A seepage field identification method, device and equipment based on a TPC-PINN and a medium

Abstract

This invention discloses a seepage field identification method, apparatus, device, and medium based on TPC-PINN. First, raw measurement point data is collected, preprocessed, and then a four-dimensional feature vector is calculated for each measurement point. This vector is then input into a pre-trained Triple Physical Constraints Physical Information Neural Network (TPC-PINN) to generate predicted resistivity as the enhanced resistivity result. Next, low resistivity region screening is performed to obtain potential seepage regions corresponding to these low resistivity regions. The seepage regions are then visualized based on morphological compactness indices, equivalent spatial correction vectors, and morphological change indices. This invention improves the physical consistency and stability of the resistivity data enhancement results by introducing triple physical constraints. Simultaneously, by constructing four-dimensional input features that include spatial location and intralayer statistical characteristics, the spatial resolution of resistivity distribution under complex geological conditions is improved. This invention achieves integrated processing of resistivity data enhancement and seepage field identification.

Description

Technical Field

[0001] This invention relates to the fields of geophysical electrical exploration and artificial intelligence inversion, and particularly to a method, apparatus, equipment and medium for identifying seepage fields based on TPC-PINN. Background Technology

[0002] Existing electrical resistivity exploration techniques primarily rely on traditional numerical inversion and geological prior constraints for subsurface resistivity inversion and seepage field identification. While these methods have achieved some success in static modeling, they often suffer from the following shortcomings when dealing with multi-period monitoring data or complex nonlinear seepage characteristics:

[0003] (1) Insufficient physical constraints lead to inconsistencies between the inversion results and the actual underground flow patterns;

[0004] (2) When the data is sparse, the model has poor stability and false anomalies appear in the augmentation results;

[0005] (3) Seepage identification relies on manual threshold judgment, and the accuracy and timeliness are difficult to guarantee.

[0006] In recent years, Physical Information Neural Networks (PINN) based on deep learning have shown potential in solving partial differential equation constraint problems. However, existing PINN models mostly focus on single-physics inversion and lack the ability to model the coupling characteristics of multiple constraints. In addition, existing PINNs often lack robustness mechanisms against noise and multi-period data in geoelectric inversion tasks, resulting in insufficient physical consistency of the enhancement results. It is difficult to balance physical consistency and spatial resolution in resistivity enhancement and seepage identification tasks. Summary of the Invention

[0007] To address the technical problems in current electrical resistivity inversion and data augmentation methods, such as insufficient physical constraints, discrepancies between augmentation results and actual geological features, and low accuracy in seepage field identification, this invention proposes a seepage field identification method, device, equipment, and medium based on Triple Physical Constraint Physical Information Neural Network (TPC-PINN). This invention utilizes a four-dimensional resistivity data augmentation, visualization, and seepage field identification system based on Triple Physical Constraint Physical Information Neural Network (TPC-PINN), which can achieve enhanced physical consistency of resistivity data under multiple physical constraints.

[0008] To achieve the above-mentioned technical objectives, the technical solution of the present invention includes:

[0009] On the one hand, the present invention provides a seepage field identification method based on TPC-PINN, comprising the following steps:

[0010] Step 1: Collect raw measurement point data obtained from electrical resistivity tomography and perform preprocessing on the raw measurement point data, including outlier removal and consistency verification.

[0011] Step 2: For the preprocessed data, firstly, all measuring points are divided into multiple sets according to elevation. Then, the mean and standard deviation of resistivity of all measuring points in each set are calculated. Then, together with the distance parameter of the measuring point along the measuring line and the elevation parameter of the measuring point, a four-dimensional feature vector of each measuring point is formed.

[0012] Step 3: Input the four-dimensional feature vector into the trained Triple Physical Constraint Physical Information Neural Network (TPC-PINN). TPC-PINN, based on a feedforward neural network structure, performs nonlinear mapping on the input four-dimensional feature vector to generate a predicted resistivity result corresponding to the spatial location of the measurement point, which is used as the enhanced resistivity result. During training, TPC-PINN optimizes and updates its parameters based on the constraints of the joint physical constraint loss function.

[0013] Step 4: Perform low resistivity region screening on the enhanced resistivity results: First, construct a low resistivity mask in the form of a continuous threshold function, then perform morphological optimization on the low resistivity mask to improve spatial continuity and boundary stability, and finally extract the closed boundary contour to obtain the potential seepage region corresponding to the low resistivity region.

[0014] Step 5: Based on the original measurement point data and the enhanced resistivity results, the potential seepage area is generated, including the morphological compactness index, the equivalent space correction vector, and the morphological change index, and then displayed in a visual form for comparison.

[0015] Preferably, in step 3, during the training of TPC-PINN, one or more sets of four-dimensional feature vectors formed by historical measurement point data are input as training data, wherein the acquisition period corresponding to each set of four-dimensional feature vectors is different; the joint physical constraint loss function used in the training is constructed to address the spatial non-uniformity, depth stratification characteristics and multi-period variation characteristics of geological resistivity data, and consists of the sum of weighted mean square error loss function, spatial smoothness constraint term, depth gradient constraint term, numerical range constraint term and parameter regularization term;

[0016] The mean square error loss term is used to measure the error between the predicted resistivity and the measured resistivity.

[0017] The spatial smoothness constraint term is used to constrain the predicted resistivity difference between adjacent measuring points, and the constraint strength is adaptively adjusted according to the spatial distance between measuring points to improve the model's ability to represent the spatial continuity of geological structures.

[0018] The depth gradient constraint term is used to impose a one-sided penalty constraint on the vertical resistivity change between adjacent measuring points so that the prediction results conform to the electrical change law of the underground medium along the depth direction.

[0019] The numerical range constraint term is used to penalize predicted resistivity values ​​that exceed the preset physical range in order to suppress the output of extreme values ​​that have no physical meaning.

[0020] The parameter regularization term is used to constrain the complexity of the parameters to prevent overfitting;

[0021] When the input is multiple sets of four-dimensional feature vectors from different acquisition times, an adaptively weighted temporal consistency constraint term is added to the joint physical constraint loss function. The temporal consistency constraint term is used to constrain the change in the predicted resistivity value between adjacent monitoring periods and to assign higher weights to measurement points with larger changes, so as to enhance the model's ability to characterize the dynamic changes of seepage.

[0022] Preferably, in step 4, the screening of low resistivity regions includes:

[0023] First, for each measurement point in each acquisition cycle, a low-resistivity region continuous mask is generated by using an adaptive seepage threshold and a smoothed continuous threshold function.

[0024] Then, closing operations are performed on the continuous mask of the low-resistivity region to fill local holes, opening operations are performed to remove isolated noise regions, and erosion and dilation operations are combined to smooth the region boundaries and enhance the region connectivity to obtain the optimized mask.

[0025] The closed boundary contour is then extracted from the optimized mask, and the area, perimeter, and centroid of the low-resistivity region are calculated by line integral and surface integral respectively to describe the geometric morphological characteristics of the low-resistivity region.

[0026] Preferably, the morphological compactness index is obtained by calculating the ratio of the area to the perimeter of the potential seepage region; the equivalent spatial correction vector is calculated based on the change in the centroid position of the potential seepage region; and the morphological change index is calculated based on the spatial regional change of the potential seepage region.

[0027] Secondly, the present invention also provides a seepage field identification device based on TPC-PINN, comprising:

[0028] The preprocessing unit is used to collect raw measurement point data obtained from electrical exploration and to perform preprocessing on the raw measurement point data, including outlier removal and consistency verification.

[0029] The four-dimensional feature vector calculation unit is used to divide all measuring points into multiple sets according to elevation after preprocessing the data. Then, it calculates the mean and standard deviation of resistivity of all measuring points in each set. Finally, it forms the four-dimensional feature vector of each measuring point together with the distance parameter of the measuring point along the measuring line and the elevation parameter of the measuring point.

[0030] The resistivity enhancement unit is used to input the four-dimensional feature vector into the trained Triple Physical Constraint Physical Information Neural Network (TPC-PINN). TPC-PINN is based on a feedforward neural network structure and performs nonlinear mapping on the input four-dimensional feature vector to generate a predicted resistivity result corresponding to the spatial location of the measurement point as the enhanced resistivity result. During training, TPC-PINN optimizes and updates its parameters based on the constraints of the joint physical constraint loss function.

[0031] The potential seepage region generation unit is used to perform low resistivity region screening on the enhanced resistivity results: First, a low resistivity mask in the form of a continuous threshold function is constructed, then morphological optimization is performed on the low resistivity mask to improve spatial continuity and boundary stability, and finally the closed boundary contour is extracted to obtain the potential seepage region corresponding to the low resistivity region.

[0032] The comparison unit is used to generate potential seepage regions based on the original measurement point data and enhanced resistivity results, including morphological compactness index, equivalent space correction vector and morphological change index, and display them in a visual form for comparison.

[0033] Preferably, in the resistivity enhancement unit, the TPC-PINN is trained by inputting one or more sets of four-dimensional feature vectors formed by historical measurement point data as training data, wherein the acquisition period corresponding to each set of four-dimensional feature vectors is different; the joint physical constraint loss function used in training is constructed to address the spatial non-uniformity, depth stratification characteristics and multi-period variation characteristics of geological resistivity data, and consists of the sum of a weighted mean square error loss function, a spatial smoothness constraint term, a depth gradient constraint term, a numerical range constraint term and a parameter regularization term;

[0034] The mean square error loss term is used to measure the error between the predicted resistivity and the measured resistivity.

[0035] The spatial smoothness constraint term is used to constrain the predicted resistivity difference between adjacent measuring points, and the constraint strength is adaptively adjusted according to the spatial distance between measuring points to improve the model's ability to represent the spatial continuity of geological structures.

[0036] The depth gradient constraint term is used to impose a one-sided penalty constraint on the vertical resistivity change between adjacent measuring points so that the prediction results conform to the electrical change law of the underground medium along the depth direction.

[0037] The numerical range constraint term is used to penalize predicted resistivity values ​​that exceed the preset physical range in order to suppress the output of extreme values ​​that have no physical meaning.

[0038] The parameter regularization term is used to constrain the complexity of the parameters to prevent overfitting;

[0039] When the input is multiple sets of four-dimensional feature vectors from different acquisition times, an adaptively weighted temporal consistency constraint term is added to the joint physical constraint loss function. The temporal consistency constraint term is used to constrain the change in the predicted resistivity value between adjacent monitoring periods and to assign higher weights to measurement points with larger changes, so as to enhance the model's ability to characterize the dynamic changes of seepage.

[0040] Preferably, in the potential seepage zone generation unit, the low resistivity zone screening includes:

[0041] First, for each measuring point, a continuous mask of the low-resistivity region is generated by using an adaptive seepage threshold and a smoothed continuous threshold function.

[0042] Then, closing operations are performed on the continuous mask of the low-resistivity region to fill local holes, opening operations are performed to remove isolated noise regions, and erosion and dilation operations are combined to smooth the region boundaries and enhance the region connectivity to obtain the optimized mask.

[0043] The closed boundary contour is then extracted from the optimized mask, and the area, perimeter, and centroid of the low-resistivity region are calculated by line integral and surface integral respectively to describe the geometric morphological characteristics of the low-resistivity region.

[0044] Preferably, in the comparison unit, the morphological compactness index is obtained by calculating the ratio of the area to the perimeter of the potential seepage region; the equivalent spatial correction vector is calculated based on the change in the centroid position of the potential seepage region; and the morphological change index is calculated based on the spatial regional change of the potential seepage region.

[0045] In three aspects, the present invention also provides an electronic device, comprising:

[0046] One or more processors;

[0047] Storage device for storing one or more programs;

[0048] When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described above.

[0049] Fourthly, the present invention also provides a computer-readable medium storing a computer program that, when executed by a processor, implements the method as described above.

[0050] Compared with the prior art, the technical advantages of this invention are as follows:

[0051] This invention introduces physical information neural networks into the field of resistivity seepage field identification and constructs a physical information neural network (TPC-PINN) model trained based on triple physical constraints. By introducing spatial smoothness constraints, depth gradient constraints, and numerical range constraints into a unified optimization framework, the model can simultaneously satisfy the physical characteristics of the geological medium in terms of spatial continuity, vertical variation, and resistivity range, thereby solving the problems of missing physical constraints and unstable results in existing methods for geological resistivity field modeling.

[0052] To address the problem of insufficient spatial resolution of resistivity distribution under complex geological conditions, this invention introduces a feature construction mechanism based on elevation stratification. On the basis of traditional spatial coordinate features, it further integrates the mean and standard deviation of resistivity within the layer to construct a four-dimensional feature vector input to the TPC-PINN model. This enables the model to perceive the overall electrical characteristics of different depth ranges while learning the local spatial information of the measurement points, thereby improving the model's ability to express complex underground structures and enhancing the spatial resolution of resistivity distribution.

[0053] To address the issue that resistivity data is susceptible to noise interference in traditional methods, this invention combines data consistency constraints with multiple physical constraints through a collaborative optimization mechanism using a joint loss function. This approach ensures data fitting accuracy while effectively suppressing abnormal fluctuations and spurious anomalies, thereby improving the stability and robustness of the enhancement results.

[0054] To address the issues of existing seepage identification methods relying on manual thresholds and producing unstable results, this invention constructs a low-resistivity region extraction method based on an adaptive threshold function and morphological optimization. By introducing a smoothed continuous threshold function and morphological processing operators, automatic extraction and boundary optimization of low-resistivity regions are achieved, improving the continuity and accuracy of seepage region identification.

[0055] To address the difficulty in quantitatively describing the dynamic changes in the seepage field, this invention introduces a morphological compactness index, an equivalent spatial correction vector, and a morphological change index to quantitatively analyze the spatial location and geometric shape of the seepage region before and after enhancement, thereby achieving interpretable expression and dynamic visualization of the seepage field identification results.

[0056] In summary, this invention achieves integrated processing of resistivity data enhancement and seepage field identification by constructing a TPC-PINN model, designing a hierarchical feature expression mechanism, and introducing dynamic seepage identification and quantification methods. This effectively improves the physical consistency and spatial resolution of resistivity distribution and enhances the accuracy and stability of seepage region identification. The TPC-PINN model of this invention enhances the physical consistency of resistivity data by embedding three types of physical constraints—smoothness, depth gradient, and numerical range—into the neural network. This invention can accurately recover the subsurface medium structure in noisy environments and achieve automatic visualization and identification of the seepage field. This invention is applicable to electrical resistivity exploration and data enhancement tasks in complex geological environments such as landslide monitoring, groundwater migration, and karst detection. Attached Figure Description

[0057] Figure 1 This is a flowchart of the present invention;

[0058] Figure 2 A simplified diagram of the TPC-PINN model architecture;

[0059] Figure 3 This is a cross-sectional view of the resistivity data in the example before enhancement;

[0060] Figure 4 This is an enhanced profile of the resistivity data in the example.

[0061] Figure 5 A schematic diagram of the low-resistivity seepage zone before enhancement for seepage identification;

[0062] Figure 6 A schematic diagram of the enhanced seepage zone for seepage identification. Detailed Implementation

[0063] The following embodiments are used to illustrate specific implementations of the present invention, but should not be construed as limiting the scope of protection of the present invention. Equivalent adjustments to parameter values, network structure, or algorithm flow made by those skilled in the art without departing from the spirit of the present invention are all within the scope of protection of the present invention.

[0064] Example 1.

[0065] This embodiment provides a seepage field identification method based on TPC-PINN. See [link to relevant documentation]. Figure 1First, raw measurement point data obtained from electrical resistivity tomography (ERT) is collected. In this embodiment, the raw measurement point data comes from a landslide monitoring area with several ERT measurement points laid out along the survey line. Each measurement point corresponds to a set of three data points (d, h, ρ), where d represents the horizontal distance of the measurement point relative to the starting point along the survey line, in meters (m). h represents the elevation value corresponding to the measurement point, in meters (m). ρ represents the apparent resistivity or equivalent resistivity value obtained by inversion at the measurement point, in ohm-meters (Ω·m).

[0066] To ensure data reliability, data preprocessing is performed to remove outliers and verify consistency of the raw data. Specifically, this includes:

[0067] (1) An anomaly detection method based on statistical distribution is adopted to jointly judge the resistivity data using box-plot and Z-score, and to remove abnormal measurement points that deviate significantly from the overall distribution.

[0068] (2) Perform a geometric consistency check on the distance-elevation data and remove invalid measurement points with obvious spatial misalignment or duplicate records.

[0069] (3) Remove missing values ​​or physically unreasonable negative resistivity data.

[0070] The purpose of the above preprocessing is to reduce the impact of measurement noise and acquisition errors on the stability of subsequent model training and use, and to enhance the physical consistency of the results.

[0071] The following describes the TPC-PINN model construction and resistivity enhancement process in this embodiment.

[0072] (1) Feature construction and hierarchical logic

[0073] To achieve a technical solution that characterizes the electrical differences of underground media by depth or elevation, in this embodiment, the effective measuring points are divided into several layers along the elevation direction according to the elevation distribution of the measuring points and the terrain undulations, with each layer corresponding to a continuous elevation interval.

[0074] Let the spatial location of the i-th measuring point be... The corresponding resistivity observation value is For a set of measuring points located within the same elevation level Calculate the statistical characteristics of the resistivity within this layer, including the mean resistivity within the layer. and standard deviation Its definition is as follows:

[0075]

[0076]

[0077] Based on the above hierarchical results, a four-dimensional feature vector is constructed for each measurement point. Its expression is:

[0078]

[0079] in, This represents the distance parameter of the measuring point along the measuring line. Indicates the elevation parameters of the measuring point. and These represent the mean and standard deviation of resistivity within the elevation layer to which measuring point i belongs, respectively, reflecting the overall electrical properties and dispersion of the subsurface medium within the corresponding depth range. By introducing intra-layer statistical characteristics, the model can learn local spatial information while also taking into account the electrical variation patterns at different depth scales.

[0080] (2) Fusion of model training and physical constraints

[0081] In this embodiment, a physical information neural network model incorporating triple physical constraints, namely the Triple Physical Constraints Physics-Informed Neural Network (TPC-PINN), is constructed for modeling and training based on four-dimensional feature vectors. After training, TPC-PINN processes the subsequent input four-dimensional feature vectors formed from measurement point data, thereby enhancing the physical consistency of resistivity data.

[0082] See Figure 2 The TPC-PINN model in this embodiment includes an input module, a neural network module, an output module, and a physical constraint loss module.

[0083] For the i-th measurement point, its four-dimensional eigenvector is defined as:

[0084]

[0085] in, This represents the distance parameter of the measuring point along the measuring line. Indicates the elevation parameters of the measuring point. This represents the average resistivity within the elevation layer to which the measuring point belongs. This represents the standard deviation of resistivity within the corresponding layer.

[0086] In this embodiment, the TPC-PINN model employs a feedforward neural network structure to learn the nonlinear mapping relationship between input features and resistivity. Its output is defined as:

[0087]

[0088] in, Indicated by network parameters A defined nonlinear mapping function, This represents the resistivity value predicted by the model at the i-th measuring point in the k-th monitoring period. This represents the four-dimensional feature vector at the i-th measuring point during the k-th monitoring period. The output module outputs the predicted resistivity results, which correspond one-to-one with the input spatial locations. These predicted resistivity results constitute the enhanced resistivity dataset.

[0089] It should be noted that the TPC-PINN model described above is a unified generative model for predicting resistivity results. In the loss function described below, all resistivity predictions refer to the physical meaning of the predictions obtained by the TPC-PINN model under the corresponding input conditions.

[0090] During the training of TPC-PINN, triple physical constraints are introduced as constraint terms into the model's joint physical constraint loss function. These constraints, working in conjunction with the data consistency objective, achieve collaborative optimization of the model parameters. The joint physical constraint loss function is expressed as:

[0091]

[0092] in, These are the weighting coefficients for each loss item, and their specific values ​​can be adjusted according to the actual geological conditions.

[0093] In this embodiment, the loss terms of the joint physical constraint loss function are defined as follows:

[0094] This represents the mean square error loss term, used to measure the error between the predicted resistivity and the measured resistivity. In this embodiment, it is defined as:

[0095]

[0096] Where N is the number of measurement points participating in model training; i represents the measurement point index, and k represents the monitoring period index; This represents the resistivity value predicted by the model at the i-th measurement point and the k-th monitoring period; This represents the measured resistivity value of the i-th measuring point during the k-th monitoring period.

[0097] To constrain the spatial continuity of the resistivity field, a spatial smoothness constraint term is introduced. This constraint is used to constrain the predicted resistivity difference between adjacent measuring points, and the constraint strength is adaptively adjusted according to the spatial distance between the measuring points to improve the model's ability to represent the spatial continuity of geological structures. In this embodiment, the spatial smoothness constraint term is the average of the squares of the predicted resistivity differences between adjacent measuring points in each monitoring period, and its form is:

[0098]

[0099] Where K represents the total number of monitoring periods involved in model training. This represents the resistivity value predicted by the model at the (i+1)th measurement point and the kth monitoring cycle.

[0100] To reflect the electrical variation of the underground medium along the depth direction, a depth gradient constraint term is introduced. This is used to apply a one-sided penalty constraint to the vertical resistivity variation between adjacent measuring points, so that the prediction results conform to the electrical variation law of the subsurface medium along the depth direction. In this embodiment, the depth gradient constraint term is the average value of the vertical difference of the predicted resistivity of adjacent measuring points under each monitoring period after one-sided penalty, and its definition is as follows:

[0101]

[0102] To avoid the model output containing physically meaningless extreme values, a numerical range constraint term is introduced. This is to penalize predicted resistivity values ​​that exceed a preset physical range, suppressing extreme values ​​that have no physical meaning. In this embodiment, the numerical range constraint term is the average value of the predicted resistivity values ​​after processing by the range penalty function over all measurement points and the monitoring period, and it is defined as follows:

[0103]

[0104] in, Used for predicting resistivity below the physical lower limit Punishment will be imposed in such circumstances. Used for predicting resistivity above the physical upper limit This constraint imposes a penalty on certain situations. Through this constraint, the model is guided during training to keep predictions within a reasonable physical range. This effectively suppresses extreme value outputs that have no physical meaning.

[0105] In addition, to prevent overfitting of the model, a parameter regularization term is introduced. , used to constrain the complexity of parameters to prevent overfitting, is defined in this embodiment as:

[0106]

[0107] Where Θ represents the parameter set of the TPC-PINN model, These are the trainable weight parameters in the neural network.

[0108] In addition, when the input training data contains monitoring information from multiple cycles, a time consistency constraint term is introduced to constrain the continuity of resistivity changes between adjacent time steps. To constrain the changes in resistivity predictions between adjacent monitoring periods, higher weights are assigned to measuring points with larger changes, thereby enhancing the model's ability to characterize dynamic changes in seepage. In this embodiment, the temporal consistency constraint term is the average of the squared differences in resistivity predictions between all measuring points in adjacent monitoring periods, and its form is as follows:

[0109]

[0110] By analyzing the above joint loss function By minimizing the training process, the model can maintain the accuracy of data fitting while ensuring that the predicted resistivity field conforms to the physical laws of the underground medium in terms of spatial continuity, vertical variation trend, numerical rationality, and temporal evolution, thereby obtaining an enhanced resistivity distribution with high physical reliability.

[0111] It should be noted that the constraint terms in the aforementioned joint loss function are not simply a combination of conventional losses, but rather are specifically designed based on the electrical distribution characteristics of the underground medium. This invention incorporates depth gradient constraint terms... Timing consistency constraints A unified physical information neural network optimization framework is introduced, working in conjunction with hierarchical statistical features, to explicitly constrain the physical rationality of resistivity field prediction in terms of vertical variation trends and temporal evolution. Through the synergistic optimization of multiple physical constraints, a TPC-PINN model with triple physical constraints is constructed, achieving a simultaneous improvement in resistivity enhancement effect and physical consistency.

[0112] In this embodiment, the resistivity enhancement result is directly output by the TPC-PINN model after training convergence. Specifically, the model uses the constructed four-dimensional feature vector as input, performs nonlinear mapping through a feedforward neural network, and optimizes and updates the network parameters under the constraints of a joint physical constraint loss function. In this embodiment, the termination condition for TPC-PINN training is preset to terminate after reaching the maximum number of training epochs. Specifically, the maximum number of training epochs is set to 3000 epochs, and training automatically terminates when this number of epochs is reached. During training, the total loss value of each epoch is recorded, and the model parameters corresponding to the historical best loss are saved as the final model. Finally, the trained TPC-PINN model is obtained. Then, the trained TPC-PINN model processes the measurement point data that needs to be enhanced. The measurement point data is preprocessed in the same way as in training, and a four-dimensional feature vector is generated and input into TPC-PINN. Finally, TPC-PINN generates predicted resistivity results that correspond one-to-one with the spatial location of each measurement point. The predicted resistivity results constitute the enhanced resistivity dataset.

[0113] The measured data show significant fluctuations in the "distance-elevation-resistivity" relationship; the profile generated after model enhancement is as follows: Figure 4 , compared with the original profile ( Figure 3 Compared to the previous model, the shallow high-resistivity zone has a more continuous boundary, the deep low-resistivity zone has a clearer outline, and the overall electrical distribution is more consistent with geological patterns. The model effectively suppresses measurement noise and spurious anomalies, improving spatial continuity and physical consistency.

[0114] The following describes the seepage field identification and dynamic visualization process in this embodiment, using the data in the table below to perform the corresponding process.

[0115] Table 1. Resistivity Sample Data of Monitoring Area

[0116] 1 0.5 135.2 890 2 1.0 134.8 1020 3 1.5 134.6 970 4 2.0 134.4 940 5 2.5 134.0 880 … … … … 135 53.5 146.1 780

[0117] Note: The data in the table is a selection of measured samples. The complete dataset contains 135 measuring points and is derived from the landslide monitoring area data.csv file.

[0118] (1) Extraction of low-resistivity seepage zone.

[0119] In this embodiment, the original resistivity profile not processed by the method of this invention is used as a comparison benchmark, and the resistivity profile enhanced by the TPC-PINN model is used as the main basis for seepage field identification and analysis. Figure 5 As shown, the corresponding resistivity profile is the original result without the enhancement method of this invention, such as... Figure 6 As shown, the resistivity profile is the enhanced result after processing using the method of the present invention.

[0120] Based on the physical principle that underground seepage areas typically exhibit low resistivity, the resistivity values ​​predicted from each measuring point are analyzed. The spatially distributed data is used to perform low-resistivity region screening to extract potential seepage areas. Specifically, a low-resistivity mask in the form of a continuous threshold function is constructed:

[0121]

[0122] in, This represents the continuous mask value of the low-resistivity region at the i-th measurement point during the k-th monitoring period. This represents the adaptive seepage threshold corresponding to the i-th measuring point during the k-th monitoring period. This represents a smoothing continuous threshold function.

[0123] (2) Morphological optimization and contour extraction.

[0124] To further improve the spatial coherence and reliability of the seepage zone identification results, the above-mentioned Morphological optimization is performed. In this embodiment, a combination of morphological operators is used. The mask is processed and represented in the following form:

[0125]

[0126] in, This describes a processing procedure composed of a combination of various morphological operators. In this embodiment, the morphological processing includes performing a closing operation on a low-resistivity mask to fill local voids, performing an opening operation to remove isolated noise regions, and combining erosion and dilation operations to smooth region boundaries and enhance region connectivity. Through this morphological optimization process, the spatial continuity and boundary stability of seepage candidate regions can be effectively improved.

[0127] Obtain the optimized mask Then, its closed boundary contour is extracted, and the corresponding geometric feature parameters are calculated, including the region area, perimeter, and centroid position, which are defined as follows:

[0128]

[0129]

[0130]

[0131] in, This represents the area of ​​the low-resistivity region during the k-th monitoring period. Indicates the perimeter of the corresponding area. Indicates the location of the region's centroid; This represents the low-resistivity region mask value of the i-th measurement point during the k-th monitoring period; This represents the area weight corresponding to the i-th measurement point; This indicates the boundary length weight corresponding to the boundary measurement point. This represents the spatial position vector of the i-th measurement point.

[0132] To screen seepage regions with clear physical meaning and stable boundaries, a morphological compactness index is introduced to characterize the geometric rationality of the profile, defined as follows:

[0133]

[0134] in This represents the closed boundary profile of the potential seepage zone. This represents the area of ​​the region enclosed by the boundary contour, used for normalization calculations of compactness.

[0135] In this embodiment, the Compactness index is used to compare and analyze the stability of the boundary morphology of the seepage zone before and after enhancement. Specifically, it is used to... Figure 5 The low-resistivity region contour corresponding to the original data shown is... Figure 6 The Compactness value of the low-resistivity region contour corresponding to the enhanced data is calculated. The comparison results show that after using the method provided by the present invention, the overall Compactness value of the low-resistivity seepage region is reduced, and the region boundary is smoother and more continuous, indicating that the method provided by the present invention can effectively reduce the influence of noise and false anomalies on the morphological identification of the seepage region.

[0136] (3) Dynamic tracking and quantification of seepage transport characteristics

[0137] To quantitatively characterize the improvement effect of the method of the present invention on the seepage field identification results, a comparative analysis was conducted on the changes in the spatial location and geometric morphology of the seepage area before and after enhancement.

[0138] Assuming the same seepage zone is Figure 5 The original recognition results shown are the same as those shown. Figure 6 The centroid positions corresponding to the enhanced recognition results shown are as follows: and Then its equivalent space correction vector is defined as:

[0139]

[0140] in, This indicates the direction and magnitude of the spatial positioning correction of the seepage area caused by the method of the present invention, which is used to quantify the degree of improvement in the spatial location of the seepage area identification results before and after enhancement.

[0141] In addition, to quantitatively characterize the boundary and morphological differences of the seepage zone before and after enhancement, a morphological change index based on the degree of regional overlap is introduced. :

[0142]

[0143] in, and These represent the spatial regions corresponding to the seepage areas before and after enhancement, respectively. This index reflects the effectiveness of the method of the present invention in improving the integrity and spatial consistency of the seepage area boundary. A larger value indicates that the enhanced seepage region has undergone significant morphological optimization compared to the original result.

[0144] By analyzing the Compactness index, the equivalent space correction vector v, and the morphological change index... The joint analysis can systematically evaluate the improvement effect of the method of the present invention in terms of seepage zone positioning accuracy, boundary stability and spatial consistency, and visualize the analysis results in the form of enhanced before and after profile comparison and vector overlay, such as... Figure 5 and Figure 6 As shown.

[0145] The above description shows that the method provided in this embodiment provides significantly improved spatial continuity and deep analysis capabilities compared to the original results. In typical landslide area applications, the low-resistivity region of the enhanced profile has good consistency with the measured slip surface location, and the seepage migration velocity can be quantitatively characterized on an engineering scale.

[0146] This embodiment also provides a seepage field identification device based on TPC-PINN. The system provided in this embodiment consists of a preprocessing unit, a four-dimensional feature vector calculation unit, a resistivity enhancement unit, a potential seepage region generation unit, and a comparison unit. Each unit operates collaboratively through data flow. The overall system functions include raw resistivity data cleaning, four-dimensional feature construction, model enhancement and seepage identification, and dynamic visualization. The preprocessing unit is used to collect raw measurement point data obtained based on electrical resistivity exploration and perform preprocessing on the raw measurement point data, including outlier removal and consistency verification.

[0147] The four-dimensional feature vector calculation unit is used to first divide all measuring points into multiple sets according to elevation after preprocessing the data. Then, it calculates the mean and standard deviation of resistivity of all measuring points in each set. Finally, it combines the distance parameter and elevation parameter of the measuring point along the measuring line to form the four-dimensional feature vector of each measuring point.

[0148] The resistivity enhancement unit is used to input the four-dimensional feature vector into the trained Triple Physical Constraints Physical Information Neural Network (TPC-PINN). TPC-PINN is based on a feedforward neural network structure and performs nonlinear mapping on the input four-dimensional feature vector to generate a predicted resistivity result corresponding to the spatial location of the measurement point as the enhanced resistivity result. During training, TPC-PINN optimizes and updates its parameters based on the constraints of the joint physical constraint loss function.

[0149] The potential seepage region generation unit is used to perform low resistivity region screening on the enhanced resistivity results: First, a low resistivity mask in the form of a continuous threshold function is constructed, then morphological optimization is performed on the low resistivity mask to improve spatial continuity and boundary stability, and finally the closed boundary contour is extracted to obtain the potential seepage region corresponding to the low resistivity region.

[0150] The comparison unit is used to generate potential seepage regions based on the original measurement point data and enhanced resistivity results, including morphological compactness index, equivalent space correction vector and morphological change index, and display them in a visual form for comparison.

[0151] According to embodiments of the present invention, the present invention also provides an electronic device and a computer-readable medium.

[0152] Electronic devices include:

[0153] One or more processors.

[0154] Storage device for storing one or more programs.

[0155] When the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned TPC-PINN-based percolation field identification method.

[0156] In practical use, users can interact with servers, which are also electronic devices, via a network to receive or send messages. Terminal devices are generally various electronic devices equipped with a display and used through a human-computer interface, including but not limited to smartphones, tablets, laptops, and desktop computers. Various specific application software can be installed on these terminal devices as needed, including but not limited to web browsers, instant messaging software, social media platforms, and shopping apps.

[0157] A server is a network service provider that offers various services. The seepage field identification method based on TPC-PINN provided in this embodiment is generally executed by the server. In practical applications, under necessary conditions, terminal devices can also directly execute the seepage field identification method based on TPC-PINN.

[0158] Similarly, the computer-readable medium of the present invention stores a computer program thereon, which, when executed by a processor, implements the TPC-PINN-based seepage field identification method of the embodiments of the present invention.

[0159] The foregoing has provided a detailed description of the seepage field identification method, apparatus, device, and medium based on TPC-PINN provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention, and the descriptions of the embodiments above are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A seepage field identification method based on TPC-PINN, characterized in that, Includes the following steps: Step 1: Collect raw measurement point data obtained from electrical resistivity tomography and perform preprocessing on the raw measurement point data; Step 2: For the preprocessed data, firstly, all measuring points are divided into multiple sets according to elevation. Then, the mean and standard deviation of resistivity of all measuring points in each set are calculated. Then, together with the distance parameter of the measuring point along the measuring line and the elevation parameter of the measuring point, a four-dimensional feature vector of each measuring point is formed. Step 3: Input the four-dimensional feature vector into the trained Triple Physical Constraint Physical Information Neural Network (TPC-PINN). TPC-PINN, based on a feedforward neural network structure, performs nonlinear mapping on the input four-dimensional feature vector to generate a predicted resistivity result corresponding to the spatial location of the measurement point, which is used as the enhanced resistivity result. During training, TPC-PINN optimizes and updates its parameters based on the constraints of the joint physical constraint loss function. Step 4: Perform low resistivity region screening on the enhanced resistivity results: First, construct a low resistivity mask in the form of a continuous threshold function, then perform morphological optimization on the low resistivity mask to improve spatial continuity and boundary stability, and finally extract the closed boundary contour to obtain the potential seepage region corresponding to the low resistivity region. Step 5: Based on the original measurement point data and potential seepage areas, generate morphological compactness index, equivalent spatial correction vector and morphological change index, and display them in a visual form for comparison.

2. The method according to claim 1, characterized in that, In step 3, during training, TPC-PINN uses one or more sets of four-dimensional feature vectors formed by historical measurement point data as training data. Each set of four-dimensional feature vectors corresponds to a different acquisition period. The joint physical constraint loss function used in training is constructed to address the spatial non-uniformity, depth stratification characteristics, and multi-period variation characteristics of geological resistivity data. It consists of the sum of a weighted mean square error loss function, a spatial smoothness constraint term, a depth gradient constraint term, a numerical range constraint term, and a parameter regularization term. The mean square error loss term is used to measure the error between the predicted resistivity and the measured resistivity. The spatial smoothness constraint term is used to constrain the predicted resistivity difference between adjacent measuring points, and the constraint strength is adaptively adjusted according to the spatial distance between measuring points to improve the model's ability to represent the spatial continuity of geological structures. The depth gradient constraint term is used to impose a one-sided penalty constraint on the vertical resistivity change between adjacent measuring points so that the prediction results conform to the electrical change law of the underground medium along the depth direction. The numerical range constraint term is used to penalize predicted resistivity values ​​that exceed the preset physical range in order to suppress the output of extreme values ​​that have no physical meaning. The parameter regularization term is used to constrain the complexity of the parameters to prevent overfitting; When the input is multiple sets of four-dimensional feature vectors from different acquisition times, an adaptively weighted temporal consistency constraint term is added to the joint physical constraint loss function. The temporal consistency constraint term is used to constrain the change in the predicted resistivity value between adjacent monitoring periods and to assign higher weights to measurement points with larger changes, so as to enhance the model's ability to characterize the dynamic changes of seepage.

3. The method according to claim 1, characterized in that, Step 4, the screening of low resistivity regions, includes: First, for each measurement point in each acquisition cycle, a low-resistivity region continuous mask is generated by using an adaptive seepage threshold and a smoothed continuous threshold function. Then, closing operations are performed on the continuous mask of the low-resistivity region to fill local holes, opening operations are performed to remove isolated noise regions, and erosion and dilation operations are combined to smooth the region boundaries and enhance the region connectivity to obtain the optimized mask. The closed boundary contour is then extracted from the optimized mask, and the area, perimeter, and centroid of the low-resistivity region are calculated by line integral and surface integral respectively to describe the geometric morphological characteristics of the low-resistivity region.

4. The method according to claim 1, characterized in that, In step 5, the morphological compactness index is obtained by calculating the ratio of the area to the perimeter of the potential seepage region; the equivalent space correction vector is calculated based on the change in the centroid position of the potential seepage region. The morphological change index is calculated based on the spatial regional changes of the potential seepage zone.

5. A seepage field identification device based on TPC-PINN, characterized in that, include: The preprocessing unit is used to collect raw measurement point data obtained from electrical resistivity tomography and to perform preprocessing on the raw measurement point data. The four-dimensional feature vector calculation unit is used to divide all measuring points into multiple sets according to elevation after preprocessing the data. Then, it calculates the mean and standard deviation of resistivity of all measuring points in each set. Finally, it forms the four-dimensional feature vector of each measuring point together with the distance parameter of the measuring point along the measuring line and the elevation parameter of the measuring point. The resistivity enhancement unit is used to input the four-dimensional feature vector into the trained Triple Physical Constraint Physical Information Neural Network (TPC-PINN). TPC-PINN is based on a feedforward neural network structure and performs nonlinear mapping on the input four-dimensional feature vector to generate a predicted resistivity result corresponding to the spatial location of the measurement point as the enhanced resistivity result. During training, TPC-PINN optimizes and updates its parameters based on the constraints of the joint physical constraint loss function. The potential seepage region generation unit is used to perform low resistivity region screening on the enhanced resistivity results: First, a low resistivity mask in the form of a continuous threshold function is constructed, then morphological optimization is performed on the low resistivity mask to improve spatial continuity and boundary stability, and finally the closed boundary contour is extracted to obtain the potential seepage region corresponding to the low resistivity region. The comparison unit is used to generate morphological compactness index, equivalent spatial correction vector and morphological change index based on the original measurement point data and potential seepage area, and to display them in a visual form for comparison.

6. The apparatus according to claim 5, characterized in that, In the resistivity enhancement unit, TPC-PINN is trained by inputting one or more sets of four-dimensional feature vectors formed by historical measurement point data as training data, where the acquisition period corresponding to each set of four-dimensional feature vectors is different; the joint physical constraint loss function used in training is constructed to address the spatial non-uniformity, depth stratification characteristics and multi-period variation characteristics of geological resistivity data, and consists of the sum of weighted mean square error loss function, spatial smoothness constraint term, depth gradient constraint term, numerical range constraint term and parameter regularization term; The mean square error loss term is used to measure the error between the predicted resistivity and the measured resistivity. The spatial smoothness constraint term is used to constrain the predicted resistivity difference between adjacent measuring points, and the constraint strength is adaptively adjusted according to the spatial distance between measuring points to improve the model's ability to represent the spatial continuity of geological structures. The depth gradient constraint term is used to impose a one-sided penalty constraint on the vertical resistivity change between adjacent measuring points so that the prediction results conform to the electrical change law of the underground medium along the depth direction. The numerical range constraint term is used to penalize predicted resistivity values ​​that exceed the preset physical range in order to suppress the output of extreme values ​​that have no physical meaning. The parameter regularization term is used to constrain the complexity of the parameters to prevent overfitting; When the input is multiple sets of four-dimensional feature vectors from different acquisition times, an adaptively weighted temporal consistency constraint term is added to the joint physical constraint loss function. The temporal consistency constraint term is used to constrain the change in the predicted resistivity value between adjacent monitoring periods and to assign higher weights to measurement points with larger changes, so as to enhance the model's ability to characterize the dynamic changes of seepage.

7. The apparatus according to claim 5, characterized in that, In the potential seepage region generation unit, the screening of low resistivity regions includes: First, for each measurement point in each acquisition cycle, a low-resistivity region continuous mask is generated by using an adaptive seepage threshold and a smoothed continuous threshold function. Then, closing operations are performed on the continuous mask of the low-resistivity region to fill local holes, opening operations are performed to remove isolated noise regions, and erosion and dilation operations are combined to smooth the region boundaries and enhance the region connectivity to obtain the optimized mask. The closed boundary contour is then extracted from the optimized mask, and the area, perimeter, and centroid of the low-resistivity region are calculated by line integral and surface integral respectively to describe the geometric morphological characteristics of the low-resistivity region.

8. The method according to claim 1, characterized in that, In the comparison unit, the morphological compactness index is obtained by calculating the ratio of the area to the perimeter of the potential seepage region; the equivalent space correction vector is calculated based on the change in the centroid position of the potential seepage region. The morphological change index is calculated based on the spatial regional changes of the potential seepage zone.

9. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-4.

10. A computer-readable medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-4.

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