distance between the scanning system and the gas cloud is generally much larger than the size of the gas cloud, and the optical paths from the same system in the gas cloud can be considered to be approximately parallel. According to the positioning method in Section 2.4, the size of the space covered by the scan can be obtained, and the monitored space is divided into H layers in the vertical direction. Taking the center of the vertical projection of the monitored space (VPMS) as the reference point, the 2-D grid expands horizontally outward until it covers the intersection field. It is assumed that without considering the height of the single layer, the VPMS is 2-D discretized and divided into N unit grids (Fig. 7). It is considered that the gas concentration in each unit grid is evenly distributed, and the latitude and longitude of each unit grid are calculated. The gas concentration integral (O) on the i-th optical path where the optical axis of the infrared field of view of the scanning FTIR remote-sensing imaging system passes through the plane to be measured is discretized and expressed by the following formula:
where ${l_{ij}}$ is the OPL of the i-th optical path passing through the j-th unit grid, and ${c_j}$ is the gas concentration in the j-th unit grid.Considering the height of the single-layer grid, it cannot be guaranteed that all optical paths of the two systems in the same layer have equal elevation angles during the measurement process. Therefore, the elevation angles of optical paths from different systems in the same layer are different. Figure 7 shows a schematic diagram of the projection of the optical path. In addition, the level of system placement causes a difference in the elevation of each optical path on the same layer. Therefore, it is necessary to correct the OPL in a single-layer 3-D grid, and Eq. (15) can be rewritten as
where ${\theta _i}$ is the elevation of the i-th optical path relative to the horizontal ground. Within the same layer, the OPL of rays in each voxel are calculated one by one to obtain the OPL sparse matrix which is defined byThe number of spectra acquired by scanning FTIR remote-sensing imaging systems is limited. To solve the concentration vector C, the relationship between p and N needs to be considered. In most cases, p < N, Eq. (18) is transformed into a solution problem of sparse underdetermined linear equations. However, methods such as least squares and singular value decomposition are unstable for this problem, and reduce the reconstruction accuracy. Therefore, the SART algorithm is considered for the single-layer reconstruction of gas clouds, and has the advantages of high stability and strong robustness. SART combines the advantages of the ART and SIRT algorithms and achieves higher reconstruction accuracy. In addition, the number of iterations of the ART algorithm is reduced, and the computation of the SIRT algorithm is simplified. The iterative process is as follows:
2.6 Calculation of the weighted concentration center for gas clouds
The diffusion of leaking gas clouds satisfies the continuous-point-source Gaussian diffusion model [29–31]. The gas cloud spreads from the high-concentration area to the low-concentration area; the closer the leak source, the higher the concentration. The gas cloud concentration is combined with WGS84, and the weighted concentration center is used to further approach the leak source and narrow the search range. This is described in the following formula:
3. Field experiment
The field experiment was carried out in the suburbs of Hefei city on December 23, 2021. The instrument placement is shown in Fig. 8. Two AG-FTIR-GS3000 systems were arranged in different directions relative to the monitored field, and the scanning field of view of each system is set. Two gas cylinders containing high-concentration CH4 and two gas cylinders containing high-concentration SF6 were placed in the area to be monitored, and the height of the gas cylinder mouth was approximately 1 m above the ground. Before the experiment, the latitude and longitude values of each system were measured, and the distance between the two systems and the azimuth of the connection line were calculated. For the first time, the SF6 gas in the pressure vessel was released. An obstacle was placed 10 cm in front of the gas cylinder mouth so that the airflow was upward to form a gas cloud, and the released source was a continuous point source. As shown in Fig. 4, the two systems simultaneously scan the monitored space and measure infrared radiation, acquiring the attitude information of the system, including the azimuth and elevation. After synchronously scanning one frame, the spectral cube, elevation matrix and azimuth matrix of each system are obtained. As shown in Fig. 8, each corner point of the monitored space is calculated based on the middle and boundary of each system's field of view. The second time, the CH4 in the pressure vessel was released, and the above measurement process was repeated. The difference between the two experiments is the released gas, so the measured process data (Table 1) are consistent.
Table 1. Measured process data for two scanning systems
The infrared radiation measured at each pixel is converted into a spectrum and then transformed into absolute radiance by radiometric calibration. A three-layer radiative transfer model is used to invert the transmittance. The CL on the measurement optical path is acquired by fitting the measured spectrum to the reference spectrum using the nonlinear least-squares method. In Fig. 9(a), the measured transmittance has an obvious absorption peak of sulfur hexafluoride at 947 cm−1, and the inversion band of CL is selected at 912–968 cm−1. In Fig. 9(b), the measured transmittance has an obvious methane absorption peak at 1300–1310 cm−1, and the inversion band of CL is selected at 1220–1310 cm−1. Figure 10 is the fusion result of the gas CL and the background image generated by the processing flow in Section 2.3. In the measurement scenario of system 2, the temperature difference between the background and the gas cloud is low, and the inversion CL of methane (Fig. 10(d)) will be lower than the true value.
Fig. 9. Results of fitting calculation between measured transmittance and reference spectrum: (a) sulfur hexafluoride, (b) methane.
Fig. 10. Corrected CL images: (a) SF6 CL image measured by system 1, (b) SF6 CL image measured by system 2, (c) CH4 CL image measured by system 1, (d) CH4 CL image measured by system 2.
4. Results and discussion
Reconstruction focuses on 3-D grid division and establishment of an OPL sparse matrix at each layer. As shown in Fig. 8, the VPMS is divided into a 9×9 2-D grid with a cell width of 0.9 m. According to the two system positions, the azimuth of the optical paths and sine theorem, the OPL of each ray in a 2-D grid within 9×9 is calculated as an OPL sparse matrix M0. The monitored space is divided into 6 layers according to the elevation in the vertical direction, and the height of a single layer is 0.8 m. By matching the optical path of the same layer, the OPL sparse matrix Mi (i = 1, 2, …, 6) is corrected by M0 and the elevation of each optical path. The number of optical paths passing through single-layer 3-D grid is 23, and the single-layer grid has 81 voxels. Mi and CL are entered into Eq. (19) to solve for the i-layer grid concentration. The results of the single-layer reconstruction are arranged in a grid, and voxels with location and concentration information for each layer are stacked into a 3-D concentration cube. The method of layered reconstruction reduces the dimensionality of the OPL sparse matrix so that incoherent layers do not affect each other during reconstruction.
Fig. 11. Three-dimensional concentration distribution of SF6 gas cloud: (a)(b) side view of gas cloud displayed by 20% threshold, (c)(d) side view of gas cloud displayed by 50% threshold.
As shown in Fig. 11 and Fig. 12 (voxels are magnified approximately 1.5 times), the parameters of each voxel (longitude, latitude, altitude, concentration) are written in the keyhole markup language (KML) and displayed on Google Earth. Then, 20% and 50% of the maximum concentration are selected as the lower boundary of the gas cloud visualization, above which it can be displayed. This display mode can further narrow the scope of the gas cloud, which is convenient for finding the leak source. Comparing Fig. 10 with Fig. 11(c) and (d) and Fig. 12(c) and (d), the 3-D gas cloud displayed by the 50% threshold is consistent with the CL image, which shows that the reconstruction method is correct. The concentration inside the gas cloud is higher than the concentration outside the gas cloud, which satisfies the diffusion model of the gas. The detailed information that can be obtained from the reconstructed gas cloud is listed in Table 2. The latitude, longitude and concentration of each voxel are input into Eq. (20) and Eq. (21) in order to calculate the weighted concentration center. If we set a higher threshold, the cloud volume shrinks, and the average concentration increases. This is progressively closer to the source of diffusion and is consistent with the diffusion of the gas.
Fig. 12. Three-dimensional concentration distribution of CH4 gas clouds: (a)(b) side view of gas cloud displayed by 20% threshold, (c)(d) side view of gas cloud displayed by 50% threshold.
Table 2. Details of reconstructed gas cloud
The morphologies of the SF6 and CH4 gas clouds are described in detail, but the measurement field boundaries need to be considered. The concentration on the south side of Fig. 11(b) and Fig. 12(b) is relatively high, and there is a small part of the gas cloud outside the boundary of the field of view. When scanning systems perform leak monitoring in chemical parks, buildings, storage tanks, etc., can be used as a reference for setting the field of view. When the gas leak location and most of the gas cloud are in the monitored space, the conversion of the gas concentration unit from ppm·m to ppm is basically successful, and then the 3-D quantitative reconstruction of the gas cloud is completed. Furthermore, the accuracy of the layered reconstruction is less affected by the height boundary, especially the intermediate layers, which are not affected. During the measurement of multiple systems, the density of the intersecting optical paths in the monitored space is not equal. Therefore, the reconstruction accuracy of each voxel is also different, and increasing the number of measurement systems can improve the gas cloud reconstruction accuracy. In addition, if the gas cloud needs to be further refined, the gas cloud can be interpolated.
5. Conclusion
The proposed method further extends the application of scanning FTIR remote-sensing imaging systems to quantify and locate 3-D gas clouds. Multiple scanning systems were placed in different positions to measure the geometric and spectral information of the monitored space. Infrared spectra were stratified by geometric parameters. The SART algorithm was used to reconstruct the concentration distribution of each layer. Layered reconstruction greatly reduces the computational complexity, and the reconstruction process between layers does not affect each other. Relying on the measurement data of GPS and nine-axis gyroscope, we can accurately locate the size and corner of the monitored space. With the complete gas cloud covered by the crossed optical path, the source of the leak can be found by calculating the weighted concentration center. Finally, the combination of multiple scanning FTIR remote-sensing imaging systems, 3-D Earth Software, and the proposed method enables automated, online leak monitoring of the monitored space.
Funding
National Natural Science Foundation of China (41941011); Key Research Program of Frontier Science, Chinese Academy of Sciences (QYZDY-SSW-DQC016); National Key Research and Development Program of China (2019YFF0303400).
Acknowledgments
The authors would like to thank anonymous reviewers for their insightful comments and constructive suggestions.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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