A method for reconstructing concentration field of surface leakage point of natural gas storage micro-leakage

Abstract

This invention discloses a method for reconstructing the surface leak point concentration field of a natural gas storage facility with micro-leakage, belonging to the field of storage facility safety monitoring and gas diffusion simulation technology. It includes: inputting real-time sparse sensor data into a pre-trained surface leak point concentration field reconstruction model, and outputting the surface leak point concentration field reconstruction result; training the surface leak point concentration field reconstruction model includes: cleaning historical sparse sensor data to obtain cleaned data; eliminating non-physical structures in the cleaned data based on multiple explicit diffusion iterations, and directionally eliminating false closed contour lines in the cleaned data based on a contour line tracing algorithm to generate an initial concentration field; generating a physical simulation dataset based on leak point information using a pre-constructed high-fidelity gas diffusion simulator; and training the surface leak point concentration field reconstruction model using the physical simulation dataset and the initial concentration field to obtain a trained surface leak point concentration field reconstruction model. This invention can achieve high-fidelity, physically compliant concentration field reconstruction.

Description

Technical Field

[0001] This invention relates to the field of gas storage safety monitoring and gas diffusion simulation technology, and in particular to a method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities. Background Technology

[0002] Natural gas storage facilities are mostly built deep underground, covering an area of ​​tens of square kilometers. They are core infrastructure for national energy strategic reserves, and their operational safety is directly related to the stability of energy supply and the safety of the surrounding ecological environment. Because these storage facilities are buried deep underground, once a leak occurs, the gas's upward migration path to the surface is complex, making it difficult for traditional methods to directly pinpoint the leak location on the surface. Tracer detection, which involves injecting sulfur hexafluoride (SF6) gas tracers underground, utilizes its chemical inertness, low background concentration, and easy detection properties. After the tracer is fully mixed with the underground stored gas, multiple detection points are set up on the surface. By detecting the surface concentration distribution of the tracer, the location and extent of the underground leak can be determined. This method has become an important means of monitoring micro-leaks in gas storage facilities.

[0003] However, surface tracer detection at gas storage facilities faces several engineering challenges: First, gas storage facilities occupy large areas, and due to cost constraints, surface detection points are sparse (typically only 4-12). Traditional Kriging and linear interpolation methods, lacking physical constraints under sparse point conditions, are prone to producing non-physical artifacts such as false closed contour lines and concentration gradient breaks, leading to misjudgments of leak sources. Second, surface detection instruments are affected by environmental factors such as temperature, humidity, wind speed, and terrain undulations, resulting in biases or anomalies in some detection data. Purely data-driven deep learning models have poor generalization ability under noisy and sparse sample conditions, and are prone to non-physical oscillations in detection blind areas, outputting prediction results that violate the laws of gas diffusion. Furthermore, existing combinations of gas diffusion simulation and deep learning models are mostly limited to a two-stage separate architecture of data generation and model training, lacking a unified framework that integrates diffusion physics laws throughout the entire process of data preprocessing, data augmentation, and model inference. Additionally, research on lightweight models for edge computing devices at gas storage facilities is lacking, failing to meet real-time monitoring requirements. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities. The method embeds Fick's diffusion law into the entire process from data processing and dataset construction to model training, and achieves high-fidelity and physically compliant concentration field reconstruction under extremely sparse sensor input conditions.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] This invention provides a method for reconstructing the concentration field of surface leak points in micro-leaks of natural gas storage facilities, including:

[0007] Acquire real-time sparse sensor data at the gas storage site;

[0008] The real-time sparse sensor data is input into a pre-trained surface leak point concentration field reconstruction model, and the surface leak point concentration field reconstruction result is output.

[0009] The training of the surface leak point concentration field reconstruction model includes:

[0010] Acquire historical sparse sensor data from the gas storage site;

[0011] The historical sparse sensor data is cleaned to obtain cleaned data;

[0012] The initial concentration field is generated by eliminating the non-physical structure of the cleaned data through multiple explicit diffusion iterations and by directionally eliminating false closed contour lines in the cleaned data based on the contour line tracking algorithm.

[0013] The pre-built high-fidelity gas diffusion simulator generates a physical simulation dataset containing different wind speeds, wind directions, and leakage source intensities based on leak point information;

[0014] The surface leak point concentration field reconstruction model is trained using the initial concentration field and physical simulation dataset, enabling the model to establish a preliminary mapping capability from sparse sensor data to a dense concentration field, thus obtaining a trained surface leak point concentration field reconstruction model.

[0015] Optionally, the real-time sparse sensor data includes real-time sensor latitude and longitude coordinates and real-time gas concentration readings.

[0016] Optionally, the historical sparse sensor data is cleaned to obtain cleaned data, including:

[0017] Historical sparse sensor data that exceeds the preset physical reasonable range is marked and removed. Invalid historical sparse sensor data is filled in using the nearest neighbor filling method to obtain clean data.

[0018] Optionally, an initial concentration field is generated by eliminating the non-physical structure of the cleaned data through multiple explicit diffusion iterations and by directionally eliminating spurious closed contour lines in the cleaned data using a contour tracing algorithm, including:

[0019] Non-physical structures in the cleaned data are eliminated through multiple explicit diffusion iterations. In each iteration, the gas concentration is diffused from the high-value region to the low-value region to dissolve isolated closed contour coils.

[0020] The algorithm of contour line tracking is used to eliminate false closed contour lines in the cleaned data. Tangential smoothing is performed along each gas concentration contour line to eliminate false jagged contour lines between sparse data points and generate an initial concentration field.

[0021] The formula for the multiple explicit diffusion iterations is:

[0022] ;

[0023] in, They represent the first sequence Interpolated concentration field after explicit diffusion iteration; Indicates the diffusion smoothing coefficient; Represents the gradient operator; express Spatial heterogeneity diffusion coefficient of location.

[0024] Optionally, the formula for the high-fidelity gas diffusion simulator is:

[0025] ;

[0026] ;

[0027] in, express time The gas concentration at the location; express Two-dimensional wind field vector at location; Represents the gradient operator; express Spatial heterogeneity diffusion coefficient of location; Indicates the source of the leak; Indicates the overall attenuation coefficient; Indicates the basic diffusion coefficient; Represents the coupling coefficient; These represent the maximum and minimum values ​​of wind speed amplitude within the current wind field, respectively. express Spatial heterogeneity perturbation term of location.

[0028] Optionally, a pre-built high-fidelity gas diffusion simulator generates a physical simulation dataset based on leak point information, including different wind speeds, wind directions, and leak source intensities, including:

[0029] For scenarios with leakage, reflection boundary conditions, gradient vanishing boundary conditions, and a soft truncation mechanism based on the tanh function are used on the computational grid of the target area to handle the concentration range, solve the high-fidelity gas diffusion simulator, obtain the gas concentration value at each grid location in the target area, and generate a physical simulation dataset containing different wind speeds, wind directions, and leakage source intensities.

[0030] For leak-free scenarios, a computational grid of multiples of the target area is constructed, and a virtual leak source is set outside the grid area to simulate the scenario of gas diffusing from the boundary into the grid area. By changing the wind speed, wind direction, and virtual leak source intensity, a physical simulation dataset containing different wind speeds, wind directions, and leak source intensities is generated.

[0031] Optionally, reflection boundary conditions, vanishing gradient boundary conditions, and a soft truncation mechanism based on the tanh function are employed to handle the concentration range, solve the high-fidelity gas diffusion simulator, and obtain the gas concentration value at each grid location within the target region, including:

[0032] Based on the preset physical concentration range, the current concentration value is mapped to the target interval. If the current concentration value exceeds the preset physical concentration range, the current concentration value is mapped to outside the target interval to obtain the normalized result.

[0033] The normalization result is hard-truncated to the target interval. The hard-truncated result is fed into the tanh function for smoothing transformation. The hard-truncated result is then smoothly mapped back to the target interval to obtain the smoothed result.

[0034] The smoothed result is inversely normalized back to the preset physical concentration range, and the gas concentration value at each grid location in the target area is obtained in the absence of negative concentration.

[0035] Optionally, it also includes using a dynamic time step based on CFL conditions, expressed by the formula:

[0036] ;

[0037] in, This represents the dynamic time step based on CFL conditions; These represent taking the maximum value and taking the minimum value, respectively. These represent the grid spacing in the x-direction and the grid spacing in the y-direction, respectively. express Two-dimensional wind field vector at location; Indicate Spatial heterogeneity diffusion coefficient of location.

[0038] Optionally, the surface leak point concentration field reconstruction model is a lightweight U-Net model;

[0039] The lightweight U-Net model is obtained by reducing the network depth, basic channel number, and parameter constraints of the U-Net model, and by replacing the upsampling method of the U-Net model from deconvolution to bilinear interpolation.

[0040] Optionally, the training loss function formula for the surface leak point concentration field reconstruction model is:

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] in, This represents the training loss function for the surface leak point concentration field reconstruction model; Indicates L1 reconstruction loss; Represents the total variational regularization term for anisotropy; Represents the Laplace smoothing constraint term; Indicates a non-negative constraint term; All represent weight parameters; Indicates the total number of pixels in the grid; These represent the model at the grid pixels. Predicted gas concentration value and actual gas concentration value at the location; These represent the model's position on the grid. Place, Place, Place, The predicted gas concentration value at the location; Indicates the model's position on the grid. The discrete Laplace operator value of the predicted gas concentration at the location; Both indicate direction; This indicates taking the maximum value.

[0048] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0049] This invention addresses the surface detection scenario of tracers in underground gas storage facilities. By embedding Fick's diffusion law into the entire process from data processing and dataset construction to model training, it constructs a full-link physical compliance constraint system, overcoming the limitations of traditional two-stage interpolation and prediction methods. Through a combination of diffusion iteration of physical smooth interpolation and contour tracking, it achieves high-fidelity, physically compliant reconstruction from sparse points to a continuous concentration field under extremely sparse sensor input conditions. This significantly reduces the residual of the diffusion equation in the reconstructed concentration field, enabling it to reach a numerically stable convergence state with small mass conservation errors. By constructing a high-fidelity gas diffusion simulator and using an off-domain leakage simulation mechanism to generate leakage-free scenario samples, it effectively expands sample diversity and significantly improves the model's anti-interference ability and robustness. By developing a fully automated system integrating data parsing, preprocessing, reconstruction, visualization, and quantitative evaluation, it supports multi-timestep and arbitrary layout sensor data input and can generate concentration field distribution maps and quantitative analysis reports with one click, significantly reducing the on-site engineering adaptation cost of gas storage facilities. Attached Figure Description

[0050] Figure 1 A schematic flowchart illustrating the surface leak point concentration field reconstruction method for micro-leakage in a natural gas storage facility provided in this embodiment of the invention.

[0051] Figure 2 A schematic diagram of the training process for the surface leak point concentration field reconstruction model provided in an embodiment of the present invention;

[0052] Figure 3 This is a schematic diagram of the structure of the surface leak point concentration field reconstruction model provided in an embodiment of the present invention;

[0053] Figure 4 A schematic diagram of the training loss function structure of the surface leak point concentration field reconstruction model provided in an embodiment of the present invention;

[0054] Figure 5 This is a contour map of the surface gas concentration distribution of the gas storage facility under time step F before enhancement, provided in an embodiment of the present invention.

[0055] Figure 6 This is a contour map of the surface gas concentration distribution of the gas storage facility under the enhanced pre-time step G provided in an embodiment of the present invention.

[0056] Figure 7 This is a contour map of the surface gas concentration distribution of the gas storage facility under time step H before enhancement, provided in an embodiment of the present invention.

[0057] Figure 8 This is a contour map of the surface gas concentration distribution of the gas storage facility under enhanced time step I provided in an embodiment of the present invention.

[0058] Figure 9This is a contour map of the surface gas concentration distribution of a gas storage facility under enhanced pre-time step J, provided in an embodiment of the present invention.

[0059] Figure 10 This is a contour map of the surface gas concentration distribution of the gas storage facility at time step F after enhancement, provided in an embodiment of the present invention.

[0060] Figure 11 This is a contour map of the surface gas concentration distribution of the gas storage facility at enhanced time step G, provided in an embodiment of the present invention.

[0061] Figure 12 This is a contour map of the surface gas concentration distribution of the gas storage facility at time step H after enhancement, provided in an embodiment of the present invention.

[0062] Figure 13 This is a contour map of the surface gas concentration distribution of the gas storage facility under enhanced time step I provided in an embodiment of the present invention.

[0063] Figure 14 The above is a contour map of the surface gas concentration distribution of the gas storage facility under enhanced time step J, provided in an embodiment of the present invention. Detailed Implementation

[0064] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0065] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0066] Example 1

[0067] This embodiment introduces a method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities, including:

[0068] Acquire real-time sparse sensor data at the gas storage site;

[0069] The real-time sparse sensor data is input into a pre-trained surface leak point concentration field reconstruction model, and the surface leak point concentration field reconstruction result is output.

[0070] The training of the surface leak point concentration field reconstruction model includes:

[0071] Acquire historical sparse sensor data from the gas storage site;

[0072] The historical sparse sensor data is cleaned to obtain cleaned data;

[0073] The initial concentration field is generated by eliminating the non-physical structure of the cleaned data through multiple explicit diffusion iterations and by directionally eliminating false closed contour lines in the cleaned data based on the contour line tracking algorithm.

[0074] The pre-built high-fidelity gas diffusion simulator generates a physical simulation dataset containing different wind speeds, wind directions, and leakage source intensities based on leak point information;

[0075] The surface leak point concentration field reconstruction model is trained using the initial concentration field and physical simulation dataset, enabling the model to establish a preliminary mapping capability from sparse sensor data to a dense concentration field, thus obtaining a trained surface leak point concentration field reconstruction model.

[0076] like Figure 1 As shown in this embodiment, a method for reconstructing the concentration field of a surface leak point in a natural gas storage facility with micro-leakage includes the following steps:

[0077] Step 1: Acquire and clean historical sparse sensor data at the natural gas storage site, specifically:

[0078] Historical sparse sensor data includes historical sensor latitude and longitude coordinates and historical gas concentration readings.

[0079] Data cleaning is performed on historical sparse sensor data to obtain cleaned data.

[0080] Automatic parsing of historical sensor latitude and longitude coordinates and historical gas concentration data; supports data input from sensors with up to 10 time steps and arbitrary layout.

[0081] Historical sparse sensor data that exceeds the preset physical reasonable range is marked and removed. Invalid historical sparse sensor data is filled in using the nearest neighbor filling method to obtain clean data and ensure data integrity.

[0082] Step 2: Interpolation processing based on the physical smoothing interpolation algorithm of the diffusion equation residuals, specifically as follows:

[0083] The initial concentration field is generated by eliminating the non-physical structure of the cleaned data through multiple explicit diffusion iterations and by directionally eliminating spurious closed contour lines in the cleaned data using a contour tracing algorithm.

[0084] Non-physical structures such as passively closed high-concentration islands in the cleaned data are eliminated through multiple explicit diffusion iterations. Each iteration corresponds to a smoothing process based on the diffusion equation, diffusing the gas concentration from high-value regions to low-value regions and dissolving isolated closed contour coils. This embodiment involves 5 explicit diffusion iterations, and the formula for multiple explicit diffusion iterations is as follows:

[0085] ;

[0086] in, They represent the first sequence Interpolated concentration field after explicit diffusion iteration; Indicates the diffusion smoothing coefficient; Represents the gradient operator; express Spatial heterogeneity diffusion coefficient of location.

[0087] The contour tracking algorithm is used to directionally eliminate false closed contour lines in the cleaned data. Tangential smoothing is performed along each gas concentration contour line to eliminate false jagged contour lines generated between sparse data points, ensuring that each contour line in the output concentration field has a smooth, continuous, and falsely closed geometric shape, thus generating the initial concentration field.

[0088] The interpolation process employs a fixed step size of 5 rounds of explicit diffusion iteration, with the step size coefficient taken as an empirical value to ensure numerical stability. The physical smooth interpolation algorithm is used to generate supervised learning labels during the training phase and to convert sparse detection point data into a grid format input acceptable to the model during the inference phase.

[0089] Step 3: Construct a high-fidelity gas diffusion simulator based on two-dimensional unsteady convection and diffusion equations, specifically as follows:

[0090] The formula for a high-fidelity gas diffusion simulator is:

[0091] ;

[0092] ;

[0093] in,, express time The gas concentration at the location; express Two-dimensional wind field vector at location; Indicates the source of the leak; Indicates the overall attenuation coefficient; Indicates the basic diffusion coefficient; Represents the coupling coefficient; These represent the maximum and minimum values ​​of wind speed amplitude within the current wind field, respectively. express The spatial heterogeneity perturbation term, with an amplitude of 0.25, better reflects the actual atmospheric diffusion pattern after being superimposed with the spatial heterogeneity perturbation.

[0094] Step 4: Generate a physical simulation dataset based on a high-fidelity gas diffusion simulator, specifically:

[0095] A pre-built high-fidelity gas diffusion simulator generates a physical simulation dataset containing different wind speeds, wind directions, and leak source intensities based on leak point information.

[0096] For scenarios with leaks, reflection boundary conditions, vanishing gradient boundary conditions, and a soft truncation mechanism based on the hyperbolic tangent (tanh) function are used on the computational grid of the target area to handle the concentration range. A high-fidelity gas diffusion simulator is then solved to obtain the gas concentration value at each grid location within the target area. This generates a physical simulation dataset containing different wind speeds, directions, and leak source intensities, avoiding the vanishing gradient problem caused by hard truncation.

[0097] Based on the preset physical concentration range, the current concentration value is mapped to the target interval. If the current concentration value exceeds the preset physical concentration range, the current concentration value is mapped to outside the target interval to obtain the normalized result.

[0098] The normalization result is hard-truncated to the target interval. The hard-truncated result is fed into the tanh function for smoothing transformation. The hard-truncated result is then smoothly mapped back to the target interval to obtain the smoothed result.

[0099] The smoothed result is inversely normalized back to the preset physical concentration range, and the gas concentration value at each grid location in the target area is obtained in the absence of negative concentration.

[0100] In this embodiment, when solving the high-fidelity gas diffusion simulator, with each step forward, the concentration value may exceed the physically reasonable range due to numerical oscillations, such as resulting in negative concentrations or unrealistically high concentrations. The three-step progressive processing includes:

[0101] First, the current concentration value C is mapped to the [0,1] interval to obtain the normalized result. The mapping is based on a pre-defined physical concentration range, with a lower limit of c_min, i.e., 1×10⁻¹. 7 The upper limit is c_max, which is 1×10⁻¹¹. If the current concentration value C is equal to the lower limit c_min, it is normalized to 0; if the current concentration value C is equal to the upper limit c_max, it is normalized to 1; if the current concentration value is not within the preset physical concentration range, it falls below 0 or above 1.

[0102] Secondly, a hard truncation of [0, 1] is performed on the normalized result. This is to prevent the input values ​​of subsequent operations from being too large or too small. It is rarely triggered under normal circumstances and is only used as a fallback in extreme cases.

[0103] Finally, the hard-truncated results are fed into the tanh function for smoothing. The tanh function is nearly linear when the input is near 0, and the compression is stronger the input deviates further from 0. Ultimately, all hard-truncated results are smoothly mapped back to the [0, 1] interval. Then, they are inversely normalized back to the [c_min, c_max] interval, and it is further ensured that the result is not less than the lower limit c_min to prevent negative concentration.

[0104] In this embodiment, the soft truncation of the tanh function is used as a step in the solution process of the high-fidelity gas diffusion simulator. Together with the upwind finite difference scheme, the reflection / gradient vanishing boundary condition, and the dynamic time step based on the Courant-Friedrichs-Lewy (CFL) condition, it constitutes a complete solution scheme for numerically solving the surface concentration field of gas storage.

[0105] In this study, a dynamic time step based on CFL conditions is used to ensure the stability of solving the high-fidelity gas diffusion simulator. The formula for the dynamic time step based on CFL conditions is as follows:

[0106] ;

[0107] in, This represents the dynamic time step based on CFL conditions; These represent taking the maximum value and taking the minimum value, respectively. They represent Directional grid spacing, Directional grid spacing.

[0108] Solving the high-fidelity gas diffusion simulator yields the concentration field data of the spatiotemporal sequence, i.e. the gas concentration values ​​at different times for each grid position within the target area. The solution results directly constitute the physical simulation dataset. Each sample in the simulation dataset is the output result of a single numerical solution of the high-fidelity gas diffusion simulator.

[0109] The dynamic time step based on the CFL condition ensures both the numerical stability of the explicit finite difference scheme and maximizes the simulation efficiency; where 0.4 and 0.45 are the CFL safety factors for the convection and diffusion terms, respectively, and an upper limit for the time step is set to ensure the stability constraint of the explicit Euler method.

[0110] For leak-free scenarios, a computational grid of multiples of the target area is constructed, and a virtual leak source is set outside the grid area to simulate the scenario of gas diffusing from the boundary into the grid area. This avoids false leak characteristics in leak-free samples. By changing the wind speed, wind direction, and virtual leak source intensity, a physical simulation dataset containing different wind speeds, wind directions, and leak source intensities is generated.

[0111] In a leak-free scenario, there is no leak source within the target area, but gas can still diffuse in from the atmospheric background outside the target area. If the simulation is initialized with all zeros directly within the target area, the model will learn the incorrect mapping that leak-free equals all zeros, becoming overly sensitive to weak leaks during inference. The extra-domain mechanism generates a realistic low-concentration background distribution diffused in from the boundary, rather than a simple all-zero field. It is actually designed to simulate a scenario where a leak occurs outside the target area, causing gas to diffuse into the target area from the outside.

[0112] In this embodiment, a computational grid twice the size of the target area is constructed, generating 500 labeled physical simulation datasets covering different wind speeds and multiple scenarios with / without leakage.

[0113] Step 5: Construct and train a surface leak point concentration field reconstruction model, specifically:

[0114] The surface leak point concentration field reconstruction model is a lightweight U-Net model;

[0115] By reducing the network depth, number of basic channels, and parameter constraints of the U-Net model, and replacing the upsampling method of the U-Net model from deconvolution to bilinear interpolation, a lightweight U-Net model is obtained.

[0116] like Figure 3 As shown, the lightweight U-Net model in this embodiment adopts a 4-layer symmetric encoder and decoder structure with a basic channel count of 64. A random dropout layer with a probability of 0.2 is added to the intermediate layer. The weights adopt the Xavier initialization strategy. The total number of model parameters does not exceed 3.5M. The single-sample inference time on a regular laptop CPU does not exceed 50ms. It supports high-resolution reconstruction of 32×32 grid density fields.

[0117] The lightweight U-Net model is a two-dimensional lightweight variant designed for the specific task of reconstructing the surface concentration field. Its specific configuration combinations in terms of network depth (4 layers), basic number of channels (64), parameter constraints (<3.5M), Dropout layer, Xavier initialization, and upsampling method (bilinear interpolation instead of deconvolution) constitute a specific engineering optimization scheme for the deployment scenario at the edge of the gas storage facility.

[0118] The lightweight U-Net model consists of four parts: an encoder, a bottleneck layer, a decoder, and an output layer, forming a U-shaped symmetrical structure. The encoder is located on the left, progressively compressing the spatial size and increasing the number of feature channels from top to bottom; the decoder is located on the right, progressively restoring the spatial size and decreasing the number of feature channels from bottom to top; the bottleneck layer is located at the narrowest point at the bottom of the U-shape; cross-layer information transfer is achieved between the encoder and decoder through four skip connections. The model input is a sparse density field mesh of 1 channel × 32 × 32, and the output is a high-resolution reconstructed density field mesh of 1 channel × 32 × 32.

[0119] The key differences between the various jump connections are as follows:

[0120] From the first to the fourth, as the encoding depth increases, the information conveyed by the jump connection shows a gradual trend from concrete to abstract, from local to global, and from spatial precision to semantic condensation.

[0121] Shallow skip connections, i.e., the first and second connections, provide spatial location accuracy, while deep skip connections, i.e., the third and fourth connections, provide semantic discrimination capabilities.

[0122] After fusing the feature information from these four levels, the decoder can not only identify the approximate area of ​​the leakage source globally, but also accurately preserve the concentration gradient and contour line morphology locally, thereby achieving high-fidelity concentration field reconstruction with a finite grid resolution of 32×32.

[0123] The surface leak point concentration field reconstruction model was trained using the initial concentration field and physical simulation dataset, enabling the model to establish a preliminary mapping ability from sparse sensor data to dense concentration field, and thus obtaining a trained surface leak point concentration field reconstruction model.

[0124] The training process employs a training strategy based on hybrid physical simulation data, such as... Figure 2 As shown, a hybrid simulation sample covering leaky scenarios (40 scenarios) and no-leak scenarios (60 scenarios) was generated to solve for the complete concentration field output by the high-fidelity gas diffusion simulator, which was then used as a supervision signal for training. The training set and validation set were divided in an 8:2 ratio, totaling 500 training samples. Figure 2 As shown, the optimizer is initialized, the model input data (training set) is obtained and input into the model, the model is forward propagated, and then the composite loss is calculated. Then the model is backpropagated, the parameters are updated through the optimizer, the validation set is used to evaluate whether the composite loss has decreased, the training is completed, and the optimal model parameters are saved.

[0125] Model training uses a composite loss function, such as Figure 4 As shown, the training loss function formula for the surface leak point concentration field reconstruction model is:

[0126] ;

[0127] in, This represents the training loss function for the surface leak point concentration field reconstruction model; This represents the L1 reconstruction loss, ensuring pixel-level reconstruction accuracy; Represent the total variational regularization term for anisotropy, and calculate the concentration field in... The weighted sum of the absolute values ​​of the gradients in two directions suppresses non-physical high-frequency oscillations; The term represents the Laplace smoothing constraint, which calculates the L1 norm of the Laplace operator for the concentration field and forces the spatial second-order smoothness of the concentration field to conform to the solution space characteristics of the diffusion equation. This represents a non-negativity constraint term that penalizes negative concentration values ​​in the model output, preventing physically impossible negative concentration outputs. All represent weight parameters. , , , .

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] ;

[0133] in, Indicates the total number of pixels in the grid; These represent the model at the grid pixels. Predicted gas concentration value and actual gas concentration value at the location; These represent the model's position on the grid. Place, Place, Place, The predicted gas concentration value at the location; Indicates the model's position on the grid. The discrete Laplace operator value of the predicted gas concentration at the location; Both indicate direction; This indicates taking the maximum value.

[0134] L1 reconstruction loss This is used to measure the numerical difference between the model's output concentration field and the true concentration field at each grid location. For each location in a 32×32 grid, the absolute value of the difference between the model's predicted value and the true value is calculated, and then the absolute values ​​of all 1024 grid locations are averaged. The smaller this loss value, the closer the reconstructed concentration field is to the true concentration field numerically.

[0135] Anisotropic total variational regularization term This is used to suppress non-physical high-frequency oscillations in the reconstructed concentration field, i.e., unwanted, noise-like fine jumps, forcing a smooth spatial transition in the concentration field. Calculations are performed separately. direction and The absolute value of the concentration difference between adjacent grid cells in the direction. Specifically, for each grid location in a 32×32 grid, along... Calculate the absolute value of the concentration difference between the grid and its adjacent grid on the right in the direction; along... Calculate the absolute value of the concentration difference between the direction and its adjacent grid below; then calculate all The absolute value of the difference in direction and all The absolute values ​​of the differences in direction are averaged separately, and the sum of the two is the loss.

[0136] Laplace smoothing constraint This is used to reconstruct the concentration field from the second-order curvature level, forcing it to conform to the geometric characteristics of the solution space of the diffusion equation. For each grid location, its Laplacian operator value is calculated. The Laplacian operator reflects the degree of convexity / concavity of the concentration at that point relative to its surrounding neighborhood; a positive value indicates that the concentration at that point is lower than the neighborhood average, and a negative value indicates that the concentration at that point is higher than the neighborhood average. Discrete calculations use a 3×3 neighborhood weighted summation template, where the center point has a weight of -4, and the four neighboring points (top, bottom, left, and right) each have a weight of 1. The summation is then divided by 4. The average of the absolute values ​​of the Laplacian operator for all grid locations is the loss term.

[0137] Non-negative constraint terms This is used to prevent physically impossible negative concentration values ​​from appearing in the reconstructed concentration field. The concentration values ​​at all 1024 grid locations in the model output are examined, and the absolute values ​​of the negative values ​​are summed and averaged. Specifically, each value in the predicted concentration field is compared to 0; for values ​​less than 0, their absolute values ​​are recorded, and all positive values ​​are treated as 0. Finally, the average value of all grid values ​​is taken. If there are no negative values ​​in the predicted concentration field, this term is 0; the more negative values ​​there are or the more severe the negativity, the greater the penalty for this term.

[0138] A specific combination of four physical constraints—L1 loss, total variational regularization, Laplace smoothing, and nonnegativity penalty—is used. These four loss terms, which respectively constrain first-order smoothness, second-order curvature compliance, numerical accuracy, and physical nonnegativity, are combined with specific weights of 1.0:0.3:0.1:0.05 to form a unified composite loss function. Addressing the unique engineering challenge of sparse sensors and dense concentration fields, a multi-dimensional physical constraint loss configuration is designed, resolving the non-physical oscillation problem of purely data-driven models under extremely sparse inputs.

[0139] Step Six: Reconstruct the surface leak point concentration field using real-time data, specifically:

[0140] Real-time sparse sensor data is input into a pre-trained surface leak point concentration field reconstruction model, and the surface leak point concentration field reconstruction results are output.

[0141] This embodiment achieves high-fidelity, physically compliant reconstruction from sparse points to a continuous concentration field under extremely sparse sensor input conditions by combining diffusion iteration with physical smoothing interpolation and contour tracing. This significantly reduces the residual of the diffusion equation in the reconstructed concentration field, enabling it to reach a numerically stable convergence state with small mass conservation error. By constructing a high-fidelity gas diffusion simulator and using an out-of-domain leakage simulation mechanism to generate leakage-free scenario samples, the diversity of samples is effectively expanded, significantly improving the model's anti-interference ability and robustness.

[0142] Example 2

[0143] Based on Example 1, this example presents an experimental example of a method for reconstructing the concentration field of surface leak points in micro-leakage of a natural gas storage facility:

[0144] This embodiment verifies the technical effectiveness of using physical simulation data for model training compared to training using only measured data through comparative experiments.

[0145] A control group and an experimental group were set up. The model before enhancement served as the control group, and the model after enhancement served as the experimental group. Both groups used the exact same network architecture: a 4-layer symmetric encoder-decoder, 64 basic channels, a Dropout probability of 0.2, Xavier initialization, no more than 3.5M parameters, the same composite loss function (L1 reconstruction loss + anisotropic total variational regularization + Laplacian smoothing constraint + non-negativity constraint) with weights of 1.0, 0.3, 0.1, and 0.05 respectively, the same optimizer (AdamW) with a learning rate of 0.001, and the same data preprocessing procedures (data cleaning, outlier filtering, and nearest neighbor imputation). The only difference between the two groups was the size and source of the training data.

[0146] Experimental process of the pre-enhancement model:

[0147] Training data was extracted solely from sparse sensor data from 10 time steps (AJ) at the gas storage site, with 4 to 12 sampling points per time step. Data preprocessing involved concentration anomaly filtering, adaptive logarithmic normalization, physical constraint interpolation based on diffusion equation residuals, gradient clipping, multi-scale Gaussian smoothing, gradient-curvature joint constraints, and closed contour line orientation elimination. The physical constraint interpolation based on diffusion equation residuals consisted of 5 explicit diffusion iterations. Finally, a 5% sparse mask was used to simulate sensor observations, generating 10 training samples. These samples were divided into training and validation sets in an 8:2 ratio and trained for 30 epochs.

[0148] Experimental process of the enhanced model:

[0149] First, a high-fidelity gas diffusion simulator was invoked to generate a hybrid simulation sample in real time, encompassing 40 leakage scenarios and 60 non-leakage scenarios. The simulator, based on a two-dimensional unsteady convection-diffusion equation, coupled with physical mechanisms such as wind field spatiotemporal heterogeneity, dynamic correlation between wind speed and diffusion coefficient, and external leakage simulation, stably solved under dynamic time step control based on CFL conditions. For each scenario, a 32×32 grid concentration field with 5 time steps was generated, resulting in 500 labeled physical simulation samples. These were divided into training and validation sets at an 8:2 ratio, and training was performed using the complete concentration field output by the simulator as the supervision signal for 10 training rounds. After training, inference and evaluation were directly performed on the measured data.

[0150] The two models were compared fairly on the same measured data validation set, namely the physical constraint interpolation results at 10 time steps. The evaluation metrics are shown in Table 1 below.

[0151] Table 1 Evaluation Indicators

[0152]

[0153] Figures 5 to 9 To enhance the previous model, it was trained using only 10 measured samples, generating gas concentration distribution contour plots at 5 key time steps from time step F to time step J. The plots reveal independent, spurious closed isotropic loops—small, isolated closed curves—appearing in multiple time steps. This is because, trained with only 10 samples, the model failed to learn the physical laws of gas diffusion, forcibly fitting between sparse data points and generating non-existent local extrema. Furthermore, the concentration gradient exhibits abrupt breaks and oscillations, inconsistent with the natural smoothness of gas diffusion.

[0154] Figures 10 to 14 To enhance the model, i.e., after pre-training with 500 sets of physical simulation data, contour maps of gas concentration distribution are generated at the same five time steps, i.e., time steps F to J. Figures 5 to 9The comparison reveals that the previously chaotic, spurious closed contour lines have been eliminated, and the concentration field exhibits a single, smooth, diffusing plume pattern consistent with the wind direction. From time step F to time step J, the change in the concentration gradient is consistent and natural, without any abrupt breaks or oscillations. This indicates that the model, through pre-training with physical simulation data, has successfully learned the physical laws behind the convection-diffusion equations, rather than simply performing a geometric fit.

[0155] Experimental results show that although both sets of experiments used the exact same network architecture, loss function, and preprocessing procedure, the pre-enhancement model trained with only 10 measured samples suffered from severe overfitting, generating numerous non-physical artifacts in sparse sensor scenarios, failing to meet the accuracy requirements for gas storage leak monitoring. However, after pre-training with 500 sets of physical simulation data, the model first learned general gas diffusion physics, and then fine-tuned its adaptation to the field scenario using measured data. The Structural Similarity Index Measure (SSIM) improved from 0.5166 to 0.7405 (+43.3%), the Peak Signal-to-Noise Ratio (PSNR) improved by 1.88 dB, and the L1 loss error decreased by 34.6%. The physical compliance and numerical accuracy of the reconstructed concentration field both met engineering monitoring requirements. This comparative experiment verifies the decisive role of large-scale physical simulation data in improving model performance in scenarios with scarce training data.

[0156] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0157] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0158] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0159] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0160] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for reconstructing the concentration field of surface leakage points of natural gas storage reservoirs with micro-leakage, characterized in that, include: Acquire real-time sparse sensor data at the gas storage site; The real-time sparse sensor data is input into a pre-trained surface leak point concentration field reconstruction model, and the surface leak point concentration field reconstruction result is output. The training of the surface leak point concentration field reconstruction model includes: Acquire historical sparse sensor data from the gas storage site; The historical sparse sensor data is cleaned to obtain cleaned data; The initial concentration field is generated by eliminating the non-physical structure of the cleaned data through multiple explicit diffusion iterations and by directionally eliminating false closed contour lines in the cleaned data based on the contour line tracking algorithm. The pre-built high-fidelity gas diffusion simulator generates a physical simulation dataset containing different wind speeds, wind directions, and leakage source intensities based on leak point information; The surface leak point concentration field reconstruction model is trained using the initial concentration field and physical simulation dataset, enabling the model to establish a preliminary mapping capability from sparse sensor data to a dense concentration field, thus obtaining a trained surface leak point concentration field reconstruction model.

2. The method for reconstructing the surface leak point concentration field of a natural gas storage micro-leakage according to claim 1, characterized in that, The real-time sparse sensor data includes real-time sensor latitude and longitude coordinates and real-time gas concentration readings.

3. The method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities according to claim 1, characterized in that, The historical sparse sensor data is cleaned to obtain cleaned data, including: Historical sparse sensor data that exceeds the preset physical reasonable range is marked and removed. Invalid historical sparse sensor data is filled in using the nearest neighbor filling method to obtain clean data.

4. The method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities according to claim 1, characterized in that, An initial concentration field is generated by eliminating non-physical structures in the cleaned data through multiple explicit diffusion iterations and by directionally eliminating spurious closed contour lines in the cleaned data using a contour tracing algorithm, including: Non-physical structures in the cleaned data are eliminated through multiple explicit diffusion iterations. In each iteration, the gas concentration is diffused from the high-value region to the low-value region to dissolve isolated closed contour coils. The algorithm of contour line tracking is used to eliminate false closed contour lines in the cleaned data. Tangential smoothing is performed along each gas concentration contour line to eliminate false jagged contour lines between sparse data points and generate an initial concentration field. The formula for the multiple explicit diffusion iterations is: ； in, They represent the first sequence Interpolated concentration field after explicit diffusion iteration; Indicates the diffusion smoothing coefficient; Represents the gradient operator; express Spatial heterogeneity diffusion coefficient of location.

5. The method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities according to claim 1, characterized in that, The formula for the high-fidelity gas diffusion simulator is: ； ； in, express time Gas concentration at location; express Two-dimensional wind field vector at location; Represents the gradient operator; express Spatial heterogeneity diffusion coefficient of location; Indicates the source of the leak; Indicates the overall attenuation coefficient; Indicates the basic diffusion coefficient; Represents the coupling coefficient; These represent the maximum and minimum values ​​of wind speed amplitude within the current wind field, respectively. express Spatial heterogeneity perturbation term of location.

6. The method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities according to claim 1, characterized in that, A pre-built high-fidelity gas diffusion simulator generates a physical simulation dataset based on leak point information, including different wind speeds, wind directions, and leak source intensities, including: For scenarios with leakage, reflection boundary conditions, gradient vanishing boundary conditions, and a soft truncation mechanism based on the tanh function are used on the computational grid of the target area to handle the concentration range, solve the high-fidelity gas diffusion simulator, obtain the gas concentration value at each grid location in the target area, and generate a physical simulation dataset containing different wind speeds, wind directions, and leakage source intensities. For leak-free scenarios, a computational grid of multiples of the target area is constructed, and a virtual leak source is set outside the grid area to simulate the scenario of gas diffusing from the boundary into the grid area. By changing the wind speed, wind direction, and virtual leak source intensity, a physical simulation dataset containing different wind speeds, wind directions, and leak source intensities is generated.

7. The method for reconstructing the surface leak point concentration field of a micro-leakage in a natural gas storage facility according to claim 6, characterized in that, By employing reflection boundary conditions, vanishing gradient boundary conditions, and a soft truncation mechanism based on the tanh function, a high-fidelity gas diffusion simulator is solved to handle the concentration range and obtain the gas concentration values ​​at each grid location within the target region, including: Based on the preset physical concentration range, the current concentration value is mapped to the target interval. If the current concentration value exceeds the preset physical concentration range, the current concentration value is mapped to outside the target interval to obtain the normalized result. The normalization result is hard-truncated to the target interval. The hard-truncated result is fed into the tanh function for smoothing transformation. The hard-truncated result is then smoothly mapped back to the target interval to obtain the smoothed result. The smoothed result is inversely normalized back to the preset physical concentration range, and the gas concentration value at each grid location in the target area is obtained in the absence of negative concentration.

8. The method for reconstructing the surface leak point concentration field of a micro-leakage in a natural gas storage facility according to claim 6, characterized in that, It also includes using a dynamic time step based on CFL conditions, expressed by the formula: ； in, This represents the dynamic time step based on CFL conditions; These represent taking the maximum value and taking the minimum value, respectively. They represent Directional grid spacing, Directional grid spacing; express Two-dimensional wind field vector at location; Indicate Spatial heterogeneity diffusion coefficient of location.

9. The method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities according to claim 1, characterized in that, The surface leak point concentration field reconstruction model is a lightweight U-Net model; The lightweight U-Net model is obtained by reducing the network depth, basic channel number, and parameter constraints of the U-Net model, and by replacing the upsampling method of the U-Net model from deconvolution to bilinear interpolation.

10. The method for reconstructing the concentration field of surface leak points in micro-leakage of natural gas storage facilities according to claim 1, characterized in that, The training loss function formula for the surface leak point concentration field reconstruction model is as follows: ； ； ； ； ； ； in, This represents the training loss function for the surface leak point concentration field reconstruction model; Indicates L1 reconstruction loss; Represents the total variational regularization term for anisotropy; Represents the Laplace smoothing constraint term; Indicates a non-negative constraint term; All represent weight parameters; Indicates the total number of pixels in the grid; These represent the model at the grid pixels. Predicted gas concentration value and actual gas concentration value at the location; These represent the model's position on the grid. Place, Place, Place, Predicted gas concentration values ​​at the location; Indicates the model's position on the grid. The discrete Laplace operator value of the predicted gas concentration at the location; Both indicate direction; This indicates taking the maximum value.

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