CN105178240A - Optimization method for drawing P-III type distribution frequency curve - Google Patents

Optimization method for drawing P-III type distribution frequency curve Download PDF

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CN105178240A
CN105178240A CN201510310171.9A CN201510310171A CN105178240A CN 105178240 A CN105178240 A CN 105178240A CN 201510310171 A CN201510310171 A CN 201510310171A CN 105178240 A CN105178240 A CN 105178240A
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frequency
iii type
flood
type distribution
frequency curve
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CN105178240B (en
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尹家波
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Wuhan University WHU
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Abstract

The invention discloses an optimization method for drawing a P-III type distribution frequency curve. By establishing a P-III type distribution frequency curve optimization model, theoretical frequency and experimental frequency are endowed with different weights, and the minimum square sum of a relative error weight serves as an objective function; according to the drainage basin general situation and the actual condition of a reservoir, constraint conditions of a parameter are added; and the parameter estimated through a moment method serves as an initial value, an improved very fast simulated annealing algorithm is adopted for solving the model, the optimal solution of the parameter is obtained, and therefore the P-III type distribution frequency curve is drawn. By means of the method, the parameter estimation result is unique, randomness caused by human factors is avoided, historical flood and catastrophic flood are also taken into account, the applicability of the P-III type distribution frequency curve is widened, and an important reference basis is provided for drawing the P-III type distribution frequency curve.

Description

A kind of optimization method drawing P-III type distribution frequency curve
Technical field
The present invention relates to a kind of optimization method of frequency curve, particularly a kind of optimization method drawing P-III type distribution frequency curve.
Background technology
Flood Frequency Analysis estimates the main contents of Design of Water Resources and Hydroelectric Projects flood, calculates the important evidence of design standard when being also hydraulic engineering construction.Carry out Design Flood Calculation by building Flood Frequency Analysis model, this model is made up of flood frequency distribution function and method for parameter estimation.The sixties in 20th century, China is according to the practical experience of a large amount of long-term flood serial analysis result and design work for many years, the distribution function that the distribution of regulation P-III type calculates as China's hydrological analysis, adopt the initial value of Moment method estimators parameter, adopt mathematic expectaion formulae discovery empirical Frequency, the numerical value of every flood and corresponding empirical Frequency point are painted on ruled paper, frequency curve is drawn with the first guess of statistical parameter, if curve and empirical Frequency point good not according to matching, adjustable statistical parameter, until curve and point better according to matching, till comparatively satisfied, determine the statistical parameter adopted thus, this method for parameter estimation is called as estimating fitting line method (CF), the Flood Frequency Analysis model of China is called as P-III/CF model.
According to the suitable line method of P-III/CF model, when frequency curve alignment, generally will look after historical flood and extraodinary flood point certificate as much as possible, on the frequency curve namely drawn, afterbody will be tried one's best near it.Because the experience of different project planner, parallax are variant, there is larger arbitrariness in the flood frequency curve adopting the method to obtain, in engineering reality, often occur that different design departments can calculate the situation of different designs result, is difficult to formulate unified Engineering Disign Standard.And, adopt the method manually repeatedly adjusting parameter, also consume a large amount of time and efforts.
(the Liu Li such as Liu Li, Zhou Jianzhong, Yang person of outstanding talent etc., particle group optimizing fits the application of collimation method in hydrologic(al) frequency analysis. the hydrology, 2009, 29 (2), 21-23.) curve-fitting method based on particle swarm optimization algorithm is proposed, and the method is applied in annual flood frequency analysis, although the method avoids the uncertainty of human factor to a certain extent, but the deviation absolute value of the estimate under same frequency that it estimates with the actual value of sample data and theoretical curve with minimum for object function, do not look after historical flood and extraodinary flood, do not meet the actual requirement of Chinese engineering design.(the Li Hongwei such as Li Hongwei, Song Songbai. the application of ant group algorithm in frequency curve parameter calculates. people the Yellow River, 2009,31 (4), 38-40.) a kind of ant group algorithm based on Gridding Method that can be applied to hydrological frequency parameter and calculate is proposed, the method not only parameter is numerous, complex operation, does not look after historical flood and extraodinary flood equally.
Summary of the invention
For the deficiency that prior art exists, the invention provides a kind of optimization method drawing P-III type distribution frequency curve.
The present invention is by setting up P-III type distribution frequency optimization of profile model, different weights is given to the relative error of theoretic frequency and empirical Frequency, minimum for object function with the quadratic sum of relative error weight, and the constraints of parameter is added according to the actual conditions of basin overview and reservoir, with the parameter of Moment method estimators for initial value, adopt very fast simulated annealing algorithm (MVFSA) solving model improved, obtain the optimal solution of parameter, thus draw out P-III type distribution frequency curve.
For solving the problems of the technologies described above, the present invention adopts following technical scheme:
Draw an optimization method for P-III type distribution frequency curve, comprise the steps:
Step 1, collects historical flood and observed flood data;
For the historical flood of collecting, if its maximum investigation phase is N, the historical flood number of investigation is m, and the year number of actual measurement series is n, and containing extraodinary flood number in actual measurement series is l; X 1, X 2..., X n-l, X n-l+1..., X n-l+mthe series of samples of to be sample capacity be n-l+m, and by order arrangement from small to large, use X jrepresent the jth value in series;
Step 2, calculates the empirical Frequency of Flood evolution, and by the parameter of moments method distribution function according to a preliminary estimate;
For the series of samples X obtained in step 1 j, its empirical Frequency is denoted as P 0(X j);
Step 3, sets up P-III type distribution frequency optimization of profile model;
Flood data in step 1 are substituted into the frequency distribution function that step 2 obtains, in the hope of different floods point according to the theoretic frequency of correspondence, P can be denoted as 1(X j), j=1,2 ..., n-l+m, thus the relative error RE (X that can obtain theoretic frequency and empirical Frequency j), to different floods point certificate, give corresponding weight α j; Adopt the quadratic sum of relative error weight minimum is object function, and adds the constraints of parameter according to the actual conditions of basin overview and reservoir, sets up P-III type distribution frequency optimization of profile model;
Step 4, adopts the model in very fast simulated annealing algorithm (MVFSA) solution procedure 3 improved, thus obtains the parameters of P-III type distribution function, thus draws frequency curve.
The very fast simulated annealing algorithm (MVFSA) of described improvement is prior art, specifically see Tongji University's journal (natural science edition) the 34th volume the 8th phase in 2006, and 1121-1125 pages, author is Chen Huagen, Li Lihua, Xu Huiping, Chen Bing.
Described weight α j, determine by the different interval importance of frequency curve, the sort order of flood sample data is larger, the weight just larger α of this flood point certificate j> 0, and
Compared with prior art, the present invention has the following advantages and beneficial effect:
The present invention is by setting up P-III type distribution frequency optimization of profile model, different weights is given to the relative error of theoretic frequency and empirical Frequency, minimum for object function with the quadratic sum of relative error weight, and the constraints of parameter is added according to the actual conditions of basin overview and reservoir, with the parameter of Moment method estimators for initial value, adopt the very fast simulated annealing algorithm solving model improved, obtain the optimal solution of parameter, thus draw out P-III type distribution frequency curve.The method parameter estimation result is unique, avoids the arbitrariness that human factor produces, can also look after historical flood and extraodinary flood, expand the applicability of P-III type distribution curve, provides important reference frame for drawing P-III type distribution frequency curve.
Accompanying drawing explanation
Fig. 1 is the flow chart of the inventive method;
Fig. 2 is the frequency curve adopting the inventive method to obtain.
Detailed description of the invention
The present invention is by setting up P-III type distribution frequency optimization of profile model, different weights is given to the relative error of theoretic frequency and empirical Frequency, minimum for object function with the quadratic sum of relative error weight, and the constraints of parameter is added according to the actual conditions of basin overview and reservoir, with the parameter of Moment method estimators for initial value, adopt very fast simulated annealing algorithm (MVFSA) solving model improved, obtain the optimal solution of parameter, thus draw out P-III type distribution frequency curve.Below in conjunction with Fig. 1, concrete steps of the present invention are described:
Step 1, collects historical flood and observed flood data;
For the historical flood of collecting, if its maximum investigation phase is N, the historical flood number of investigation is m, and the year number of actual measurement series is n, and containing extraodinary flood number in actual measurement series is l.X 1, X 2..., X m+l, X m+l+1..., X n-l+mthe series of samples of to be sample capacity be n-l+m, and by order arrangement from big to small, use X jrepresent the jth value in series.
Step 2, calculates the empirical Frequency of Flood evolution, and by the parameter of moments method distribution function according to a preliminary estimate;
The empirical frequency formula that the present invention recommends is the empirical frequency formula not connecting sequence sample:
P r = r N + 1 ( r = 1,2 , . . . , m )
P j = m N + 1 + ( 1 - m N + 1 ) j n + 1 ( j = 1,2 , . . . , n )
In formula, P rrepresent the empirical Frequency of r field historical flood, P jrepresent the empirical Frequency of jth field observed flood.
For the series of samples obtained in step 1, for X j, its empirical Frequency is denoted as P 0(X j).
Step 3, sets up P-III type distribution frequency optimization of profile model;
Flood data in step 1 are substituted into the frequency distribution function that step 2 obtains, in the hope of different floods point according to the theoretic frequency of correspondence, P can be denoted as 1(X j), j=1,2 ..., n-l+m, thus the relative error RE (X that can obtain theoretic frequency and empirical Frequency j), to different floods point certificate, give corresponding weight α j.Adopt the quadratic sum of relative error weight minimum is object function, and adds the constraints of parameter according to the actual conditions of basin overview and reservoir, so set up P-III type distribution frequency optimization of profile model.
Relative error about weight α in Optimized model jassignment method can adopt experience assignment method, the Bayesian model method of average, arithmetic mean method or fuzzy reasoning method etc.Generally, for weight α j, determine by the different interval importance of frequency curve, the sort order of flood sample data is larger, the weight just larger α of this flood point certificate j> 0, and
For constraints, the regulation of different basins to P-III distribution function parameters is distinguished to some extent, but generally requires C v/ C s>=2.This detailed description of the invention only adds this point constraints, and the constraints continuing to add other in practical application does not exceed protection scope of the present invention.
Step 4, with the parameter estimated in step 2 for initial value, adopts the model in very fast simulated annealing algorithm (MVFSA) solution procedure 3 improved, thus obtains the parameters of P-III type distribution function, thus draw frequency curve.
Adopting that very fast simulated annealing algorithm (MVFSA) solves local optimum problem is the ordinary skill in the art, and it will not go into details.
Fig. 2 gives the schematic diagram of the frequency curve adopting the present invention to obtain, and the upper afterbody matching of frequency curve is good as we can see from the figure, meets the actual demand of Chinese engineering.
To sum up, the present invention is by setting up P-III type distribution frequency optimization of profile model, different weights is given to the relative error of theoretic frequency and empirical Frequency, minimum for object function with the quadratic sum of relative error weight, and the constraints of parameter is added according to the actual conditions of basin overview and reservoir, with the parameter of Moment method estimators for initial value, adopt very fast simulated annealing algorithm (MVFSA) solving model improved, obtain the optimal solution of parameter, thus draw out P-III type distribution frequency curve.The method parameter estimation result is unique, avoids the arbitrariness that human factor produces, can also look after historical flood and extraodinary flood, expand the applicability of P-III type distribution curve, provides important reference frame for drawing P-III type distribution frequency curve.

Claims (5)

1. draw an optimization method for P-III type distribution frequency curve, it is characterized in that comprising the steps:
Step (1), collects historical flood and observed flood data;
Step (2), calculates the empirical Frequency of Flood evolution, and by the parameter of moments method distribution function according to a preliminary estimate;
Step (3), sets up P-III type distribution frequency optimization of profile model;
Step (4), with the parameter estimated in step (2) for initial value, adopt the model in the very fast simulated annealing algorithm solution procedure (3) improved, obtain the parameters of P-III type distribution function, thus draw frequency curve.
2. a kind of optimization method drawing P-III type distribution frequency curve as claimed in claim 1, it is characterized in that: in step (1), for the historical flood of collecting, if its maximum investigation phase is N, the historical flood number of investigation is m, the year number of actual measurement series is n, and containing extraodinary flood number in actual measurement series is l; X 1, X 2..., X n-l, X n-l+1..., X n-l+mthe series of samples of to be sample capacity be n-l+m, and by order arrangement from small to large, use X jrepresent the jth value in series.
3. a kind of optimization method drawing P-III type distribution frequency curve as claimed in claim 1, it is characterized in that: in step (2), described empirical frequency formula is the empirical frequency formula not connecting sequence sample; For the series of samples X obtained in step (1) j, its empirical Frequency is denoted as P 0(X j).
4. a kind of optimization method drawing P-III type distribution frequency curve as claimed in claim 1, it is characterized in that: in step (3), flood data in step (1) are substituted into the frequency distribution function that step (2) obtains, try to achieve different flood points according to the theoretic frequency of correspondence, be denoted as P 1(X j), j=1,2 ..., n-l+m, thus the relative error RE (X obtaining theoretic frequency and empirical Frequency j), to different floods point certificate, give corresponding weight α j; Adopt the quadratic sum of relative error weight minimum is object function, and adds the constraints of parameter according to the actual conditions of basin overview and reservoir, sets up P-III type distribution frequency optimization of profile model.
5. a kind of optimization method drawing P-III type distribution frequency curve as claimed in claim 4, is characterized in that: described weight α j, determine by the different interval importance of frequency curve, the sort order of flood sample data is larger, the weight just larger α of this flood point certificate j> 0, and
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CN105887751A (en) * 2016-04-28 2016-08-24 武汉大学 Multi-variable flood recurrence period calculating method considering reservoir flood routing calculation
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CN112085298A (en) * 2020-09-23 2020-12-15 中国电建集团成都勘测设计研究院有限公司 Non-continuous sequence flood frequency analysis method considering historical flood
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