CN117540582B - Unit line time period conversion method based on S curve interpolation - Google Patents
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Abstract
The invention provides a base onSThe curve interpolation unit line period conversion method comprises obtaining unit lineq(t) The method also comprises the following steps: based on the unit lineq(t) Construction based onSA unit line period conversion model for curve interpolation; obtaining a target period of time to be convertedThe method comprises the steps of carrying out a first treatment on the surface of the Setting the target period of timeInputting the unit line time period conversion model, and calculating the converted unit line sequenceq(,t 2 ) The method comprises the steps of carrying out a first treatment on the surface of the At the target time periodTo interval from the converted unit lineq(,t 2 ) And picking the time interval unit line, namely the converted time interval unit line. The invention provides a method based onSThe curve interpolation unit line period conversion method can realize the unit line conversion of 1-bit decimal period, is easy to program and realize, and improves the scientificity and the calculation efficiency of the unit line period conversion.
Description
Technical Field
The invention relates to the technical field of water conservancy model construction, in particular to a hydraulic model-based hydraulic model construction methodSA unit line period conversion method of curve interpolation.
Background
The unit line is a surface runoff (direct runoff) process line formed by a unit net rainfall which is uniformly distributed in space-time on a given river basin in a unit period at the outlet section of the river basin. The method is widely applied to flood design and hydrologic forecasting, and plays an important role in hydrologic history.
The unit line is deduced based on the rainfall runoff data observed, and since the observed data is time period data, the deduced time period length of the unit line is the same as the observed data time period length. When the unit line is applied, the actual rainfall duration is often not consistent with the time period length of the known unit line, and the unit line cannot be used at will, so that the time period conversion is required for the unit line. When the time period conversion is carried out on the unit line in the field of the hydrology of the water conservancy industry engineering, the original unit line is firstly accumulated time period by time period to obtain a process line, which is called asSCurve and then pair againSAnd interpolating the curve to obtain an S-curve of the conversion target period. In the prior art, regarding unit line period conversion, interpolation methods are not described, but specific values of certain field unit line period conversion are given in an example table, so that in actual operation, technicians have no clear method and basis pairSThe curve is calculated by scientific and reasonable interpolation, and the current method adopts empirical calculation, so that the problems of larger randomness and low calculation efficiency are solved.
In the book of hydrological forecast, main edition Lin Sanyi published by Water conservancy and electric Press, month 11 of 2001, the content of the topic of Unit line period conversion is disclosed, and the third part of the content proposes to adoptSThe curve is used for solving the problem of unit line conversion of different time periods. The method has the defects that a specific interpolation calculation method of the S curve during unit line period conversion is not provided, and the method has the problems of high randomness and low calculation efficiency.
An article of Li Weihe Liu Yang entitled "drainage basin conflux unit line period conversion application analysis" is published in the journal of Heilongjiang water conservancy science and technology, volume 40, 1 st 2012, and the article proposes that when a drainage basin flood period rain information period changes under special conditions, the drainage basin conflux unit line must be subjected to period conversion in advance before being used for actual flood forecast. Based on the measured hydrologic raw data, according to the special requirements of the example watershed in hydrologic forecasting work,by usingSThe curve method performs example conversion and application analysis on the flow field confluence unit line. The analysis result accords with the standard precision standard of the related industry, the specific use condition and the application range of the analysis result are provided, and the result can be used as an alternative method in actual work. The method has the disadvantage that only the whole period conversion method from 12 hours to 24 hours is given, no period conversion method of any period is given, and universality is not realized.
Disclosure of Invention
In order to solve the technical problems, the invention provides a device based onSThe curve interpolation unit line period conversion method can realize the unit line conversion of 1-bit decimal period, is easy to program and realize, and improves the scientificity and the calculation efficiency of the unit line period conversion.
The invention aims to provide a device based onSThe curve interpolation unit line period conversion method comprises obtaining unit lineq(t) The method also comprises the following steps:
step 1: based on the unit lineq(t) Construction based onSA unit line period conversion model for curve interpolation;
step 2: obtaining a target period of time to be converted；
Step 3: setting the target period of timeInputting the unit line time period conversion model, and calculating the converted unit line sequenceq(/>,t 2 )；
Step 4: at the target time periodFor spacing from said converted unit line sequenceq(/>,t 2 ) Picking the time interval unit line to obtain a converted time interval unit line;
wherein,t=1,2,…,n，nis the number of data in a unit line,nis an odd number greater than 1,t 2 =1,2,…,n 1 ，n 1 is combined withS' number of curve data.
Preferably, the unit wireq(t) The time period length of (2) is。
In any of the above schemes, preferably, the step 1 includes the following substeps:
step 11: for the unit lineq(t) Accumulating time-by-time to obtainSA curve;
step 12: adopts a unitary quadratic polynomial pairSPerforming sectional fitting on the curve;
step 13: interpolation calculation is carried out on the piecewise fitting polynomial at the interval of 0.1 hour, and the piecewise fitting polynomial is combined to obtainS' curve;
step 14: will follow the order of segment fittingS' Curve reordering combined, combinedS' Curve data number is recorded asn 1 。
In any of the above embodiments, it is preferable that theSThe calculation formula of the curve is
S(t)=S(t-1)+q(t)
Wherein,S(t) Is the firsttEnd of time periodSOrdinate value of curve (m 3 /s)，S(0)=0。
In any of the above aspects, preferably, the piecewise fitting employs a three-point data fitting comprisingS(1)、S(2)、S(3)，S(3)、S(4)、S(5)，S(5)、S(6)、S(7)，……，S(n-2)、S(n-1)、S(n)。
In any of the above schemes, preferably, the calculation formula of the piecewise fitting is as follows
，
Wherein,a、b、cin order to fit the parameters of the formula,t’=1,3,5,…,n-2。
in any of the above embodiments, it is preferable that theSThe calculation formula of the piecewise interpolation of the 'curve' is
S’ (t 1 )=at 1 2 +bt 1 +c
Wherein,t 1 =0.1,0.2,0.3,…,。
in any of the above embodiments, it is preferred that, when saidS' the curve is larger than theSAt the maximum of the curve, theSThe' curve is modified as describedSMaximum of the curve.
In any of the above embodiments, it is preferable that the converted unit line sequenceq(,t 2 ) The calculation formula of (2) is
，
The invention provides a method based onSThe unit line time period conversion method of curve interpolation can meet the requirements of flood design and flood forecast in the water conservancy field on the calculation time period, is more scientific, has universality and easy programming realization, avoids the randomness of an empirical method, and improves the calculation efficiency.
Drawings
FIG. 1 is a schematic diagram of a base station according to the inventionSA flow chart of a preferred embodiment of a unit line period conversion method of curve interpolation.
FIG. 2 is a schematic diagram of a base station according to the inventionSUnit line period conversion for curve interpolationA computational flow diagram of another preferred embodiment of the method.
FIG. 3 is a schematic diagram of a base station according to the present inventionSPage 1 of one embodiment of a unit line conversion calculation process table of a unit line period conversion method of curve interpolation is schematically shown.
FIG. 4 is a schematic diagram of a base station according to the present inventionSPage 2 of an embodiment of a unit line conversion calculation process table of a unit line period conversion method of curve interpolation is schematically shown.
FIG. 5 is a schematic diagram of a base station according to the present inventionSPage 3 of one embodiment of a unit line conversion calculation process table of a unit line period conversion method of curve interpolation.
FIG. 6 is a schematic diagram of a base station according to the inventionSPage 4 of an embodiment of a unit line conversion calculation process table of a unit line period conversion method of curve interpolation is schematically shown.
FIG. 7 is a schematic diagram of a base station according to the inventionSA schematic diagram of an embodiment of a 3h unit line example and calculation contrast of a unit line period conversion method of curve interpolation.
FIG. 8 is a schematic diagram of a base station according to the present inventionSA schematic diagram of an embodiment of a 9h unit line example of a curve interpolated unit line period conversion method versus computation.
FIG. 9 is a schematic diagram of a base station in accordance with the present inventionSA comparative schematic of one embodiment of a 20mm unit line conversion outcome of the curve interpolated unit line period conversion method.
FIG. 10 is a schematic diagram of a base station in accordance with the present inventionSA comparative schematic of one embodiment of a 40mm unit line conversion outcome of the curve interpolated unit line period conversion method.
FIG. 11 is a schematic diagram of a base station in accordance with the present inventionSA comparative schematic of one embodiment of a 60mm unit line conversion outcome of the curve interpolated unit line period conversion method.
FIG. 12 is a schematic diagram of a base station in accordance with the present inventionSA comparative schematic of one embodiment of the 80mm unit line conversion outcome of the curve interpolated unit line period conversion method.
FIG. 13 is a schematic diagram of a base station in accordance with the inventionSImplementation of 100mm Unit line conversion outcome of Unit line period conversion method for Curve interpolationComparative schematic of examples.
Detailed Description
The invention is further illustrated by the following figures and specific examples.
Example 1
As shown in fig. 1, one is based onSThe curve interpolation unit line time period conversion method is executed to step 100 to obtain a unit lineq(t)，t=1,2,…,n，nIs the number of data in a unit line,nodd number greater than 1, unit lineq(t) The time period length of (2) isThe unit is hours.
Executing step 110 based on the unit lineq(t) Construction based onSA unit line period conversion model for curve interpolation, comprising the sub-steps of:
step 111 is executed to the unit lineq(t) Accumulating time-by-time to obtainSThe curve is formed by a curve of the curve,Sthe calculation formula of the curve isS(t)=S(t-1)+q(t) Wherein, the method comprises the steps of, wherein,S(t) Is the firsttEnd of time periodSOrdinate value of curve (m 3 /s)，S(0)=0。
Step 112 is executed to adopt a unitary quadratic polynomial pairSThe curve is subjected to piecewise fitting, and the piecewise fitting adopts three-point data fitting, comprisingS(1)、S(2)、S(3)，S(3)、S(4)、S(5)，S(5)、S(6)、S(7)，……，S(n-2)、S(n-1)、S(n) The method comprises the steps of carrying out a first treatment on the surface of the The calculation formula of the piecewise fitting is as follows
，
Wherein,a、b、cin order to fit the parameters of the formula,t’=1,3,5,…,n-2。
step 113 is executed, the polynomial fitted to the segment is interpolated at intervals of 0.1 hour, and the combination is obtainedSThe curve of the 'curve' is shown,Sthe calculation formula of the piecewise interpolation of the 'curve' is
S’ (t 1 )=at 1 2 +bt 1 +c
Wherein,t 1 =0.1,0.2,0.3,…,。
in step 113, when theS' the curve is larger than theSAt the maximum of the curve, theSThe' curve is modified as describedSMaximum of the curve.
Step 114 is executed to match the segments in the order of segment fittingS' Curve reordering combined, combinedS' Curve data number is recorded asn 1 。
Step 120 is executed to obtain the target period of time to be converted；
Executing step 130 to obtain the target time periodInputting the unit line time period conversion model, and calculating the converted unit line sequenceq(/>,t 2 ) Converted unit line sequenceq(/>,t 2 ) The calculation formula of (2) is
，
Wherein,t 2 =1,2,…,n 1 。
step 4: at the target time periodFor spacing from said converted unit line sequenceq(/>,t 2 ) And picking the time interval unit line, namely the converted time interval unit line.
Example two
As shown in fig. 2, the present embodiment discloses a method based onSThe specific calculation method of the unit line period conversion method of curve interpolation comprises the following steps:
known unit wireq(t)，t=1,2,…,n，nThe data number of the unit line is an odd number which is larger than 1; the period is (hours), reserving 1-bit fraction.
Step 1: to unit lineq(t) Accumulating time-by-time to obtainSAnd (3) a curve and a calculation formula is (1).
S(t)=S(t-1)+q(t) （1）
Step 2: adopts a unitary quadratic polynomial pairSAnd (5) performing segment fitting on the curve. Segmentation using three-point data fitting, e.g.S(1)、S(2)、S(3)，S(3)、S(4)、S(5)，S(5)、S(6)、S(7)，……，S(n-2)、S(n-1)、S(n). The segmentation fitting calculation formula is shown as (2), and the segmentation fitting unitary quadratic polynomial parameter can be obtained by solving the (2)a、b、c。
，
t’=1,3,5,…,n-2 （2）
Step 3: interpolation calculation is carried out on the piecewise fitting polynomial at the interval of 0.1 hour, and the piecewise fitting polynomial is combined to obtainS'curve'. The piecewise interpolation calculation formula is shown in (3).
S’(t 1 )=at 1 2 +bt 1 +c t 1 =0.1,0.2,0.3,…, （3）
Step 4: will follow the order of segment fittingS' Curve reordering combined, combinedS' Curve data number is recorded asn 1 。
Step 5: according toCalculating a converted sequence of unit lines, wherein +.>Reserving 1-bit fraction (unit: hours) for a target period of conversion;t 2 =1,2,…,n 1 。
step 6: to be used forFor spacing fromq(/>,t 2 ) And picking the time interval unit line, namely the converted time interval unit line.
Note that: segment calculation at step 3SIn the 'curve', the calculated result may be due to fitting errorsS' Curve is greater thanSThe maximum of the curve may cause the converted unit line to appear as an unreasonable negative value. Thus, if it occursS' Curve is greater thanSThe maximum value of the curve needs to be corrected toSMaximum of the curve.
The method has the following characteristics:
according toSThe characteristics of the curve are fitted according to 3 point data segments by adopting a unitary quadratic polynomial, and the curve is more accurately representedSA curve;
fitting the fitted pairs with a period of 0.1 hourSThe curve is calculated, and on the premise of ensuring the calculation efficiency, the requirements of the water conservancy field for designing flood and forecasting flood on the calculation period can be met.
The method is more scientific, has universality, is easy to program and realize, avoids the randomness of an experience method, and improves the calculation efficiency.
Example III
The present embodiment discloses a specific method of converting a unit line with a period of 6h into 3h and 9h unit lines.
As shown in FIGS. 3 to 6, column (1) in Table 1 is time (h), and columns (2) and (3) are originalTime period unit line of =6 hours.
Step 1: accumulating the unit line values of each period to obtainSA curve is stored in a (3) th column;
step 2: adopts a unitary quadratic polynomial pairSPerforming segment fitting on the curve, and fitting parametersa、b、cStoring in a (4) th column;
step 3: performing interpolation calculation on the piecewise fitted polynomial at time interval of 0.1 hour;
step 4: combining the calculation results of the step 3 to obtainS' Curve, stored in columns (6), (7), in this embodiment, is taken only for a whole hour periodS' Curve values;
step 5: calculation ofTime period unit line of 3 hours. Calculation ofS’(t-10/>) Storing in a (8) th column; calculation ofStoring in a (9) th column;
step 6: to be used forTaking time interval unit line from (9) column at intervals of 3 hr, rounding and storing in (11) column, and storing in (10) column with corresponding time sequence to obtain converted +.>Time period unit line of 3 hours.
To be used forRepeating steps 5 and 6 for 9 hr, and storing the results in columns (12) - (15) to obtain converted +.>=9 hour period unit line.
The results of comparison are shown in Table 1, FIG. 7 and FIG. 8. Compared with example achievements, the deviation after 3h unit line conversion is slightly larger, the flood peak deviation is-19.2%, and the errors in other time periods are smaller; the result after 9h unit line conversion is very close, and the flood peak error is only-1.2%.
TABLE 1 conversion of 6h Unit lines to 3h, 9h Unit lines
，
It should be noted that, in this example, the period length is an integer, and for period conversion in which the period length is 1 bit fraction (the period length is always reserved by 1 bit fraction in hydrologic calculation), the method is also applicable.
Example IV
In the 'heavy rain flood atlas of small river basin design in certain province', the time period conversion results of 5 unit lines of 20, 40, 60, 80 and 100mm net rain intensity are shown in tables 2-6, and the comparison result of the calculation result and the example result is shown in figures 9-13. Compared with the example result, the flood peak errors after conversion are respectively-2.3%, -6.5%, -3.4%, -3.5%, -5.1%, and the flood peak errors are all within a reasonable range.
In tables 2 to 6, columns 1 and 2 are the original unit lines, column 3 is the time after conversion, column 4 is the flow in the original example, and column 5 is the flow calculated by the present method.
TABLE 2 20mm Unit line conversion results
，
TABLE 3 40mm Unit line conversion results
，
TABLE 4 60mm Unit line conversion results
，
TABLE 5 80mm Unit line conversion results
，
TABLE 6 100mm Unit line conversion results
，
The foregoing description of the invention has been presented for purposes of illustration and description, but is not intended to be limiting. Any simple modification of the above embodiments according to the technical substance of the present invention still falls within the scope of the technical solution of the present invention. In this specification, each embodiment is mainly described in the specification as a difference from other embodiments, and the same or similar parts between the embodiments need to be referred to each other. For system embodiments, the description is relatively simple as it essentially corresponds to method embodiments, and reference should be made to the description of method embodiments for relevant points.
Claims (5)
1. Based onSThe curve interpolation unit line period conversion method comprises obtaining unit lineq(t) The method also comprises the following steps:
step 1: based on the unit lineq(t) Construction based onSA unit line period conversion model for curve interpolation, comprising the sub-steps of:
step 11: for the unit lineq(t) Accumulating time-by-time to obtainSA curve;
step 12: adopts a unitary quadratic polynomial pairSPerforming segment fitting on the curve, wherein the calculation formula of the segment fitting is as follows
，
Wherein,a、b、cin order to fit the parameters of the formula,t’=1,3,5,…,n-2, the unit lineq(t) The time period length of (2) is；
Step 13: interpolation calculation is carried out on the piecewise fitting polynomial at the interval of 0.1 hour, and the piecewise fitting polynomial is combined to obtainS' curve;
step 14: will follow the order of segment fittingS' Curve reordering combined, combinedS' Curve data number is recorded asn 1 ；
Step 2: obtaining a target period of time to be converted；
Step 3: setting the target period of timeInputting the unit line time period conversion model, and calculating the converted unit line sequenceq(/>,t 2 )；
Step 4: at the target time periodFor spacing from said converted unit line sequenceq(/>,t 2 ) Picking time interval unit line, i.e. convertedTime interval unit line with a calculation formula of
，
Wherein,t=1,2,…,n，nis the number of data in a unit line, nis an odd number greater than 1,t 2 =1,2,…,n 1 ，n 1 is combined withS' number of curve data;
the unit line is a surface runoff process line formed by the unit net rainfall which is uniformly distributed on a given river basin in a space-time manner in a unit period at the outlet section of the river basin.
2. The base of claim 1SA unit line period conversion method of curve interpolation, characterized in thatSThe calculation formula of the curve is
S(t)= S(t-1)+q(t)
Wherein,S(t) Is the firsttEnd of time periodSThe ordinate value of the curve,S(0)=0。
3. the base of claim 2SThe unit line period conversion method of curve interpolation is characterized in that the piecewise fitting adopts three-point data fitting, comprising the following steps ofS(1)、S(2)、S(3)，S(3)、S(4)、S(5)，S(5)、S(6)、S(7)，……，S(n-2)、S(n-1)、S(n)。
4. A base according to claim 3SA unit line period conversion method of curve interpolation, characterized in thatSThe calculation formula of the piecewise interpolation of the 'curve' is
S’ (t 1 )=at 1 2 +bt 1 +c
Wherein,t 1 =0.1,0.2,0.3,…,。
5. the base of claim 4SA method for converting unit line time periods of curve interpolation, characterized in that when the following is adoptedS' the curve is larger than theSAt the maximum of the curve, theSThe' curve is modified as describedSMaximum of the curve.
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| US20090040218A1 (en) * | 2007-08-06 | 2009-02-12 | Ken Museth | Fitting curves from one model to another |
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| CN115907061A (en) * | 2022-02-22 | 2023-04-04 | 河南大学 | Hydrological forecasting method based on improved unit line |
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