CN105260607A - Serial connection and parallel connection coupling multi-model hydrological forecasting method - Google Patents

Abstract

The invention relates to the hydrological forecasting field of the hydrology, and discloses a serial connection and parallel connection coupling multi-model hydrological forecasting method. The advantages of two traditional methods including correction and combination forecasting are fully performed to establish a serial connection and parallel connection coupling hydrological forecasting model. The multi-model hydrological forecasting method is divided into three forms, i.e., a method that parallel connection is carried out after serial connection, a method that serial connection is carried out after parallel connection, and an integral coupling method, according to different coupling ways, wherein the method that parallel connection is carried out after serial connection is characterized in that the calculation results of the hydrological models are firstly subjected to serial connection correction, and then, the correction results of the models are subjected to parallel connection correction; the method that serial connection is carried out after parallel connection is characterized in that the calculation results of the hydrological models are firstly subjected to the parallel connection correction, and then, the result of the combination forecasting is subjected to the serial connection correction; and the integral coupling method establishes a target function of a serial connection and parallel connection coupling correction result on the basis of a forecasting error minimum principle, and simultaneously calibrates the parameters of the parallel connection correction and the serial connection correction. The hydrological forecasting method can reduce forecasting errors to a maximum degree, improves forecasting precision and can be widely applied to real-time hydrological forecasting.

Description

A kind of multi-model hydrologic forecasting method of connection in series-parallel coupling

Technical field

The invention belongs to the hydrologic forecast field in hydrology, relate to the multi-model hydrologic forecasting method of a kind of connection in series-parallel coupling.The method can provide theoretical foundation and technical support for water conservancy administration department realizes high-precision hydrologic forecast.

Background technology

Hydrologic forecast, by making scientific forecasting to following hydrologic regime (as crest discharge), particularly makes accurate forecast to disastrous hydrology phenomenon, thus realizes flood control and disaster reduction and rational development of water resources utilization.Improve the important content that the precision of hydrologic forecast is hydrologic forecast work, to flood control and disaster reduction, protect people life property safety, give full play to that benefit of water project is improved the ecological environment etc. and play vital effect.

The method of existing raising hydrological factor mainly contains real time correction and combining prediction two kinds of methods.Real-time correction method make use of the correlative character of prediction error sequence self, the error amount of prediction future time instance, thus realize the real time correction (method for optimizing as patent CN201010106038.9-real-time correction models in flood forecast system) to hydrologic forecast result.Combining prediction method is on the basis of current application various hydrologic forecast model widely, utilize the complementarity between model, incorporate the thought of model-weight method, several hydrological models chosen application basin is comparatively suitable for set up combining prediction scheme, carry out hydrologic forecast (hydrologic forecasting method as patent CN200910234628.7-a kind of different mechanisms hydrological model combination).

Summary of the invention

Real time correction and combining prediction two kinds of methods are not combined closely by current methods, set up the hydrologic forecast calibration model of more system and science.The present invention proposes the hydrologic forecasting method that real time correction is coupled with combining prediction, i.e. a kind of multi-model hydrologic forecasting method of connection in series-parallel coupling, to give full play to the advantage of real time correction and combining prediction, thus improve precision and the level of hydrologic forecast to greatest extent.

The present invention is on the basis of existing real time correction and combining prediction model, creatively combine the advantage of the two, have developed the multi-model hydrologic forecasting method of a kind of connection in series-parallel coupling, according to the difference of coupling scheme, altogether three kinds of effective forms are proposed, namely first after string and method, elder generation and after go here and there method and integrated coupling process.The present invention decreases prediction error to greatest extent, improves forecast precision, thus achieves high-precision real-time hydrological forecasting.

For solving the problems of the technologies described above, the present invention adopts following technical scheme:

Step 1: select forecast section, obtains the actual measurement rainfall and flow data of this section period of history, data is divided into rate regularly and probative term two parts; The data that employing rate is regular, the parameter of calibration hydrological model, adopts the data of probative term, the effect of inspection hydrological model.Set up multiple hydrologic forecast model, as Xinanjiang model, tank model and API (AntecedentPrecipitationIndex) model etc., forecast the run-off of this section respectively.

Step 2: the hydrologic forecast model setting up connection in series-parallel coupling.

The present invention have developed the multi-model hydrologic forecasting method of a kind of connection in series-parallel coupling, by the difference of coupling scheme, is divided into three kinds of forms, namely first after string and method, elder generation afterwards string method and integrated coupling model.

(1) first string after and method

1. first, the result of single hydrologic forecast model is corrected, complete the process of series connection forecast.

Based on the forecasting runoff of each hydrological model in actual measurement and step 1, obtain the prediction error sequence of each forecasting model.According to the autocorrelation performance of prediction error sequence, set up autogression of error calibration model.Specific as follows:

Order actual measurement sequence is Q _t=(Q ₁, Q ₂..., Q _n), n is the length of sequence, and forecasting sequence is forecasting sequence is error sequence with the difference of actual measurement sequence, is designated as e _t=(e ₁, e ₂..., e _n).The mathematic(al) representation of autogression of error model is:

e _t＝θ ₁e _t-1+θ ₂e _t-2+…+θ _qe _t-q+ξ

In formula, θ _i(i=1,2 ..., q) be the parameter of autoregressive model.Adopt above formula, set up q rank autoregressive model AR (q).In order to make the fitting effect of selected autoregressive model to data best, carried out the exponent number of Confirming model by AIC criterion.AIC (q) value of q rank autoregressive model AR (q) is:

$AIC\left(q\right)=nln\left(\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{(Q_i-{\hat{Q}}_i)}^2}\right)+2(2q+1)$

Select to calculate below the q rank autoregressive model that probative term AIC (Akaikeinformationcriterion) value is minimum participates in.By the prediction error e of the autoregressive model prediction t of foundation _t, adopt the prediction error value obtained to correct forecast result.For each hydrologic forecast model, utilize said method, obtain the series connection forecast result of each forecasting model in this section forecasting runoff.

2. secondly, the result of comprehensive each single model series connection forecast, completes Parallel Adjustment process.

Based on m hydrological model series connection prediction sequence set up Parallel Adjustment model, as follows:

$F_t={\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}$

In formula, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrologic forecast model, and the ω that satisfies condition ₁+ ω ₂+ ... + ω _m=1.Least square method is adopted to calculate the weight of forecast in parallel.Resulting in the result of calculation of the rear also coupling model of first string.

(2) first and after go here and there method

1. based on the prediction sequence Q of m hydrological model _1t, Q _2t..., Q _mt, set up Parallel Adjustment model, as follows:

F _t＝ω ₁Q _1t+ω ₂Q _2t+…+ω _mQ _mt

In formula, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrologic forecast model, and the ω that satisfies condition ₁+ ω ₂+ ... + ω _m=1.Least square method is adopted to calculate the weight of each model in Parallel Adjustment.

2. according to the result of Parallel Adjustment, the error sequence of Parallel Adjustment is obtained.Utilize above-mentioned autoregressive model principle, set up autogression of error cascade compensation model AR (q), based on the exponent number of AIC criterion Confirming model, cascade compensation is carried out to the Parallel Adjustment result of multiple forecasting model.Resulting in the result of calculation of first and rear string coupling model.

(3) integrated coupling process

Utilize the run-off of section measured runoff and each hydrologic forecast model Simulation prediction, set up integrated coupling model.Note hydrological model number is m, and actual measurement sequence is Q _t, the forecast result of each hydrological model is Q _1t, Q _2t..., Q _mt.Each model is adopted to the error sequence e of autogression of error model prediction t _t, expression formula is as follows:

$\left\{\begin{array}{c}{e}_{1t}={\mathrm{\α}}_{11}{e}_{1(t-1)}+{\mathrm{\α}}_{21}{e}_{1(t-2)}\\ e_{2t}={\mathrm{\α}}_{12}{e}_{2(t-1)}+{\mathrm{\α}}_{22}{e}_{2(t-2)}\\ .\\ .\\ .\\ e_{mt}={\mathrm{\α}}_{1m}{e}_{m(t-1)}+{\mathrm{\α}}_{2m}{e}_{m(t-2)}\end{array}\right.$

In formula, (α ₁₁, α ₂₁), (α ₁₂, α ₂₂) ..., (α _1m, α _2m) be regression coefficient.Adopt above-mentioned prediction error value to correct forecast result, obtain the flow sequence after each model cascade compensation

On the basis of each model series connection forecast result, utilize least square method, carry out the Parallel Adjustment of multiple model, the result of Parallel Adjustment is F _t:

$F_t={\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}$

In formula, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrologic forecast model, and the ω that satisfies condition ₁+ ω ₂+ ... + ω _m=1.

Adopt the method (integral method) of global optimization to ask the parameter obtaining cascade compensation and Parallel Adjustment simultaneously.The error of Parallel Adjustment result is made to be F _t-Q _t, the expectation of its error is designated as E (F _t-Q _t) ².In order to make the expectation value E (F of error _t-Q _t) ²minimum, obtain following objective function:

$\left\{\begin{array}{c}MinE{(F_t-Q_t)}^2=MinE{({\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}-Q_t)}^2\\ =MinE{\left({\mathrm{\ω}}_1\right(e_{1t}+Q_t)+{\mathrm{\ω}}_2(e_{2t}+Q_t)+...+{\mathrm{\ω}}_m(e_{mt}+Q_t)-Q_t)}^2\\ =MinE{({\mathrm{\ω}}_1{e}_{1t}+{\mathrm{\ω}}_2{e}_{2t}+...+{\mathrm{\ω}}_m{e}_{mt})}^2\\ =MinE\left({\mathrm{\ω}}_1\right({\mathrm{\α}}_{11}{e}_{1(t-1)}+{\mathrm{\α}}_{21}{e}_{1(t-2)})+{\mathrm{\ω}}_2({\mathrm{\α}}_{12}{e}_{2(t-1)}+{\mathrm{\α}}_{22}{e}_{2(t-2)})\\ +...+{\mathrm{\ω}}_m({\mathrm{\α}}_{1m}{e}_{m(t-1)}+{\mathrm{\α}}_{2m}{e}_{m(t-2)}){)}^2\\ \begin{array}{cc}s.t.& {\mathrm{\ω}}_1+{\mathrm{\ω}}_2+...+{\mathrm{\ω}}_m=1\end{array}\end{array}\right.$

In formula, its parameter comprises regression coefficient (α ₁₁, α ₂₁), (α ₁₂, α ₂₂) ..., (α _1m, α _2m) and weight coefficient ω ₁, ω ₂..., ω _mtwo parts, altogether 3m undetermined parameter.

Introduce population intelligent optimization algorithm (ParticleSwarmOptimizer, PSO) and solve these parameters simultaneously.After obtaining these parameters, first adopt cascade compensation method, cascade compensation is carried out to the forecasting runoff of each hydrological model, obtains cascade compensation result; Then, utilize Parallel Adjustment method, Parallel Adjustment is carried out to the result after each hydrological model real time correction.Resulting in the result of calculation of integrated coupling process.

Step 3: choose the conventional accuracy assessment indexs such as mean absolute error, average relative error, deterministic coefficient and root-mean-square error, accuracy assessment is carried out to the result of the connection in series-parallel coupling model of three kinds of forms.

Compared with prior art, the present invention has the following advantages and effect:

(1) prior art only adopts real time correction technology or combining prediction method to improve the precision of hydrologic forecast, and the two is not combined consideration.The present invention is on the basis of comprehensive real time correction and combining prediction advantage, propose the multi-model hydrologic forecasting method of a kind of connection in series-parallel coupling, correct the result that result significantly will be better than simple real time correction or combining prediction, decrease prediction error to greatest extent, improve precision and the level of hydrologic forecast.

(2) prior art adopts least square method to calculate the parameter of cascade compensation and Parallel Adjustment, when this method for parameter estimation is applied to coupling model, lacks and holds the entirety of calibration result.The present invention utilizes particle swarm optimization algorithm, the parameter that calibration connection in series-parallel coupling simultaneously corrects, i.e. integrated coupling model.With first go here and there after and and first and rear string method compare, the forecast precision of integrated coupling model is the highest.

Accompanying drawing explanation

Fig. 1 is the multi-model hydrologic forecasting method process flow diagram of connection in series-parallel of the present invention coupling.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.In addition, if below in described each embodiment of the present invention involved technical characteristic do not form conflict each other and just can mutually combine.

The present invention proposes the multi-model hydrologic forecasting method of a kind of connection in series-parallel coupling, according to the difference of coupling scheme, model have three kinds of forms namely first after string and method, elder generation string method afterwards, and integrated coupling model.By the complementarity between the autocorrelation of prediction error sequence and hydrological model, decrease prediction error, improve forecast precision, thus achieve high-precision real-time hydrological forecasting, for science bridle flood provides theoretical foundation and technical support.As shown in Figure 1, be the multi-model hydrologic forecasting method idiographic flow of connection in series-parallel coupling of the present invention, said method comprising the steps of:

Step 1: select forecast section, obtains the actual measurement rainfall and flow data of this section period of history, data is divided into rate regularly and probative term two parts; The data that employing rate is regular, the parameter of calibration model, adopts the data of probative term, the effect of testing model.Set up multiple hydrologic forecast model, as Xinanjiang model, tank model and API model etc., forecast the run-off of this section respectively.

Step 2: the hydrologic forecast model setting up connection in series-parallel coupling.

The present invention proposes the hydrologic forecasting method of a kind of connection in series-parallel coupling, different by coupling scheme, be divided into three kinds of forms, namely first after string and method, elder generation and after go here and there method and integrated coupling model.

(1) first string after and method

1. based on measured discharge and forecasting runoff, prediction error sequence is obtained.According to prediction error sequence, set up autogression of error cascade compensation model.

Concrete modeling method is as follows:

Order actual measurement sequence is Q _t=(Q ₁, Q ₂..., Q _n), n is the length of sequence, and forecasting sequence is forecasting sequence is error sequence with the difference of actual measurement sequence, is designated as e _t=(e ₁, e ₂..., e _n).The mathematic(al) representation of autogression of error model is:

e _t＝θ ₁e _t-1+θ ₂e _t-2+…+θ _qe _t-q+ξ

In formula, q is the exponent number of autogression of error model, θ ₁, θ ₂..., θ _qfor regression coefficient, ξ is average is zero, variance is the white noise signal of certain value.

Adopt above formula, set up q rank autoregressive model AR (q), q=2,3 ..., 30.Based on the data that rate is regular, utilize the parameter of least square method calibration model; Based on the data of probative term, the effect of testing model.

The exponent number of Selection Model is carried out by AIC criterion.AIC (q) value of q rank autoregressive model AR (q) is:

$AIC\left(q\right)=nln\left(\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{(Q_i-{\hat{Q}}_i)}^2}\right)+2(2q+1)$

The autoregressive model selecting probative term AIC value minimum, as optimization model, participates in correcting.

Finally, by the prediction error e of built autoregressive model prediction t _t, and forecast result is corrected.For each hydrologic forecast model, utilize said method, obtain the cascade compensation result of each forecasting model in this section forecasting runoff.

2. according to section measured discharge and 1. in the cascade compensation result of each hydrological model, set up Parallel Adjustment model.If the hydrological model number participating in Parallel Adjustment is m, the forecast result after each hydrological model corrects is respectively can be expressed as:

$\left\{\begin{array}{c}{\hat{Q}}_{1t}-\left({\hat{Q}}_{11},{\hat{Q}}_{12},\mathrm{...},{\hat{Q}}_{1n}\right)\\ {\hat{Q}}_{2t}-\left({\hat{Q}}_{21},{\hat{Q}}_{22},\mathrm{...},{\hat{Q}}_{2n}\right)\\ .\\ .\\ .\\ {\hat{Q}}_{mt}-\left({\hat{Q}}_{m1},{\hat{Q}}_{m2},\mathrm{...},{\hat{Q}}_{mn}\right)\end{array}\right.$

The result of Parallel Adjustment is calculated by following formula:

$F_t={\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}$

Wherein, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrological model, and the ω that satisfies condition ₁+ ω ₂+ ... + ω _m=1.

Least square method is adopted to determine the weight of Parallel Adjustment, specific as follows.

Calculate the error sequence of each model, the error sequence obtaining each model is as follows:

$\left\{\begin{array}{c}{e}_{1t}=(e_{11},e_{12},...,e_{1n})\\ e_{2t}=(e_{21},e_{22},...,e_{2n})\\ .\\ .\\ .\\ e_{mt}=(e_{m1},e_{m2},...,e_{mn})\end{array}\right.$

The error sequence of Parallel Adjustment result is designated as (F _t-Q _t), represent expectation value with symbol E, the expectation value of error sequence square is designated as E (F _t-Q _t) ², its calculating formula is as follows:

$E{(F_t-Q_t)}^2=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{(F_i-Q_i)}^2$

In order to make the expectation value of Parallel Adjustment resultant error square minimum, the problem of each Model Weight value under this target that solves is converted into and solves following linear programming problem:

$\left\{\begin{array}{c}MinE{(F_t-Q_t)}^2=MinE{({\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}-Q_t)}^2\\ =MinE{\[{\mathrm{\ω}}_1(e_{1t}+Q_t)+{\mathrm{\ω}}_2(e_{2t}+Q_t)+...+{\mathrm{\ω}}_m(e_{mt}+Q_t)-Q_t\]}^2\\ =MinE{({\mathrm{\ω}}_1{e}_{1t}+{\mathrm{\ω}}_2{e}_{2t}+...+{\mathrm{\ω}}_m{e}_{mt})}^2\\ \begin{array}{cc}s.t.& {\mathrm{\ω}}_1+{\mathrm{\ω}}_2+...+{\mathrm{\ω}}_m=1\end{array}\end{array}\right.$

Introduce Lagrange multiplier λ, establishing target function:

L(ω ₁,ω ₂,...,ω _m,λ)＝E(ω ₁e _1t+ω ₂e _2t+…+ω _me _mt) ²+λ(ω ₁+ω ₂+…+ω _m-1)

Objective function is respectively to ω ₁, ω ₂..., ω _m, λ asks local derviation, and makes its local derviation equal 0, obtains following system of equations:

$\left\{\begin{array}{c}\frac{\∂L}{\∂{\mathrm{\ω}}_1}=2{\mathrm{\ω}}_{1}E\left(e_{1t}{e}_{1t}\right)+2{\mathrm{\ω}}_{2}E\left(e_{1t}{e}_{2t}\right)+...+2{\mathrm{\ω}}_{m}E\left(e_{1t}{e}_{mt}\right)+\mathrm{\λ}=0\\ \frac{\∂L}{\∂{\mathrm{\ω}}_2}=2{\mathrm{\ω}}_{1}E\left(e_{2t}{e}_{1t}\right)+2{\mathrm{\ω}}_{2}E\left(e_{2t}{e}_{2t}\right)+...+2{\mathrm{\ω}}_{m}E\left(e_{2t}{e}_{mt}\right)+\mathrm{\λ}=0\\ .\\ .\\ .\\ \frac{\∂L}{\∂{\mathrm{\ω}}_m}=2{\mathrm{\ω}}_{1}E\left(e_{mt}{e}_{1t}\right)+2{\mathrm{\ω}}_{2}E\left(e_{mt}{e}_{2t}\right)+...+2{\mathrm{\ω}}_{m}E\left(e_{mt}{e}_{mt}\right)+\mathrm{\λ}=0\\ \frac{\∂L}{\∂\mathrm{\λ}}={\mathrm{\ω}}_1+{\mathrm{\ω}}_2+...+{\mathrm{\ω}}_m-1=0\end{array}\right.$

Wherein, $E\left(e_{jt}{e}_{kt}\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}(e_{ji}\·e_{ki}),(j,k=1,2,...,m).$

By solving equation group, the coupling weights omega of each hydrological model can be obtained ₁, ω ₂..., ω _mvalue.

(2) first and after go here and there method

1. based on the prediction sequence Q of m hydrological model _1t, Q _2t..., Q _mt, set up Parallel Adjustment model, as follows:

F _t＝ω ₁Q _1t+ω ₂Q _2t+…+ω _mQ _mt

In formula, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrologic forecast model, and meet ω ₁+ ω ₂+ ... + ω _m=1.Above-mentioned principle of least square method is utilized to solve coupling weights omega ₁, ω ₂..., ω _m, resulting in the Parallel Adjustment result of multiple forecasting model.

2. forecast the forecast result in parallel of run-off according to section measured runoff and multiple forecasting model at this section, set up the real-time cascade compensation model of the autogression of error.Utilize above-mentioned autoregressive model principle, cascade compensation is carried out to the Parallel Adjustment result of multiple forecasting model.Resulting in the result of calculation of first and rear string method.

(3) integrated coupling process

1. utilize the run-off of section measured runoff and each hydrologic forecast model Simulation prediction, set up integrated coupling model.Note hydrologic forecast model number is m, and actual measurement sequence is Q _t, the forecast result of each hydrological model is Q _1t, Q _2t..., Q _mt.Adopt autogression of error model to correct to each model, remember that the error correction expression formula of each model is as follows:

$\left\{\begin{array}{c}{e}_{1t}={\mathrm{\α}}_{11}{e}_{1(t-1)}+{\mathrm{\α}}_{21}{e}_{1(t-2)}\\ e_{2t}={\mathrm{\α}}_{12}{e}_{2(t-1)}+{\mathrm{\α}}_{22}{e}_{2(t-2)}\\ .\\ .\\ .\\ e_{mt}={\mathrm{\α}}_{1m}{e}_{m(t-1)}+{\mathrm{\α}}_{2m}{e}_{m(t-2)}\end{array}\right.$

On the basis of cascade compensation result obtaining each model, utilize least square method, carry out the Parallel Adjustment of multiple model.The result of Parallel Adjustment is as follows:

$F_t={\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}$

In formula, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrologic forecast model, and meet ω ₁+ ω ₂+ ... + ω _m=1.

The error of combining prediction result is designated as F _t-Q _t, what it was expected square is designated as E (F _t-Q _t) ², in order to make E (F _t-Q _t) ²minimum, obtain following objective function:

$\left\{\begin{array}{c}MinE{(F_t-Q_t)}^2=MinE{({\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}-Q_t)}^2\\ =MinE{\left({\mathrm{\ω}}_1\right(e_{1t}+Q_t)+{\mathrm{\ω}}_2(e_{2t}+Q_t)+...+{\mathrm{\ω}}_m(e_{mt}+Q_t)-Q_t)}^2\\ =MinE{({\mathrm{\ω}}_1{e}_{1t}+{\mathrm{\ω}}_2{e}_{2t}+...+{\mathrm{\ω}}_m{e}_{mt})}^2\\ =MinE\left({\mathrm{\ω}}_1\right({\mathrm{\α}}_{11}{e}_{1(t-1)}+{\mathrm{\α}}_{21}{e}_{1(t-2)})+{\mathrm{\ω}}_2({\mathrm{\α}}_{12}{e}_{2(t-1)}+{\mathrm{\α}}_{22}{e}_{2(t-2)})\\ +...+{\mathrm{\ω}}_m({\mathrm{\α}}_{1m}{e}_{m(t-1)}+{\mathrm{\α}}_{2m}{e}_{m(t-2)}){)}^2\\ \begin{array}{cc}s.t.& {\mathrm{\ω}}_1+{\mathrm{\ω}}_2+...+{\mathrm{\ω}}_m=1\end{array}\end{array}\right.$

In formula, its parameter comprises regression coefficient (α ₁₁, α ₂₁), (α ₁₂, α ₂₂) ..., (α _1m, α _2m) and weight coefficient ω ₁, ω ₂..., ω _mtwo parts, altogether 3m undetermined parameter.

Introduce population intelligent optimization algorithm (ParticleSwarmOptimizer, PSO) and solve these parameters simultaneously.After obtaining these parameters, first adopt cascade compensation method, cascade compensation is carried out to the forecasting runoff of each hydrological model, obtains cascade compensation result; Then, utilize Parallel Adjustment method, Parallel Adjustment is carried out to the result after each hydrological model cascade compensation.Resulting in the result of calculation of integrated coupling process.

Step 3: choose the forecast precision deliberated index that mean absolute error, average relative error, deterministic coefficient and root-mean-square error etc. are conventional, carries out accuracy assessment to the result that master mould and connection in series-parallel coupling correct.Each accuracy assessment index is defined as follows:

1. mean absolute error (MAE)

Mean absolute error is shown below:

$MAE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}|Q_i-{\hat{Q}}_i|$

In formula, Q _ifor measured value, for predicted value, n is prediction sequence length.

2. average relative error (MRE)

Average relative error is shown below:

$MRE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{\[(Q_i-{\hat{Q}}_i)/Q_i\]}^2$

3. deterministic coefficient (DC)

Deterministic coefficient is shown below:

$DC=1-\[\underset{i=1}{\overset{n}{\Σ}}{(Q_i-{\hat{Q}}_i)}^2\]/\underset{i=1}{\overset{n}{\Σ}}{(Q_i-\stackrel{\‾}{Q_i})}^2\]$

In formula, for the mean value of measured value in prediction sequence length, DC reflects the degree of agreement between flood forecasting process and actual measurement process, and DC value is higher, and degree of agreement is higher.

4. root-mean-square error (RMSE)

Root-mean-square error is shown below:

$RMSE=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{(Q_i-{\hat{Q}}_i)}^2}$

Adopt the Xinanjiang River, water tank, neural network and gray model forecast Three Gorges Reservoir reservoir inflow sequence, its accuracy assessment result is as shown in table 1; Utilize the present invention to carry connection in series-parallel coupling model to correct forecast result, its accuracy assessment result is as shown in table 2.

Table 1 single hydrological model forecast precision evaluation result

Table 2 is coupled hydrologic forecast model accuracy assessment result

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (10)

1. a multi-model hydrologic forecasting method for connection in series-parallel coupling, is characterized in that, comprise the steps:

Step 1: select forecast section, obtains the actual measurement rainfall and flow data of this section period of history, data is divided into rate regularly and probative term two parts; The data that employing rate is regular, the parameter of calibration hydrological model, adopts the data of probative term, the effect of inspection hydrological model; Set up multiple hydrologic forecast model, forecast the run-off of this section respectively;

Step 2: the hydrologic forecast model setting up connection in series-parallel coupling, by the difference of coupling scheme, is divided into three kinds of forms, namely first after string and method, elder generation afterwards string method and integrated coupling model;

Step 3: choose the conventional accuracy assessment indexs such as mean absolute error, average relative error, deterministic coefficient and root-mean-square error, accuracy assessment is carried out to the result of the connection in series-parallel coupling model of three kinds of forms.

2. the method for claim 1, is characterized in that, the first string in described step 2 afterwards and method be specially:

1. first, the result of single hydrologic forecast model is corrected, complete the process of series connection forecast;

Based on the forecasting runoff of each hydrological model in actual measurement and step 1, obtain the prediction error sequence of each forecasting model; According to the autocorrelation performance of prediction error sequence, set up autogression of error calibration model; Specific as follows:

Order actual measurement sequence is Q _t=(Q ₁, Q ₂..., Q _n), n is the length of sequence, and forecasting sequence is forecasting sequence is error sequence with the difference of actual measurement sequence, is designated as e _t=(e ₁, e ₂..., e _n); The mathematic(al) representation of autogression of error model is:

e _t＝θ ₁e _t-1+θ ₂e _t-2+…+θ _qe _t-q+ξ

In formula, θ _i(i=1,2 ..., q) be the parameter of autoregressive model; Adopt above formula, set up q rank autoregressive model AR (q); AIC (q) value of q rank autoregressive model AR (q) is:

$AIC\left(q\right)=nln\left(\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{(Q_i-{\hat{Q}}_i)}^2}\right)+2(2q+1)$

Select to calculate below the q rank autoregressive model that probative term AIC value is minimum participates in: by the prediction error e of the autoregressive model prediction t of foundation _t, adopt the prediction error value obtained to correct forecast result; For each hydrologic forecast model, utilize said method, obtain the series connection forecast result of each forecasting model in this section forecasting runoff;

2. secondly, the result of comprehensive each single model series connection forecast, completes Parallel Adjustment process;

Based on m hydrological model series connection prediction sequence set up Parallel Adjustment model, as follows:

$F_t={\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}$

In formula, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrologic forecast model, and the ω that satisfies condition ₁+ ω ₂+ ... + ω _m=1; Resulting in the result of calculation of the rear also coupling model of first string.

3. the method for claim 1, is characterized in that, the elder generation in described step 2 rear string method are specially:

1. based on the prediction sequence Q of m hydrological model _1t, Q _2t..., Q _mt, set up Parallel Adjustment model, as follows:

F _t＝ω ₁Q _1t+ω ₂Q _2t+…+ω _mQ _mt

In formula, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrologic forecast model, and the ω that satisfies condition ₁+ ω ₂+ ... + ω _m=1; Least square method is adopted to calculate the weight of each model in Parallel Adjustment;

2. according to the result of Parallel Adjustment, the error sequence of Parallel Adjustment is obtained; Utilize autoregressive model principle, set up autogression of error cascade compensation model AR (q), based on the exponent number of AIC criterion Confirming model, cascade compensation is carried out to the Parallel Adjustment result of multiple forecasting model; Resulting in the result of calculation of first and rear string coupling model.

4. the method for claim 1, is characterized in that, the integrated coupling process in described step 2 is specially:

Utilize the run-off of section measured runoff and each hydrologic forecast model Simulation prediction, set up integrated coupling model; Note hydrological model number is m, and actual measurement sequence is Q _t, the forecast result of each hydrological model is Q _1t, Q _2t..., Q _mt; Each model is adopted to the error sequence e of autogression of error model prediction t _t, expression formula is as follows:

$\left\{\begin{array}{c}{e}_{1t}={\mathrm{\α}}_{11}{e}_{1(t-1)}+{\mathrm{\α}}_{21}{e}_{1(t-2)}\\ e_{2t}={\mathrm{\α}}_{12}{e}_{2(t-1)}+{\mathrm{\α}}_{22}{e}_{2(t-2)}\\ \begin{array}{c}.\\ .\\ .\end{array}\\ e_{mt}={\mathrm{\α}}_{1m}{e}_{m(t-1)}+{\mathrm{\α}}_{2m}{e}_{m(t-2)}\end{array}\right.$

In formula, (α ₁₁, α ₂₁), (α ₁₂, α ₂₂) ..., (α _1m, α _2m) be regression coefficient; Adopt above-mentioned prediction error value to correct forecast result, obtain the flow sequence after each model cascade compensation

On the basis of each model series connection forecast result, utilize least square method, carry out the Parallel Adjustment of multiple model, the result of Parallel Adjustment is F _t:

$F_t={\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}$

In formula, ω ₁, ω ₂..., ω _mbe respectively the coupling weight of each hydrologic forecast model, and the ω that satisfies condition ₁+ ω ₂+ ... + ω _m=1;

Adopt the method for global optimization to ask the parameter obtaining cascade compensation and Parallel Adjustment simultaneously; The error of Parallel Adjustment result is made to be F _t-Q _t, the expectation of its error is designated as E (F _t-Q _t) ²; In order to make the expectation value E (F of error _t-Q _t) ²minimum, obtain following objective function:

$\left\{\begin{array}{c}MinE{(F_t-Q_t)}^2=MinE{({\mathrm{\ω}}_1{\hat{Q}}_{1t}+{\mathrm{\ω}}_2{\hat{Q}}_{2t}+...+{\mathrm{\ω}}_m{\hat{Q}}_{mt}-Q_t)}^2\\ =MinE{\left({\mathrm{\ω}}_1\right(e_{1t}+Q_t)+{\mathrm{\ω}}_2(e_{2t}+Q_t)+...+{\mathrm{\ω}}_m(e_{mt}+Q_t)-Q_t)}^2\\ =MinE{({\mathrm{\ω}}_1{e}_{1t}+{\mathrm{\ω}}_2{e}_{2t}+...+{\mathrm{\ω}}_m{e}_{mt})}^2\\ =MinE({\mathrm{\ω}}_1\left({\mathrm{\α}}_{11}{e}_{1(t-1)}+{\mathrm{\α}}_{21}{e}_{1(t-2)}\right)+{\mathrm{\ω}}_2\left({\mathrm{\α}}_{12}{e}_{2(t-1)}+{\mathrm{\α}}_{22}{e}_{2(t-2)}\right)\\ +...+{\mathrm{\ω}}_m\left({\mathrm{\α}}_{1m}{e}_{m(t-1)}+{\mathrm{\α}}_{2m}{e}_{m(t-2)}\right){)}^2\\ \begin{array}{cc}s.t.& {\mathrm{\ω}}_1+{\mathrm{\ω}}_2+...+{\mathrm{\ω}}_m=1\end{array}\end{array}\right.$

In formula, its parameter comprises regression coefficient (α ₁₁, α ₂₁), (α ₁₂, α ₂₂) ..., (α _1m, α _2m) and weight coefficient ω ₁, ω ₂..., ω _mtwo parts, altogether 3m undetermined parameter;

Introduce population intelligent optimization algorithm and solve these parameters simultaneously; After obtaining these parameters, first adopt cascade compensation method, cascade compensation is carried out to the forecasting runoff of each hydrological model, obtains cascade compensation result; Then, utilize Parallel Adjustment method, Parallel Adjustment is carried out to the result after each hydrological model real time correction; Resulting in the result of calculation of integrated coupling process.

5. the method as described in any one of claim 1-4, is characterized in that, the accuracy assessment index in described step 3 comprise following one or more: mean absolute error, average relative error, deterministic coefficient and root-mean-square error.

6. method as claimed in claim 5, it is characterized in that, described mean absolute error MAE is shown below:

$MAE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}|Q_i-{\hat{Q}}_i|$

In formula, Q _ifor measured value, for predicted value, n is prediction sequence length.

7. method as claimed in claim 5, it is characterized in that, described average relative error MRE is shown below:

$MRE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{\[(Q_i-{\hat{Q}}_i)/Q_i\]}^2$

In formula, Q _ifor measured value, for predicted value, n is prediction sequence length.

8. method as claimed in claim 5, it is characterized in that, described deterministic coefficient DC is shown below:

$DC=1-\[\underset{i=1}{\overset{n}{\Σ}}{(Q_i-{\hat{Q}}_i)}^2\]/\underset{i=1}{\overset{n}{\Σ}}{(Q_i-{\stackrel{\‾}{Q}}_i)}^2\]$

In formula, for the mean value of measured value in prediction sequence length, Q _ifor measured value, for predicted value, n is prediction sequence length.

9. method as claimed in claim 5, it is characterized in that, described root-mean-square error RMSE is shown below:

$RMSE=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{(Q_i-{\hat{Q}}_i)}^2}$

In formula, Q _ifor measured value, for predicted value, n is prediction sequence length.

10. method as claimed in claim 1 or 2, is characterized in that, the hydrologic forecast model in described step 1 comprises following one or more: Xinanjiang model, tank model and API model.