CN117057221A - Coastal heterogeneous aquifer characterization realization method and device based on machine learning - Google Patents
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Abstract
The invention discloses a method and a device for describing a coastal heterogeneous aquifer based on machine learning, wherein a seawater invasion numerical model is used for obtaining simulation data outputted by a plurality of groups of hydraulic conductivity coefficients randomly generated from parameter prior distribution and corresponding models thereof; generating a plurality of samples of the parameter difference value and the analog data difference value from the prior set by two-phase subtraction between the samples; training a machine learning model by using the data, and constructing a mapping relation between the simulated data difference value and the parameter difference value; inputting the difference value between the observed data and the priori simulation data set into a trained machine learning model, and adding the obtained output and the priori parameter set to obtain an updating result of the priori hydraulic conductivity coefficient set; and carrying out iterative updating to obtain the iterative hydraulic conductivity. The method can identify complex features from training data and learn nonlinear relations, and obtains better inversion effect in the problem of describing the complex non-Gaussian coastal aquifer.
Description
Technical Field
The invention belongs to the technical field of hydrogeology, and particularly relates to a coastal heterogeneous aquifer characterization realization method and device based on machine learning.
Background
The phenomenon that coastal aquifer salty-fresh water interfaces develop to inland due to over exploitation of coastal aquifer fresh water resources and land utilization change in coastal areas is called seawater invasion. Seawater intrusion will seriously threaten the water use safety in coastal areas. In order to realize scientific management and control of the coastal aquifer, accurate prediction of the seawater invasion process is needed, and a numerical model is a universal means. Therefore, in order to realize accurate prediction of seawater invasion, accurate characterization of a coastal heterogeneous aquifer is a crucial step. However, performing exploration activities such as drilling to obtain an accurate depiction of the coastal aquifer requires a significant cost investment, so that this approach may be considered impractical. One possible solution is to use other relatively easily available observations to obtain a depiction of the coastal heterogeneous aquifer by a data assimilation method.
In the field of data assimilation, the mainstream methods include Markov chain Monte Carlo, kalman filtering, variational methods, ESMDA and other algorithms. The Markov chain Monte Carlo algorithm (MCMC) is a Monte Carlo method based on a Markov chain, a large number of samples need to be extracted to obtain enough information, the calculation cost caused by multiple forward model calculation when the algorithm runs is huge, and a convergence problem may exist in the sample extraction process. Even though the MCMC algorithm has a complete theory, it is considered to be incapable of handling high-dimensional, nonlinear and non-gaussian problems due to its computational cost limitations. The kalman filter algorithm is a recursive filter algorithm that can be used to estimate the system state from noise measurements. The kalman filter algorithm has advantages in dealing with gaussian noise and time-varying systems, but has limitations for non-linear and non-gaussian systems. The variational method is an optimization method and can be used for calculating posterior distribution and edge distribution in the probability model. The variational method replaces the true posterior distribution by approximating the posterior distribution to simplify complex calculations. The variational method has advantages in processing large-scale data and model parameter learning, but cannot process complex posterior distributions such as non-Gaussian. The ESMDA algorithm is an ensemble learning-based method for estimating parameters and implicit variables in a probabilistic model. The ESMDA algorithm improves accuracy by integrating the predictions of multiple models with multiple data sources. The ESMDA algorithm has advantages in the case of processing multiple data sources, but it is difficult to achieve satisfactory results in non-gaussian systems. Clearly, none of the current data assimilation algorithms is capable of applying well in the characterization of such high-dimensional, non-linear, non-gaussian problems in coastal aquifers. Therefore, developing a good data assimilation algorithm for the coastal heterogeneous aquifer characterization problem becomes a current urgent problem to be solved.
Disclosure of Invention
The invention aims to: in the problem of coastal heterogeneous aquifer characterization, the invention provides a method and a device for coastal heterogeneous aquifer characterization based on machine learning, and the obtained inversion effect is superior to an ESMDA algorithm based on Kalman updating.
The technical scheme is as follows: the invention provides a method for realizing coastal heterogeneous aquifer characterization based on machine learning, which comprises the following steps:
(1) Obtaining simulation data outputted by a plurality of groups of hydraulic conductivity coefficients randomly generated from parameter prior distribution and the seawater intrusion numerical model by the seawater intrusion numerical model;
(2) Generating a plurality of samples of the parameter difference value and the analog data difference value from the prior set by two-by-two subtraction between the samples;
(3) Training a machine learning model by using the data, and constructing a mapping relation between the simulated data difference value and the parameter difference value;
(4) Inputting the difference value between the observed data and the priori simulation data set into a trained machine learning model, and adding the obtained output and the hydraulic conductivity coefficient set to obtain an updating result of the priori hydraulic conductivity coefficient set;
(5) Repeating the steps (2) to (4) until the iteration is finished, and obtaining the iterative hydraulic conductivity coefficient.
Further, the simulation data in the step (1) are water head, sea water concentration and land pollutant concentration.
Further, the implementation process of the step (1) is as follows:
randomly selecting N from a priori distribution of hydraulic conductivity coefficients e Group hydraulic conductivity sample Substitution of COMSOL Multiphysics-based seawater intrusion numerical model ∈> Obtaining simulation data output by a corresponding model: />Wherein->
Further, the seawater intrusion numerical model comprises a flow model and an migration model;
the flow model:
wherein u is darcy speed; k is the hydraulic conductivity; p is pore pressure; ρ is the fluid density; g is gravity acceleration; e-shaped article P (-) is porosity; q (Q) m Is a source sink item;
the migration model:
wherein c i Represents the concentration of the i-type substance in the liquid, c P,i Represents the adsorption amount of solid particles; j (J) i Diffusing a flux vector for the mass flux; r is R i An expression representing a reaction rate of the substance; s is S i Is an arbitrary source term; indicating the effective diffusion coefficient of the liquid i; d (D) F,i Is the fluid diffusion coefficient; d (D) D,i Representing the dispersion tensor of the liquid i.
Further, the implementation process of the step (2) is as follows:
from { X ] (0) ,Y (0) Non-repeated samples of two groups were subtracted to give n=n e (N e -1)/2 sets of training data, namely:
wherein ε ij Random samples of the observed error;is the analog data difference;is the parameter difference.
Further, the implementation process of the step (3) is as follows:
will beAs input, < >>Training a machine learning model as an output to obtain a mapping relationship +.>
Further, the implementation process of the step (4) is as follows:
wherein,namely, the updated hydraulic conductivity coefficient set, < + >>Is the observation data.
Further, the implementation process of the step (5) is as follows:
setting the iteration number as N iter First from { X (t-1) ,Y (t-1 ) Generation of models for training machine learningData of-> The set updates are as follows:through N iter After the secondary update, the final parameter set is that
The invention also provides an apparatus device comprising a memory and a processor, wherein:
a memory for storing a computer program capable of running on the processor;
a processor for executing the steps of the machine learning based coastal heterogeneous aquifer characterization implementation method as described above when running the computer program.
The invention also provides a storage medium having stored thereon a computer program which, when executed by at least one processor, implements the steps of a machine learning based coastal heterogeneous aquifer characterization implementation method as described above.
The beneficial effects are that: compared with the prior art, the invention has the beneficial effects that: according to the invention, a machine learning model is used for replacing a Kalman gain formula in ESMDA, so that Gaussian assumption required by the Kalman gain formula is avoided; secondly, the machine learning model used in the invention has the capability of extracting complex (including non-Gaussian) characteristics and learning nonlinear relations from a large amount of training data, and in the coastal heterogeneous aquifer characterization problem, the obtained inversion effect is superior to an ESMDA algorithm based on Kalman update.
Drawings
FIG. 1 is a schematic diagram of a method for describing and realizing a coastal heterogeneous aquifer based on machine learning;
FIG. 2 is a schematic diagram of a seawater intrusion numerical model in an embodiment;
FIG. 3 is a diagram showing the comparison of reference fields and the effect of the characterization; wherein (a) is an embodiment hydraulic conductivity reference field pattern; (b) is an embodiment observation well profile; (c) depicting effect patterns for implementation case ESMDA; (d) For embodiment case DA ML Drawing an effect graph;
FIG. 4 is a schematic diagram of a machine learning model used in an embodiment;
FIG. 5 shows the ESMDA and DA in the embodiment ML And (5) obtaining a root mean square error curve graph of the mean value of the hydraulic conductivity coefficient and the reference value.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The invention provides a coastal heterogeneous aquifer characterization realization method (DA) based on machine learning ML ) As shown in fig. 1, the method comprises the following steps:
s1, obtaining simulation data (namely, water head, sea water concentration and land pollutant concentration) output by a plurality of groups of parameter samples (namely, hydraulic conductivity coefficients) randomly generated from parameter prior distribution and corresponding models by a sea water intrusion numerical model.
Randomly selecting 500 groups of hydraulic conductivity coefficient samples from hydraulic conductivity coefficient prior distribution Substitution model->Obtaining simulation data output by a corresponding model: /> Wherein->
The seawater intrusion and land-based contaminant migration were simulated by coupling the two modules "Darcy's Law" and "The Transport of Diluted Species in Porous Media" in COMSOL Multiphysics, and the flow and migration models were solved sequentially by a separate solver.
For the flow model:
wherein u (m/s) is Darcy speed; k (m/s) is the hydraulic conductivity; p (Pa) is pore pressure; ρ (kg/m) 3 ) Is the fluid density; g (m/s) 2 ) Gravitational acceleration; e-shaped article P (-) is porosity; q (Q) m (kg/(m 3 S)) is a source sink item.
For the migration model:
wherein c i (mol/m 3 ) Represents the concentration of the i-type substance in the liquid, c P,i (-) represents the solid particle adsorption amount (i.e., moles of solid per dry weight); j (J) i (mol/m 2 S) is a mass flux diffusion flux vector; r is R i (mol/m 3 S) represents a reaction rate expression of the substance; s is S i (kg/(m 3 S)) is any source term;indicating the effective diffusion coefficient of the liquid i; d (D) F,i (m 2 S) is the fluid diffusion coefficient; d (D) D,i (m 2 S) represents the dispersion tensor of the liquid i.
S2, generating a large number of samples of the parameter difference value and the analog data difference value from the prior set by subtracting the samples from each other.
From { X ] (0) ,Y (0) Subtracting the two non-repeated samples from each other to obtain training data of n=500 (500-1)/2= 124750, namely: wherein: epsilon ij Random samples of the observed error;is the analog data difference; />Is the parameter difference.
S3, training a machine learning model by using the data, and constructing a mapping relation between the simulated data difference value and the parameter difference value.
Will beAs input, < >>Training as output substituted into a machine learning model named DenseNet shown in figure 4 to obtain mapping relationship of analog data difference value to parameter difference value ≡>
S4: inputting the difference value between the observed data (namely, the actual observed value of the water head, the sea water concentration and the land pollutant concentration) and the prior simulation data set into a trained machine learning model, and adding the obtained output (the prediction of the difference value between the prior parameter and the parameter true value) and the prior parameter (namely, the hydraulic conductivity coefficient) set to obtain the updating result of the prior hydraulic conductivity coefficient set:
wherein,namely, the updated hydraulic conductivity coefficient set, < + >>Is the observation data.
And S5, for the strong nonlinearity problem, repeating the steps S2 to S4 to the iteration end to obtain the parameter (hydraulic conductivity coefficient) after the iteration, namely the description of the coastal aquifer.
Setting the iteration number as N iter First from { X (t-1) ,Y (t-1) Generation of models for training machine learningData of-> The set updates are as follows:through N iter After the secondary update, the final parameter set is that
Based on the same inventive concept, the present invention also provides an apparatus device comprising a memory and a processor, wherein: a memory for storing a computer program capable of running on the processor; a processor for executing the steps of the machine learning based coastal heterogeneous aquifer characterization implementation method as described above when running the computer program.
The invention also provides a storage medium having stored thereon a computer program which, when executed by at least one processor, implements the steps of a machine learning based coastal heterogeneous aquifer characterization implementation method as described above.
In order to verify that the method can be used for describing the coastal heterogeneous aquifer, the implementation case considers a two-dimensional elevation coastal aquifer. As shown in fig. 2, the size of the study area is lxb=240×30m, and the left side is a constant fresh water head h f =31.6m, concentration is C f ＝0kg/m 3 . The right side is a constant seawater head h s =31m, concentration of C s ＝35kg/m 3 . The upper and lower are watertight boundaries. The total simulated time for this study was 4500 days, and the area was filled with fresh water having a head of 30m at the initial time. A pumping well with a diameter of 0.5m at (100, 25) pumps water at a rate of 2000kg/d from 1000 d. Square area with side length of 0.5m at the position of upper left corner (20, 25) is 35 kg/(m) within 1500-2500d 3 The intensity of d) releases the land-based contaminant outwards.
In this numerical case, the observed data (i.e., actual observed values of head, sea water concentration, land-based contaminant concentration) are calculated by substituting the reference field of 91×241-dimensional hydraulic conductivity (K) shown in fig. 3 (a) into a numerical model and adding the values to conform to the normal distributionObtained by measuring the error of the measurement. Wherein the head, sea water concentration, land-based contaminant concentration data are based on the observation well shown in fig. 3 (b) at t= [300,600..4500, respectively]d、t＝[300,600,...,4500]d、t＝[1800,2100,...,4500]And d, obtaining the time.
Fig. 3 (c) shows the mean field of K obtained by ESMDA algorithm. Obviously, ESMDA algorithm only characterizes part of the reference field through observation data, andthe channel characteristics exhibited in the reference field are poorly characterized. And as shown in FIG. 3 (d), is formed by DA ML The algorithm inversion obtains that the hydraulic conductivity coefficient mean value field is closer to the reference field than ESMDA, and the method is characterized by better connectivity of the reference field and almost all channel characteristics of the reference field. As can be seen from FIG. 5, from DA ML The root mean square error (Root mean squared error, RMSE) between the hydraulic conductivity obtained by the algorithm and the reference value is significantly smaller than the root mean square error between the simulated head value and the observed head value obtained by the ESMDA algorithm. The DA can be considered by integrating various evaluation criteria ML The inversion effect of the method in the non-Gaussian hypothesis groundwater parameter inversion problem is superior to ESMDA.
Through the analysis, the coastal heterogeneous aquifer characterization realization method based on machine learning has the capability of characterizing the complex coastal heterogeneous aquifer.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereto, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the present invention.
Claims (10)
1. The coastal heterogeneous aquifer characterization realization method based on machine learning is characterized by comprising the following steps of:
(1) Obtaining simulation data outputted by a plurality of groups of hydraulic conductivity coefficients randomly generated from parameter prior distribution and the seawater intrusion numerical model by the seawater intrusion numerical model;
(2) Generating a plurality of samples of the parameter difference value and the analog data difference value from the prior set by two-by-two subtraction between the samples;
(3) Training a machine learning model by using the data, and constructing a mapping relation between the simulated data difference value and the parameter difference value;
(4) Inputting the difference value between the observed data and the priori simulation data set into a trained machine learning model, and adding the obtained output and the hydraulic conductivity coefficient set to obtain an updating result of the priori hydraulic conductivity coefficient set;
(5) Repeating the steps (2) to (4) until the iteration is finished, and obtaining the iterative hydraulic conductivity coefficient.
2. The method for describing the coastal heterogeneous aquifer based on machine learning according to claim 1, wherein the simulation data of the step (1) are water head, sea water concentration and land pollutant concentration.
3. The method for describing the coastal heterogeneous aquifer based on machine learning according to claim 1, wherein the implementation process of the step (1) is as follows:
randomly selecting N from a priori distribution of hydraulic conductivity coefficients e Group hydraulic conductivity sample Substitution of COMSOL Multiphysics-based seawater intrusion numerical model ∈> Obtaining simulation data output by a corresponding model: />Wherein->
4. The machine learning based coastal heterogeneous aquifer characterization implementation method of claim 1, wherein the seawater intrusion numerical model comprises a flow model and an migration model;
the flow model:
wherein u is darcy speed; k is the hydraulic conductivity; o is pore pressure; ρ is the fluid density; g is gravity acceleration; e-shaped article P (-) is porosity; q (Q) m Is a source sink item;
the migration model:
wherein c i Represents the concentration of the i-type substance in the liquid, c P,i Represents the adsorption amount of solid particles; j (J) i Diffusing a flux vector for the mass flux; r is R i An expression representing a reaction rate of the substance; s is S i Is an arbitrary source term; indicating the effective diffusion coefficient of the liquid i; d (D) F,i Is the fluid diffusion coefficient; d (D) D,i Representing the dispersion tensor of the liquid i.
5. The method for describing the coastal heterogeneous aquifer based on machine learning according to claim 1, wherein the implementation process of the step (2) is as follows:
from { X ] (0) ,Y (0) Non-repeated samples of two groups were subtracted to give n=n e (N e -1)/2 sets of training data, namely:
wherein ε ij Random samples of the observed error;is the analog data difference;is the parameter difference.
6. The method for describing the coastal heterogeneous aquifer based on machine learning according to claim 1, wherein the implementation process of the step (3) is as follows:
will beAs input, < >>Training a machine learning model as an output to obtain a mapping relationship +.>
7. The method for realizing the coastal heterogeneous aquifer characterization based on machine learning according to claim 1, wherein the implementation process of the step (4) is as follows:
wherein,namely, the updated hydraulic conductivity coefficient set, < + >>Is the observation data.
8. The method for realizing the coastal heterogeneous aquifer characterization based on machine learning according to claim 1, wherein the implementation process of the step (5) is as follows:
setting the iteration number as N iter First from { X (t-1) ,Y (t-1) Generation of models for training machine learningIs a function of the data of (a), the set updates are as follows:through N iter After the secondary update, the final parameter set is that
9. An apparatus device comprising a memory and a processor, wherein:
a memory for storing a computer program capable of running on the processor;
a processor for performing the steps of the machine learning based coastal heterogeneous aquifer characterization implementation method as defined in any one of claims 1-8 when the computer program is run.
10. A storage medium having stored thereon a computer program which, when executed by at least one processor, performs the steps of the machine learning based coastal heterogeneous aquifer characterization implementation method of any one of claims 1-8.
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