CN109190280A - A kind of pollution source of groundwater inverting recognition methods based on core extreme learning machine alternative model - Google Patents
A kind of pollution source of groundwater inverting recognition methods based on core extreme learning machine alternative model Download PDFInfo
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Abstract
The invention discloses a kind of pollution source of groundwater inverting recognition methods based on core extreme learning machine alternative model, steps are as follows: the generation of S10, training set；The foundation of S20, core extreme learning machine alternative model；S30, the foundation of substitution-Optimized model: it in traditional analog-optimization link, introduces core extreme learning machine alternative model and replaces simulation model；S40, it solves substitution-Optimized model: iteratively solving above-mentioned Optimized model respectively by genetic algorithm, after objective function convergence, decision variable value corresponding to optimal objective function, as corresponding pollution sources discharge history.The experimental results showed that, for multiple pollution sources the situations such as release, irregular shape research area and unsteady flow, which occur, for the present invention good recognition effect, identify that pollution source of groundwater release history precision is higher, compared to directlying adopt fast ten times of calculating speed of simulation model.
Description
Technical field
The present invention relates to a kind of pollution source of groundwater processing techniques, more particularly to a kind of core extreme learning machine that is based on to substitute mould
The pollution source of groundwater inverting recognition methods of type.
Background technique
Underground water pollution problem constitutes a serious threat to drinking water safety and ecological environment.Since underground water pollution has
The hysteresis quality feature of existing concealment and discovery, causes people for the situation of pollution source of groundwater, including in water-bearing layer
The information such as spatial position, the release history of lower pollution entering the water are all short in understanding and grasp.This sets to underground water pollution recovery scenario
Meter, risk assessment and liability for polution identification all bring very big difficulty.Therefore, what related pollution source of groundwater inverting identified grinds
Studying carefully seems increasingly important.
Pollution source of groundwater inverting identification refers to according to limited level of ground water, water-quality observation data, to underground water solute
Transported simulation model carries out inverting solution, identifies the feature in relation to pollution source of groundwater, including pollution source position, release history
Etc. information.
Currently, the research of pollution source of groundwater inverting identification is still in developing stage, influences pollution source of groundwater inverting knowledge
The factor of other effect is numerous, including observe the accuracys of data, the modeling method of alternative model, the classification of unknown variable with wait ask
Variable number etc..Therefore how above-mentioned influence factor is dealt carefully with, and then improve pollution source of groundwater inverting accuracy of identification
It is the problem in science of urgent need to resolve.
Currently, when solving pollution source of groundwater inversion problem using simulation-optimization method, require thousands of to adjust secondaryly
With groundwater solute transfer simulation model (abbreviation simulation model), since the calculation amount of running simulation model is relatively large, calculates
Time is longer, therefore huge calculated load and interminable calculating time can be generated during iterative solution, this can seriously be limited
Application of the simulation-optimization method in pollution source of groundwater recognitive engineering problem.
The calculated load of underground water pollution sources inversion problem can be effectively reduced using alternative model, and then is improved and calculated effect
Rate.Alternative model is the approximate substitution model of simulation model, has similar input-output response relation with simulation model.Compared with
Simulation model, alternative model is easier to solve, therefore can reduce and a large amount of calculate time and calculated load.
The present Research and development trend that alternative model is applied in underground water pollution identifing source have a characteristic that substitution mould
The modeling method of type is relatively single, mainly Artificial Neural Network, and the substitution mould established based on artificial neural network method
That there are stability is poor for type, there is the deficiency to be improved to the fitting precision of simulation model.
There has been no core extreme learning machine alternative model is embedded in simulation-optimization method to solve underground water pollution in China at present
The research of source inversion problem is reported.
Summary of the invention
For the drawbacks described above of existing research, the present invention provides a kind of undergrounds based on core extreme learning machine alternative model
Pollution entering the water inverting recognition methods.In traditional analog-optimization link, core extreme learning machine alternative model is added, not only possesses
Preferable precision, and interminable inverse time and huge calculated load are decreased, improve the computational efficiency of refutation process.
The present invention solves technical problem and adopts the following technical scheme that a kind of underground based on core extreme learning machine alternative model
Pollution entering the water inverting recognition methods, comprising the following steps:
The generation of S10, training set
In order to portray Contaminants Transport rule in underground water, need to build for practical contaminated site condition or experiment condition
Found corresponding underground water pollution simulation of water quality model.For petroleum hydrocarbons, its migration mechanism is described, that is, is dissolved in
The mathematical model of the processes such as convection current, hydrodynamic dispersion and the biochemical reaction of the petroleum hydrocarbons in underground water such as formula (1).
Petroleum hydrocarbons enter underground environment, and there are Multiphase Flow, multiphase flow multicomponent pollutant transport mass-conservation equations are as follows:
In formula: k is number of components, including water (k=1), oily (k=2)；L is the number of phases, including water phase (l=1), oily phase (l=
2)；φ is porosity；For the total concentration of component k (with volume fraction)；ρkFor the density [ML of component k-3]；CklFor component k
Concentration in l phase (with volume fraction)；For the Darcy velocity [LT of l phase-1]；SlFor the saturation degree of l phase；For component k
Dispersion coefficient tensor [L in l phase2T-1]；RkFor the source sink term [ML of component k-3T-1]。
Above-mentioned multiphase flow multicomponent pollutant transport mass-conservation equation adds primary condition appropriate and boundary condition,
Constitute underground water pollution simulation of water quality model.It can by the calculating of underground water pollution simulation of water quality model by known input data
Output data is obtained, it thus can be by input-output data set composing training collection.
The foundation of S20, core extreme learning machine alternative model
Core extreme learning machine alternative model is a kind of alternative model with good accuracy and stability, it with for practical
Contaminated site condition or experiment condition have extremely phase to portray the simulation model that Contaminants Transport rule is established in underground water
Close Input output Relationship can be used to replace simulation model, calculate time and calculated load to reduce, improve computational efficiency.
For N number of training sample (xj,tj), j=1,2 ... .N, the original optimization problem expression of core extreme learning machine method
Are as follows:
s.t.h(xi)Tβ=ti-ξi (2)
In formula: β represents a vector of feature space F, and C represents regularization parameter, εiRepresentative errors, h (xi) represent input
Mapping of the variable x in the space F.The parameter that core extreme learning machine alternative model need to determine is regularization coefficient C.Regularization coefficient C
Play the role of balance training error and algorithm complexity, C value is smaller, and bigger to the tolerance of training error, C value is excessive, can
It can lead to the problem of over-fitting.
The output function expression of core extreme learning machine is as follows:
In formula: H is the hidden layer output matrix of core extreme learning machine, i.e.,HTIt is the transposed matrix of H, K is
Kernel function, KELMFor nuclear matrix, t is output matrix.Core extreme learning machine alternative model parameter is trained according to training set, further according to
Approximation quality evaluation index carrys out the precision that test stone measures core extreme learning machine alternative model, and it is good for selecting inspection result
Alternative model.
S30, the foundation of substitution-Optimized model
Alternative model is embedded into formation substitution-Optimized model in the constraint condition of Optimized model, expression is such as
Under:
In formula: NtIndicate period, NdIndicate inspection well quantity, Ck(t) the simulating pollution concentration of sample point k period t is indicated
Value,Indicate sample point k period t pollutant concentration actual measured value,It is the vector of measured concentration value composition,It is
The vector of source flux,WithIt is source flux value range is respectively up-and-down boundary.Formula (4) expression is to find unknown variable
Objective function is set to reach minimum.The expression formula of objective function is meant for NtA period, NdThe simulation of a inspection well calculates dense
The quadratic sum of the difference of angle value and measured concentration value reaches minimum (least square).Formula (5) is core extreme learning machine alternative model
Expression formula shorthand, expression be simulation calculate concentration value meet solute transport, that is to say, that simulation calculate concentration
Value is calculated according to core extreme learning machine alternative model.Formula (6) indicates the amplitude of variation restrictive condition of release history.
S40, substitution-Optimized model is solved
Iteratively solve above-mentioned Optimized model respectively by heuritic approach, after objective function convergence, optimal objective function
Corresponding decision variable value, as corresponding pollution sources discharge history.
Compared with prior art, the invention has the following beneficial effects:
1. the situations such as release, irregular shape research area and unsteady flow, which occur, for multiple pollution sources good identification
Effect, identification pollution source of groundwater release history precision are higher.
2. the alternative model based on the foundation of core extreme learning machine method is to simulation mould in contrast to artificial neural network alternative model
Type has better approximation ratio, is also relatively substituted based on artificial neural network by the inversion result of core extreme learning machine alternative model
The recognition result accuracy of model is higher.
3. using core extreme learning machine alternative model than directlying adopt fast ten times of calculating speed of simulation model.
Detailed description of the invention
The accompanying drawings constituting a part of this application is used to provide further understanding of the present application, and the application's shows
Meaning property embodiment and its explanation are not constituted an undue limitation on the present application for explaining the application.
Fig. 1 is a kind of flow chart of pollution source of groundwater inverting recognition methods based on core extreme learning machine alternative model
Fig. 2 is 1 water-bearing layer floor map of embodiment
Fig. 3 is 1 pollution sources of embodiment release history recognition result and true value comparison diagram
Fig. 4 is 2 water-bearing layer floor map of embodiment
Fig. 5 is 2 pollution sources of embodiment release history recognition result and true value comparison diagram
Specific embodiment
It is further elaborated below with reference to technical solution of the embodiment to invention.It will be appreciated that described embodiment
It is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, ordinary skill
Personnel's all other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
Those skilled in the art should know it is further that following specific embodiments or specific embodiment, which are the present invention,
The set-up mode of series of optimum explaining specific summary of the invention and enumerating, and being between those set-up modes can be mutual
In conjunction with or it is interrelated use, unless clearly proposing some of them or a certain specific embodiment or embodiment party in the present invention
Formula can not be associated setting or is used in conjunction with other embodiments or embodiment.Meanwhile following specific embodiment or
Embodiment is only as the set-up mode optimized, and not as the understanding limited the scope of protection of the present invention.
Embodiment 1:
It in research area is one of rectangle homogeneous aquifer more preferred embodiment that following embodiment, which is the present invention, only
As a preferred method for being further elaborated on thinking of the invention, and not as the restriction of specific protection scope of the invention
Understand.
1, the generation of training set
Table 1
| Aquifer parameter | Numerical value |
| Infiltration coefficient on the direction x, Kxx(m/s) | 0.0002 |
| Infiltration coefficient on the direction y, Kyy(m/s) | 0.0002 |
| Effecive porosity, θ | 0.25 |
| Vertical dispersivity, αL(m) | 40.0 |
| Level dispersivity, αT(m) | 9.6 |
| Water-bearing layer thickness, b (m) | 30.5 |
| The direction x mesh generation length, Δ x (m) | 100 |
| The direction y mesh generation length, Δ y (m) | 100 |
| Period Length, Δ t (month) | 3 |
| Initial concentration (g/L) | 0.1 |
The description in rectangular uniform water-bearing layer is as shown in table 1, and water-bearing layer floor map is as shown in Figure 2.Alternative model input
Data are obtained by the methods of sampling, and what present case was taken is that Latin Hypercube Sampling method obtains input data, pass through fortune later
Turn groundwater solute transfer simulation model, and by the solution of the MODFLOW and MT3DMS software in GMS software, obtains case 1
Each inspection well day part pollutant concentration value (as output data).Inspection well concentration is as the actual observation in inverting
Value, and using pollution sources feature as known variables processing.
It repeats the above steps 100 times, and then obtains 100 groups of input-output sample data collection.This is as the defeated of alternative model
Enter-output data, for training and examining the parameter of alternative model.Wherein, it is used for training parameter for first 90 groups, latter 10 groups for examining
Test the precision of alternative model.
2, the foundation of core extreme learning machine alternative model
The output function expression of core extreme learning machine is as follows:
By can get the parameter of alternative model based on 90 groups of sample data sets for training.For each situation, often
The alternative model of mouth well trained after parameter, requires to test respectively 10 times, selects the alternative model by inspection, with
Ensure that the parameter of alternative model training is effective.
3, substitution-Optimized model foundation
Optimized model is established as follows:
0 < σm< 100, m=1,2 ... 12 (10)
Formula (8) tabular form finds unknown variable σ1To σ12(4 period × 3 pollution sources) make objective function Z reach minimum.Target
Function expression is meant that the simulation for 6 inspection wells, 20 periods calculates the difference of concentration value and measured concentration value
Quadratic sum reaches minimum.Formula (9) indicates that calculating concentration value meets solute transport, and calculating concentration value here is according to substitution
Model is calculated, wherein f1What is indicated is the alternative model of situation 1.Above and below the amplitude of variation of formula (10) expression release history
Boundary condition.
4, substitution-Optimized model is solved
Iteratively solve above-mentioned Optimized model respectively by genetic algorithm, after objective function convergence, optimal objective function institute
Corresponding decision variable value, as corresponding pollution sources discharge history.Find out for convenience and mould is substituted based on core extreme learning machine
The recognition result of type and the difference of the true release characteristic of pollution sources, depict Fig. 3.
Embodiment 2:
Following embodiment is that the present invention is studying the more preferred implementation that area is irregular and heterogeneous water-bearing layer
Example is only used as a preferred method for being further elaborated on thinking of the invention, and not as specific protection model of the invention
The restriction enclosed understands.
1, the generation of training set
Table 2
| Aquifer parameter | Numerical value |
| Infiltration coefficient, K1(m/s) | 0.0004 |
| Infiltration coefficient, K2(m/s) | 0.0002 |
| Infiltration coefficient, K3(m/s) | 0.0001 |
| Infiltration coefficient, K4(m/s) | 0.0003 |
| Infiltration coefficient, K5(m/s) | 0.0007 |
| Effecive porosity, θ | 0.30 |
| Vertical dispersivity, αL(m) | 40.0 |
| Level dispersivity, αT(m) | 4.0 |
| Water-bearing layer thickness, b (m) | 30.0 |
| The direction x mesh generation length, Δ x (m) | 100 |
| The direction y mesh generation length, Δ y (m) | 100 |
| Period Length, Δ t (month) | 6 |
| Initial concentration (g/L) | 0 |
Irregular and water-bearing layer property is that heterogeneous description is as shown in table 2, water-bearing layer floor map such as Fig. 4 institute
Show.Alternative model input data is obtained by the methods of sampling, and what present case was taken is that Latin Hypercube Sampling method is inputted
Data later by operating groundwater solute transfer simulation model, and pass through MODFLOW the and MT3DMS software in GMS software
Solution, obtain case 2 each inspection well day part pollutant concentration value (as output data).Inspection well concentration is as anti-
Actual observed value in drilling, and using pollution sources feature as known variables processing.
It repeats the above steps 100 times, and then obtains 100 groups of input-output sample data collection.This is as the defeated of alternative model
Enter-output data, for training and examining the parameter of alternative model.Wherein, it is used for training parameter for first 90 groups, latter 10 groups for examining
Test the precision of alternative model.
2, the foundation of core extreme learning machine alternative model
The output function expression of core extreme learning machine is as follows:
By can get the parameter of alternative model based on 90 groups of sample data sets for training.For each situation, often
The alternative model of mouth well trained after parameter, requires to test respectively 10 times, selects the alternative model by inspection, with
Ensure that the parameter of alternative model training is effective.
3, substitution-Optimized model foundation
Optimized model is established as follows:
0 < σm< 100, m=1,2 ... 8 (14)
Formula (12) tabular form finds unknown variable σ1To σ8(4 period × 2 pollution sources) make objective function z reach minimum.Target
Function expression is meant that the simulation for 7 inspection wells, 20 periods calculates the difference of concentration value and measured concentration value
Quadratic sum reaches minimum.Formula (13) indicates that calculating concentration value meets solute transport, and calculating concentration value here is according to substitution
Model is calculated, wherein f2What is indicated is the alternative model of situation 2.Formula (14) indicates the upper of the amplitude of variation of release history
Downstream condition.
4, substitution-Optimized model is solved
Iteratively solve above-mentioned Optimized model respectively by genetic algorithm, after objective function convergence, optimal objective function institute
Corresponding decision variable value, as corresponding pollution sources discharge history.Find out for convenience and mould is substituted based on core extreme learning machine
The recognition result of type and the difference of the true release characteristic of pollution sources, depict Fig. 5.
Claims (2)
1. a kind of pollution source of groundwater inverting recognition methods based on core extreme learning machine alternative model, which is characterized in that utilize
Core extreme learning machine alternative model replaces the simulation model in simulation-optimization method, makes target letter using heuristic search algorithm
Number is restrained, and decision variable value corresponding to optimal objective function discharges history to obtain corresponding pollution sources.
2. according to claim 1 based on the pollution source of groundwater inverting recognition methods of core extreme learning machine alternative model, packet
Include following steps:
The generation of S10, training set
In order to portray Contaminants Transport rule in underground water, need to establish phase for practical contaminated site condition or experiment condition
Corresponding underground water pollution simulation of water quality model；For petroleum hydrocarbons, its migration mechanism is described, that is, is dissolved in underground
The mathematical model of the processes such as convection current, hydrodynamic dispersion and the biochemical reaction of the petroleum hydrocarbons in water such as formula (1)；Petroleum
Pollutant enters underground environment, and there are Multiphase Flow, multiphase flow multicomponent pollutant transport mass-conservation equations are as follows:
In formula: k is number of components, including water (k=1), oily (k=2)；L is the number of phases, including water phase (l=1), oily phase (l=2)；φ
For porosity；For the total concentration of component k (with volume fraction)；ρkFor the density [ML of component k-3]；CklIt is component k in l phase
In concentration (with volume fraction)；For the Darcy velocity [LT of l phase-1]；SlFor the saturation degree of l phase；It is component k in l phase
In dispersion coefficient tensor [L2T-1]；RkFor the source sink term [ML of component k-3T-1]；
Above-mentioned multiphase flow multicomponent pollutant transport mass-conservation equation adds primary condition appropriate and boundary condition, i.e. structure
At underground water pollution simulation of water quality model；Known input data can be calculated by underground water pollution simulation of water quality model
Output data, thus can be by input-output data set composing training collection；
The foundation of S20, core extreme learning machine alternative model
Core extreme learning machine alternative model is a kind of alternative model with good accuracy and stability, it is polluted with for practical
Site condition or experiment condition come portray the simulation model that Contaminants Transport rule is established in underground water have it is extremely similar
Input output Relationship can be used to replace simulation model, calculate time and calculated load to reduce, improve computational efficiency；
For N number of training sample (xj,tj), j=1,2 ... .N, the original optimization problem expression of core extreme learning machine method are as follows:
s.t.h(xi)Tβ=ti-ξi (2)
In formula: β represents a vector of feature space F, and C represents regularization parameter, εiRepresentative errors, h (xi) represent input variable
Mapping of the x in the space F；The parameter that core extreme learning machine alternative model need to determine is regularization coefficient C；Regularization coefficient C is played
The effect of balance training error and algorithm complexity, C value is smaller, bigger to the tolerance of training error, and C value is excessive, may
Lead to the problem of over-fitting；
The output function expression of core extreme learning machine is as follows:
In formula: H is the hidden layer output matrix of core extreme learning machine, i.e.,HTIt is the transposed matrix of H, K is core letter
Number, KELMFor nuclear matrix, t is output matrix.According to training set training core extreme learning machine alternative model parameter, further according to approximation
Precision evaluation index carrys out the precision that test stone measures core extreme learning machine alternative model, and selecting inspection result is good substitution
Model；
S30, the foundation of substitution-Optimized model
It is as follows that alternative model is embedded into formation substitution-Optimized model, expression in the constraint condition of Optimized model:
In formula: NtIndicate period, NdIndicate inspection well quantity, Ck(t) the simulating pollution concentration value of sample point k period t is indicated,Indicate sample point k period t pollutant concentration actual measured value,It is the vector of measured concentration value composition,It is source
The vector of flow,WithIt is source flux value range is respectively up-and-down boundary；Formula (4) expression is to find unknown variable to make
Objective function reaches minimum；The expression formula of objective function is meant for NtA period, NdThe simulation of a inspection well calculates concentration
The quadratic sum of the difference of value and measured concentration value reaches minimum (least square)；Formula (5) is core extreme learning machine alternative model
Expression formula shorthand, expression is that simulation calculating concentration value meets solute transport, that is to say, that simulation calculates concentration value
It is to be calculated according to core extreme learning machine alternative model；Formula (6) indicates the amplitude of variation restrictive condition of release history；
S40, substitution-Optimized model is solved
Iteratively solve above-mentioned Optimized model respectively by heuritic approach, after objective function convergence, optimal objective function institute is right
The decision variable value answered, as corresponding pollution sources discharge history.
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