CN107341346A - A kind of hydrologic forecasting method - Google Patents
A kind of hydrologic forecasting method Download PDFInfo
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Abstract
The invention discloses a kind of bound section hydrologic forecasting method based on ideal boundary and multiple linear regression.The present invention is respectively adopted same multiple proportions amplification and reduces the preferable bound border of method construct of measured discharge, it is periodically the structure and parameter that principle determines multiple linear regression upper and lower bound model by target and least square method of preferable upper and lower limit border in rate, percent of pass is periodically and the bound forecast result of probative term realizes bound section hydrologic forecast.Rate, relative width, symmetry and root-mean-square error (using section intermediate value to be used as predicted value) are included as accuracy assessment index using prediction interval, the regression model interval prediction result of existing neural net method and different relative widths is contrasted, method proposed by the present invention shows preferable forecast precision and the value of forecasting.The method that the present invention uses calculates simple and fast, avoids substantial amounts of parameter optimization search procedure and optimized algorithm is absorbed in the possibility of local optimum, significantly shorten the hydrologic forecast time.
Description
Technical field
The invention belongs to the short-term runoff hydrologic forecast field in hydrology, and ideal edge is based on more particularly, to one kind
Boundary and the bound section hydrologic forecasting method of multiple linear regression.
Background technology
Existing hydrologic forecasting method mainly has experience correlation method and model method, and experience correlation technique is included as based on more
The hydrologic forecasting method of first Return Law, this method is by establishing between multiple variables linearly or nonlinearly mathematical modeling quantitative relation
The statistical method of formula, so as to reflect the rule between the quantity of a kind of phenomenon or things and a variety of phenomenons or the variation of quantity of things
Rule.Probability numerical solution method includes the Probability numerical solution model such as based on bayesian theory, and this method is first assumed to survey number
According to prior distribution and Posterior distrbutionp type, using prior distribution and the likelihood function of forecast data based on measured data, really
Determine the Posterior distrbutionp parameter of Bayes's forecast, realize the Probability numerical solution under confidence degree.
The existing hydrologic forecasting method based on image factoring can realize the forecast to the related hydrology variable such as flow, but
It is that this method does not account for the uncertainty of hydrologic process, it is impossible to quantitative carry out uncertainty forecast, therefore this method is not
Hydrologic process can be reflected completely.
It is pre- that the existing probability forecast for assuming error distribution and DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM calculate the probability that can be produced under confidence degree
Report, but its calculating process is complicated.The method of interval prediction is carried out again because of black-box model internal structure using neural network model
Complexity, and its optimized algorithm is easily trapped into local optimum, causes model prediction precision undesirable.
The problem of summary Current Hydrologic forecasting procedure is present, hydrologic forecasting method is in forecast precision, algorithm optimization, meter
Calculating efficiency etc. still has deficiency, it is necessary to develop new hydrologic forecasting method.
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, the invention provides one kind to be based on ideal boundary and polynary line
Property the bound section hydrologic forecasting method that returns, its object is to, there is provided one kind calculates area simple and convenient, and be easily achieved
Between hydrologic forecasting method, it is intended to ensure to shorten under conditions of forecast precision to call time in advance.
The present invention is using a kind of following bound section hydrologic forecast side based on ideal boundary and multiple linear regression
Method：
Step 1：Hydrologic forecast section is selected, obtains forecast section and its upstream section period of history measured discharge data,
And by data on flows be divided into rate periodically and probative term two parts,
Step 2：To rate periodic data, using the measured discharge of section to be forecast, construct based on absolute width ideally
Lower limit or the preferable bound border based on relative width so that the preferable bound of construction meets following formula：
Q∈[QL,QU]
Wherein, Q is measured discharge, unit m3/ s, QLFor ideally limit flow, QUFor ideal bound flow,
(1) the preferable bound boundary formation method based on absolute width
In preferable bound boundary formation method based on absolute width, one is set by all measured discharges of synthesis
Preferable interval width constant WA, then preferable bound flow represented with following formula：
Wherein, Q is measured discharge, WAFor preferable interval width constant, WAFirm discharge value is taken,For based on absolute width
The ideally limit flow of degree,For the ideal bound flow based on absolute width so that preferable bound absolute width
(2) the preferable bound boundary formation method based on relative width
In preferable bound boundary formation method based on relative width, one is set by all measured discharges of synthesis
Preferable section relative width constant WR, then preferable bound flow represented with following formula：
Wherein, Q is measured discharge, WRFor preferable section relative width constant,For based on relative width ideally
Limit flow,For the ideal bound flow based on relative width, WRValue depend on Q, such as can in Practical Project practice
Take WR=0.3Q, then the relative width in preferable bound section is following formula：
Step 3：According to the regular measured discharge data of section rate and preferable bound border sequence, determine that multiple linear returns
Return the regression parameter of upper-lower limit, specifically,
Multiple linear regression upper-lower limit is as described in following formula：
Q'=b+a1Q1+a2Q2+...+akQk+ε
Wherein, Q' is measured discharge, and k is factor of influence number, Qm(m=1,2 ..., be k) factor of influence, b is constant term,
am(m=1,2 ..., be k) regression coefficient, ε is error term,
In error sum of squares ∑ ε2On the premise of for minimum, regression parameter is solved with least square method, regression parameter includes
b、a1、a2、……、ak。
Step 4：Using the regression parameter of step 3, calculate probative term data, using prediction interval include rate, relative width,
Symmetry and forecasting runoff and the root-mean-square error of measured discharge are as accuracy assessment index, to bound interval prediction result
Precision evaluation is carried out, the actual recurrence for choosing value of forecasting optimum regression parameter as multiple linear regression upper-lower limit is joined
Number, wherein,
Prediction interval is comprising rate：
Wherein, n is sample number, if measured discharge yi∈[QLi,QUi], then ci=1, otherwise ci=0, lower limit ideally
Under conditions of border, PICP=100%, QUiFor t=i when upper limit forecasting runoff, QLiFor t=i when lower limit forecasting runoff,
Prediction interval relative width：
Using the average of prediction interval width and the ratio of measured discharge as evaluation criterion, than prediction interval is used alone
Width, it is more representative, wherein, QiFor t=i when measured discharge, other specification meaning is same as above,
Prediction interval symmetry：
Wherein, PIS represents the symmetry of prediction interval upper and lower bound geometry, the PIS=under the conditions of ideal interval
0%,
Prediction interval root-mean-square error：
Wherein parameter meaning is same as above,
Using the bound intermediate value of prediction interval as predicted value, RMSE reflects the levels of precision of predicted value and measured value.
Step 5：The actual regression parameter of the multiple linear regression upper-lower limit determined using step 4, when calculating following
Carve upper and lower bound data on flows and issue interval prediction result.
In general, by the contemplated above technical scheme of the present invention, following beneficial effect can be obtained：
Prior art, which is distributed using hypothesis error mostly or is carried out a large amount of DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEMs, realizes Probability numerical solution, these
Method is respectively provided with cumbersome calculating process and longer pre- called time.In recent years the method using neutral net estimation bound is proposed
Interval prediction is carried out, although this method saves calculates the time, but the intrinsic nerve meta structure of neural network model can not have
Body is presented, and neural network model is also easily absorbed in local optimum, very big uncertainty is brought to hydrologic forecast.
The present invention proposes a kind of method for constructing preferable bound border according to relative width and absolute width, is managed with this
It is target to think bound border, structure multiple linear regression upper-lower limit realize section traffic forecast, the construction ideally under
Limit boundary method can make a response rapidly according to the requirement of manager, realize the section hydrologic forecast under various confidence levels, fixed
The forecast hydrological uncertainty of amount, data supporting is provided for basin and water reservoir management person.
The present invention proposes that the method calculating that bound section is constructed using multiple linear regression model is simple and convenient, keeps away simultaneously
The problem of having exempted from parameter optimization algorithm search procedure and local optimum, it will be apparent that shorten simulation and call time in advance.In addition, this hair
The model of bright proposition reduces prediction error to greatest extent, has compared with the interval prediction result of neural network model construction
Higher forecast precision, and the section hydrologic forecast under various confidence levels can be realized, the uncertainty of quantitative hydrologic forecast, it is
River basin planning and Cascade Reservoirs optimization operation provide more abundant data supporting.
Brief description of the drawings
Fig. 1 is the bound section hydrologic forecasting method based on ideal boundary and multiple linear regression in the embodiment of the present invention
Flow chart.
The interval prediction result of flood season in 1954 of MLR-LUBE model predictions when Fig. 2 is W=0.32.
The interval prediction result of flood season in 1998 of MLR-LUBE model predictions when Fig. 3 is W=0.32.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that specific embodiment described herein is only to explain the present invention, not
For limiting the present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below that
Conflict can is not formed between this to be mutually combined.
The invention discloses a kind of bound section hydrologic forecasting method based on ideal boundary and multiple linear regression.This
Invention is respectively adopted same multiple proportions amplification and reduces the preferable bound border of method construct of measured discharge, in rate periodically with ideal
Upper and lower limit border is target and least square method is structure and ginseng that principle determines multiple linear regression upper and lower bound model
Number, percent of pass is regular and the bound forecast result of probative term realizes bound section hydrologic forecast.With prediction interval include rate,
Relative width, symmetry and root-mean-square error (using section intermediate value as predicted value) contrast existing god for accuracy assessment index
Regression model interval prediction result through network method and different relative widths, method proposed by the present invention show preferably pre-
Report precision and the value of forecasting.Method that the present invention uses calculates simple and fast, avoid substantial amounts of parameter optimization search procedure with
And optimized algorithm is absorbed in the possibility of local optimum, the hydrologic forecast time is significantly shortened.
The inventive method is further illustrated with reference to specific embodiment, based on ideal boundary and multiple linear regression
Bound section hydrologic forecasting method, comprises the following steps：
Step 1：Hydrologic forecast section is selected, obtains forecast section and its upstream section period of history measured discharge data,
1953~2007 years common 55a of above-mentioned six websites flood season day (June to September) data on flows is chosen in this example.By data on flows point
For regular (1953~1987) and probative term (1988~2007) two parts of rate.
Step 2：To rate periodic data, using the measured discharge of section to be forecast, construct based on absolute width ideally
Lower limit or the preferable bound border based on relative width so that the preferable bound of construction meets following formula：
Q∈[QL,QU]
Q is measured discharge, unit m3/s。QLFor ideally limit flow, QUFor ideal bound flow.
(1) the preferable bound building method based on absolute width
Preferable bound building method based on absolute width is exactly that comprehensive all measured discharges determine a preferable area
Between width constant WA, then preferable bound flow represented with following formula：
Q is measured discharge, WAFor regulatable interval width constant,For the ideally limit flow based on absolute width,For the ideal bound flow based on absolute width.WATake fixed value so that preferable bound absolute width
(2) the preferable bound building method based on relative width
Preferable bound building method based on relative width is exactly that comprehensive all measured discharges determine a preferable area
Between width constant WR, then preferable bound flow represented with following formula：
Wherein, Q is measured discharge, WRFor regulatable relatively wide angle value,For the ideally current limliting based on relative width
Amount,For the ideal bound flow based on relative width.
WRValue depend on Q, such as desirable WR=0.3Q so that preferable bound relative width：
Step 3：According to section measured discharge data and preferable bound sequence, the parameter of regression model is determined, is distinguished
The forecast result of preferable bound is obtained, generates the prediction interval of measured discharge.
Multiple linear regression model principle：
Q'=b+a1Q1+a2Q2+...+akQk+ε
Wherein k is factor of influence number, Qm(m=1,2 ..., be k) factor of influence, b is constant term, am(m=1,2 ...,
K) it is regression coefficient, ε is error term.In error sum of squares ∑ ε2On the premise of for minimum, solved with least square method and return ginseng
Number, regression parameter include b, a1、a2、……、ak。
Step 4：Using the regression parameter of step 3, calculate probative term data, using prediction interval include rate, relative width,
Symmetry and forecasting runoff and the root-mean-square error of measured discharge are entered as accuracy assessment index to bound interval prediction result
Row precision evaluation, actual regression parameter of the value of forecasting optimum regression parameter as multiple linear regression upper-lower limit is chosen,.
Prediction interval includes rate：
Wherein, n is sample number, if measured discharge yi∈[QLi,QUi], then ci=1, otherwise ci=0.In ideal interval
Under the conditions of PICP=100%.QUiFor t=i when upper limit forecasting runoff, QLiFor t=i when lower limit forecasting runoff,
Prediction interval relative width：
Using the average of prediction interval width and the ratio of measured discharge as evaluation criterion, than prediction interval is used alone
Width, it is more representative.Wherein, QiFor t=i when measured discharge, other specification meaning is same as above.
Prediction interval symmetry：
PIS represents the symmetry of prediction interval upper and lower bound geometry, the PIS=0% under the conditions of ideal interval, ginseng
Number meaning is same as above.
Prediction interval root-mean-square error：
Using the bound intermediate value of prediction interval as predicted value, RMSE reflects the measure of precision of predicted value and measured value,
Parameter meaning is same as above.
Step 5：The upper and lower bound model regression parameter determined with step 4, calculate future time instance bound data on flows
And issue interval prediction result.
In order to illustrate further the effect obtained compared with prior art of the inventive method, combine further below specific
Embodiment comparative illustration.
Using neutral net bound section hydrologic forecasting method (referred to as：BP-LUBE) and different relative widths ideal
Bound multiple linear regression model section hydrologic forecasting method is (referred to as：MLR-LUBE discharge at Yichang station sequence) is forecast, its essence
It is as shown in table 1 to spend evaluation result.Wherein, W is the relative width of ideal interval in table 1.
Specifically, when ideal interval relative width is 0.30 as can be seen from Table 1, multiple linear regression interval prediction side
Method is bigger than BP-LUBE method statistics result 93.4% in the regular PICP values 93.9% of rate, and PIRAW, PIS, RMSE compare BP-LUBE
Method statistic end value is small.In the phase of checking, PICP, PIRAW, PIS, RMSE are smaller than BP-LUBE method statistic end values.Phase
Answer, when ideal interval relative width is 0.32 and 0.34, rate is periodically both greater than BP-LUBE side with the PICP values of checking phase
Method, PIRAW, PIS, RMSE are smaller than BP-LUBE method statistic end values.Because the target of interval prediction is PICP maximums,
PIRAW, PIS, RMSE are minimum, so, multiple linear regression interval prediction method only when ideal interval relative width is 0.30,
The checking phase is slightly less than BP-LUBE methods comprising rate, and each indices prediction effect in remaining period is better than BP-LUBE methods.This table
Bright, multiple linear regression interval prediction method is higher compared with BP-LUBE method forecast precisions, using the teaching of the invention it is possible to provide more accurate hydrologic forecast
As a result.
In addition, contrasting the MLR-LUBE forecast results of different ideal interval width, it is wide that PIRAW is approximately equal to ideal interval
Degree, this explanation multiple linear regression model interval prediction method have reached the expected value of forecasting.Moreover, as ideal interval is wide
The increase of degree, PICP become big, and this is consistent with PICP the and PIRAW implications and actual conditions of interval prediction method.
Comprehensive each model prediction result is understood：During W=0.32, interval prediction result includes rate PICP, interval width
PIRAW, symmetry PIS are superior to neutral net bound section hydrologic forecasting method.Therefore model during W=0.32 is taken as most
Good forecasting model, it is determined that after the parameter of model, forecast to Yichang Station 1954 and flood season flow in 1998, interval prediction
The interval prediction result of flood season in 1954 of MLR-LUBE model predictions when being as a result W=0.32 such as Fig. 2 and Fig. 3, Fig. 2.Fig. 3 is W
The interval prediction result of flood season in 1998 of MLR-LUBE model predictions when=0.32.
It can be seen that by Fig. 2~3：Interval prediction can cover measured discharge well, and have preferable symmetry.
Great flood occurs for flood season especially when flow is more than 40000m3During/s, acting the phase of rising and disappearing to fall the phase in play flood, measured discharge is more
Close to the upper limit.In time of peak, flow is then closer to the average value among bound.
Contrast understands that MLR-LUBE models provided by the invention reduce prediction error to greatest extent, with BP-LUBE moulds
Type forecast result shows the preferable value of forecasting compared to having higher forecast precision, can for water management and
Flood control and disaster reduction provides more reliable foundation.
The bound section hydrological factor evaluation result of table 1
In summary, a kind of bound section hydrology based on ideal boundary and multiple linear regression proposed by the present invention is pre-
Reporting method, the regression model interval prediction result of existing neural net method and different relative widths is contrasted, it is proposed by the present invention
Method shows preferable forecast precision and the value of forecasting.
The method that the present invention uses calculates simple and fast, avoids substantial amounts of parameter optimization search procedure and optimized algorithm
The possibility of local optimum is absorbed in, significantly shortens the hydrologic forecast time.In addition, construction proposed by the present invention is preferable
Bound boundary method can make a response rapidly according to the requirement of manager, realize that the section hydrology under various confidence levels is pre-
Report, fast and accurately decision information is provided for basin and water reservoir management person.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, all any modification, equivalent and improvement made within the spirit and principles of the invention etc., all should be included
Within protection scope of the present invention.
Claims (7)
1. a kind of hydrologic forecasting method, it is characterised in that comprise the following steps：
Step 1：Hydrologic forecast section is selected, obtains section to be forecast and its upstream section period of history measured discharge data, and
By data on flows be divided into rate periodically and probative term two parts,
Step 2：To rate periodic data, using the measured discharge of section to be forecast, the preferable bound based on absolute width is established
Border or the preferable bound border based on relative width, preferable bound border meet following formula：
Q∈[QL,QU]
Wherein, Q is measured discharge, unit m3/ s, QLFor ideally limit flow, QUFor ideal bound flow,
Step 3：According to the regular measured discharge data of section rate and preferable bound border sequence, determine on multiple linear regression
The regression parameter of lower limit model, specifically,
Multiple linear regression upper-lower limit is as described in following formula：
Q'=b+a1Q1+a2Q2+...+akQk+ε
Wherein, Q' is measured discharge, and k is factor of influence number, Qm(m=1,2 ..., be k) factor of influence, b is constant term, am(m
=1,2 ..., be k) regression coefficient, ε is error term,
In error sum of squares ∑ ε2On the premise of for minimum, regression parameter is solved with least square method, regression parameter includes b, a1、
a2、……、ak,
Step 4：Using the regression parameter of step 3, probative term data are calculated, it is right using prediction interval as accuracy assessment index
Bound interval prediction result carries out precision evaluation, chooses value of forecasting optimum regression parameter as multiple linear regression bound
The actual regression parameter of model,
Forecast precision deliberated index, which includes the root mean square comprising rate, relative width, symmetry, forecasting runoff and measured discharge, to be missed
Difference.
2. the method as described in claim 1, it is characterised in that in the step 2, establish based on absolute width ideally under
Limiting boundary method is specially：
In preferable bound border method for building up based on absolute width, an ideal is set by all measured discharges of synthesis
Interval width constant WA, then preferable bound flow represented with following formula：
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Ideal bound flow based on absolute width, WATake firm discharge value so that preferable bound absolute width
3. method as claimed in claim 2, it is characterised in that establish the preferable bound boundary method tool based on absolute width
Body is as follows：
In preferable bound border method for building up based on relative width, an ideal is set by all measured discharges of synthesis
Section relative width constant WR, then preferable bound flow represented with following formula：
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Wherein, Q is measured discharge, WRFor regulatable relatively wide angle value,For the ideally limit flow based on relative width,
For the ideal bound flow based on relative width, WRValue depend on Q, take WR=0.3Q so that preferable bound relative width
4. method as claimed in claim 3, it is characterised in that what forecast precision deliberated index included includes rate such as following formula institute
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Under conditions of, PICP=100%, QUiFor t=i when upper limit forecasting runoff, QLiFor t=i when lower limit forecasting runoff.
5. method as claimed in claim 4, it is characterised in that the relative width that forecast precision deliberated index includes such as following formula institute
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6. method as claimed in claim 5, it is characterised in that the symmetry of forecast precision deliberated index is shown below：
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Wherein, PIS represents the symmetry of prediction interval upper and lower bound geometry, PIS=0%, Q under the conditions of ideal intervali
For t=i when measured discharge, n is sample number, QUiFor t=i when upper limit forecasting runoff, QLiFor t=i when lower limit forecast stream
Amount.
7. method as claimed in claim 6, it is characterised in that the root-mean-square error of forecast precision deliberated index such as following formula institute
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<mi>n</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>(</mo>
<mrow>
<msub>
<mi>Q</mi>
<mrow>
<mi>U</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>Q</mi>
<mrow>
<mi>L</mi>
<mi>i</mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
<mo>/</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>n</mi>
</mfrac>
</msqrt>
</mrow>
Wherein, QiFor t=i when measured discharge, n is sample number, QUiFor t=i when upper limit forecasting runoff, QLiFor t=i when
Lower limit forecasting runoff.
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