Machine learning-based aquifer hydraulic conductivity field description method for water head and tracing data analysis of independent pre-processing and fused post-processing

Abstract

The invention relates to the technical field of aquifer hydraulic conductivity, and discloses an aquifer hydraulic conductivity field description method based on machine learning independent pretreatment and fused post-treatment water head and tracing data analysis. Comprising the following steps: S1, collecting original detection data: obtaining original data of underground water hydraulic head data H and tracer experiment concentration data C, and taking the original data as a data set for model training; s2, constructing an HC-Net model, wherein the HC-Net model comprises an input layer, a full-connection layer, a merging layer, a convolution layer and an output layer, and the full-connection layer comprises a first full-connection layer, a second full-connection layer, a third full-connection layer, a fourth full-connection layer, a fifth full-connection layer and a sixth full-connection layer which are connected in sequence; the convolution layer comprises a convolution layer I, a convolution layer II to a convolution layer N which are connected in sequence, the full connection layer I is connected with the input layer, the merging layer is connected with the input layer, the full connection layer N and the convolution layer I, and the convolution layer N is connected with the output layer. According to the method, the performance and practicability of underground water pollution source identification are remarkably improved in the aspects of reducing the calculation cost, reducing the operation complexity, improving the prediction precision, processing complex geological conditions, improving the data utilization efficiency, reducing the prediction uncertainty and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulic conductivity of aquifers, and in particular to a method for characterizing hydraulic conductivity field of aquifers by analyzing head and tracer data based on independent pre-processing and fusion post-processing of machine learning. Background Art

[0002] Aquifer characterization is key to effectively manage groundwater resources and control pollution incidents. In recent years, aquifer characterization methods have developed in two promising directions: (1) integrating various types of data, such as hydraulic head (H) and tracer concentration (C) data; and (2) using machine learning methods in the field of artificial intelligence. However, there is currently no machine learning model that can effectively fuse H and C data for aquifer characterization. These two data types are in different forms: H data is spatial data and C data is temporal data. This difference poses a challenge to data integration.

[0003] Aquifer hydraulic conductivity (K) is an important parameter for describing groundwater flow, and data are usually obtained through well interference experiments and tracer experiments. Well interference experiments infer the distribution of hydraulic conductivity of aquifers by conducting pumping tests at different well locations and measuring the changes in hydraulic head. Tracer experiments, on the other hand, obtain information about the dispersion and conductivity of aquifers by injecting tracers and monitoring their propagation in aquifers.

[0004] In order to meet these challenges, researchers have proposed a variety of machine learning models, such as convolutional neural networks (CNNs) and long short-term memory networks (LSTMs), to process and analyze the hydraulic properties of aquifers. However, these models usually only process a single type of data and it is difficult to effectively integrate spatial and temporal data to improve the characterization accuracy. Therefore, a method for characterizing the hydraulic conductivity field of aquifers based on independent pre-processing and fusion post-processing of head and tracer data analysis based on machine learning is proposed. Summary of the invention

[0005] In order to solve the technical problems existing in the prior art, the present invention provides a method for characterizing the hydraulic conductivity field of an aquifer by analyzing the head and tracer data based on independent pre-processing and fusion post-processing of machine learning.

[0006] The present invention is implemented by the following technical solution: a method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis by machine learning, comprising the following steps:

[0007] S1 collects raw test data:

[0008] Obtain the original data of groundwater hydraulic head data H and tracer experiment concentration data C, and use the original data as the data set for model training;

[0009] S2 builds the HC-Net model:

[0010] Among them, the HC-Net model includes an input layer, a convolutional layer module 1, a fully connected layer, a convolutional layer module 2, a merging layer and an output layer. The fully connected layer includes the fully connected layer 1, the fully connected layer 2...the fully connected layer N connected in sequence; the convolutional layer module 1 includes the convolutional layer A1, the convolutional layer A2...the convolutional layer AN connected in sequence; the convolutional layer module 2 includes the convolutional layer B1, the convolutional layer B2...the convolutional layer BN connected in sequence; the input layer is connected to the convolutional layer A1 and the fully connected layer 1, the merging layer is connected to the convolutional layer AN, the fully connected layer N and the convolutional layer B1, and the convolutional layer BN is connected to the output layer;

[0011] S3 preprocesses the data of the dataset and divides it into a training set and a validation set;

[0012] S4 model training:

[0013] Input the training set data into the model for model training and optimize the model;

[0014] S5 Model Validation Evaluation:

[0015] The validation set data is input into the trained and optimized model for prediction, and the hydraulic conductivity field is output. The prediction results are converted into a two-dimensional grid and displayed through a color-coded graph. The prediction results are compared with the actual hydraulic conductivity field to evaluate the prediction accuracy and reliability of the model.

[0016] As a further improvement of the above solution, step S1 further includes the following steps:

[0017] a. Configuration of synthetic aquifers:

[0018] Firstly, the scope of the aquifer sampling area and the scope of the aquifer buffer zone are determined, and the hydraulic head boundary conditions of the aquifer are determined;

[0019] b. Generate a random hydraulic conductivity field:

[0020] The hydraulic conductivity distribution map is generated by using GS-tool software, and hydraulic conductivity nodes are generated on the hydraulic conductivity distribution map by grid formation;

[0021] c. Collect hydraulic head data H using the well-to-well interference pumping test method:

[0022] A location is selected on the synthetic aquifer as a sampling point of a sampling well, and then the hydraulic head data H of the sampling well is collected by using a pumping sampling method on the sampling well;

[0023] d. Collect tracer experiment concentration data C using tracer experiment method:

[0024] The tracer is injected into the boundary position of the sampling well, and the concentration of the tracer is collected downstream of the aquifer to obtain the tracer experimental concentration data C.

[0025] As a further improvement of the above scheme, the well-to-well interference pumping test method includes the following steps:

[0026] Select sampling points: Choose appropriate locations as sampling wells based on the structure and hydraulic conditions of the aquifer;

[0027] Install pumping equipment: Install pumping equipment in the sampling well to ensure that the equipment can operate stably;

[0028] Pumping process: Start the pumping equipment, continue pumping, and record the water level changes in real time during the pumping process;

[0029] Data recording: collect hydraulic head data H;

[0030] Among them, the hydraulic head data H includes the following specific contents:

[0031] Time series data: records the water level changes from the start to the end of pumping;

[0032] Water level depth: water level depth data at different time points;

[0033] Pumping rate: the rate at which water flows during the pumping process;

[0034] Hydraulic gradient: records the changes in hydraulic gradient produced during the pumping process.

[0035] As a further improvement of the above scheme, the tracer experiment comprises the following steps:

[0036] Select injection and collection points: Select the injection point of the tracer at the boundary of the sampling well and set the collection point downstream of the aquifer;

[0037] Prepare tracer: Select appropriate tracer and prepare tracer solution according to experimental requirements;

[0038] Injection of tracer: Inject the tracer into the boundary of the sampling well to ensure that the tracer is evenly distributed in the aquifer;

[0039] Data recording: Collect tracer experiment concentration data C;

[0040] Among them, the tracer experiment concentration data C includes the following specific contents:

[0041] Time series data: tracer concentration data collected at downstream collection points at different time points;

[0042] Spatial distribution data: record the tracer concentration at different locations to reflect the migration path of the tracer in the aquifer;

[0043] Concentration change rate: record the rate of change of tracer concentration over time;

[0044] Sampling frequency: Determine the sampling frequency based on the experimental design to ensure that the acquired concentration data has sufficient temporal and spatial resolution;

[0045] These detailed data will be used for model training and validation to ensure that the model can accurately predict the hydraulic conductivity field of the aquifer.

[0046] As a further improvement of the above scheme, the input layer in step S2 is used to input the acquired processed hydraulic head data H and tracer experiment concentration data C; the convolution layer module 1 is used to transform the hydraulic head data H; the fully connected layer is used to reduce the dimension; the merging layer is used to combine the reduced dimension tracer experiment concentration data C with the transformed hydraulic head data H; the convolution layer module 2 extracts and refines the merged data; and the output layer is used to output test data.

[0047] As a further improvement of the above scheme, the data set preprocessing step in step S3 is:

[0048] The acquired data set is preprocessed using the standard deviation. The standard deviation formula is:

[0049] Among them, x is the original data; mean is the sample mean; σ is the sample standard deviation; z is the standardized result;

[0050] The preprocessed data is divided into a training set and a validation set, where the training set requires more than 4,000 samples and the validation set requires more than 500 samples.

[0051] As a further improvement of the above solution, the activation function of the model in step S4 is Relu, and the specific formula is as follows:

[0052] ReLU(x)=max(0,x), Relu(x) represents the Relu loss function, and x represents the output value of each layer.

[0053] As a further improvement of the above solution, in step S4, a back propagation algorithm is used to adjust the model. The specific steps of the back propagation algorithm are:

[0054] Forward propagation: using activation function to calculate model output;

[0055] Error calculation: Calculate the mean square error between the predicted value and the true value;

[0056] Back propagation: calculate gradients via the chain rule;

[0057] Parameter Update: Update the model parameters using the gradient descent algorithm.

[0058] As a further improvement of the above scheme, in step S4, the training results are verified using the validation set data, the validation set data is input into the trained optimized model, the predicted hydraulic conductivity field is output, and the mean square error (MSE) is used to evaluate the deviation between the predicted result and the true value; wherein the mean square error (MSE) formula is:

[0059] X represents the predicted value, Y represents the true value, i represents the value number, n represents the amount of data, and ∑ is the accumulation operator.

[0060] As a further improvement of the above scheme, the method recorded in step S5 is as follows: inputting the validation set data into the trained and optimized model for prediction, outputting the hydraulic conductivity field, converting the prediction results into a two-dimensional grid, and displaying the prediction results through a color-coded diagram, and comparing the prediction results with the actual hydraulic conductivity field, so as to evaluate the prediction accuracy and reliability of the model;

[0061] During the evaluation, the error between the predicted results and the actual results was calculated, the mean and standard deviation of the statistical error were used for comparative analysis, and the correlation coefficient (R) and mean square error (MSE) were used to determine the prediction accuracy.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] 1. The present invention uses an artificial neural network (ANN) model to directly predict the properties of pollution sources instead of traditional simulation / optimization methods. By eliminating the need for optimization algorithms, the consumption of computing resources and time costs are greatly reduced, and efficiency is greatly improved;

[0064] 2. The present invention uses One-hot encoding technology to transform the spatial distribution task of pollution sources into a classification problem, and uses the model to directly output the probability of the pollution source location; it simplifies the operation process, eliminates the need for complex optimization algorithm selection and implementation, and enables non-professionals to quickly master and apply the method;

[0065] 3. The present invention optimizes the number of layers and the number of neurons in each layer of the ANN model to ensure that the model can effectively learn and capture the complex relationship between pollution sources and monitoring data; the optimized model shows high prediction accuracy in the pollution source identification task, can accurately estimate the location and intensity parameters of the pollution source, and reduce the prediction error;

[0066] 4. The present invention uses One-hot coding to represent the existence probability of pollution sources in different spatial regions and converts it into classification problem processing; through probabilistic prediction, the uncertainty brought by single position prediction is reduced, the reliability of identification results is improved, and the environmental management department can locate the pollution source more accurately and take corresponding control measures.

[0067] 5. The present invention significantly improves the performance and practicality of groundwater pollution source identification in terms of reducing computing costs, reducing operational complexity, improving prediction accuracy, handling complex geological conditions, improving data utilization efficiency and reducing prediction uncertainty. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A schematic diagram of the structure of the HC-Net model provided by the present invention;

[0069] Figure 2 A schematic diagram of the distribution of pumping wells for an interference pumping test in the well-to-well interference pumping test method in Example 2 provided by the present invention;

[0070] Figure 3 A schematic diagram of the distribution of pumping wells collected by the tracer experiment method in Example 2 provided by the present invention;

[0071] Figure 4 A distribution diagram of the actual hydraulic conductivity field provided by the present invention;

[0072] Figure 5 This is a prediction diagram of the hydraulic conductivity field after prediction by the HC-Net1 model provided by the present invention. DETAILED DESCRIPTION

[0073] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods. It should be noted that, under the premise of no conflict, the various embodiments or technical features described below can be arbitrarily combined to form a new embodiment.

[0074] Embodiment 1:

[0075] Please combine Figure 1 The present embodiment provides a method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis by machine learning, comprising the following steps:

[0076] S1 collects raw test data:

[0077] Obtain the original data of groundwater hydraulic head data H and tracer experiment concentration data C, and use the original data as the data set for model training;

[0078] S2 builds the HC-Net model:

[0079] Among them, the HC-Net model includes an input layer, a convolutional layer module 1, a fully connected layer, a convolutional layer module 2, a merging layer and an output layer. The fully connected layer includes the fully connected layer 1, the fully connected layer 2...the fully connected layer N connected in sequence; the convolutional layer module 1 includes the convolutional layer A1, the convolutional layer A2...the convolutional layer AN connected in sequence; the convolutional layer module 2 includes the convolutional layer B1, the convolutional layer B2...the convolutional layer BN connected in sequence; the input layer is connected to the convolutional layer A1 and the fully connected layer 1, the merging layer is connected to the convolutional layer AN, the fully connected layer N and the convolutional layer B1, and the convolutional layer BN is connected to the output layer;

[0080] S3 preprocesses the data of the dataset and divides it into a training set and a validation set;

[0081] S4 model training:

[0082] Input the training set data into the model for model training and optimize the model;

[0083] S5 Model Validation Evaluation:

[0084] The validation set data is input into the trained and optimized model for prediction, and the hydraulic conductivity field is output. The prediction results are converted into a two-dimensional grid and displayed through a color-coded graph. The prediction results are compared with the actual hydraulic conductivity field to evaluate the prediction accuracy and reliability of the model.

[0085] The step S1 further comprises the following steps:

[0086] a. Configuration of synthetic aquifers:

[0087] Firstly, the scope of the aquifer sampling area and the scope of the aquifer buffer zone are determined, and the hydraulic head boundary conditions of the aquifer are determined;

[0088] b. Generate a random hydraulic conductivity field:

[0089] The hydraulic conductivity distribution map is generated by using GS-tool software, and hydraulic conductivity nodes are generated on the hydraulic conductivity distribution map by grid formation;

[0090] c. Collect hydraulic head data H using the well-to-well interference pumping test method:

[0091] A location is selected on the synthetic aquifer as a sampling point of a sampling well, and then the hydraulic head data H of the sampling well is collected by using a pumping sampling method on the sampling well;

[0092] d. Collect tracer experiment concentration data C using tracer experiment method:

[0093] The tracer is injected into the boundary position of the sampling well, and the concentration of the tracer is collected downstream of the aquifer to obtain the tracer experimental concentration data C.

[0094] The well-to-well interference pumping test method comprises the following steps:

[0095] Select sampling points: Choose appropriate locations as sampling wells based on the structure and hydraulic conditions of the aquifer;

[0096] Install pumping equipment: Install pumping equipment in the sampling well to ensure that the equipment can operate stably;

[0097] Pumping process: Start the pumping equipment, continue pumping, and record the water level changes in real time during the pumping process;

[0098] Data recording: collect hydraulic head data H;

[0099] Among them, the hydraulic head data H includes the following specific contents:

[0100] Time series data: records the water level changes from the start to the end of pumping;

[0101] Water level depth: water level depth data at different time points;

[0102] Pumping rate: the rate at which water flows during the pumping process;

[0103] Hydraulic gradient: records the changes in hydraulic gradient produced during the pumping process.

[0104] The tracer experiment comprises the following steps:

[0105] Select injection and collection points: Select the injection point of the tracer at the boundary of the sampling well and set the collection point downstream of the aquifer;

[0106] Prepare tracer: Select appropriate tracer and prepare tracer solution according to experimental requirements;

[0107] Injection of tracer: Inject the tracer into the boundary of the sampling well to ensure that the tracer is evenly distributed in the aquifer;

[0108] Data recording: Collect tracer experiment concentration data C;

[0109] Among them, the tracer experiment concentration data C includes the following specific contents:

[0110] Time series data: tracer concentration data collected at downstream collection points at different time points;

[0111] Spatial distribution data: record the tracer concentration at different locations to reflect the migration path of the tracer in the aquifer;

[0112] Concentration change rate: record the rate of change of tracer concentration over time;

[0113] Sampling frequency: Determine the sampling frequency based on the experimental design to ensure that the acquired concentration data has sufficient temporal and spatial resolution;

[0114] These detailed data will be used for model training and validation to ensure that the model can accurately predict the hydraulic conductivity field of the aquifer.

[0115] In the step S2, the input layer is used to input the acquired processed hydraulic head data H and tracer experiment concentration data C; the convolution layer module 1 is used to transform the hydraulic head data H; the fully connected layer is used to reduce the dimension; the merging layer is used to combine the reduced dimension tracer experiment concentration data C with the transformed hydraulic head data H; the convolution layer module 2 extracts and refines the merged data; and the output layer is used to output the test data.

[0116] The data set preprocessing steps in step S3 are:

[0117] The acquired data set is preprocessed using the standard deviation. The standard deviation formula is:

[0118] Among them, x is the original data; mean is the sample mean; σ is the sample standard deviation; z is the standardized result;

[0119] The preprocessed data is divided into a training set and a validation set, where the training set requires more than 4,000 samples and the validation set requires more than 500 samples.

[0120] The activation function of the model in step S4 is Relu, and the specific formula is as follows:

[0121] ReLU(x)=max(0,x), Relu(x) represents the Relu loss function, and x represents the output value of each layer.

[0122] In step S4, the back propagation algorithm is used to adjust the model. The specific steps of the back propagation algorithm are:

[0123] Forward propagation: using activation function to calculate model output;

[0124] Error calculation: Calculate the mean square error between the predicted value and the true value;

[0125] Backward propagation: Gradients are calculated using the chain rule, a fundamental rule in calculus that states that if there are two differentiable functions y = g(x) and z = f(g(x)), then the derivative of z with respect to x is:

[0126] In the context of neural networks, if we want to calculate the impact of a certain weight on the final loss, we will apply the chain rule to trace and calculate the derivatives at each step from the output layer back to the input layer (or weight layer). This method allows us to accurately calculate the gradient of each parameter, even if the network is complex;

[0127] Parameter update: Update model parameters using the gradient descent algorithm, where gradient descent is an optimization algorithm used to find the local minimum of a function in an iterative manner; in neural networks, gradient descent is used to minimize the loss function, that is, adjust network parameters (such as weights and biases) to reduce prediction errors;

[0128] Specific content includes:

[0129] Calculate gradients: First, use the back-propagation algorithm to calculate the gradient of the loss function with respect to each parameter;

[0130] Parameter Update: Then, each parameter is updated using the following formula: Among them, θ represents the parameter, L is the learning rate, is the gradient of the loss function J with respect to θ; the direction of the gradient points to the direction of fastest increase, so when updating the parameters we make adjustments in the opposite direction of the gradient in the hope of reducing the loss.

[0131] In step S4, the training result is verified using the validation set data, the validation set data is input into the trained optimized model, the predicted hydraulic conductivity field is output, and the mean square error (MSE) is used to evaluate the deviation between the predicted result and the true value; wherein the mean square error (MSE) formula is:

[0132] X represents the predicted value, Y represents the true value, i represents the value number, n represents the amount of data, and ∑ is the accumulation operator.

[0133] The method described in step S5 includes: inputting the validation set data into the trained and optimized model for prediction, outputting the hydraulic conductivity field, converting the prediction results into a two-dimensional grid, and displaying the prediction results through a color-coded diagram, and comparing the prediction results with the actual hydraulic conductivity field, so as to evaluate the prediction accuracy and reliability of the model;

[0134] During the evaluation, the error between the predicted results and the actual results was calculated, the mean and standard deviation of the statistical error were used for comparative analysis, and the correlation coefficient (R) and mean square error (MSE) were used to determine the prediction accuracy.

[0135] Embodiment 2:

[0136] The raw detection data collection also includes the following steps:

[0137] a. Configuration of synthetic aquifers:

[0138] First, a two-dimensional (2-D) aquifer in a fully saturated state is determined. The sampling point area is located within the aquifer with an area of ​​10×10 square kilometers. A buffer zone is set around it to expand the total area of ​​the aquifer to 25×25 square kilometers to reduce the boundary effect and simulate the natural extension of the aquifer. At the same time, the hydraulic conductivity field in the sampling point area has specific heterogeneous properties. A homogeneous property is set in the buffer zone, and the hydraulic conductivity is set to 10 -2 m / s, the porosity of the entire aquifer remains at 30%;

[0139] The aquifer has a hydraulic head boundary condition, defined by the equation: hboundary = (500-x / 100) [m], where 500 represents a baseline groundwater hydraulic head in meters, simulating a general groundwater level, and -x / 100 establishes a natural hydraulic gradient, meaning that the hydraulic head decreases by 1 meter for every 100 meters traveled in the x direction. This setting indicates that the hydraulic head at the left boundary is higher than the right boundary. In the absence of human intervention, groundwater in the aquifer naturally flows from left to right. This condition remains unchanged throughout the simulation and determines the hydraulic head boundary condition of the aquifer;

[0140] b. Generate a random hydraulic conductivity field:

[0141] Generate 10×10km using GS-tool software package 2 The distribution of hydraulic conductivity within the sampling point area. These random fields have a uniform spacing of 200 meters, forming a grid structure of 51×51 nodes. Each node represents a specific spatial point. Hydraulic properties are generated at the spatial point. This dense grid can capture the detailed heterogeneity and variability of the subsurface environment. After the initial random field is generated, the spatial values ​​between the 200-meter grid points are filled by linear interpolation;

[0142] c. Collect hydraulic head data H using the well-to-well interference pumping test method:

[0143] Five disturbance pumping tests were conducted in the synthetic aquifer in five wells (P1, P2, P3, P4 and P5), as Figure 2 As shown. The coordinates of the pumping wells are: P1 (-4000, -4000), P2 (-4000, 0), P3 (-4000, 4000), P4 (0, 4000), P5 (0, 0), and the five wells are pumped in sequence (one at a time). The pumping rate for all tests is the same: 3.6 [kg / (m×h)], the number of observation wells is 100, and the hydraulic head (H) is recorded at all monitoring points. These recorded hydraulic head values ​​will be used to form a data set for model learning to estimate the hydraulic conductivity field of the synthetic aquifer;

[0144] d. Collect tracer experiment concentration data C using tracer experiment method:

[0145] Five tracer experiments were conducted in the synthetic aquifer. The five tracer injection wells were located at the western boundary of the study area, namely I1 (-4000, -4000), I2 (-4000, 0), I3 (-4000, 4000), I4 (0, 4000), and I5 (0, 0). Figure 3 As shown, 1.25×10 5 The injection of the tracer pulse has no effect on the original flow field. Ten concentration monitoring wells were placed downstream to record the concentration values ​​(C). These recorded values ​​were then used to back-estimate the hydraulic conductivity field of the synthetic aquifer. In five tracer experiments, there were ten monitoring wells each time, and a total of 50 breakthrough curves were generated. These 50 breakthrough curves were sequentially merged to form a comprehensive data set that will be used in the model to estimate the hydraulic conductivity field of the synthetic aquifer.

[0146] Embodiment 3:

[0147] The HC-Net model includes an input layer, a convolutional layer module 1, a fully connected layer, a convolutional layer module 2, a merging layer and an output layer. The fully connected layer includes the fully connected layer 1, the fully connected layer 2 and the fully connected layer 3 connected in sequence; the convolutional layer module 1 includes the convolutional layer A1, the convolutional layer A2, the convolutional layer A3, the convolutional layer A4 and the convolutional layer A5 connected in sequence; the convolutional layer module 2 includes the convolutional layer B1, the convolutional layer B2 and the convolutional layer B3 connected in sequence; the input layer is connected to the convolutional layer A1 and the fully connected layer 1, the merging layer is connected to the convolutional layer A5, the fully connected layer 3 and the convolutional layer B1, and the convolutional layer B3 is connected to the output layer;

[0148] The input layer is used to input the processed hydraulic head data H and tracer experiment concentration data C; the convolution layer module 1 is used to transform the hydraulic head data H; the fully connected layer is used to reduce the dimension of the tracer experiment concentration data C with the transformed hydraulic head data H; the convolution layer module 2 extracts and refines the merged data; the output layer is used to output the test data;

[0149] Among them, the convolutional layer module 1 converts the merged data (5×10×10) into a single-channel output of size 2×51×51, representing the predicted hydraulic conductivity field (expressed in logarithmic form).

[0150] The specific steps are as follows:

[0151] Convolutional layer A1: padding and upsampling layer, expanding each 10×10 input to 12×12, and then further upsampling through transposed convolution, outputting feature maps of size 24×24. Convolution kernel size: 4×4; convolution stride: 2; padding: 1.

[0152] Convolutional layer A2: The transposed convolutional layer upsamples the feature map to 48×48, and additional padding adjustment brings the size to 51×51 to match the output dimension. Convolution kernel size: 4×4; convolution stride: 2; padding: 1.

[0153] Convolutional layer A3: extracts and refines features from the extended data. Convolution kernel size: 3×3; convolution stride: 1; padding: 1.

[0154] Convolutional layer A4: Continues the process of extracting and refining features. Convolution kernel size: 3×3; convolution step: 1; padding: 1.

[0155] Convolutional layer A5: The final convolutional layer converts the 8-channel feature map into a single-channel output of size 2×51×51, representing the predicted hydraulic conductivity field. Convolution kernel size: 3×3; convolution step: 1; padding: 1;

[0156] The fully connected layer converts the linear C data, which is originally 5000-dimensional, into 5202 elements, which are then reshaped into a 2×51×51 dual-channel output to make the output format of H data and C data consistent;

[0157] The specific steps are as follows:

[0158] Fully connected layer 1: The 5000-dimensional linear C data is converted into 2000 elements through the fully connected layer 1, using the ReLU activation function;

[0159] Fully connected layer 2: The 2000-dimensional data is converted into 1024 elements through the fully connected layer 2, using the ReLU activation function;

[0160] Fully connected layer 3: The 1024-dimensional data is converted into 5202 elements through the fully connected layer 3, using the ReLU activation function and reshaped into a 2×51×51 dual-channel output;

[0161] The merging layer combines the processed C data (2×51×51) with the H data (2×51×51), resulting in a combined dataset of 4×51×51;

[0162] The HC-Net2 model effectively integrates and processes spatial hydraulic head data and time tracer concentration data through this multimodal neural network architecture, improving the accuracy and efficiency of characterizing the hydraulic conductivity field of the aquifer;

[0163] Convolutional layer module 2 converts the four-channel data into a single-channel output of size 51×51 through convolutional layers B1, B2, and B3, representing the predicted hydraulic conductivity field (K field) expressed in logarithmic form. The convolution kernel size is 3×3; the stride is 1; and the padding is 1.

[0164] The present invention uses an artificial neural network (ANN) model to directly predict the properties of pollution sources, rather than traditional simulation / optimization methods. By eliminating the need for optimization algorithms, the consumption of computing resources and time costs are greatly reduced, and efficiency is greatly improved.

[0165] One-hot encoding technology is used to transform the spatial distribution task of pollution sources into a classification problem, and the model is used to directly output the probability of the location of pollution sources. This simplifies the operation process and eliminates the need for complex optimization algorithm selection and implementation, allowing non-professionals to quickly master and apply the method.

[0166] By optimizing the number of layers and the number of neurons in each layer of the ANN model, the model can effectively learn and capture the complex relationship between pollution sources and monitoring data. The optimized model shows high prediction accuracy in the pollution source identification task, and can accurately estimate the location and intensity parameters of the pollution source, reducing the prediction error.

[0167] One-hot coding is used to represent the existence probability of pollution sources in different spatial areas and transform it into a classification problem. Through probabilistic prediction, the uncertainty brought by single-location prediction is reduced, the reliability of identification results is improved, and environmental management departments can locate pollution sources more accurately and take corresponding control measures.

[0168] In summary, the present invention significantly improves the performance and practicality of groundwater pollution source identification in terms of reducing computational costs, reducing operational complexity, improving prediction accuracy, handling complex geological conditions, improving data utilization efficiency, and reducing prediction uncertainty.

[0169] The above-mentioned embodiments are only preferred embodiments of the present invention and cannot be used to limit the scope of protection of the present invention. Any non-substantial changes and substitutions made by technicians in this field on the basis of the present invention shall fall within the scope of protection required by the present invention.

Claims

1. A method for characterizing the hydraulic conductivity field of aquifers based on independent pre-processing and fusion post-processing of head and tracer data analysis, It is characterized in that The following steps are involved: S1 collects raw test data: Obtain the original data of groundwater hydraulic head data H and tracer experiment concentration data C, and use the original data as the data set for model training; S2 builds the HC-Net model: Among them, the HC-Net model includes an input layer, a convolutional layer module 1, a fully connected layer, a convolutional layer module 2, a merging layer and an output layer. The fully connected layer includes the fully connected layer 1, the fully connected layer 2...the fully connected layer N connected in sequence; the convolutional layer module 1 includes the convolutional layer A1, the convolutional layer A2...the convolutional layer AN connected in sequence; the convolutional layer module 2 includes the convolutional layer B1, the convolutional layer B2...the convolutional layer BN connected in sequence; the input layer is connected to the convolutional layer A1 and the fully connected layer 1, the merging layer is connected to the convolutional layer AN, the fully connected layer N and the convolutional layer B1, and the convolutional layer BN is connected to the output layer; S3 preprocesses the data of the dataset and divides it into a training set and a validation set; S4 model training: Input the training set data into the model for model training and optimize the model; S5 Model Validation Evaluation: The validation set data is input into the trained and optimized model for prediction, and the hydraulic conductivity field is output. The prediction results are converted into a two-dimensional grid and displayed through a color-coded graph. The prediction results are compared with the actual hydraulic conductivity field to evaluate the prediction accuracy and reliability of the model.

2. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis based on machine learning as claimed in claim 1, It is characterized in that The step S1 further comprises the following steps: a. Configuration of synthetic aquifers: Firstly, the scope of the aquifer sampling area and the scope of the aquifer buffer zone are determined, and the hydraulic head boundary conditions of the aquifer are determined; b. Generate a random hydraulic conductivity field: The hydraulic conductivity distribution map is generated by using GS-tool software, and hydraulic conductivity nodes are generated on the hydraulic conductivity distribution map by grid formation; c. Collect hydraulic head data H using the well-to-well interference pumping test method: A location is selected on the synthetic aquifer as a sampling point of a sampling well, and then the hydraulic head data H of the sampling well is collected by using a pumping sampling method on the sampling well; d. Collect tracer experiment concentration data C using tracer experiment method: The tracer is injected into the boundary position of the sampling well, and the concentration of the tracer is collected downstream of the aquifer to obtain the tracer experimental concentration data C.

3. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis by machine learning as claimed in claim 2, It is characterized in that The well-to-well interference pumping test method comprises the following steps: Select sampling points: Choose appropriate locations as sampling wells based on the structure and hydraulic conditions of the aquifer; Install pumping equipment: Install pumping equipment in the sampling well to ensure that the equipment can operate stably; Pumping process: Start the pumping equipment, continue pumping, and record the water level changes in real time during the pumping process; Data recording: collect hydraulic head data H; Among them, the hydraulic head data H includes the following specific contents: Time series data: records the water level changes from the start to the end of pumping; Water level depth: water level depth data at different time points; Pumping rate: the rate at which water flows during the pumping process; Hydraulic gradient: records the changes in hydraulic gradient produced during the pumping process.

4. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis based on machine learning as claimed in claim 2, It is characterized in that The tracer experiment comprises the following steps: Select injection and collection points: Select the injection point of the tracer at the boundary of the sampling well and set the collection point downstream of the aquifer; Prepare tracer: Select appropriate tracer and prepare tracer solution according to experimental requirements; Injection of tracer: Inject the tracer into the boundary of the sampling well to ensure that the tracer is evenly distributed in the aquifer; Data recording: Collect tracer experiment concentration data C; Among them, the tracer experiment concentration data C includes the following specific contents: Time series data: tracer concentration data collected at downstream collection points at different time points; Spatial distribution data: record the tracer concentration at different locations to reflect the migration path of the tracer in the aquifer; Concentration change rate: record the rate of change of tracer concentration over time; Sampling frequency: Determine the sampling frequency based on the experimental design to ensure that the acquired concentration data has sufficient temporal and spatial resolution; These detailed data will be used for model training and validation to ensure that the model can accurately predict the hydraulic conductivity field of the aquifer.

5. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis by machine learning as claimed in claim 1, It is characterized in that In the step S2, the input layer is used to input the acquired processed hydraulic head data H and tracer experiment concentration data C; the convolution layer module 1 is used to transform the hydraulic head data H; the fully connected layer is used to reduce the dimension; the merging layer is used to combine the reduced dimension tracer experiment concentration data C with the transformed hydraulic head data H; the convolution layer module 2 extracts and refines the merged data; and the output layer is used to output the test data.

6. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis by machine learning as claimed in claim 1, It is characterized in that The data set preprocessing steps in step S3 are: The acquired data set is preprocessed using the standard deviation. The standard deviation formula is: Among them, x is the original data; mean is the sample mean; σ is the sample standard deviation; z is the standardized result; The preprocessed data is divided into a training set and a validation set, where the training set requires more than 4,000 samples and the validation set requires more than 500 samples.

7. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis based on machine learning as claimed in claim 1, It is characterized in that The activation function of the model in step S4 is Relu, and the specific formula is as follows: ReLU(x)=max(0,x), Relu(x) represents the Relu loss function, and x represents the output value of each layer.

8. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis by machine learning as claimed in claim 1, It is characterized in that In step S4, the back propagation algorithm is used to adjust the model. The specific steps of the back propagation algorithm are: Forward propagation: using activation function to calculate model output; Error calculation: Calculate the mean square error between the predicted value and the true value; Back propagation: calculate gradients via the chain rule; Parameter Update: Update the model parameters using the gradient descent algorithm.

9. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis by machine learning as claimed in claim 1, It is characterized in that In step S4, the training result is verified using the validation set data, the validation set data is input into the trained optimized model, the predicted hydraulic conductivity field is output, and the mean square error (MSE) is used to evaluate the deviation between the predicted result and the true value; wherein the mean square error (MSE) formula is: X represents the predicted value, Y represents the true value, i represents the value number, n represents the amount of data, and ∑ is the accumulation operator.

10. A method for characterizing the hydraulic conductivity field of an aquifer based on independent pre-processing and fusion post-processing of head and tracer data analysis based on machine learning as claimed in claim 1, It is characterized in that The method described in step S5 includes: inputting the validation set data into the trained and optimized model for prediction, outputting the hydraulic conductivity field, converting the prediction results into a two-dimensional grid, and displaying the prediction results through a color-coded diagram, and comparing the prediction results with the actual hydraulic conductivity field, so as to evaluate the prediction accuracy and reliability of the model; During the evaluation, the error between the predicted results and the actual results was calculated, the mean and standard deviation of the statistical error were used for comparative analysis, and the correlation coefficient (R) and mean square error (MSE) were used to determine the prediction accuracy.

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