CN114611832B - Seawater intrusion prediction method based on Bayesian multi-model set pair analysis - Google Patents
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Abstract
The invention discloses a seawater intrusion prediction method based on Bayesian multi-model set pair analysis, which comprises the following steps of: selecting model parameters, setting and optimizing parameter value ranges, and constructing seawater intrusion numerical models of different schemes; updating model weights of different schemes by combining chloride ion concentration observation data and prediction data and utilizing a Bayesian multi-model set pair analysis technology; and carrying out weighted average on the prediction result of the seawater intrusion model to obtain the integrated space-time distribution of the chloride ion concentration. The invention organically combines the Bayes theorem with the set pair analysis method, improves the weight calculation based on the similarity of a plurality of sets of set pairs, and proves the feasibility of the Bayes multi-model set pair analysis method in predicting the migration of underground water pollutants.
Description
Technical Field
The invention relates to the field of hydrology statistics, in particular to a seawater intrusion prediction method based on Bayesian multi-model set pair analysis.
Background
Seawater intrusion disasters are widely regarded as threatening coastal underground fresh water resources. With the advance of the urbanization process in China, unreasonable water resource development leads to the destruction of the balance between the fresh water in the land aquifer and the ocean seawater, so that the seawater (or the salt water which is in hydraulic connection with the seawater) invades towards the land along the aquifer to form the seawater invasion phenomenon, and the land and underground fresh water is greatly polluted. The accurate and reliable prediction of seawater invasion is crucial to effectively preventing and controlling groundwater pollution and improving aquifer remediation efficiency.
Groundwater numerical simulation is an important means for studying the seawater invasion process. For example, a numerical model based on physical processes, such as MT3DMS, sewwat, PARFLOW, etc., can simulate continuous water flow and solute transport processes in three-dimensional space, providing flow fields and pollutant distributions. However, the model construction process is usually artificially simplified to a certain extent, and due to the lack of observation data, an effective checking mechanism of the system is lacked after the model is established, and the model parameters are selected unreasonably, so that the model results are deviated. This is because the models are equivalent, and the models can achieve the same simulation result through different parameter combinations. Therefore, the reasonable selection of the model parameters is very key for accurately predicting the seawater invasion process. However, most of the current research only relies on a single model for pollutant prediction, and few techniques for multi-model integration considering uncertainty of model parameters exist.
Multi-model integration can be used to estimate a wider range of parameter uncertainty, so as to be more likely to include unknown true predictors. The set pair analysis theory is a novel system analysis method for processing uncertainty problems by using the contact degree. The method carries out systematic mathematical analysis on the determinacy and uncertainty of two sets with certain correlation in the set pair and the interaction between the determinacy and the uncertainty, and is a new theoretical method for integrally researching the determinacy and the uncertainty. However, current research on set-up analysis methods is rarely applied to solve the actual groundwater contamination problem. More importantly, the existing set pair analysis method only considers the similarity influence of a single set pair (namely a pair formed by two sets) when calculating the weight of the scheme, and the determined scheme weight may have one-sidedness and cause large deviation on an evaluation result.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects of the background technology, the invention discloses a seawater intrusion prediction method based on Bayes multi-model set pair analysis, which comprises the steps of fusing a Bayes theorem and a set pair analysis method, innovating a Bayes multi-model set pair analysis technology, considering various models under the situation of different parameters (such as permeability coefficient, water storage rate and longitudinal dispersion), updating the posterior probability of the models by utilizing the similarity of training data set pairs, obtaining model weights of different schemes, and further weighting and averaging to predict seawater intrusion.
The technical scheme is as follows: the invention discloses a seawater intrusion prediction method based on Bayesian multi-model set pair analysis, which comprises the following steps:
s1, establishing a seawater intrusion model based on a physical process, selecting model parameters which have obvious influence on a chloride ion concentration output result, optimizing and determining value ranges of the parameters;
s2, setting and constructing different parameter combination schemes based on the value range of the model parameter selected in the S1, and predicting the global chloride ion concentration distribution under different construction schemes by utilizing the established seawater intrusion model;
s3, updating and solving the weights of the seawater intrusion model with different schemes by utilizing a Bayesian multi-model set pair analysis technology according to the difference between the chloride ion concentration observation data and the prediction data at the observation well;
and S4, according to the model weight obtained in the S3, integrating the seawater intrusion model prediction results under different parameter setting schemes and obtaining the integrated chloride ion concentration distribution.
In S1, the seawater intrusion model is a groundwater solute transport model based on a physical process, and the selected model parameters which have obvious influences on the output result of the chloride ion concentration are permeability coefficient K and water storage rate S s And longitudinal dispersion degree alpha L And the chloride ion concentration is a variable which is variable in time and space and is output by a seawater intrusion model.
Further, in S2, based on the parameter value range in S1, a Latin hypercube sampling method is adopted to respectively measure the permeability coefficient K and the water storage rate S s Longitudinal dispersion alpha L Sampling and constructing M different model parameter combination schemes; based on a Monte Carlo method, seawater invasion numerical simulation models are respectively operated to obtain corresponding global chloride ion concentration fields under different construction schemes.
Further, S3 specifically includes the following steps:
s3.1, randomly dividing all observation wells into a training group and a verification group, and respectively obtaining chloride ion concentration simulation values of the observation wells of the training group and the verification group at different time under different construction schemes (M =1 \ 8230M);
s3.2, constructing a scheme g aiming at a certain model m All observation sequences A of the training set obs With its analog sequence B sim Are combined into a set of pairs S { A obs ,B sim And dividing the total number N of elements in the sequence into the following classes according to a difference sequence between observation and simulation: the number of the same characteristic elements in the same class is I m The number of the difference characteristic elements is D m And pairs, the number of opposite characteristic elements is C m ；
Calculating the contact degree mu based on a contact degree formula in a set pair analysis method m ：
And then calculating set pair weight omega based on set pair weight function m ：
Repeating the above process by using the difference values of all the observation sequences and the simulated sequence data of the verification group, and calculating the pair weights theta of different model sets m ；
S3.3, according to the Bayes statistical principle, the set pair weight omega obtained by the training set is subjected to m As a priori probability Pr (g) m ) Set pair weight θ obtained by verifying group m As likelihood value Pr (data | g) m ) Updating posterior probabilities of different models, namely Bayesian set pair weight:
further, in S4, the multi-model output results (O) under different schemes are collected m ) And carrying out weighted average to finally obtain the output result (O) of the seawater intrusion integrated model:
the model output result obtained in the above formula is the chloride ion contaminant concentration, which is variable in space and time.
Has the advantages that: compared with the prior art: according to the method, bayes 'theorem and a set pair analysis method are organically combined, weight calculation is improved based on the similarity of a plurality of sets of set pairs, and the feasibility of the Bayes' multi-model set pair analysis method in the aspect of predicting underground water pollutant migration (taking chloride ion migration in the process of seawater intrusion as an example) is verified; according to the method, a multi-scheme integrated modeling is adopted, an aggregate model under different situations such as permeability coefficient, water storage rate and longitudinal dispersity is considered, and deviation caused by unreasonable parameter selection in a single model is reduced; the Bayesian set pair analysis technology quantifies the similarity of a plurality of groups of data set pairs, is an improved weight evaluation algorithm, reduces the estimation error, and has higher accuracy and reliability.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a region model mesh under investigation in an example embodiment;
FIG. 3 is a graph showing the correlation between 27 models calculated by using the training set and the validation set in the example;
FIG. 4 is a comparison graph of the predicted chloride ion concentration value and the observed value of the training set output by the integrated model and a comparison graph of the predicted chloride ion concentration value and the observed value of the validation set output by the integrated model in the embodiment.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
The seawater intrusion prediction method based on the Bayesian multi-model set pair analysis, as shown in FIG. 1, comprises the following steps:
s1: the invention can effectively predict seawater invasion based on Bayes multi-model set pair analysis technology when being verified in an unsteady confined aquifer. As shown in figure 2, the area 374 square kilometers and the thickness of the aquifer is about 10-15 meters, and the area is a concentrated water supply area in a city, and the south sea water invades inland due to excessive pumping. Firstly, an underground water solute transport model based on a physical process is established for the region, the embodiment is a seawater intrusion model, local grid refinement is carried out on a heavy spot region, a coarse grid is 200mx 200m, the refined grid is 50mx 50m, the total dispersion is 36660 quadrilateral grids, the peripheral boundaries of the region are all given water head boundaries, the south boundary is a fixed concentration boundary, the initial pollutant concentration of an aquifer is set to be 0mg/L, a plurality of observation wells are arranged in the region to monitor the chloride ion concentration, the chloride ion concentration is the output result of the seawater intrusion model and is a variable in space and time, and a SEAWAT is utilized to solve an underground water flow equation and a chloride ion transport equation.
After the model is checked, other underground water flow and solute transport parameters are as follows: the permeability coefficient was 55m/day, the water storage rate was 2.2104E-05, the porosity was 0.3, the longitudinal dispersibility was 1m, and the ratio of the transverse dispersibility to the longitudinal dispersibility was set to 0.1. For this embodiment, the total simulation duration is 23741 days, i.e., from the beginning of 1945 to the end of 2009, and each month is set as a time step, for 780 time steps. After the model is established and checked, three parameters (the permeability coefficient K of the aquifer and the water storage rate S) which have great influence on the simulation result of the chloride ion concentration are selected s Longitudinal dispersion alpha L ) And constructing a multi-model combination scheme.
S2: the parameters obtained after model checking are mean values, and Gaussian distribution is met. According to different parameter sensitivities of each model, a Latin hypercube sampling method is adopted to respectively measure the permeability coefficient K and the water storage rate S s Longitudinal dispersion alpha L Sampling is carried out, and as shown in table 1, three values are taken for each parameter to consider errors caused by non-uniqueness of parameter selection, and 27 model parameter combination schemes are constructed. Based on a Monte Carlo (Monte Carlo) method, seawater invasion numerical models under different parameter combinations are respectively operated to obtain corresponding space-time scale chloride ion concentrations.
Table 1 27 sets of model parameter selection and combination schemes
S3: and (3) acquiring chloride ion concentration simulation values at observation wells of a training group and a verification group aiming at 27 (m =1 \ 8230; 27) model construction schemes. In this embodiment, for each solution model, the training set pair consists of 225 observed values and simulated values of chloride ions, and the verification set pair consists of 117 observed values and simulated values of chloride ions. Taking the degree of three-way relation as an example, according to the relative error between the observed value and the analog value, the training set pair sequence is firstly divided into three types: the same class (the relative error is less than 1.0%), the difference class (the relative error is between 1.0% and 4.5%) and the opposite class (the relative error is more than 4.5%), and counting the corresponding number I m 、D m And C m And calculating the contact degree:
and then calculating the pair weight omega of the training set based on the set pair weight function 1 -ω 27 ：
Similarly, the above process is repeated using the relative errors between all the observed sequences and their simulated sequences in the validation set, and set-to-weight θ of the 27 models in the validation set is calculated 1 -θ 27 . As shown in fig. 3, the relationship between the 27 models calculated by using the training set and the validation set data is used to quantify the uncertainty of the model, and the smaller the relationship, the larger the uncertainty of the model and the lower the weight.
Finally, according to Bayesian statistical principle, the set pair weight omega obtained from the training set is used m As a prior probability Pr (g) m ) Verify group derived set-to-set weight θ m As likelihoodValue Pr (data | g) m ) And updating posterior probabilities of the 27 models:
s4: and (3) collecting the multi-model output results under 27 different schemes, and performing weighted average to finally obtain the chloride ion concentration output of the seawater intrusion integration model in the research area:
as shown in fig. 4 and table 2, the coincidence degree of the chloride ion concentration value and the observed value of the integrated model is high, the performance of the integrated model is good, and the prediction capability is strong.
Table 2 shows the fitting degree and error of the predicted value and the observed value of the chloride ion concentration of the training set and the verification set obtained by integrating the models
| Index (I) | Training set | Authentication group |
| Coefficient of correlation (r) | 0.9756 | 0.8160 |
| Root Mean Square Error (RMSE) | 11.9679 | 8.2191 |
| Nash coefficient of efficiency (NSE) | 0.9519 | 0.6658 |
| Mean relative error (MARE) | 2.7729 | 2.3502 |
Through the analysis, the integrated model created by the Bayesian multi-model set pair analysis technology can effectively predict seawater intrusion. Compared with other technologies, the method improves the weight evaluation algorithm, and the calculation precision and reliability are higher.
Claims (2)
1. A seawater intrusion prediction method based on Bayesian multi-model set pair analysis is characterized by comprising the following steps:
s1, establishing a seawater intrusion model based on a physical process, selecting model parameters which have obvious influence on a chloride ion concentration output result, optimizing and determining value ranges of the parameters;
the seawater invasion model is a physical process-based underground water solute transport model, and the selected model parameters which have obvious influence on the output result of the chloride ion concentration are permeability coefficient K and water storage rate S s And longitudinal dispersion degree alpha L The concentration of the chloride ions is a time-space variable which is an output result of the seawater intrusion model;
s2, setting and constructing different parameter combination schemes based on the value range of the model parameter selected in the S1, and predicting the global chloride ion concentration distribution under different construction schemes by utilizing the established seawater intrusion model;
specifically, a Latin hypercube sampling method is adopted to respectively measure the permeability coefficient K and the water storage rate S s Longitudinal dispersion alpha L Sampling and constructing M different model parameter combination schemes; respectively operating a seawater invasion numerical simulation model based on a Monte Carlo method to obtain corresponding global chloride ion concentration fields under different construction schemes;
s3, updating and solving the weights of the seawater intrusion model with different schemes by utilizing a Bayesian multi-model set pair analysis technology according to the difference between the chloride ion concentration observation data and the prediction data at the observation well;
the method specifically comprises the following steps:
s3.1, randomly dividing all observation wells into a training group and a verification group, and respectively obtaining chloride ion concentration simulation values of the observation wells of the training group and the verification group at different time under different construction schemes (M =1 \ 8230M);
s3.2, constructing a scheme g aiming at a certain model m All observation sequences A of the training set obs With its analog sequence B sim Combined into a set of pairs S { A } obs ,B sim And dividing the total number N of elements in the sequence into the following classes according to a difference sequence between observation and simulation: the number of the same characteristic elements is I m The number of the difference characteristic elements is D m And pairs, the number of opposite characteristic elements is C m ；
Calculating the contact degree mu based on a contact degree formula in a set pair analysis method m ：
And then calculating set pair weight omega based on set pair weight function m ：
Repeating the above process by using the difference values of all observation sequences and simulated sequence data of the verification group, and calculating the pair weights theta of different model sets m ；
S3.3, according to the Bayes statistical principle, the set pair weight omega obtained by the training set is weighted m As a prior probability Pr (g) m ) Set pair weight θ obtained by verifying group m As likelihood value Pr (data | g) m ) Updating different modelsPosterior probability, i.e. bayes set pair weight:
and S4, according to the model weight obtained in the S3, integrating the seawater intrusion model prediction results under different parameter setting schemes and obtaining the integrated chloride ion concentration distribution.
2. The seawater intrusion prediction method based on Bayesian multi-model set pair analysis according to claim 1, characterized in that: s4, collecting multi-model output results O under different schemes m And carrying out weighted average to finally obtain an output result O of the seawater intrusion integration model:
the model output result obtained in the above formula is the chloride ion contaminant concentration, which is variable in space and time.
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