Underground water system aquifer parameter inversion method, device and system and storage medium

Abstract

The invention discloses an underground water system aquifer parameter inversion method, device and system, and a storage medium. The method comprises the following steps: S1, constructing a water pumping test scene; s2, establishing a numerical model for simulating the water pumping test process; s3, establishing a substitution model of the numerical model by using a deep neural network; s4, according to observation data, the substitution model and aquifer parameter prior information, establishing a nonlinear optimization model taking an inversion identification model parameter as a target; and according to constraint conditions in the nonlinear optimization model, searching an optimal model parameter by using an elk swarm optimization algorithm, and taking the optimal model parameter as an inversion identification result of the aquifer parameter. By adopting the technical scheme provided by the invention, the inversion result can be accurately given.

Description

Technical Field

[0001] The present invention belongs to the technical field of groundwater inversion, and particularly relates to a method and device, a system, and a storage medium for inverting aquifer parameters of a groundwater system. Background Art

[0002] Groundwater is an important fresh water resource on the earth and is crucial for human production and life. At the same time, groundwater is also an important factor in the evolution of the geological environment and the formation of geological disasters. Correctly understanding the spatio-temporal evolution law of groundwater is of great significance for the sustainable utilization of water resources, ecological environment protection, and disaster prevention and mitigation.

[0003] Groundwater models are an important means to reveal the movement and evolution laws of groundwater. However, due to the complexity of the groundwater system and the heterogeneity of the aquifer structure, accurately obtaining the hydrogeological parameter information of the aquifer has always been an important challenge in the field of groundwater science. In early engineering practices, the analytical curve-matching method based on the drawdown data of pumping tests was the main means to estimate aquifer parameters. This method has high applicability when the mathematical model has a clear analytical solution. For example, under the condition of a homogeneous confined aquifer, the hydrogeological parameters of the aquifer can be obtained according to the Theis formula. However, in order to more precisely depict the flow field state under actual site conditions, the heterogeneous conditions of aquifer parameters must be fully considered. At this time, simply relying on the traditional analytical curve-matching method cannot meet the actual needs. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method and device, a system, and a storage medium for inverting aquifer parameters of a groundwater system.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for inverting aquifer parameters of a groundwater system includes:

[0007] Step S1: Set up a pumping test scenario including one pumping well and several observation wells in the target site; wherein, pumping work is performed on the target aquifer in the pumping well, and the water level decline change data during the pumping test and the water level recovery change data after the pumping test are obtained in the observation wells; the observation data is recorded as a vector:

[0008] Step S2: For the pumping test scenario in Step S1, establish a numerical model to simulate the pumping test process; at the same time, determine the upper and lower limits of the value of the parameter m to be inverted in the model according to the prior information, and record them as: m L and m U ;

[0009] Step S3: According to the upper and lower limits m of the aquifer parametersL and m U , obtain the parameter sample data set M = [m 1 , …, m M by using the Latin hypercube sampling method, and obtain the simulation results Y = [y obs corresponding to the space-time coordinates of the observed data y 1 , …, y M at the space-time coordinates of the observed data y in step S1 by using the numerical model in step S2, and establish the sample data set D = {M, Y} required for training the surrogate model; then, according to the sample data set D, establish a surrogate model of the numerical model in step S2 by using a deep neural network;

[0010] Step S4: Establish a non-linear optimization model with the inversion and identification of the model parameter m as the objective according to the observed data, the surrogate model, and the prior information of the aquifer parameters; then, according to the constraint conditions in the non-linear optimization model, use the elk herd optimization algorithm to search for the optimal model parameter m * , as the inversion and identification result of the aquifer parameters.

[0011] Preferably, the basic form of the non-linear optimization model in step S4 is:

[0012]

[0013] m L ≤ m ≤ m U

[0014] F S (m) ≈ F HF (m)

[0015] where: F HF (·) and F S (·) respectively represent the high-fidelity numerical model operator and the surrogate model operator; represents the observed data vector.

[0016] Preferably, the parameter m to be inverted includes: permeability parameter and compressibility coefficient.

[0017] The present invention also provides a device for inverting the aquifer parameters of a groundwater system, including:

[0018] A first processing module, configured to set a pumping test scenario including a pumping well and several observation wells in a target site; wherein, pumping work is performed on a target aquifer in the pumping well, and water level decline change data during the pumping test and water level recovery change data after the pumping test are obtained in the observation wells; the observed data is denoted as a vector:

[0019] The second processing module is used to establish a numerical model for simulating the pumping test process; meanwhile, determine the upper and lower limits of the parameter m to be inverted in the model according to prior information, denoted as: m L and m U ;

[0020] The third processing module is used to obtain a parameter sample data set M = [m L and m U , …, m 1 by using the Latin hypercube sampling method according to the upper and lower limits m M of the aquifer parameters, and obtain the simulation results Y = [y obs , …, y 1 at the corresponding spatio-temporal coordinates of the pumping test observation data y M by using the numerical model, and establish a sample data set D = {M, Y} required for training the surrogate model; then, according to the sample data set D, establish a surrogate model of the numerical model by using a deep neural network;

[0021] The fourth processing module establishes a non-linear optimization model with the parameter m of the inversion identification model as the objective according to the observation data, the surrogate model and the prior information of the aquifer parameters; then, according to the constraint conditions in the non-linear optimization model, uses the elk herd optimization algorithm to search for the optimal model parameter m * , as the inversion identification result of the aquifer parameters.

[0022] Preferably, the non-linear optimization model is:

[0023]

[0024] m L ≤ m ≤ m U

[0025] F S (m) ≈ F HF (m)

[0026] where: F HF (·) and F S (·) respectively represent the high-fidelity numerical model operator and the surrogate model operator; represents the observation data vector.

[0027] Preferably, the parameter m to be inverted includes: permeability parameter and compressibility coefficient.

[0028] The present invention also provides a groundwater system aquifer parameter inversion system, including: a memory and a processor, where a computer program run by the processor is stored on the memory, and the computer program executes the groundwater system aquifer parameter inversion method when run by the processor.

[0029] The present invention also provides a storage medium, on which a computer program is stored, and the computer program executes the groundwater system aquifer parameter inversion method when running.

[0030] The surrogate model established by the present invention using the deep residual network 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 observed information; on the premise of ensuring the prediction accuracy of the surrogate model and sufficient inversion constraint conditions, the elk herd optimization algorithm can accurately give the inversion results of the aquifer parameters. Description of the Drawings

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention, and for those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0032] Figure 1 It is a flowchart of the groundwater system aquifer parameter inversion method according to the embodiment of the present invention;

[0033] Figure 2 It is a pumping test model for simulating the groundwater system. Detailed Embodiments

[0034] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present invention.

[0035] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0036] Embodiment 1:

[0037] As Figure 1 shown, the embodiment of the present invention provides a groundwater system aquifer parameter inversion method, including:

[0038] Step S1. Define the parameters m to be inverted for the aquifer in the target site, where the parameters m to be inverted include: permeability parameter and compressibility. Set up a pumping test scenario in the target site that includes one pumping well and several observation wells. Perform pumping work on the target aquifer in the pumping well, and obtain the water level decline change data during the pumping test and the water level recovery change data after the pumping test in the observation wells; record the observed data as a vector:

[0039] Step S2. For the pumping test scenario in Step S1, establish a numerical model to simulate the pumping test process; meanwhile, according to the geological conditions and prior information of expert experience, determine the upper and lower limits of the values of the parameters m to be inverted in the model, denoted as: m L and m U .

[0040] Step S3. According to the upper and lower limits m L and m U of the aquifer parameters, use the Latin hypercube sampling method to obtain a parameter sample data set M = [m 1 , …, m M , and use the numerical model in Step S2 to obtain the simulation results Y = [y obs , …, y 1 , …, y M at the spatio-temporal coordinates corresponding to the pumping test observed data y obs in Step S1, so as to establish a sample data set D = {M, Y} required for training the surrogate model. Then, according to the sample data set D, use a deep neural network to establish a surrogate model for the numerical model in Step S2;

[0041] Step S4. According to the observed data, the surrogate model, and the prior information of the aquifer parameters, establish a non-linear optimization model with the goal of inverting and identifying the model parameters m; then, according to the constraint conditions in the non-linear optimization model, use the elk herd optimization algorithm to search for the optimal model parameters m * , as the inversion and identification result of the aquifer parameters.

[0042] As an implementation manner of this embodiment of the present invention, the pumping test in Step S1 is performed at a constant flow rate Q, and the water level data at different times in the observation wells are obtained during the pumping process. After the water level data are basically stable, stop pumping, and record the water level data at different times in different observation wells during the water level recovery process. Specifically, use a pumping test numerical model to simulate the groundwater system, as Figure 2 shown. The simulation area of the numerical model is 1000 m × 1000 m, and all four boundaries are constant head boundaries. The numerical model is established using TOUGH2, a total of 4 parameter partitions (R1 - R4) are set, and the permeability parameters (k 1 -k 4 , unit: m2 ) and compressibility coefficient (α 1 -α 4 , unit: pa -1 ) are used as the parameters to be inverted. The prior information of the aquifer parameters involved in the numerical model follows a uniform distribution. The prior information value ranges of k i and α i are [5.0×10 -14 , 5.0×10 -13 and [1.0×10 -10 , 9.9×10 -9 respectively. The model area is discretized into 10,000 grid cells (100×100). The pumping well is set in the grid of the 51st row and 51st column, with the corresponding coordinates of (505m, 505m). The pumping test is carried out for 72 hours. Among them, 0 - 24 hours is the pumping period, and the flow rate is Q = 0.3 kg / s. After 24 hours, the pumping stops. A total of 24 water level change observation wells are set. The observation data is generated by adding Gaussian perturbation noise to the predicted results of the true values obtained from the numerical simulation. The ratio of the perturbed data to the simulated data follows 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 will be obtained for each observation point.

[0043] As an implementation manner of an embodiment of the present invention, the numerical model in step S2 is established by the porous media multiphase flow simulation program tough2. In tough2, the conditions of the numerical model are set according to the initial conditions, boundary conditions, pumping well location and pumping flow rate of the groundwater level in the target site, and the number and location of the observation wells are specified in the numerical model. At the same time, the time for which observations need to be performed is specified, and the parameters to be inverted in the numerical model are clarified.

[0044] As an implementation manner of an embodiment of the present invention, the deep neural network for establishing the surrogate model in step S3 includes: a data preprocessing module, a residual neural network module, and an output layer module. The specific introductions are as follows:

[0045] The function of the data preprocessing module is to map the model parameter vector data m of any dimension into a fixed 6400-dimensional vector data; then, through the reshape operation, a single-channel matrix data structure with a fixed shape of 1×80×80 is obtained.

[0046] The residual neural network module is constructed with ResNet-18 based on two-dimensional convolution. Its input is the 1×80×80 single-channel matrix data obtained from the data preprocessing module. After passing through the various hidden layers of ResNet-18, the finally output data is flattened into vector data.

[0047] The output layer module is a fully connected neural network that maps the vector data obtained by the residual neural network module into data results with the same dimension as the pumping test observation data y in step S1. The activation function of the output layer is the Sigmoid function. obs Further, in step S3, during the training process of the surrogate model, the training sample data set needs to be normalized to 0-1; the ranges of the normalized model parameters and model response data are both within 0-1. The specific formula for normalization is as follows:

[0048]

[0049]

[0050] In the formula: y min and y max respectively represent the vectors composed of the maximum and minimum values corresponding to each dimension of y i .

[0051]

[0051] Further, the loss function for training the surrogate model in step S3 is established based on the L1 norm:

[0052]

[0053] The update formula for the weight parameter is:

[0054]

[0055] Among them, ω d in formula (2) represents the regularization term weight decay coefficient, which is used to alleviate overfitting during the DNN training process. and in formula (3) respectively represent the weight parameters of the k-th and k+1-th iterations.

[0056] The above process of establishing the surrogate model based on the deep neural network is developed and completed using the third-party deep learning library pytorch for python3.

[0057] As an implementation manner of the embodiment of the present invention, in step S4, the process of the elk herd optimization algorithm searching for the optimal model parameter m * specifically includes the following 5 steps to implement:

[0058] Step S4-1, Elk population initialization: According to the value range of the model parameter m L and m U , randomly generate a model parameter data set with the number of EHS as the initialized elk population EH = [m 1 , m 2 , …, m EHS . T。And calculate the fitness function values corresponding to each individual in EH.

[0059] Step S4-2, Elk population family division: Divide the population EH into B population families according to the preset male proportion parameter Br.

[0060] Step S4-3, Calving season: This step mainly takes the families in Step S4-2 as units, and generates new elk calves by inheriting the characteristics of the female deer groups and male deer in the family.

[0061] Step S4-4, Selection season: Combine all the male deer, female deer and newborn calf individuals into a new population matrix EH temp . According to the fitness function values of all individuals in EH temp , sort them, and select the top EHS individuals with the smallest fitness function values to form the next generation of elk population.

[0062] Step S4-5, Iteration and termination conditions: Repeat the above Steps S4-2 to S4-4. When the termination condition is met, take the individual with the smallest fitness function value in the population obtained in the last time as the final inversion result m of the model parameters * .

[0063] Preferably, the basic form of the nonlinear optimization model in Step S4 is:

[0064]

[0065] In the formula: F HF (·) and F S (·) respectively represent the high-fidelity numerical model operator and the surrogate model operator; represents the observed data vector.

[0066] Furthermore, each individual in the elk population EH in Step S4-1 is generated according to the following formula:

[0067]

[0068] In the formula: and respectively represent the lower limit and upper limit of the j-th dimension of the model parameter; 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 according to the objective function of the nonlinear optimization model in formula (5): f(m i), i = 1, …, EHS.

[0070] Further, the number of population families in step S4-2 is calculated according to B = |Br × EHS|. The B populations with the smallest fitness value f(m i ) in step S4-1 are used as the stags in each deer herd family. The set of stag populations B is expressed as:

[0071]

[0072] The remaining individuals other than these are regarded as does. All does will be assigned to one of the stags in, and finally B families are obtained. The specific assignment method adopts a roulette wheel selection mechanism (roulette-wheel selection) based on the fitness function value. First, a selection probability p is assigned to all the stag individuals m i , (i = 1, …, B) in the set, and its calculation formula is as follows: i

[0073]

[0074] Then, the stags are sorted in ascending order according to the fitness function value f(m i ), and the position occupied by each stag individual on the roulette wheel is determined according to the p i value. According to the result of generating a random number from a standard uniform distribution, the remaining doe individuals are sequentially assigned to the corresponding stags. After the family division of the does is completed, the vector H = [h 1 , h 2 , …, h k , (k = EHS - B) is used to represent the stag number corresponding to each doe individual.

[0075] Further, the method for generating new elk calves in step S4-3 is: by traversing the elk individuals in each family, the corresponding next-generation individuals are generated.

[0076] When the traversal index j is a stag in the family, the generation of elk calves is calculated according to the following formula:

[0077]

[0078] where: k ∈ (1, …, EHS) is a random individual in the population; α is a random number between 0 and 1, which is used to control the proportion of the inherited characteristics of the randomly selected elk m k (t).

[0079] And when the traversal index j is a doe in the family, the generation formula of elk calves is:

[0080]

[0081] Where: h j represents the buck number corresponding to the j-th doe; r represents a buck individual randomly selected from. In nature, there may be a small probability event, that is, a doe in a certain family mates with a buck in other families to give birth to a calf. β and γ are two random numbers between [0, 2] used to describe this phenomenon, and are used to determine the part of the attributes inherited from the previously generated elk cubs.

[0082] Furthermore, the termination condition in step S4-5 is set according to the maximum number of iterations, generally set to be greater than 200 iterations.

[0083] Embodiment 2:

[0084] The embodiment of the present invention further provides a device for inverting aquifer parameters of a groundwater system, including:

[0085] A first processing module, configured to set a pumping test scenario including one pumping well and several observation wells in a target site; wherein, pumping work is performed on the target aquifer in the pumping well, and water level decline change data during the pumping test and water level recovery change data after the pumping test are obtained in the observation wells; the observed data is recorded as a vector:

[0086] A second processing module, configured to establish a numerical model for simulating the pumping test process; at the same time, determine the upper and lower limits of the parameter m to be inverted in the model according to prior information, and record them as: m L and m U ;

[0087] A third processing module, configured to obtain a parameter sample data set M = [m L and m U , …, m 1 , …, m M by using the Latin hypercube sampling method according to the upper and lower limits m obs of the aquifer parameters, and obtain the simulation results Y = [y 1 , …, y M at the corresponding space-time coordinates of the pumping test observed data y

[0088] The fourth processing module establishes a non - linear optimization model with the goal of inversely identifying the model parameter m based on the observed data, the surrogate model, and the prior information of the aquifer parameters; then, according to the constraint conditions in the non - linear optimization model, the elk herd optimization algorithm is used to search for the optimal model parameter m * , as the inversion and identification result of the aquifer parameters.

[0089] As an implementation manner of an embodiment of the present invention, the non - linear optimization model is:

[0090]

[0091] m L ≤m≤m U

[0092] F S (m)≈F HF (m)

[0093] where: F HF (·) and F S (·) respectively represent the high - fidelity numerical model operator and the surrogate model operator; represents the observed data vector.

[0094] As an implementation manner of an embodiment of the present invention, the parameter m to be inverted includes: permeability parameter and compressibility.

[0095] Example 3:

[0096] The embodiment of the present invention also provides a groundwater system aquifer parameter inversion system, including: a memory and a processor. A computer program is stored on the memory and run by the processor. When the computer program is run by the processor, it executes the groundwater system aquifer parameter inversion method.

[0097] Example 4:

[0098] The embodiment of the present invention also provides a storage medium. A computer program is stored on the storage medium. When the computer program runs, it executes the groundwater system aquifer parameter inversion method.

[0099] The above - described embodiments are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for inverting parameters of aquifers in a groundwater system, characterized in that: include: Step S1, setting a pumping test scene including a pumping well and several observation wells at the target site; wherein, pumping work is performed on the target aquifer in the pumping well, and the water level drop change data during the pumping test and the water level recovery change data after the pumping test are obtained in the observation well; the observation data is recorded as a vector: Step S2: for the pumping test scenario in step S1, a numerical model simulating the pumping test process is established; at the same time, the upper and lower limits of the value of the parameter m to be inverted in the model are determined according to the prior information, which are respectively denoted as: m L and m U ; Step S3: According to the upper and lower limits m of the aquifer parameters L and m U , using the Latin hypercube sampling method to obtain the parameter sample data set M = [m1,…,m M ], and use the numerical model in step S2 to obtain the pumping test observation data y in step S1 obs The simulation result at the corresponding space-time coordinate is Y=[y1,…,y M ], establish a sample data set D = {M, Y} required for training the alternative model; then, based on the sample data set D, use a deep neural network to establish an alternative model for the numerical model in step S2; Step S4: Based on the observed data, the alternative model and the prior information of the aquifer parameters, a nonlinear optimization model with the inversion identification model parameter m as the goal is established; and then, based on the constraints in the nonlinear optimization model, the elk herd optimization algorithm is used to search for the optimal model parameter m. * , as the inversion identification result of aquifer parameters.

2. The method for inversion of groundwater system aquifer parameters according to claim 1, characterized in that: The basic form of the nonlinear optimization model in step S4 is: Among them: F HF (·) and F S (·) denotes the high-fidelity numerical model operator and the surrogate model operator, respectively; Represents the observed data vector.

3. The method for inversion of groundwater system aquifer parameters according to claim 2, characterized in that: The parameter m to be inverted includes: a permeability parameter and a compressibility coefficient.

4. A groundwater system aquifer parameter inversion device, characterized in that: include: The first processing module is used to set up a pumping test scenario including a pumping well and several observation wells at the target site; wherein, pumping work is performed on the target aquifer in the pumping well, and the water level drop change data during the pumping test and the water level recovery change data after the pumping test are obtained in the observation well; the observation data is recorded as a vector: The second processing module is used to establish a numerical model for simulating the pumping test process; at the same time, the upper and lower limits of the value of the parameter m to be inverted in the model are determined according to the prior information, which are respectively denoted as: m L and m U ; The third processing module is used to calculate the upper and lower limits m of the aquifer parameters. L and m U , using the Latin hypercube sampling method to obtain the parameter sample data set M = [m1,…,m M ], and the numerical model was used to obtain the pumping test observation data y obs The simulation result at the corresponding space-time coordinate is Y=[y1,…,y M ], establish the sample data set D = {M, Y} required for training the alternative model; then, based on the sample data set D, use the deep neural network to establish the alternative model of the numerical model; The fourth processing module establishes a nonlinear optimization model with the inversion identification model parameter m as the goal based on the observed data, the alternative model and the prior information of the aquifer parameters; then, according to the constraints in the nonlinear optimization model, the elk group optimization algorithm is used to search for the optimal model parameter m. * , as the inversion identification result of aquifer parameters.

5. The groundwater system aquifer parameter inversion device according to claim 4, characterized in that: The nonlinear optimization model is: Among them: F HF (·) and F S (·) denotes the high-fidelity numerical model operator and the surrogate model operator, respectively; Represents the observed data vector.

6. The groundwater system aquifer parameter inversion device according to claim 5, characterized in that: The parameter m to be inverted includes: a permeability parameter and a compressibility coefficient.

7. A groundwater system aquifer parameter inversion system, characterized in that: include: A memory and a processor, wherein the memory stores a computer program executed by the processor, and when the computer program is executed by the processor, the method for inverting the parameters of aquifers in a groundwater system as described in any one of claims 1 to 3 is executed.

8. A storage medium, characterized in that: The storage medium stores a computer program, which, when running, executes the method for inverting parameters of aquifers in a groundwater system as described in any one of claims 1 to 3.

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