CN109460526A - The composite type hydrographic(al) network assessment models combined based on Copula function and information entropy theory - Google Patents
The composite type hydrographic(al) network assessment models combined based on Copula function and information entropy theory Download PDFInfo
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Abstract
The present invention discloses a kind of composite type hydrographic(al) network assessment models combined based on Copula function and information entropy theory, the following steps are included: using the preferably potential Archimedean race Copula of half parameter evaluation method, calculating the total correlation amount (Total correlation, TC) of two variable mutual informations and multiple variables；Combination based on Copula function theory and information entropy principle, Mutual Information Estimation value under multidimensional variable has been determined using Copula function theory, propose MACE website Optimality Criteria (minimizing absolute value of copula entropy, MACE), the single deficiency estimated using comentropy mutual information is compensated for well.The present invention also uses the evaluation index of three kinds of posteriority to have final evaluation: (1) Nash-Sutcliffe efficiency factor to modelling effect；(2) the negative Copula entropy after equalization；(3) united information entropy.
Description
Technical field
The present invention relates to hydrographic(al) network optimisation techniques, and in particular to one kind is based on Copula function and information entropy theory phase
In conjunction with composite type hydrographic(al) network assessment models.
Background technique
Hydrometric station is one and sets up on river or basin, is mainly used for observing and collecting rivers and lakes and water
The hydrology mechanism, base of the water bodys correlation hydrology such as library and meteorological data, by early period to field data it is complete collection and control,
Enough data supports are provided for the work that the later period probes into basic hydrology function, largely meet hydrologic forecast, water
Literary information, water resources assessment work and the primary demand of hydroscience research.Therefore plan that reasonable hydrographic(al) network can be sufficiently anti-
Hydrology Characteristics of spatio-temporal is reflected, makes it to collect accurate detailed hydrographic information, this is clearly that it is necessary to probe into more objectively
Theoretical method support hydrographic(al) network is made rational planning for.Forefathers can substantially be summarized as following in the research method that station network planning is drawn
It is several:
1, mathematical statistics method, this method application earliest, but require researcher to have abundance to recognize water resource system structure
Know；Meanwhile the principle by mathematical statistics is limited, the selection of statistical analysis technique and sample size will all analyze data
Conclusion produce bigger effect；And this method can only determine website by the relationship between estimated accuracy and sample size
Quantity, the purpose to the spatial configuration optimal of website is not achieved.
2, kriging analysis method needs to make subjective assessment to the improvement of hydrology variable estimation error on the diagram, if estimation
The standard deviation of error is greater than the range of given standard deviation, then needs to add website in space, otherwise should just reduce website,
The bigger precision of this method subjectivity is not high enough in practical application.
3, comentropy method is based in comentropy progress hydrographic(al) network optimizing research previous, was often with amount of transmitted information
Foundation selects a certain index to carry out station on-Line review valence optimization, and single piece of information entropy index tends not to reflect that website combines institute comprehensively
An important factor for decisions station net effectiveness such as informational capacity, information redundancy degree for including.The estimation of transfer entropy between standing pair is very big
The reasonable estimation of joint probability density function is limited in degree.
Summary of the invention
Goal of the invention: it is an object of the invention to solve the deficiencies in the prior art, provides a kind of based on Copula
The composite type hydrographic(al) network assessment models that function and information entropy theory combine, in conjunction with Copula function between multivariable
The advantage of relevance quantitative description proposes MACE website Optimality Criteria and uses a kind of evaluation index of posteriority formula to mould
The effect of type carries out overall merit.
Technical solution: the present invention is a kind of composite type hydrometric station combined based on Copula function and information entropy theory
Net assessment models, in turn include the following steps:
(1) based on semi-parametric approach (semiparametric approach, SP) to potential Archimedean Copula
Family of functions is fitted: firstly, within the scope of the Archimedean Copula family of functions for being usually used in hydrology field, based on half
Parametric method and Cram é r-von Mises data (Sn) find out the parameter θ value for characterizing Copula function and best Copula function
Type；The wherein Archimedean Copula family of functions refers to Frank, G-H and Clayton Copula function；It is assumed that
[X1,X2,…,XN] the station net formed under N number of website number is represented, N is the website number of first initial station net.XitRepresent website Xi's
T-th observation is by homogenization treated value, and wherein t=1,2 ..., n, n are the data samples that each website is collected into
Size.For Marginal distribution estimation value, then semi-parametric approach can be expressed as follows:
This estimator is replaced in log-likelihood function, and maximum estimator method can be made to show out that copula joins
Number:
(2) MACE criterion: the thought of criterion core the most is to minimize the information redundancy amount in the net of station to obtain with this
Optimal website combination.Wherein the mutual information TC (Total correlation) of multivariable can be derived by following formula:
TC(X1,X2,…,Xd)=- Hc(u1,u2,…,ud)
Hc(u1,u2,…,ud)=- ∫ c (u1,u2,…,ud)logc(u1,u2,…,ud)dU
=-E [logc (u1,u2,…,ud)]
Wherein, d indicates the number (d≤N) of website in website combination, uiRepresent the marginal distribution function of the i-th website.Through
It after going through Copula function preferably and has obtained TC value, can quickly show that optimal website combines by third formula.
(3) three kinds of model-evaluation indexes: (a) Nash-Sutcliffe coefficient (NSC) mainly features residual variation coefficient
Size, theoretically NSC value then shows residual values with regard to smaller closer to 1；(b) negative Copula entropy mean value (MNCE) is then respective
Hydrographic information redundancy value under website combination；(c) united information entropy (JE) is the total letter described under the combination of the point of selective calling
Breath amount size.Specific calculation formula is as follows:
Wherein n is the length of Hydrological Time Series, SAtIt is the observation under lower t-th of the time series of given website combination
Mean value (can be run-off either rainfall), TAtIt is original station observation data mean value off the net,Indicate n time series
Mean value under length.
It is assumed that the MNCE value that d website has been selected under optimal website combination so combination can indicate are as follows:
Wherein, ui,ujRepresent the marginal distribution function of i-th and j website.
United information entropy can indicate are as follows:
Wherein, p (x1,x2,…,xd) it is joint probability density function under d website.
The utility model has the advantages that one aspect of the present invention has drawn Copula function for the advantage of portraying of multivariate joint distribution, separately
On the one hand information entropy theory is utilized to the strong point of hydrographic information amount quantitative description, compensates for traditional station on-Line review well and estimates
The difficulty and deficiency portrayed in method for the probability density function in the case of higher-dimension.First with semi-parametric approach (SP) to
Out Copula function parameter and optimal Archimedean Copula letter is obtained using Cram é r-von Mises evaluation index
Number show that optimal website combines eventually by MACE criterion.The model-evaluation index used herein, can be preferred to model
Result compare comprehensive evaluation.
The present invention mainly includes following advantages:
(1) it overcomes conventional method and limitation is estimated for the joint probability density function between multivariable.It uses herein
Semi-parametric approach is that a kind of nonparametric is estimated due to using single argument empirical distribution function instead of the marginal distribution function of hypothesis
Metering avoids the subjective factor to limit distribution, so the Copula function finally obtained is the data with sample well
What structure was more suitable for.
(2) solution of the MACE criterion based on simple target function can be relatively easy to realize, avoid multiple target
Adjusting and optimizing difficult point.Model posteriority evaluation index has comprehensively considered residual values minimum, information redundancy amount minimum and total information
Maximum principle is measured, more intuitive embodiment has been carried out to the effect of website combination.
In conclusion the composite type hydrographic(al) network assessment mould that Copula function of the invention and information entropy theory combine
Type can not only realize the quantitative analysis to station net information, but also can carry out posteriority assessment to model result, with reasonability and effectively
Property.
Detailed description of the invention
Fig. 1 is flow diagram in the present invention；
Fig. 2 is website layout drawing of the invention；
Fig. 3 is that all websites illustrate corresponding optimal Copula type function and parameter θ value in the net of station in embodiment
Figure；
Fig. 4 (a) is comparative analysis figure of each station to lower experience Copula and theory Copula；Wherein A represent website 4 with
The website pair that website 7 forms, similarly B is website 1 and 3, and C is website 4 and 6, and D is website 2 and 5；
Fig. 4 (b) is comparative analysis figure of each station to lower experience Copula and theory Copula；Wherein E represent website 3 with
The website pair that website 4 forms, similarly F website 5 and 7, G are website 10 and 11, and H is website 6 and 9；Fig. 5 (a) is different phase relations
Several lower histogram methods and Copula entropy method Mutual Information Estimation amount comparison diagram；
Fig. 5 (b) is histogram method and Copula entropy method Mutual Information Estimation error analysis figure under different related coefficients；
Fig. 6 (a) is rear evaluation index MNCE and NSC calculated result in embodiment；
Fig. 6 (b) is rear evaluation index JE calculated result in embodiment.
Specific embodiment
Technical solution of the present invention is described in detail below, but protection scope of the present invention is not limited to the reality
Apply example.
It is of the invention for ease of understanding, do following explanation:
Entropy is the probabilistic measurement of stochastic variable in statistics.If X is a discrete random variable, letter
Table valued space is U, probability density function p (x)=Pr (X=x), x ∈ U.The entropy H (X) of one discrete random variable X is fixed
Justice is
The case where for two variables, amount of transmitted information I (X between the twoi,XjWith mutual information be able to calculate (Shannon,
2001):
I(Xi,Xj)=H (Xi)+H(Xj)-H(Xi,Xi)
According to Sklar theorem (Zeng et al, 2011), d Victoria C opula are as follows:
Wherein: P represents multidimensional Cumulative Distribution Function,Corresponding variable XiMarginal probability distribution function.θ is
Coupla parameter.Thus derive that Copula density function is that wherein dimensional Co pula entropy and mutual information have following relationship:
I(Xi,Xj)=- Hc(ui,uj)
By above equation it can be concluded that dimensional Co pula entropy is exactly mutual information negative value, and this conclusion is generalized to higher-dimension
Situation, it may be assumed that
TC(X1,X2,…,Xd)=- Hc(u1,u2,…,ud)
Wherein TC (X1,X2,…,Xd) represent the TC value that d ties up variable.
Therefore, the information redundancy amount that available higher-dimension Copula entropy goes to inquire under multi-site can be used as Copula
The good combination of function and comentropy.
As shown in Figure 1, the composite type hydrometric station on-Line review of the invention combined based on Copula function and information entropy theory
Estimate model, specifically successively the following steps are included:
Step 1. is fitted Copula function using semi-parametric approach: being built upon specifically in the calculating of Copula entropy
On the basis of Copula function model, so selecting one, rationally objectively method goes preferred Copula function just to seem especially
It is important.Semi-parametric approach (Semiparametric Approach, SP) solves the problems, such as all rightly more than, certain Cram é r-
Von Mises data (Sn) preferred procedure of Copula function is also largely accelerated, specific steps are as follows:
Using the observation data of each website as the observation x of stochastic variablei(i=1,2 ..., n).
Step 1 calculates empirical distribution function: carrying out the edge experience that homogenization processing obtains each website to former data
Probability function
Step 2 considers two-dimensional situation first: obtaining accumulative experience Copula functional value of each website under；
Step 3 is found out the parameter θ value of Copula based on semi-parametric approach, and combines Cram é r-von Mises data (Sn)
It minimizes ground principle and selects suitable Copula type function.
This estimator is replaced in log-likelihood function, and maximum estimator method can be made to show out that copula joins
Number:
Step 2. is based on the preferred website of MACE criterion: finding out Copula entropy first, this process is related to certain preferred step
Suddenly.It is specific as follows:
1) assume Website Hosting S0For the set of the preferred website of initial placement, original station net collective is F.
2) it is primarily based on edge maximum entropy principle and selects core site imparting Website Hosting S1, and by original site set
In select this website leave out.
3) set S is updatediAnd F.
4) preferably go out to meet the website for minimizing Copula entropy based on MACE criterion below and be attributed to set Si。
5) step 3) is constantly repeated and 4) until reaching satisfied website number.
TC(X1,X2,…,Xd)=- Hc(u1,u2,…,ud)
Hc(u1,u2,…,ud)=- ∫ c (u1,u2,…,ud)logc(u1,u2,…,ud)dU
=-E [logc (u1,u2,…,ud)]
Wherein, d indicates the number (d≤N) of website in website combination, uiRepresent the marginal distribution function of the i-th website.Through
It after going through Copula function preferably and has obtained TC value, can quickly show that optimal website combines by third formula.
The rear evaluation of step 3. station net optimum combination: since the mathematical model based on Copula function and comentropy obtains
Optimal website combined effect lacks certain inspection mechanism, so three evaluation indexes that this step proposes preferably are filled up
This blank.
Three kinds of model-evaluation indexes: (a) Nash-Sutcliffe coefficient (NSC) mainly features residual variation coefficient
Size, theoretically NSC value then shows residual values with regard to smaller closer to 1；(b) negative Copula entropy mean value (MNCE) is then respectively to stand
Hydrographic information redundancy value under point combination；(c) united information entropy (JE) is the total information described under the combination of the point of selective calling
Measure size.Specific calculation formula is as follows:
Wherein n is the length of Hydrological Time Series, SAtIt is the observation under lower t-th of the time series of given website combination
Mean value (can be run-off either rainfall), TAtIt is original station observation data mean value off the net,Indicate n time series
Mean value under length.
It is assumed that the MNCE value that d website has been selected under optimal website combination so combination can indicate are as follows:
Wherein, ui,ujRepresent the marginal distribution function of i-th and j website.
United information entropy can indicate are as follows:
Wherein, p (x1,x2,…,xd) it is joint probability density function under d website.
Whether the station net Optimized model for being intended to judge Copula function and comentropy based on these three evaluation indexes can reach
To expected effect.Following instance is needed to give to prove thus.
Embodiment 1: this implementation is optimized using Yi-Luo river basin hydrographic(al) network as practical application
By taking the station net of 13 hydrometric station compositions of Yi-Luo river basin as an example, using the monthly flow sequence of 2003-2013 as sample
This, comments the station net with the composite type hydrographic(al) network assessment models combined based on Copula function and information entropy theory
Valence and optimization.
(1) basin overview
The data information of the present embodiment derives from Yellow River basin Luo He, Yi He and Yi Luohe, -2013 years in January, 2001
December equal data on flows month by month.Yi Luohe, is the abbreviation of Yi Heyu Luo He, or refers to the appellation after two water cross.But,
The Lip river the Yi Heyu river facies in ancient times meets at Yanshi western part, or even former Luoyang is domestic.It is recorded according to local chronicle, Yi Heyou rises suddenly and sharply several times, out
Behind gantry mouthful, fling outside direct north, that is, the modern Luoyang Southern Pass, converging with Luo He makes Yi He change its course.Yuan Chu Luonan County, Shaanxi Province, China county
The northwestward, east enter Henan and are included in Luo He through Lushi, Luoning, Yiyang, Luoyang to Yanshi, inject the Yellow River to the Luokou in Gongxian county.Yi Luo
River is the Yellow River tributary.She is river overall length 264.88km, belongs to the level-one tributary of the Yellow River, drainage area 6029km2, have along journey
Luanchuan, pool head, Dong Wan, the land hydrometric station Hun Deng；It wherein hence obtains one's name, makees on the tributary crossdrift river of crossdrift valley erect-position Yu Luohe
For the representative station of Lip river river upstream region, area coverage 53.56km2, channel length 43.9km.Lip river river overall length 447, basin face
Product 18881km2, the hydrometric stations (see Fig. 2, table 1) such as Ling Kou, Chang Shui, black stone pass are equipped with along journey.
1 Yiluohe river hydrometric station list of table
(2) model running
(1~13) is numbered to 13 websites in Yi-Luo river basin hydrographic(al) network first, since 13 websites can produce
Life 78 () website is combined, for that can show that preferred Copula function chooses process, the present embodiment
Show that Copula functional simulation of eight stations between the results are shown in Table 2.
The Copula function preferred result of 28 pairs of websites of table combination
Note: in table 2, overstriking font represents optimal Copula function；aThe number of website centering has corresponded to website distribution
The number of website in Fig. 2.
Higher-dimension Copula type function and evaluation index TC value under 3 optimum combination of table
(3) it stands on-Line review valence
The font of overstriking is each station to selected Copula function type in table 2, by Copula functional simulation knot in table 2
Copula function of the different stations between is diverse known to fruit, and semi-parametric approach can be obtained relatively easily suitably
Parameter θ, absolute error also control preferably, and Cram é r-von Mises evaluation index can obtain consistent knot with L-L criterion
By so the method that this model uses is applicable in this example.In order to intuitively react the fitting effect of Copula function,
The contour comparison diagram that 8 pairs of Copula type function and corresponding experience Copula function are shown in -4 figure (b) of Fig. 4 (a), by Fig. 4
Know that preferred Copula type function can be preferably fitted unanimously with experience Copula function.
It can also be found in Fig. 3, the most of type function structures of 78 pairs of website centerings meet G-H Copula type function.
And in Fig. 3, F represents Frank Copula function, and G represents G-H function, and C represents Clayton function.
(4) it stands network optimization
In order to compare the accuracy that Copula entropy estimate obtains mutual information numerical value, the method for also taking emulation experiment, at random
The Gauss number for generating 5 dimensions, in this, as the data source of analysis.It has obtained in Fig. 5 (a)-Fig. 5 (b) based on Copula
The Mutual Information Estimation value comparative analysis that the association relationship and joint histogram that the method for entropy obtains obtain is as a result, it can thus be appreciated that base
Mutual Information Estimation value based on Copula entropy is an advantage over joint distribution histogram method.
Finally need to correspond to the reasonability of the optimum combination under website number by three indexs, this part discusses 13 stations
Point preferably 10 websites situation, by Fig. 6 (a)-Fig. 6 (b) it is found that this three indexs the result is that all can achieve expected
Effect, also show that the optimum combination that model obtains is reasonable from a side.
In conclusion method of the present invention using Copula entropy, taken into account informational capacity and evaluated error value because
Element objective can reasonably obtain optimal station net combination, make rational planning for for hydrographic(al) network and screening provide technical support.
Claims (1)
1. a kind of composite type hydrographic(al) network assessment models combined based on Copula function and information entropy theory successively include such as
Lower step:
(1) potential Archimedean Copula family of functions is fitted based on semi-parametric approach SP；I.e. in hydrology field
Within the scope of Archimedean Copula family of functions, it is based on semi-parametric approach and Cram é r-von Mises data (Sn) find out characterization
The parameter θ value of Copula function and best Copula function；Archimedean Copula family of functions refers to Frank, G-H
With Clayton Copula function；
It is assumed that [X1,X2,…,XN] the station net formed under N number of website number is represented, N is the website number of first initial station net；XitRepresent station
Point XiT-th of observation by homogenization treated value, wherein t=1,2 ..., n, n are the data that each website is collected into
Size；For Marginal distribution estimation value, then semi-parametric approach is expressed as follows:
Above-mentioned gained Marginal distribution estimation value is replaced in log-likelihood functionObtain maximum estimator method
Copula parameter:
Wherein, θ is theoretical Copula parameter,For Copula estimates of parameters, c represents Copula density function, xNtFor N-dimensional
N-th variable under variable situation；
(2) it is carried out preferably by MACE criterion, i.e., the information redundancy amount minimum in the net of station is obtained into optimal site groups with this
It closes, wherein the mutual information TC of multivariable is derived by following formula:
TC(X1,X2,…,Xd)=- Hc(u1,u2,…,ud) (3)
Wherein, d indicates the number and d≤N, u of website in website combinationiRepresent the marginal distribution function of the i-th website；
Then it after living through Copula function preferably and obtains TC value, is combined by the website that formula (5) is calculated quickly optimal fastly；
(3) optimum combination is verified by following three kinds of model-evaluation indexes:
(a) size that Nash-Sutcliffe coefficient describes residual variation coefficient is first passed through；
(b) the hydrographic information redundancy value under respective website combination is then calculated by negative Copula entropy mean value, that is, MNCE value；
(c) using total information content size under the united information entropy JE description point of selective calling combination, specific calculation formula is such as
Under:
Wherein, n is the length of Hydrological Time Series, SAtIt is the observation mean value under lower t-th of the time series of given website combination,
TAtIt is original station observation data mean value off the net,Indicate the mean value under n length of time series；
It is assumed that d website is selected in optimal website combination, then the MNCE value of the optimal website combination indicates are as follows:
Wherein, ui,ujRepresent the marginal distribution function of i-th and j website；
United information entropy indicates are as follows:
Wherein, p (x1,x2,…,xd) it is joint probability density function under d website.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110348701A (en) * | 2019-06-21 | 2019-10-18 | 华中科技大学 | A kind of multi-reservoir flood control operation risk transfer law analysis method |
| CN111949933A (en) * | 2020-07-16 | 2020-11-17 | 南京邮电大学 | Parameter estimation method of Frank Copula function in hydrological frequency analysis under small sample condition |
| CN113128076A (en) * | 2021-05-18 | 2021-07-16 | 北京邮电大学 | Power dispatching automation system fault tracing method based on bidirectional weighted graph model |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106897530A (en) * | 2017-03-06 | 2017-06-27 | 南京大学 | A kind of hydrographic(al) network Optimized model based on Copula entropys |
| CN106909616A (en) * | 2017-01-13 | 2017-06-30 | 南京大学 | Multiple target hydrographic(al) network Optimized model based on comentropy |
| CN107885959A (en) * | 2017-12-06 | 2018-04-06 | 华北电力大学 | A kind of wind-powered electricity generation modeling and performance estimating method based on confidence equivalent power curve belt |
-
2018
- 2018-09-18 CN CN201811085127.2A patent/CN109460526A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106909616A (en) * | 2017-01-13 | 2017-06-30 | 南京大学 | Multiple target hydrographic(al) network Optimized model based on comentropy |
| CN106897530A (en) * | 2017-03-06 | 2017-06-27 | 南京大学 | A kind of hydrographic(al) network Optimized model based on Copula entropys |
| CN107885959A (en) * | 2017-12-06 | 2018-04-06 | 华北电力大学 | A kind of wind-powered electricity generation modeling and performance estimating method based on confidence equivalent power curve belt |
Non-Patent Citations (1)
| Title |
|---|
| PENGCHENG XU等: "A two-phase copula entropy-based multiobjective optimization approach to hydrometeorological gauge network design", 《JOURNAL OF HYDROLOGY》 * |
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| CN110348701B (en) * | 2019-06-21 | 2021-10-08 | 华中科技大学 | Reservoir group flood control scheduling risk transfer rule analysis method |
| CN111949933A (en) * | 2020-07-16 | 2020-11-17 | 南京邮电大学 | Parameter estimation method of Frank Copula function in hydrological frequency analysis under small sample condition |
| CN111949933B (en) * | 2020-07-16 | 2023-07-25 | 南京邮电大学 | Parameter estimation method of Frank Copula function in hydrologic frequency analysis under small sample condition |
| CN113128076A (en) * | 2021-05-18 | 2021-07-16 | 北京邮电大学 | Power dispatching automation system fault tracing method based on bidirectional weighted graph model |
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