Groundwater system aquifer parameter inversion method and device, system and storage medium
By combining pumping tests with Latin hypercube sampling, deep neural networks, and elk herd optimization algorithms, the problem of parameter inversion in heterogeneous aquifers was solved, and high-precision parameter identification was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA UNIV OF MINING & TECH
- Filing Date
- 2025-02-26
- Publication Date
- 2026-05-19
AI Technical Summary
Existing technologies are insufficient to accurately obtain the hydrogeological parameters of heterogeneous aquifers, and traditional analytical wiring methods cannot meet practical needs.
By combining pumping tests with Latin hypercube sampling, deep neural networks, and elk herd optimization algorithms, alternative models and nonlinear optimization models were established, and aquifer parameters were retrieved from pumping test data.
It enables accurate inversion of aquifer parameters under heterogeneous conditions, improving the model's prediction accuracy and parameter identification accuracy.
Smart Images
Figure CN120145830B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of groundwater inversion technology, and particularly relates to a method, device, system, and storage medium for inverting aquifer parameters in a groundwater system. Background Technology
[0002] Groundwater is an important freshwater resource on Earth, vital to human production and daily life. At the same time, groundwater is also a significant factor in geological environmental evolution and the formation of geological disasters. A correct understanding of the spatiotemporal evolution of groundwater is of great importance for the sustainable use of water resources, ecological environmental protection, and disaster prevention and mitigation.
[0003] Groundwater models are crucial for revealing the movement and evolution of groundwater. However, due to the complexity of groundwater systems and the heterogeneity of aquifer structures, accurately obtaining hydrogeological parameters of aquifers remains a significant challenge in groundwater science. In early engineering practice, analytical fitting methods based on drawdown data from pumping tests were the primary means of estimating aquifer parameters. This method is highly applicable when the mathematical model has a definite analytical solution. For example, under homogeneous confined aquifer conditions, the hydrogeological parameters of the aquifer can be obtained using the Theis formula. However, to more precisely characterize the flow field under actual site conditions, the heterogeneity of aquifer parameters must be fully considered. In this case, simply relying on traditional analytical fitting methods cannot meet practical needs. Summary of the Invention
[0004] The technical problem to be solved by the present invention is to provide a method, apparatus, system, and storage medium for inverting aquifer parameters in a groundwater system.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] A method for inverting aquifer parameters in a groundwater system includes:
[0007] Step S1: Set up a pumping test scenario at the target site, including one pumping well and several observation wells; wherein, pumping is performed on the target aquifer in the pumping well, and water level drop data during the pumping test and water level recovery data after the pumping test are acquired in the observation wells; the observation data are denoted as a vector:
[0008] Step S2: For the pumping test scenario in Step S1, establish a numerical model simulating the pumping test process; simultaneously, based on prior information, determine the upper and lower limits of the values of the parameter m to be inverted in the model, denoted as: m L and m U ;
[0009] Step S3: Based on the upper and lower limits m of the aquifer parametersL and m U The parameter sample dataset M = [m1, ..., m] is obtained using the Latin hypercube sampling method. M The numerical model in step S2 is used to obtain the pumping test observation data y from step S1. obs The simulation result at the corresponding spatiotemporal coordinates is Y = [y1,…,y]. M ] , establish the sample dataset D = {M, Y} required for training the alternative model; then, based on the sample dataset D, use a deep neural network to establish an alternative model for the numerical model in step S2;
[0010] Step S4: Based on observational data, the substitution model, and prior information on aquifer parameters, establish a nonlinear optimization model with the objective of retrieving and identifying model parameters m; then, based on the constraints in the nonlinear optimization model, use the elk herd optimization algorithm to search for the optimal model parameters m. * The results are used as inversion identification of aquifer parameters.
[0011] As a preferred option, the basic form of the nonlinear optimization model in step S4 is:
[0012]
[0013] m L ≤m≤m U
[0014] F S (m)≈F HF (m)
[0015] Wherein: F HF (·) and F S (·) denote the high-fidelity numerical model operator and the substitution model operator, respectively; This represents the observation data vector.
[0016] Preferably, the parameter m to be inverted includes: a permeability parameter and a compressibility factor.
[0017] The present invention also provides an aquifer parameter inversion device for a groundwater system, comprising:
[0018] The first processing module is used to set up a pumping test scenario at the target site, including one pumping well and several observation wells. Specifically, it performs pumping operations on the target aquifer in the pumping well and acquires data on water level decline during the pumping test and water level recovery after the pumping test in the observation wells. The observation data is denoted as a vector.
[0019] The second processing module is used to establish a numerical model simulating the pumping test process; simultaneously, based on prior information, it determines the upper and lower limits of the values of the parameter m to be inverted in the model, denoted as: m L and m U ;
[0020] The third processing module is used to determine the upper and lower limits m of the aquifer parameters. L and m U The parameter sample dataset M = [m1, ..., m] is obtained using the Latin hypercube sampling method. M ], and used a numerical model to obtain the pumping test observation data y obs The simulation result at the corresponding spatiotemporal coordinates is Y = [y1,…,y]. M First, establish the sample dataset D = {M, Y} required for training the alternative model; then, based on the sample dataset D, use a deep neural network to establish an alternative model for the numerical model.
[0021] The fourth processing module establishes a nonlinear optimization model with the objective of retrieving and identifying model parameters m based on observational data, alternative models, and prior information on aquifer parameters. Then, based on the constraints in the nonlinear optimization model, it uses the elk herd optimization algorithm to search for the optimal model parameters m. * The results are used as inversion identification of aquifer parameters.
[0022] As a preferred option, the nonlinear optimization model is:
[0023]
[0024] m L ≤m≤m U
[0025] F S (m)≈F HF (m)
[0026] Wherein: F HF (·) and F S (·) denote the high-fidelity numerical model operator and the substitution model operator, respectively; This represents the observation data vector.
[0027] Preferably, the parameter m to be inverted includes: a permeability parameter and a compressibility factor.
[0028] The present invention also provides a groundwater system aquifer parameter inversion system, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a groundwater system aquifer parameter inversion method when executed by the processor.
[0029] The present invention also provides a storage medium storing a computer program, which executes a groundwater system aquifer parameter inversion method when running.
[0030] This invention utilizes a deep residual network to establish a substitute model for the numerical model, which can accurately approximate the prediction results of the numerical model; the elk herd optimization algorithm can accurately correct the consistency between the simulation prediction results of the numerical model and the observation information; under the premise of ensuring the prediction accuracy of the substitute model and sufficient inversion constraints, the elk herd optimization algorithm can accurately provide the inversion results of aquifer parameters. Attached Figure Description
[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0032] Figure 1 This is a flowchart of the groundwater system aquifer parameter inversion method according to an embodiment of the present invention;
[0033] Figure 2 A pumping test model to simulate a groundwater system. Detailed Implementation
[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0035] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0036] Example 1:
[0037] like Figure 1 As shown, this embodiment of the invention provides a method for inverting aquifer parameters in a groundwater system, including:
[0038] Step S1: Determine the parameters to be inverted for the aquifer at the target site, m, which include: permeability parameter and compressibility coefficient. Set up a pumping test scenario at the target site, including one pumping well and several observation wells. Perform pumping operations on the target aquifer in the pumping well, and acquire data on water level drop during the pumping test and water level recovery after the pumping test from the observation wells; denote the observation data as a vector:
[0039] Step S2: For the pumping test scenario in Step S1, establish a numerical model simulating the pumping test process; simultaneously, based on geological conditions and prior information from expert experience, determine the upper and lower limits of the values of the parameter m to be inverted in the model, denoted as: m L and m U .
[0040] Step S3: Based on the upper and lower limits m of the aquifer parameters L and m U The parameter sample dataset M = [m1, ..., m] is obtained using the Latin hypercube sampling method. M The numerical model in step S2 is used to obtain the pumping test observation data y from step S1. obs The simulation result at the corresponding spatiotemporal coordinates is Y = [y1,…,y]. M This establishes the sample dataset D = {M, Y} required for training the alternative model. Then, based on the sample dataset D, a substitute model for the numerical model in step S2 is built using a deep neural network.
[0041] Step S4: Based on observational data, the substitution model, and prior information on aquifer parameters, establish a nonlinear optimization model with the objective of retrieving and identifying model parameters m; then, based on the constraints in the nonlinear optimization model, use the elk herd optimization algorithm to search for the optimal model parameters m. * The results are used as inversion identification of aquifer parameters.
[0042] In one embodiment of the present invention, the pumping test in step S1 is performed at a constant flow rate Q, and water level data at different times in the observation wells are acquired during the pumping process. After the water level data stabilizes, pumping is stopped, and water level data at different times in different observation wells are recorded during the water level recovery process. Specifically, a pumping test numerical model is used to simulate the groundwater system, such as... Figure 2 As shown. The simulation region of the numerical model is 1000m × 1000m, and all four boundaries are constant head boundaries. The numerical model is built using TOUGH2, with a total of 4 parameter partitions (R1-R4), and the permeability parameters (k1-k4, unit: m) in each parameter partition are set. 2 ) and compressibility coefficients (α1-α4, unit: Pa) -1) are used as parameters to be inverted. The prior information of the aquifer parameters involved in the numerical model all follow a uniform distribution, k i and α i The prior information values range from [5.0 × 10⁻⁶] to [5.0 × 10⁻⁶]. -14 5.0×10 -13 ] and [1.0×10 -10 9.9×10 -9 The model region was discretized into 10,000 grid cells (100×100). The pumping well was located in the 51st row and 51st column of the grid, corresponding to coordinates (505m, 505m). The pumping test lasted for 72 hours. Pumping was conducted from 0 to 24 hours at a flow rate of Q = 0.3 kg / s, and pumping was stopped after 24 hours. A total of 24 water level observation wells were set up. The observation data were generated by adding Gaussian perturbation noise to the predicted values obtained from the numerical simulation. The ratio of the perturbed data to the simulated data followed a Gaussian distribution with a mean of 1 and a standard deviation of 0.01: N(1, 0.01). 2 The observation data is recorded every 4 hours, and 18 observation data points will be obtained for each observation point.
[0043] In one embodiment of the present invention, the numerical model in step S2 is established using the porous media multiphase flow simulation program Tough2. In Tough2, the conditions of the numerical model are set according to the initial conditions of the groundwater level, boundary conditions, pumping well locations, and pumping flow rates at the target site. The number and locations of observation wells are specified in the numerical model, as well as the time for observation to be performed, and the parameters to be inverted in the numerical model are defined.
[0044] As one embodiment of the present invention, the deep neural network for establishing the alternative model in step S3 includes: a data preprocessing module, a residual neural network module, and an output layer module. Detailed descriptions are as follows:
[0045] The data preprocessing module maps the arbitrary-dimensional model parameter vector data m to a fixed 6400-dimensional vector data; then, through the reshape operation, it obtains a single-channel matrix data structure with a fixed shape of 1×80×80.
[0046] The residual neural network module is constructed using ResNet-18 based on two-dimensional convolution, and its input is a 1×80×80 single-channel matrix data obtained from the data preprocessing module. After passing through the hidden layers of ResNet-18, the final output data is flattened into vector data.
[0047] The output layer module is a fully connected neural network, which maps the vector data obtained from the residual neural network module to the pumping test observation data y in step S1. obsData results with consistent dimensions. The activation function of the output layer is the Sigmoid function.
[0048] Furthermore, in step S3, the training sample dataset needs to be normalized to 0-1 during the training of the alternative model; the normalized model parameters and model response data are both within the range of 0-1. The specific formula for normalization is as follows:
[0049]
[0050] In the formula: y min and y max They represent y respectively i A vector consisting of the maximum and minimum values in each dimension.
[0051] Furthermore, the loss function for training the alternative model in step S3 is obtained based on the L1 norm:
[0052]
[0053] Weight parameters The update formula is:
[0054]
[0055] Wherein, ω in formula (2) d This represents the weight decay coefficient of the regularization term, used to alleviate overfitting during DNN training. In formula (3) and These represent the weight parameters for the k-th and k+1-th iterations, respectively.
[0056] The above-mentioned process of establishing an alternative model based on deep neural networks was completed using PyTorch, a third-party deep learning library in Python 3.
[0057] In one embodiment of the present invention, in step S4, the elk herd optimization algorithm searches for the optimal model parameters m. * The process involves the following five steps:
[0058] Step S4-1, Initialization of the Père David's Deer Population: Based on the range of model parameters m L and m U A randomized dataset of model parameters, EHS in size, is generated as the initial population of elk, EH = [m]. 1 ,m 2 ,…,m EHS ] T And the fitness function value corresponding to each individual in EH is calculated.
[0059] Step S4-2, Deer Population Family Division: Based on the preset male deer proportion parameter Br, the population EH is divided into B population families.
[0060] Step S4-3, Calving Season: This step mainly follows the family unit from Step S4-2, inheriting the herd of female deer within the family. and the Bucks To generate new elk calves based on their characteristics.
[0061] Step S4-4: Select Season: Merge all male deer, female deer, and newborn calves into a new population matrix EH. temp According to EH temp The fitness function values of all individuals are sorted, and the top 10 individuals with the smallest fitness function (EHS) are selected to form the next generation of Père David's deer population.
[0062] Step S4-5, Iteration and Termination Condition: Repeat steps S4-2 to S4-4 above. When the termination condition is met, take the individual with the smallest fitness function value in the last obtained population as the final inversion result m of the model parameters. * .
[0063] As a preferred option, the basic form of the nonlinear optimization model in step S4 is:
[0064]
[0065] In the formula: F HF (·) and F S (·) denote the high-fidelity numerical model operator and the substitution model operator, respectively; This represents the observation data vector.
[0066] Furthermore, in step S4-1, each individual in the elk population EH... The generation is obtained according to the following formula:
[0067]
[0068] In the formula: and represents the lower limit and upper limit of the j-th dimension of the model parameter, respectively; U(0,1) represents a random number obtained according to the standard uniform distribution.
[0069] Furthermore, the fitness function value corresponding to each individual in step S4-1 is calculated based on the objective function of the nonlinear optimization model in formula (5): f(m i ), i = 1, ..., EHS.
[0070] Furthermore, the number of population families in step S4-2 is calculated using B = |Br × EHS|. The fitness value f(m) from step S4-1 is then calculated. i The smallest B populations are selected as the stags in each herd family. The set of stag populations B is represented as:
[0071]
[0072] All other individuals are considered female deer. All female deer will be allocated... One stag from the set is ultimately assigned to B families. The specific allocation method employs a roulette-wheel selection mechanism based on a fitness function value. First, the set... All male deer individuals m i Assign a selection probability p to each of the following (i = 1, ..., B): i The calculation formula is as follows:
[0073]
[0074] Then, based on the fitness function value f(m) of the stags... i Perform a roulette wheel sort from smallest to largest, and then sort according to p. i The value determines the position of each male deer on the roulette wheel. Then, based on the results of generating random numbers from a standard uniform distribution, the remaining female deer are sequentially assigned to their corresponding males. After the female deer are divided into families, a vector H = [h1, h2, ..., h...] is used. k ], (k = EHS-B) is used to represent the buck number corresponding to each female deer.
[0075] Furthermore, the new method for generating elk calves in step S4-3 is as follows: by traversing the elk individuals in each family, the corresponding next generation individuals are generated.
[0076] When the traversal index j is a male deer in the family, the generation of elk calves is calculated according to the following formula:
[0077]
[0078] In the formula: k∈(1,…,EHS) represents a random individual in the population; α is a random number between 0 and 1, which is used to control the random selection of elk m in the population. k (t) The proportion of inherited characteristics.
[0079] When the traversal index j is a female deer in the family, the formula for generating elk calves is:
[0080]
[0081] Where: hj This represents the buck number corresponding to the j-th female deer; r represents... A randomly selected male deer. In nature, there is a low-probability event where a female deer from one family mates with a male deer from another family to produce a calf. β and γ are two random numbers between [0,2] used to describe this phenomenon and to determine the attribute portion inherited from previously generated elk calves.
[0082] Furthermore, the termination condition in steps S4-5 is set according to the maximum number of iterations, which is generally set to more than 200 iterations.
[0083] Example 2:
[0084] This invention also provides an aquifer parameter inversion device for a groundwater system, comprising:
[0085] The first processing module is used to set up a pumping test scenario at the target site, including one pumping well and several observation wells. Specifically, it performs pumping operations on the target aquifer in the pumping well and acquires data on water level decline during the pumping test and water level recovery after the pumping test in the observation wells. The observation data is denoted as a vector.
[0086] The second processing module is used to establish a numerical model simulating the pumping test process; simultaneously, based on prior information, it determines the upper and lower limits of the values of the parameter m to be inverted in the model, denoted as: m L and m U ;
[0087] The third processing module is used to determine the upper and lower limits m of the aquifer parameters. L and m U The parameter sample dataset M = [m1, ..., m] is obtained using the Latin hypercube sampling method. M ], and used a numerical model to obtain the pumping test observation data y obs The simulation result at the corresponding spatiotemporal coordinates is Y = [y1,…,y]. M First, establish the sample dataset D = {M, Y} required for training the alternative model; then, based on the sample dataset D, use a deep neural network to establish an alternative model for the numerical model.
[0088] The fourth processing module establishes a nonlinear optimization model with the objective of retrieving and identifying model parameters m based on observational data, alternative models, and prior information on aquifer parameters. Then, based on the constraints in the nonlinear optimization model, it uses the elk herd optimization algorithm to search for the optimal model parameters m. * The results are used as inversion identification of aquifer parameters.
[0089] As one embodiment of the present invention, the nonlinear optimization model is as follows:
[0090]
[0091] m L ≤m≤m U
[0092] F S (m)≈F HF (m)
[0093] Wherein: F HF (·) and F S (·) denote the high-fidelity numerical model operator and the substitution model operator, respectively; This represents the observation data vector.
[0094] As one embodiment of the present invention, the parameter m to be inverted includes: a permeability parameter and a compressibility coefficient.
[0095] Example 3:
[0096] This invention also provides a groundwater system aquifer parameter inversion system, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a groundwater system aquifer parameter inversion method when executed by the processor.
[0097] Example 4:
[0098] This invention also provides a storage medium storing a computer program, which executes a groundwater system aquifer parameter inversion method during runtime.
[0099] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. A method for inverting aquifer parameters in a groundwater system, characterized in that, include: Step S1: Set up a pumping test scenario at the target site, including one pumping well and several observation wells; wherein, pumping is performed on the target aquifer in the pumping well, and water level drop data during the pumping test and water level recovery data after the pumping test are acquired in the observation wells; the observation data are denoted as a vector: ; Step S2: For the pumping test scenario in Step S1, establish a numerical model simulating the pumping test process; simultaneously, determine the parameters to be inverted in the model based on prior information. m The upper and lower limits of the value of are denoted as: and ; Step S3: Based on the upper and lower limits of aquifer parameters and The parameter sample dataset was obtained using the Latin hypercube sampling method. M =[ m 1,…, m M The numerical model in step S2 is used to obtain the pumping test observation data in step S1. Simulation results at corresponding spatiotemporal coordinates Y =[y1,…,y M [Build the sample dataset needed to train the alternative model] D ={ M , Y }; then based on the sample dataset D A replacement model for the numerical model in step S2 is established using a deep neural network. Step S4: Based on observation data, alternative models, and prior information on aquifer parameters, establish a model for identifying parameters through inversion. m A nonlinear optimization model is established with the objective as the target; then, based on the constraints in the nonlinear optimization model, the optimal model parameters are searched using the elk herd optimization algorithm. m * The results of the inversion identification of aquifer parameters; The basic form of the nonlinear optimization model in step S4 is: ； in: and These represent the high-fidelity numerical model operator and the substitution model operator, respectively; Represents the observation data vector; The parameters to be inverted m Includes: permeability parameter and compressibility factor.
2. A device for inverting aquifer parameters in a groundwater system, characterized in that, include: The first processing module is used to set up a pumping test scenario at the target site, including one pumping well and several observation wells. Specifically, it performs pumping operations on the target aquifer in the pumping well and acquires data on water level decline during the pumping test and water level recovery after the pumping test in the observation wells. The observation data is denoted as a vector. ; The second processing module is used to establish a numerical model simulating the pumping test process; and simultaneously determine the parameters to be inverted in the model based on prior information. m The upper and lower limits of the value of are denoted as: and ; The third processing module is used to determine the upper and lower limits of aquifer parameters. and The parameter sample dataset was obtained using the Latin hypercube sampling method. M =[ m 1,…, m M ], and used numerical models to obtain pumping test observation data. Simulation results at corresponding spatiotemporal coordinates Y =[y1,…,y M [Build the sample dataset needed to train the alternative model] D ={ M , Y }; then based on the sample dataset D An alternative model for numerical models is built using deep neural networks; The fourth processing module, based on observational data, alternative models, and prior information on aquifer parameters, establishes a system for identifying model parameters through inversion. m A nonlinear optimization model is established with the objective as the target; then, based on the constraints in the nonlinear optimization model, the optimal model parameters are searched using the elk herd optimization algorithm. m * The results of the inversion identification of aquifer parameters; The nonlinear optimization model is as follows: ； in: and These represent the high-fidelity numerical model operator and the substitution model operator, respectively; Represents the observation data vector; The parameters to be inverted m Includes: permeability parameter and compressibility factor.
3. A groundwater system aquifer parameter inversion system, characterized in that, include: The system includes a memory and a processor, wherein the memory stores a computer program that is executed by the processor, and the computer program, when executed by the processor, performs the groundwater system aquifer parameter inversion method as described in claim 1.
4. A storage medium, characterized in that, The storage medium stores a computer program, which executes the groundwater system aquifer parameter inversion method as described in claim 1 when running.