CN106815473B - Hydrological simulation Uncertainty Analysis Method and device - Google Patents
Hydrological simulation Uncertainty Analysis Method and device Download PDFInfo
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Abstract
The invention discloses a hydrological simulation uncertainty analysis method and a hydrological simulation uncertainty analysis device. The method comprises the following steps: acquiring parameter space and flood flow data to which hydrological model parameters belong; constructing a minimum maximum robustness regret value target function and a minimum maximum Nash efficiency coefficient function regret value target function based on hydrological model parameters and flood flow data; according to the parameter space and the flood water flow data, the hydrological model parameters are calibrated according to a minimum maximum robustness regret value target function and a minimum maximum Nash efficiency coefficient function regret value target function, and an optimal parameter space of the hydrological model parameters is obtained; and analyzing uncertainty of hydrologic simulation according to the optimal parameter space. According to the method, when the hydrological model parameters are calibrated, the robustness of the hydrological model parameters is considered, so that the rationality of the calibrated hydrological model parameters is improved, and the uncertainty of the hydrological model can be better analyzed.
Description
Technical field
The present embodiments relate to hydrological simulations not to know technology more particularly to a kind of hydrological simulation analysis of uncertainty side
Method and device.
Background technique
Hydrological simulation uncertainty has important influence to the utilizability of flood forecasting and forecast result.Reasonably measure
Change the uncertain of hydrological simulation to have great importance to raising flood control safety and guarantee people's lives property safety.
The hydrological simulation Uncertainty Analysis Method being commonly used is using flood simulation precision index as likelihood function.
It is limited in that flood simulation precision index is unable to the robustness of representative model parameter, therefore tradition using these likelihood functions
Hydrological simulation Uncertainty Analysis Method cannot consider the robustness of effective analog parameter, thus influence the model parameter of calibration
Reasonability, and then reduce the accuracy of analysis of uncertainty.
Summary of the invention
In view of this, the embodiment of the present invention provides a kind of hydrological simulation Uncertainty Analysis Method and device, based on steady
Strong property calibration Hydro-Model Parameter Calibration Technology, improves the accuracy of analysis of uncertainty.
In a first aspect, the embodiment of the invention provides a kind of hydrological simulation Uncertainty Analysis Methods, which comprises
Obtain parameter space and flood discharge data belonging to Hydro-Model Parameter Calibration Technology；
Based on Hydro-Model Parameter Calibration Technology and flood discharge data, minimax robustness regret value objective function and minimum are constructed
Maximum receives assorted efficiency factor function regret value objective function；
According to the parameter space and the flood discharge data, according to minimax robustness regret value objective function and
Minimax receives assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains hydrological model most
Excellent parameter space；
According to the optimized parameter space, the uncertainty of hydrological simulation is analyzed.
Further, Hydro-Model Parameter Calibration Technology and flood discharge data are based on, minimax robustness regret value target is constructed
Function and minimax receive assorted efficiency factor function regret value objective function and include:
The assorted efficiency factor of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data is determined according to following formula:
Wherein, NSE (x, s) is the assorted efficiency factor of receiving for the flow that hydrological model is simulated according to Hydro-Model Parameter Calibration Technology, and x is water
Literary model parameter, s are s floods in flood discharge data, and M is the flood data period number in flood discharge data,
qobs·sIt (t) is flow value of the s floods in t flood data period in flood discharge data, qsim·xIt (t) is hydrology mould
The flow value for the t flood data period that type is simulated according to Hydro-Model Parameter Calibration Technology,It is the flow value in flood discharge data
Mean value；
Assorted efficiency factor is received according to described, determines following assorted efficiency factor function of receiving:
NS (x, s)=1-NSE (x, s)
Wherein, NS (x, s) is the assorted efficiency factor function of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data；
The disturbance section of Hydro-Model Parameter Calibration Technology is determined based on the rate of excitation of Hydro-Model Parameter Calibration Technology, based on the disturbance section with
It is described to receive assorted efficiency factor function, the robustness function of Hydro-Model Parameter Calibration Technology is constructed, as follows:
Wherein, R (x, s) is the robustness function of Hydro-Model Parameter Calibration Technology, NSP(x, s) is Hydro-Model Parameter Calibration Technology in perturbing area
Between (x (1-xp),x·(1+xp)) in the maximum value for receiving assorted efficiency factor function, xpIt is the rate of excitation of Hydro-Model Parameter Calibration Technology,
For a number between 0 to 1；
According to the robustness function and it is described receive assorted efficiency factor function, construct minimax robustness regret value target
Function and minimax receive assorted efficiency factor function regret value objective function, as follows:
Wherein, Rminimax-regretIt is minimax robustness regret value objective function, NSminimax-regretIt is minimax
Receive assorted efficiency factor function regret value objective function；R*It is the theoretially optimum value of robustness function, NS*It is to receive assorted efficiency factor letter
Several theoretially optimum values, X are the parameter spaces, and S is the flood discharge data.
Further, according to the parameter space and the flood discharge data, according to minimax robustness regret value
Objective function and minimax receive assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains water
The optimized parameter space of literary model includes:
According to the parameter space and the flood discharge data, according to minimax robustness regret value objective function and
Minimax receives assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains Pareto forward position；
The Pareto forward position is divided into the subregion of predetermined number, and weighs the minimax robustness regret value
Objective function and minimax receive assorted efficiency factor function regret value objective function, determine the best sub-district in the Pareto forward position
Domain；
The parameter space that the best subregion is determined is as the optimized parameter space.
Further, according to the parameter space and the flood discharge data, according to minimax robustness regret value
Objective function and minimax receive assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains pa
Tired support forward position includes:
Obtain the rate of excitation and parameter sampling number of at least two groups Hydro-Model Parameter Calibration Technology；
Respectively according to every group of rate of excitation and parameter sampling number and the parameter space and the data on flows, foundation
Minimax robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, described in calibration
Hydro-Model Parameter Calibration Technology obtains Pareto forward position.
Further, respectively according to every group of rate of excitation and parameter sampling number and the parameter space and the flow
Data receive assorted efficiency factor function regret value target letter according to minimax robustness regret value objective function and minimax
It counts, Hydro-Model Parameter Calibration Technology described in calibration, obtaining Pareto forward position includes:
S1, according to the parameter space, obtain the value of Hydro-Model Parameter Calibration Technology；
S2, according to every group of rate of excitation and parameter sampling number, determine the disturbance section of the value of the Hydro-Model Parameter Calibration Technology；
S3, from it is described disturbance section in extract the parameter sampling number Hydro-Model Parameter Calibration Technology sample value；
S4, according to the sample value, determine the sample value for receiving assorted efficiency factor function of the parameter sampling number, and really
Maximum value in the fixed sample value；
S5, according to the sample value of the Hydro-Model Parameter Calibration Technology, the maximum value and the flood discharge data, determine minimum
Maximum robustness regret value and minimax receive assorted efficiency factor function regret value；
S6, S1 to S5 is repeated, until the minimax robustness regret value and minimax that obtain default logarithm are received
Assorted efficiency factor function regret value；
S7, using the minimax robustness regret value as ordinate, the minimax is received after assorted efficiency factor function
Regreting value is abscissa, and picture obtains the Pareto forward position.
Second aspect, the embodiment of the invention also provides a kind of hydrological simulation analysis of uncertainty device, described device packets
It includes:
Data acquisition module, for obtaining parameter space belonging to Hydro-Model Parameter Calibration Technology and flood discharge data；
Objective function constructs module, and for being based on Hydro-Model Parameter Calibration Technology and flood discharge data, building minimax is steady
Property regret value objective function and minimax receive assorted efficiency factor function regret value objective function；
Parameter calibration module, for according to the parameter space and the flood discharge data, foundation minimax to be steady
Property regret value objective function and minimax receive assorted efficiency factor function regret value objective function, the ginseng of hydrological model described in calibration
Number, obtains the optimized parameter space of hydrological model；
Analysis of uncertainty module, for analyzing the uncertainty of hydrological simulation according to the optimized parameter space.
Further, the objective function building module is specifically used for:
The assorted efficiency factor of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data is determined according to following formula:
Wherein, NSE (x, s) is the assorted efficiency factor of receiving for the flow that hydrological model is simulated according to Hydro-Model Parameter Calibration Technology, and x is water
Literary model parameter, s are s floods in flood discharge data, and M is the flood data period number in flood discharge data,
qobs·sIt (t) is flow value of the s floods in t flood data period in flood discharge data, qsim·xIt (t) is hydrology mould
The flow value for the t flood data period that type is simulated according to Hydro-Model Parameter Calibration Technology,It is the flow value in flood discharge data
Mean value；
Assorted efficiency factor is received according to described, determines following assorted efficiency factor function of receiving:
NS (x, s)=1-NSE (x, s)
Wherein, NS (x, s) is the assorted efficiency factor function of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data；
The disturbance section of Hydro-Model Parameter Calibration Technology is determined based on the rate of excitation of Hydro-Model Parameter Calibration Technology, based on the disturbance section with
It is described to receive assorted efficiency factor function, the robustness function of Hydro-Model Parameter Calibration Technology is constructed, as follows:
Wherein, R (x, s) is the robustness function of Hydro-Model Parameter Calibration Technology, NSP(x, s) is Hydro-Model Parameter Calibration Technology in perturbing area
Between (x (1-xp),x·(1+xp)) in the maximum value for receiving assorted efficiency factor function, xpIt is the rate of excitation of Hydro-Model Parameter Calibration Technology,
For a number between 0 to 1；
According to the robustness function and it is described receive assorted efficiency factor function, construct minimax robustness regret value target
Function and minimax receive assorted efficiency factor function regret value objective function, as follows:
Wherein, Rminimax-regretIt is minimax robustness regret value objective function, NSminimax-regretIt is minimax
Receive assorted efficiency factor function regret value objective function；R*It is the theoretially optimum value of robustness function, NS*It is to receive assorted efficiency factor letter
Several theoretially optimum values, X are the parameter spaces, and S is the flood discharge data.
Further, the parameter calibration module includes:
Pareto forward position determination unit, for according to the parameter space and the flood discharge data, foundation to be minimum most
Big robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, hydrology mould described in calibration
Shape parameter obtains Pareto forward position；
Best subregion determination unit, for the Pareto forward position to be divided into the subregion of predetermined number, and weighs
The minimax robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, determine
The best subregion in the Pareto forward position；
Parameter optimization space determination unit, the parameter space for determining the best subregion is as the optimal ginseng
Number space.
Further, Pareto forward position determination unit includes:
Disturbance parameter obtains subelement, for obtaining the rate of excitation and parameter sampling of at least two groups Hydro-Model Parameter Calibration Technology
Number；
Pareto forward position determines subelement, for respectively according to every group of rate of excitation and parameter sampling number and the ginseng
Number space and the data on flows receive assorted efficiency factor letter according to minimax robustness regret value objective function and minimax
Regret value objective function is counted, Hydro-Model Parameter Calibration Technology described in calibration obtains Pareto forward position.
Further, the Pareto forward position determines that subelement is specifically used for:
According to the parameter space, the value of Hydro-Model Parameter Calibration Technology is obtained；
According to every group of rate of excitation and parameter sampling number, the disturbance section of the value of the Hydro-Model Parameter Calibration Technology is determined；
The sample value of the Hydro-Model Parameter Calibration Technology of the parameter sampling number is extracted from the disturbance section；
According to the sample value, the sample value for receiving assorted efficiency factor function of the parameter sampling number is determined, and determine
Maximum value in the sample value；
According to the sample value of the Hydro-Model Parameter Calibration Technology, the maximum value and the flood discharge data, minimum is determined most
Big robustness regret value and minimax receive assorted efficiency factor function regret value；
It returns and executes according to the parameter space, obtain the operation of the value of Hydro-Model Parameter Calibration Technology, until obtaining default logarithm
Minimax robustness regret value and minimax receive assorted efficiency factor function regret value；
Using the minimax robustness regret value as ordinate, the minimax receives assorted efficiency factor function regret value
For abscissa, picture obtains the Pareto forward position.
The technical solution of the present embodiment, due in calibration Hydro-Model Parameter Calibration Technology, it is contemplated that Hydro-Model Parameter Calibration Technology it is steady
Property, to improve the reasonability of the Hydro-Model Parameter Calibration Technology of calibration, and then improve the accuracy of analysis of uncertainty.
Detailed description of the invention
Fig. 1 is a kind of flow chart for hydrological simulation Uncertainty Analysis Method that the embodiment of the present invention one provides；
Fig. 2 is a kind of flow chart of hydrological simulation Uncertainty Analysis Method provided by Embodiment 2 of the present invention；
Fig. 3 is that the calibration Hydro-Model Parameter Calibration Technology in hydrological simulation Uncertainty Analysis Method provided in an embodiment of the present invention obtains
To the flow chart in Pareto forward position；
Fig. 4 is being determined in hydrological simulation Uncertainty Analysis Method provided in an embodiment of the present invention according to Pareto forward position
The schematic diagram of best subregion；
Fig. 5 is the emulation in the Pareto forward position in the hydrological simulation Uncertainty Analysis Method that the embodiment of the present invention three provides
Figure；
Fig. 6 be the embodiment of the present invention three provide hydrological simulation Uncertainty Analysis Method in rate of excitation be 0.3 when, make
The analogous diagram that the analysis of uncertainty result of 3 sub-regions is compared with green stream river valley 1991-07-21 flood；
Fig. 7 be the embodiment of the present invention three provide hydrological simulation Uncertainty Analysis Method in rate of excitation be 0.5 when, make
The analogous diagram that the analysis of uncertainty result of 3 sub-regions is compared with green stream river valley 1991-07-21 flood；
Fig. 8 is a kind of structural schematic diagram for hydrological simulation analysis of uncertainty device that the embodiment of the present invention four provides.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawings and examples.It is understood that this place is retouched
The specific embodiment stated is used only for explaining the present invention rather than limiting the invention.It also should be noted that in order to just
In description, only some but not all contents related to the present invention are shown in the drawings.
Embodiment one
Fig. 1 is a kind of flow chart for hydrological simulation Uncertainty Analysis Method that the embodiment of the present invention one provides, this implementation
Example is applicable to the robustness based on Hydro-Model Parameter Calibration Technology to analyze the situation of hydrological simulation uncertainty, and this method can be by water
Text simulates analysis of uncertainty device to execute, which can be realized by software and/or hardware, can generally be integrated in calculating
In machine, this method specifically comprises the following steps:
Step 110, parameter space and flood discharge data belonging to Hydro-Model Parameter Calibration Technology are obtained.
Wherein, the parameter space can be determined by user according to the observational data and experience of existing flood；Flood
Data on flows is the data of existing flood, including time, rainfall and data on flows.
Hydro-Model Parameter Calibration Technology is related with hydrological model, and after hydrological model determines, the Hydro-Model Parameter Calibration Technology needed can be true
Fixed, general Hydro-Model Parameter Calibration Technology will include multiple parameters, i.e. one group of parameter.Hydrological model refers to the complicated hydrology with analogy method
Phenomenon and process are through approximate scientific model given by generalization.Hydrological model can be divided into hydrology physical model by analog form
(physical model, scale model) and two kinds of fundamental types of hydrological system model.Hydrology physical model is with prototype (i.e. research pair
As) model of Main physical property, such as a basin is moved to experiment by principle of similitude diminution, or by original soil sample in the lab
The experiment etc. that room is done；Hydrological system model is then to follow the similar principle of mathematic(al) representation to describe hydrology phenomenon physical process
Model, do not consider the physical essence of prototype but, such as converge, laboratory is neither moved in section, does not also copy a race
Duan Jinhang experiment, but being different from the but equation with same mathematical expression formula with a physical essence indicates to converge, from
And the physical process actually converged is depicted.There is close connections between both models, because of the research of physical model
It is the basis of mathematical model, and mathematical model is then the strong expression way of physical model.
Step 120, Hydro-Model Parameter Calibration Technology and flood discharge data are based on, minimax robustness regret value target letter is constructed
Several and minimax receives assorted efficiency factor function regret value objective function.
Robustness represents transfer ability of the Hydro-Model Parameter Calibration Technology in different analogue datas, i.e., in the case of different analogue datas
There can be preferable simulation precision.Since flood simulation is needed using multi-group data calibration and verifying Hydro-Model Parameter Calibration Technology,
Consider that the robustness of Hydro-Model Parameter Calibration Technology is necessary.Receive assorted efficiency factor (Nash-Sutcliffe efficiency
Coefficient, NSE), the general quality to verify hydrological model analog result.
When carrying out hydrological simulation analysis of uncertainty, first construct relevant to Hydro-Model Parameter Calibration Technology and flood discharge data
Minimax regret value objective function based on robustness and Na Shi efficiency factor, i.e., the described minimax robustness regret value mesh
Scalar functions and minimax receive assorted efficiency factor function regret value objective function, carry out calibration Hydro-Model Parameter Calibration Technology.
Wherein, Hydro-Model Parameter Calibration Technology and flood discharge data are based on, minimax robustness regret value objective function is constructed
Receive that assorted efficiency factor function regret value objective function is optional to include: with minimax
The assorted efficiency factor of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data is determined according to following formula:
Wherein, NSE (x, s) is the assorted efficiency factor of receiving for the flow that hydrological model is simulated according to Hydro-Model Parameter Calibration Technology, and x is water
Literary model parameter, s are s floods in flood discharge data, and M is the flood data period number in flood discharge data,
qobs·sIt (t) is flow value of the s floods in t flood data period in flood discharge data, qsim·xIt (t) is hydrology mould
The flow value for the t flood data period that type is simulated according to Hydro-Model Parameter Calibration Technology,It is the flow value in flood discharge data
Mean value；
Assorted efficiency factor is received according to described, determines following assorted efficiency factor function of receiving:
NS (x, s)=1-NSE (x, s) (2)
Wherein, NS (x, s) is the assorted efficiency factor function of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data；
The disturbance section of Hydro-Model Parameter Calibration Technology is determined based on the rate of excitation of Hydro-Model Parameter Calibration Technology, based on the disturbance section with
It is described to receive assorted efficiency factor function, the robustness function of Hydro-Model Parameter Calibration Technology is constructed, as follows:
Wherein, R (x, s) is the robustness function of Hydro-Model Parameter Calibration Technology, NSP(x, s) is Hydro-Model Parameter Calibration Technology in perturbing area
Between (x (1-xp),x·(1+xp)) in the maximum value for receiving assorted efficiency factor function, xpIt is the rate of excitation of Hydro-Model Parameter Calibration Technology,
For a number between 0 to 1；
According to the robustness function and it is described receive assorted efficiency factor function, construct minimax robustness regret value target
Function and minimax receive assorted efficiency factor function regret value objective function, as follows:
Wherein, Rminimax-regretIt is minimax robustness regret value objective function, NSminimax-regretIt is minimax
Receive assorted efficiency factor function regret value objective function；R*It is the theoretially optimum value of robustness function, NS*It is to receive assorted efficiency factor letter
Several theoretially optimum values, X are the parameter spaces, and S is the flood discharge data.
Step 130, according to the parameter space and the flood discharge data, according to minimax robustness regret value mesh
Scalar functions and minimax receive assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains the hydrology
The optimized parameter space of model.
According to the parameter space, the Hydro-Model Parameter Calibration Technology of preset group number is determined, according to the hydrology mould of the preset group number
Shape parameter and the flood discharge data, to seek the optimal value and minimum of the minimax robustness regret value objective function
Maximum receives the optimal value of assorted efficiency factor function regret value objective function, when reaching the optimal value of default logarithm, this default pair
Several optimal values forms Pareto forward position, Pareto forward position is divided into multiple regions, respectively by the hydrological model of corresponding region
Parameter input hydrological model is simulated, obtain it is uncertain as a result, according to uncertainty as a result, choose optimal region, should
The parameter space of the corresponding Hydro-Model Parameter Calibration Technology composition in region is the optimized parameter space.
Optionally, according to the parameter space and the flood discharge data, according to minimax robustness regret value mesh
Scalar functions and minimax receive assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains the hydrology
The optimized parameter space of model includes:
According to the parameter space and the flood discharge data, according to minimax robustness regret value objective function and
Minimax receives assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains Pareto forward position；
The Pareto forward position is divided into the subregion of predetermined number, and weighs the minimax robustness regret value
Objective function and minimax receive assorted efficiency factor function regret value objective function, determine the best sub-district in the Pareto forward position
Domain；
The parameter space that the best subregion is determined is as the optimized parameter space.
By choosing the value of the Hydro-Model Parameter Calibration Technology of preset group number from the parameter space, by the hydrology of this preset group number
The value substitution minimax robustness regret value objective function and minimax of model parameter are received after assorted efficiency factor function
Regret the Hydro-Model Parameter Calibration Technology in value objective function, obtains a pair of of regret value (i.e. above-mentioned optimal value).Again from the parameter space
The value of the middle Hydro-Model Parameter Calibration Technology for choosing preset group number, obtains a pair of of regret value, until obtaining the regret value of default logarithm, by this
The regret value of default logarithm draws to obtain Pareto forward position.The Pareto forward position is divided into the subregion of predetermined number, so that
The data volume (i.e. the logarithm of regret value) of each subregion is identical, weighs minimum according to the Hydro-Model Parameter Calibration Technology of each subregion
Maximum robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, determine best sub-district
Domain.Determine that obtaining parameter space belonging to the Hydro-Model Parameter Calibration Technology of the best subregion is the optimized parameter space.Pass through
Pareto forward position is obtained, and the division of subregion is carried out to determine optimized parameter space to Pareto forward position, so that the ginseng determined
Number space is more reasonable, to further increase the accuracy of analysis of uncertainty.
Step 140, according to the optimized parameter space, the uncertainty of hydrological simulation is analyzed.
Hydro-Model Parameter Calibration Technology in the optimized parameter space is inputted into hydrological model, the model for the flow value simulated
It encloses, range, that is, hydrological simulation uncertainty of the flow value.
The technical solution of the present embodiment, by obtaining parameter space and flood discharge data belonging to Hydro-Model Parameter Calibration Technology,
Based on Hydro-Model Parameter Calibration Technology and flood discharge data, construct minimax robustness regret value objective function and minimax receive it is assorted
Efficiency factor function regret value objective function is steady according to minimax according to the parameter space and the flood discharge data
Strong property regret value objective function and minimax receive assorted efficiency factor function regret value objective function, the ginseng of hydrological model described in calibration
Number, obtains the optimized parameter space of hydrological model；According to the optimized parameter space, the uncertainty of hydrological simulation is analyzed, by
In in calibration Hydro-Model Parameter Calibration Technology, it is contemplated that the robustness of Hydro-Model Parameter Calibration Technology, to improve the hydrological model ginseng of calibration
Several reasonability, and then improve the accuracy of analysis of uncertainty.
Embodiment two
Fig. 2 is a kind of flow chart of hydrological simulation Uncertainty Analysis Method provided by Embodiment 2 of the present invention, this implementation
Example is optimized on the basis of the above embodiments, will be " according to the parameter space and the flood discharge data, according to most
Small maximum robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, water described in calibration
Literary model parameter obtains Pareto forward position " it advanced optimizes " to obtain the rate of excitation and parameter of at least two groups Hydro-Model Parameter Calibration Technology
Sampling number；Respectively according to every group of rate of excitation and parameter sampling number and the parameter space and the data on flows, foundation
Minimax robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, described in calibration
Hydro-Model Parameter Calibration Technology obtains Pareto forward position ", this method specifically comprises the following steps:
Step 210, parameter space and flood discharge data belonging to Hydro-Model Parameter Calibration Technology are obtained.
Step 220, Hydro-Model Parameter Calibration Technology and flood discharge data are based on, minimax robustness regret value target letter is constructed
Several and minimax receives assorted efficiency factor function regret value objective function.
Step 230, the rate of excitation and parameter sampling number of at least two groups Hydro-Model Parameter Calibration Technology are obtained.
Use minimax regret value objective function (including minimax robustness regret value objective function and minimax
Receive assorted efficiency factor function regret value objective function) calibration Hydro-Model Parameter Calibration Technology, the smaller calibration result of target function value is more excellent.By
In parameter perturbation rate xpHave an impact with Pareto forward position of the parameter sampling number N to calibration, not for preferably analysis mode
Certainty, it should select multiple groups xpWith N value calibration.
First have to obtain the rate of excitation x of the Hydro-Model Parameter Calibration Technology of at least two groupspWith parameter sampling number N.
Step 240, respectively according to every group of rate of excitation and parameter sampling number and the parameter space and the flow number
According to, assorted efficiency factor function regret value objective function is received according to minimax robustness regret value objective function and minimax,
Hydro-Model Parameter Calibration Technology described in calibration obtains Pareto forward position.
One group of rate of excitation and parameter sampling number determine a Pareto forward position, then the rate of excitation and parameter of at least two groups
Sampling number determines that at least two Pareto forward positions, this comprehensive at least two Paretos forward position determine the best of Pareto forward position
Subregion.
Fig. 3 is that the calibration Hydro-Model Parameter Calibration Technology in hydrological simulation Uncertainty Analysis Method provided in an embodiment of the present invention obtains
To the flow chart in Pareto forward position, as shown in figure 3, respectively according to every group of rate of excitation and parameter sampling number and the parameter
Space and the data on flows receive assorted efficiency factor function according to minimax robustness regret value objective function and minimax
Regret value objective function, Hydro-Model Parameter Calibration Technology described in calibration, obtaining Pareto forward position includes:
Step 241, according to the parameter space, the value of Hydro-Model Parameter Calibration Technology is obtained；
The value of the Hydro-Model Parameter Calibration Technology of preset group number (being assumed to be M group) is determined from the parameter space.
Step 242, according to every group of rate of excitation and parameter sampling number, the perturbing area of the value of the Hydro-Model Parameter Calibration Technology is determined
Between；
According to one group of given rate of excitation xpWith parameter sampling number N, determine what the value of every group of Hydro-Model Parameter Calibration Technology x determined
Disturb section (x (1-xp),x·(1+xp)), the disturbance section of preset group number is obtained to get M disturbance section is arrived.Wherein, it disturbs
Dynamic rate xpFor a number between 0 to 1.
Step 243, the sample value of the Hydro-Model Parameter Calibration Technology of the parameter sampling number is extracted from the disturbance section；
From a disturbance section (x (1-xp),x·(1+xp)) in, the value of the Hydro-Model Parameter Calibration Technology of N group is extracted, as N
The sample value of the Hydro-Model Parameter Calibration Technology of group.
Step 244, according to the sample value, the sampling for receiving assorted efficiency factor function of the parameter sampling number is determined
Value, and determine the maximum value in the sample value；
By the sample value of the Hydro-Model Parameter Calibration Technology of N group, substitutes into receive assorted efficiency factor function i.e. formula (2) respectively, obtain N number of
It receives the sample value of assorted efficiency factor function, compares this N number of sample value for receiving assorted efficiency factor function, obtain a maximum value, it should
Maximum value, that is, NSP(x,s).According to the sample value of the N group Hydro-Model Parameter Calibration Technology in the disturbance section of preset group number, respectively obtain pre-
If group number receives maximum value of the assorted efficiency factor function in disturbance section to get to a maximum for receiving assorted efficiency factor function of M
Value.
Step 245, according to the sample value of the Hydro-Model Parameter Calibration Technology, the maximum value and the flood discharge data, really
Determine minimax robustness regret value and minimax receives assorted efficiency factor function regret value；
By the hydrological model for the N group that each disturbance section determines in the disturbance section (i.e. M disturbance section) of preset group number
The sample value of parameter, the maximum value NSP(x, s) and the flood discharge data substitute into formula (4) and obtain a pair of of minimax
Robustness regret value and minimax receive assorted efficiency factor function regret value.
Step 246, judge that minimax robustness regret value and minimax receive pair of assorted efficiency factor function regret value
Whether number reaches default logarithm, if so, 247 are thened follow the steps, if otherwise returning to step 241；
Step 247, using the minimax robustness regret value as ordinate, the minimax receives assorted efficiency factor letter
Number regret value is abscissa, and picture obtains the Pareto forward position.
One group of rate of excitation and parameter sampling number obtain a Pareto forward position.It is determined by step 241- step 247
Pareto forward position is more accurate, can be further improved the accuracy of analysis of uncertainty.
Step 250, the Pareto forward position is divided into the subregion of predetermined number, and it is steady to weigh the minimax
Property regret value objective function and minimax receive assorted efficiency factor function regret value objective function, determine the Pareto forward position
Best subregion.
Each Pareto forward position is divided into the subregion of same number, and the hydrological model for obtaining each subregion is joined
Number input hydrological model, obtains the uncertainty of the corresponding hydrological simulation of each subregion, according to the hydrology mould of each subregion
Quasi- uncertainty, tradeoff determine the best subregion in the Pareto forward position.
Illustratively, Fig. 4 is tired according to pa in hydrological simulation Uncertainty Analysis Method provided in an embodiment of the present invention
Support forward position determines that the schematic diagram of best subregion is respectively as follows: as shown in figure 4, Pareto forward position 10 is divided into three sub-regions
First area 11, second area 12 and third region 13, respectively by first area 11, the water of second area 12 and third region 13
Literary model parameter inputs hydrological model, obtains analysis of uncertainty as a result, the i.e. corresponding analysis of uncertainty knot in first area 11
Fruit 21, the corresponding analysis of uncertainty result 22 of second area 12, the corresponding analysis of uncertainty result 23 in third region 13.?
In analysis of uncertainty result 21,22 and 23, the range of indeterminacy 32 of the flow including actual flow 31 and simulation.First
In region 11, second area 12 and third region 13, range of indeterminacy 32 can surround actual flow 31 and most narrow region
I.e. second area 12 is best subregion.
Step 260, the parameter space best subregion determined is as the optimized parameter space.
Step 270, according to the optimized parameter space, the uncertainty of hydrological simulation is analyzed.
Illustratively, the analysis of uncertainty result 22 in Fig. 4 can be extracted i.e. by the parameter optimization space point
The uncertainty of the hydrological simulation of analysis.
The technical solution of the present embodiment, on the basis of the above embodiments, by obtaining at least two groups Hydro-Model Parameter Calibration Technology
Rate of excitation and parameter sampling number, respectively according to every group of rate of excitation and parameter sampling number and the parameter space and institute
It states data on flows, receives assorted efficiency factor function regret value mesh according to minimax robustness regret value objective function and minimax
Scalar functions, Hydro-Model Parameter Calibration Technology described in calibration, obtain Pareto forward position, can preferably analyze the uncertainty of hydrological simulation,
Further improve the accuracy of analysis of uncertainty.
Embodiment three
The embodiment of the present invention three provides a kind of hydrological simulation Uncertainty Analysis Method, and the present embodiment is in above-mentioned implementation
A preferred embodiment on the basis of example, the present embodiment carry out analysis of uncertainty with the flood simulation to green stream river valley.
Select green stream river valley 1984-06-15 flood and 1997-08-19 flood as flood stream in the present embodiment
Data are measured, calibration Hydro-Model Parameter Calibration Technology is carried out.
Wherein, green stream river valley is located at northeast China, Liaoning Province southern areas, south depends on the Huanghai Sea, the west neighbour Bohai Sea, topography by
Northeast southwester tilts, and upstream belongs to low-relief terrain.Basin June to September is flood season, and rainfall is big, intensity is big, range is wide, the duration of flood
It is shorter.742.8 millimeters of basin mean annual precipitation, average annual runoff is 294.5 millimeters deep.Green stream river valley area is
2814km2.Mean annual temperature is 10.6 DEG C.
Fig. 5 is the imitative of the Pareto forward position in the Uncertainty Analysis Method for the hydrological simulation that the embodiment of the present invention three provides
True figure, as shown in figure 5, coefficient of disturbance, that is, rate of excitation is respectively 0.3 and 0.5, parameter sampling number is respectively 10,30 and 50, is obtained
To 6 Pareto forward positions, each Pareto forward position is divided into three sub-regions, respectively first area 51,52 and of second area
Third region 53.
Fig. 6 be the embodiment of the present invention three provide hydrological simulation Uncertainty Analysis Method in rate of excitation be 0.3 when
The analogous diagram that the analysis of uncertainty result of 3 sub-regions is compared using green stream river valley 1991-07-21 flood,
Fig. 7 is the rate of excitation in the Uncertainty Analysis Method for the hydrological simulation that the embodiment of the present invention three provides when being 0.5 using green stream
The analogous diagram that river valley 1991-07-21 flood is compared the analysis of uncertainty result of 3 sub-regions.Fig. 6 and Fig. 7
In used parameter sampling number 10,30 and 50 3 kind of situation.In Fig. 6 and Fig. 7, rainfall 63 and runoff 62 are the defeated of hydrological model
Enter, range of indeterminacy 61 is that the output of hydrological model, as can be seen from Figures 6 and 7 selection region 2 and region 3 carry out flood
Frequency analysis is more appropriate, because the range of indeterminacy 61 in region 2 and region 3 can wrap girth diameter stream 62 substantially, i.e., actually
Flow.Therefore, region 2 or region 3 can be used as best subregion.
The technical solution of the present embodiment carries out analysis of uncertainty with the flood simulation to green stream river valley, due to considering
The robustness of Hydro-Model Parameter Calibration Technology, can preferably analyze the uncertainty of hydrological simulation.
Example IV
Fig. 8 is a kind of structural schematic diagram for hydrological simulation analysis of uncertainty device that the embodiment of the present invention four provides, such as
Shown in Fig. 8, hydrological simulation analysis of uncertainty device described in the present embodiment includes: data acquisition module 810, objective function structure
Model block 820, parameter calibration module 830 and analysis of uncertainty module 840.
Wherein, data acquisition module, for obtaining parameter space belonging to Hydro-Model Parameter Calibration Technology and flood discharge data；
Objective function constructs module, and for being based on Hydro-Model Parameter Calibration Technology and flood discharge data, building minimax is steady
Property regret value objective function and minimax receive assorted efficiency factor function regret value objective function；
Parameter calibration module, for according to the parameter space and the flood discharge data, foundation minimax to be steady
Property regret value objective function and minimax receive assorted efficiency factor function regret value objective function, the ginseng of hydrological model described in calibration
Number, obtains the optimized parameter space of hydrological model；
Analysis of uncertainty module, for analyzing the uncertainty of hydrological simulation according to the parameter optimization space.
Optionally, the objective function building module is specifically used for:
The assorted efficiency factor of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data is determined according to following formula:
Wherein, NSE (x, s) is the assorted efficiency factor of receiving for the flow that hydrological model is simulated according to Hydro-Model Parameter Calibration Technology, and x is water
Literary model parameter, s are s floods in flood discharge data, and M is the flood data period number in flood discharge data,
qobs·sIt (t) is flow value of the s floods in t flood data period in flood discharge data, qsim·xIt (t) is hydrology mould
The flow value for the t flood data period that type is simulated according to Hydro-Model Parameter Calibration Technology,It is the flow value in flood discharge data
Mean value；
Assorted efficiency factor is received according to described, determines following assorted efficiency factor function of receiving:
NS (x, s)=1-NSE (x, s)
Wherein, NS (x, s) is the assorted efficiency factor function of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data；
The disturbance section of Hydro-Model Parameter Calibration Technology is determined based on the rate of excitation of Hydro-Model Parameter Calibration Technology, based on the disturbance section with
It is described to receive assorted efficiency factor function, the robustness function of Hydro-Model Parameter Calibration Technology is constructed, as follows:
Wherein, R (x, s) is the robustness function of Hydro-Model Parameter Calibration Technology, NSP(x, s) is Hydro-Model Parameter Calibration Technology in perturbing area
Between (x (1-xp),x·(1+xp)) in the maximum value for receiving assorted efficiency factor function, xpIt is the rate of excitation of Hydro-Model Parameter Calibration Technology,
For a number between 0 to 1；
According to the robustness function and it is described receive assorted efficiency factor function, construct minimax robustness regret value target
Function and minimax receive assorted efficiency factor function regret value objective function, as follows:
Wherein, Rminimax-regretIt is minimax robustness regret value objective function, NSminimax-regretIt is minimax
Receive assorted efficiency factor function regret value objective function；R*It is the theoretially optimum value of robustness function, NS*It is to receive assorted efficiency factor letter
Several theoretially optimum values, X are the parameter spaces, and S is the flood discharge data.
Optionally, the parameter calibration module includes:
Pareto forward position determination unit, for according to the parameter space and the flood discharge data, foundation to be minimum most
Big robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, hydrology mould described in calibration
Shape parameter obtains Pareto forward position；
Best subregion determination unit, for the Pareto forward position to be divided into the subregion of predetermined number, and weighs
The minimax robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, determine
The best subregion in the Pareto forward position；
Parameter optimization space determination unit, the parameter space for determining the best subregion is as the optimal ginseng
Number space.
Optionally, Pareto forward position determination unit includes:
Disturbance parameter obtains subelement, for obtaining the rate of excitation and parameter sampling of at least two groups Hydro-Model Parameter Calibration Technology
Number；
Pareto forward position determines subelement, for respectively according to every group of rate of excitation and parameter sampling number and the ginseng
Number space and the data on flows, minimax robustness regret value objective function and minimax described in calibration receive assorted efficiency system
Hydro-Model Parameter Calibration Technology in number function regret value objective function, obtains Pareto forward position.
Optionally, the Pareto forward position determines that subelement is specifically used for:
According to the parameter space, the value of Hydro-Model Parameter Calibration Technology is obtained；
According to every group of rate of excitation and parameter sampling number, the disturbance section of the value of the Hydro-Model Parameter Calibration Technology is determined；
The sample value of the Hydro-Model Parameter Calibration Technology of the parameter sampling number is extracted from the disturbance section；
According to the sample value, the sample value for receiving assorted efficiency factor function of the parameter sampling number is determined, and determine
Maximum value in the sample value；
According to the sample value of the Hydro-Model Parameter Calibration Technology, the maximum value and the flood discharge data, minimum is determined most
Big robustness regret value and minimax receive assorted efficiency factor function regret value；
It returns and executes according to the parameter space, obtain the operation of the value of Hydro-Model Parameter Calibration Technology, until obtaining default logarithm
Minimax robustness regret value and minimax receive assorted efficiency factor function regret value；
Using the minimax robustness regret value as ordinate, the minimax receives assorted efficiency factor function regret value
For abscissa, picture obtains the Pareto forward position.
Hydrological simulation provided by any embodiment of the invention can be performed not in above-mentioned hydrological simulation analysis of uncertainty device
Deterministic parsing method has the corresponding functional module of execution method and beneficial effect.Not detailed description in the present embodiment
Technical detail, reference can be made to the hydrological simulation Uncertainty Analysis Method that any embodiment of that present invention provides.
Note that the above is only a better embodiment of the present invention and the applied technical principle.It will be appreciated by those skilled in the art that
The invention is not limited to the specific embodiments described herein, be able to carry out for a person skilled in the art it is various it is apparent variation,
It readjusts and substitutes without departing from protection scope of the present invention.Therefore, although being carried out by above embodiments to the present invention
It is described in further detail, but the present invention is not limited to the above embodiments only, without departing from the inventive concept, also
It may include more other equivalent embodiments, and the scope of the invention is determined by the scope of the appended claims.
Claims (2)
1. a kind of hydrological simulation Uncertainty Analysis Method, which is characterized in that the described method includes:
Obtain parameter space and flood discharge data belonging to Hydro-Model Parameter Calibration Technology；
Based on Hydro-Model Parameter Calibration Technology and flood discharge data, minimax robustness regret value objective function and minimax are constructed
Receive assorted efficiency factor function regret value objective function；
According to the parameter space and the flood discharge data, according to minimax robustness regret value objective function and minimum
Maximum receives assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains Hydro-Model Parameter Calibration Technology most
Excellent parameter space；
According to the optimized parameter space, the uncertainty of hydrological simulation is analyzed；
Wherein, Hydro-Model Parameter Calibration Technology and flood discharge data are based on, minimax robustness regret value objective function and most is constructed
Small maximum receives assorted efficiency factor function regret value objective function and includes:
The assorted efficiency factor of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data is determined according to following formula:
Wherein, NSE (x, s) is the assorted efficiency factor of receiving for the flow that hydrological model is simulated according to Hydro-Model Parameter Calibration Technology, and x is hydrology mould
Shape parameter, s are s floods in flood discharge data, and M is the flood data period number in flood discharge data, qobs·s
It (t) is flow value of the s floods in t flood data period in flood discharge data, qsim·xIt (t) is hydrological model root
According to Hydro-Model Parameter Calibration Technology simulation t flood data period flow value,It is the equal of the flow value in flood discharge data
Value；
Assorted efficiency factor is received according to described, determines following assorted efficiency factor function of receiving:
NS (x, s)=1-NSE (x, s)
Wherein, NS (x, s) is the assorted efficiency factor function of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data；
The disturbance section of Hydro-Model Parameter Calibration Technology is determined based on the rate of excitation of Hydro-Model Parameter Calibration Technology, based on the disturbance section and described
It receives assorted efficiency factor function, constructs the robustness function of Hydro-Model Parameter Calibration Technology, as follows:
Wherein, R (x, s) is the robustness function of Hydro-Model Parameter Calibration Technology, NSP(x, s) is Hydro-Model Parameter Calibration Technology in disturbance section (x
(1-xp),x·(1+xp)) in the maximum value for receiving assorted efficiency factor function, xpIt is the rate of excitation of Hydro-Model Parameter Calibration Technology, is 0 to 1
Between a number；
According to the robustness function and it is described receive assorted efficiency factor function, construct minimax robustness regret value objective function
Assorted efficiency factor function regret value objective function is received with minimax, as follows:
Wherein, Rminimax-regretIt is minimax robustness regret value objective function, NSminimax-regretIt is that minimax receives assorted effect
Rate coefficient function regret value objective function；R*It is the theoretially optimum value of robustness function, NS*It is to receive the reason of assorted efficiency factor function
By optimal value, X is the parameter space, and S is the flood discharge data；
According to the parameter space and the flood discharge data, according to minimax robustness regret value objective function and minimum
Maximum receives assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains Hydro-Model Parameter Calibration Technology most
Excellent parameter space includes:
According to the parameter space and the flood discharge data, according to minimax robustness regret value objective function and minimum
Maximum receives assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration obtains Pareto forward position；
The Pareto forward position is divided into the subregion of predetermined number, and weighs the minimax robustness regret value target
Function and minimax receive assorted efficiency factor function regret value objective function, determine the best subregion in the Pareto forward position；
The parameter space that the best subregion is determined is as the optimized parameter space；
According to the parameter space and the flood discharge data, according to minimax robustness regret value objective function and minimum
Maximum receives assorted efficiency factor function regret value objective function, and Hydro-Model Parameter Calibration Technology described in calibration, obtaining Pareto forward position includes:
Obtain the rate of excitation and parameter sampling number of at least two groups Hydro-Model Parameter Calibration Technology；
Respectively according to every group of rate of excitation and parameter sampling number and the parameter space and the flood discharge data, foundation
Minimax robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, described in calibration
Hydro-Model Parameter Calibration Technology obtains Pareto forward position；
Correspondingly, respectively according to every group of rate of excitation and parameter sampling number and the parameter space and the data on flows, according to
Assorted efficiency factor function regret value objective function is received according to minimax robustness regret value objective function and minimax, calibration institute
Hydro-Model Parameter Calibration Technology is stated, obtaining Pareto forward position includes:
S1, according to the parameter space, obtain the value of Hydro-Model Parameter Calibration Technology；
S2, according to every group of rate of excitation and parameter sampling number, determine the disturbance section of the value of the Hydro-Model Parameter Calibration Technology；
S3, from it is described disturbance section in extract the parameter sampling number Hydro-Model Parameter Calibration Technology sample value；
S4, according to the sample value, determine the sample value for receiving assorted efficiency factor function of the parameter sampling number, and determine institute
State the maximum value in sample value；
S5, according to the sample value of the Hydro-Model Parameter Calibration Technology, the maximum value and the flood discharge data, determine minimax
Robustness regret value and minimax receive assorted efficiency factor function regret value；
S6, S1 to S5 is repeated, until the minimax robustness regret value and minimax that obtain default logarithm receive assorted effect
Rate coefficient function regret value；
S7, using the minimax robustness regret value as ordinate, the minimax receives assorted efficiency factor function regret value
For abscissa, picture obtains the Pareto forward position.
2. a kind of hydrological simulation analysis of uncertainty device, which is characterized in that described device includes:
Data acquisition module, for obtaining parameter space belonging to Hydro-Model Parameter Calibration Technology and flood discharge data；
Objective function constructs module, for being based on Hydro-Model Parameter Calibration Technology and flood discharge data, after constructing minimax robustness
Regret value objective function and minimax and receives assorted efficiency factor function regret value objective function；
Parameter calibration module is used for according to the parameter space and the flood discharge data, according to after minimax robustness
Regret value objective function and minimax and receive assorted efficiency factor function regret value objective function, Hydro-Model Parameter Calibration Technology described in calibration obtains
To the optimized parameter space of hydrological model；
Analysis of uncertainty module, for analyzing the uncertainty of hydrological simulation according to the optimized parameter space；
Wherein, the objective function building module is specifically used for:
The assorted efficiency factor of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data is determined according to following formula:
Wherein, NSE (x, s) is the assorted efficiency factor of receiving for the flow that hydrological model is simulated according to Hydro-Model Parameter Calibration Technology, and x is hydrology mould
Shape parameter, s are s floods in flood discharge data, and M is the flood data period number in flood discharge data, qobs·s
It (t) is flow value of the s floods in t flood data period in flood discharge data, qsim·xIt (t) is hydrological model root
According to Hydro-Model Parameter Calibration Technology simulation t flood data period flow value,It is the equal of the flow value in flood discharge data
Value；
Assorted efficiency factor is received according to described, determines following assorted efficiency factor function of receiving:
NS (x, s)=1-NSE (x, s)
Wherein, NS (x, s) is the assorted efficiency factor function of receiving based on Hydro-Model Parameter Calibration Technology and flood discharge data；
The disturbance section of Hydro-Model Parameter Calibration Technology is determined based on the rate of excitation of Hydro-Model Parameter Calibration Technology, based on the disturbance section and described
It receives assorted efficiency factor function, constructs the robustness function of Hydro-Model Parameter Calibration Technology, as follows:
Wherein, R (x, s) is the robustness function of Hydro-Model Parameter Calibration Technology, NSP(x, s) is Hydro-Model Parameter Calibration Technology in disturbance section (x
(1-xp),x·(1+xp)) in the maximum value for receiving assorted efficiency factor function, xpIt is the rate of excitation of Hydro-Model Parameter Calibration Technology, is 0 to 1
Between a number；
According to the robustness function and it is described receive assorted efficiency factor function, construct minimax robustness regret value objective function
Assorted efficiency factor function regret value objective function is received with minimax, as follows:
Wherein, Rminimax-regretIt is minimax robustness regret value objective function, NSminimax-regretIt is that minimax receives assorted effect
Rate coefficient function regret value objective function；R*It is the theoretially optimum value of robustness function, NS*It is to receive the reason of assorted efficiency factor function
By optimal value, X is the parameter space, and S is the flood discharge data；
The parameter calibration module includes:
Pareto forward position determination unit, for according to the parameter space and the flood discharge data, foundation minimax to be steady
Strong property regret value objective function and minimax receive assorted efficiency factor function regret value objective function, the ginseng of hydrological model described in calibration
Number, obtains Pareto forward position；
Best subregion determination unit, for the Pareto forward position to be divided into the subregion of predetermined number, and described in tradeoff
Minimax robustness regret value objective function and minimax receive assorted efficiency factor function regret value objective function, determine described in
The best subregion in Pareto forward position；
Optimized parameter space determination unit, the parameter space for determining the best subregion are empty as the optimized parameter
Between；
Pareto forward position determination unit includes:
Disturbance parameter obtains subelement, for obtaining the rate of excitation and parameter sampling number of at least two groups Hydro-Model Parameter Calibration Technology；
Pareto forward position determines subelement, for empty according to every group of rate of excitation and parameter sampling number and the parameter respectively
Between and the flood discharge data, receive assorted efficiency factor letter according to minimax robustness regret value objective function and minimax
Regret value objective function is counted, Hydro-Model Parameter Calibration Technology described in calibration obtains Pareto forward position；
Correspondingly, the Pareto forward position determines that subelement is specifically used for:
According to the parameter space, the value of Hydro-Model Parameter Calibration Technology is obtained；
According to every group of rate of excitation and parameter sampling number, the disturbance section of the value of the Hydro-Model Parameter Calibration Technology is determined；
The sample value of the Hydro-Model Parameter Calibration Technology of the parameter sampling number is extracted from the disturbance section；
According to the sample value, the sample value for receiving assorted efficiency factor function of the parameter sampling number is determined, and described in determining
Maximum value in sample value；
According to the sample value of the Hydro-Model Parameter Calibration Technology, the maximum value and the flood discharge data, determine that minimax is steady
Strong property regret value and minimax receive assorted efficiency factor function regret value；
It returns and executes according to the parameter space, obtain the operation of the value of Hydro-Model Parameter Calibration Technology, until obtaining default logarithm most
Small maximum robustness regret value and minimax receive assorted efficiency factor function regret value；
Using the minimax robustness regret value as ordinate, the minimax receives assorted efficiency factor function regret value as cross
Coordinate, picture obtain the Pareto forward position.
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