CN112085298A - Non-continuous sequence flood frequency analysis method considering historical flood - Google Patents
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Abstract
The invention belongs to the technical field of flood frequency analysis, aims to solve the problem of low accuracy of non-continuous sequence flood frequency analysis in the prior art, and provides a non-continuous sequence flood frequency analysis method considering historical flood, and the scheme is summarized as follows: collecting and organizing flood data of a hydrological station in a research basin; determining optimal flood frequency distribution according to the fitting degree of the actually measured flood data and a plurality of flood frequency distribution line types; initially estimating statistical parameters of optimal flood frequency distribution, and determining the value range of the statistical parameters; determining an empirical frequency correction formula of the non-sequential flood sample, establishing an optimized line fitting method based on an SCE-UA algorithm, and calculating an optimal value of a statistical parameter; and calculating the design flood in the appointed recurrence period according to the optimal flood frequency distribution and the optimal value of the statistical parameter. The invention improves the accuracy of the non-continuous sequence flood frequency analysis.
Description
Technical Field
The invention belongs to the technical field of flood frequency analysis, and particularly relates to a non-sequential flood frequency analysis method considering historical flood.
Background
The scientific and reasonable design of flood is the primary task of water conservancy and hydropower engineering design, is also an important basis for determining the engineering scale, flood prevention and flood control and operation scheduling, and is always one of the hot spots and difficult problems in the field of hydrological analysis and calculation of international engineering. At present, Flood design at home and abroad is mainly carried out by a Flood Frequency Analysis (FFA) approach, according to actually measured Flood or historical Flood (including ancient Flood) data and widely combining regional Flood laws, fitting a Flood Frequency distribution curve, estimating Flood Frequency distribution parameters, extending the Frequency curve according to the Flood Frequency distribution parameters and calculating the design Flood at each recurrence period. In order to fully utilize more flood information, historical flood data are added in flood frequency analysis, actually measured floods and historical floods jointly form a non-continuous sequence flood series, and the non-continuous sequence flood frequency analysis is carried out, so that the representativeness of the flood series is effectively increased, powerful support is provided for determining the epitaxial trend of a flood frequency curve at the rare frequency, and the quality of designed flood results can be remarkably improved.
Parameter estimation is the most critical technical link in flood frequency analysis, and the accuracy of the parameter estimation directly influences the reliability of design flood. In the existing' flood calculation Specification for Water conservancy and hydropower engineering (SL 44-2006), for non-sequential flood frequency analysis considering historical flood, a wire Fitting method (CF) is recommended, and the basic idea is that firstly, a certain specific probability distribution is assumed to be a flood frequency distribution line type; then, fitting a flood frequency distribution curve on probability graph paper by using sample point data, and estimating statistical parameters of the flood frequency distribution curve, wherein the sample point data of actual measurement flood and historical flood is calculated by adopting an empirical frequency formula provided by money iron (1964); and finally, calculating each standard design flood according to the flood frequency distribution line type and the parameter values thereof. Through the development of recent decades, hydrologics and foreign scientists at home and abroad successively provide experience frequency formulas of non-continuous flood series samples, and the experience frequency formulas are widely applied in practice; the comparison is typically the theoretical formula proposed by qian-fe (1964), Hirsch (1987), guoshengli (1990), etc.
However, the theoretical formulas are derived on the premise that the information of the historical flood in each examination period in the historical flood data is real, reliable and complete. Because historical floods often occur in long-term, historical literature records are deficient, and human cognition is limited, only a few of historically-occurring flood waters or extra-large flood waters can be roughly quantified in each examination period, and most of the flood waters are difficult to be quantified exactly. Therefore, in practice, the historical flood survey inevitably omits flood or extra-flood data, which causes the number, the arrangement and other aspects of the historical flood to be often not very exact, and causes the preconditions derived from the theoretical formulas to be often difficult to satisfy in practice. Therefore, the traditional non-continuous sequence flood sample empirical frequency formula is adopted to perform non-continuous sequence flood frequency analysis, and systematic deviation may exist in the designed flood result, so that the accuracy of the flood frequency analysis calculation result is low.
Disclosure of Invention
The invention aims to solve the problem of low accuracy of non-continuous sequence flood frequency analysis in the prior art, and provides a non-continuous sequence flood frequency analysis method considering historical flood.
The invention solves the technical problem, and adopts the technical scheme that: a non-sequential flood frequency analysis method considering historical flood comprises the following steps:
step 2, determining optimal flood frequency distribution according to the fitting degree of the actually measured flood data and a plurality of flood frequency distribution line types and by combining and researching the law of the flood frequency distribution line types in the region of the drainage basin;
step 3, initially estimating statistical parameters of the optimal flood frequency distribution by adopting a linear moment method considering historical flood, and determining the value range of the statistical parameters by combining with the regional distribution rule of the parameters;
step 4, determining an empirical frequency correction formula of the non-continuous flood sample, establishing an optimized line fitting method based on an SCE-UA algorithm, and calculating the optimal value of the statistical parameter of the optimal flood frequency distribution;
and 5, calculating the design flood in the appointed recurrence period according to the optimal flood frequency distribution and the optimal value of the statistical parameter.
Further, the method for determining the fitting degree of the actually measured flood data and the flood frequency distribution line type comprises the following steps:
estimating expected values and standard deviations of actually measured flood series by adopting a Ksdensity nuclear density estimation method;
supposing that the actually measured flood series obeys a certain flood frequency distribution line type, calculating an expected value series of numerical order statistics;
and calculating the maximum value of the absolute value of the difference value of the actually measured flood series and the expected value series of the numerical order statistics based on a Kolmogorov-Similov test method, wherein the smaller the maximum value is, the better the fitting degree of the actually measured flood data and the flood frequency distribution line is.
Further, the method for calculating the series of expected values of the numerical order statistic comprises:
assuming that the probability density function and the probability distribution function of the flood random variable X are f (X) and F (X), respectively, if the simple random sample of the flood random variable X is (X)1，X2，…，Xn) Defining a numerical order statistic X(m)Take (x)1，x2，…，xn) The m-th item value after the middle is arranged from big to small, then the m-th X(m)Expected value of E (X)(m)) The calculation formula is as follows:
wherein n is the measured flood series length, and x (F) is the inverse function of the probability distribution curve F (x).
Further, when the optimal flood frequency distribution is P-III type distribution, the random variable X of the flood to be researched is assumed to obey the P-III type distribution and is recorded as X to (X; a, alpha, beta), and the calculation formulas of the probability density function f (X) and the probability distribution function F (X) are respectively:
in the formula, a is a position parameter, namely the minimum value of a flood random variable X, alpha is a shape parameter, and beta is a scale parameter;
the flood frequency distribution statistical parameters comprise expected values Ex, variation coefficients Cv and skewness coefficients Cs, and the mathematical relations among the position parameters a, the shape parameters alpha and the scale parameters beta are as follows:
Further, the value range of the flood frequency distribution statistical parameter should satisfy:
Ex∈[Ex0×0.3，Ex0×1.7]；
Cv∈[Cv0×0.4，Cv0×1.6]；
Cs∈[Cs0×0.5，Cs0×1.5]，Cs∈[0，2]；
in the formula, the expected value Ex0, the variation coefficient Cv0 and the skewness coefficient Cs0 are initially estimated flood frequency distribution statistical parameters, and xminIs the minimum value in the measured flood series.
Further, the method for determining the empirical frequency correction formula of the non-sequential flood sample comprises the following steps:
combining the actual measurement flood series and the historical flood series into a non-continuous flood series, wherein the number of the historical flood examination periods is M, and N is respectively1，…，Nm，Nm+1，…，NMThe corresponding flood threshold values are respectively S1，…，Sm，Sm+1，…，SMThe number of floods greater than each flood threshold is k1，…，km，km+1，…，kMThe number of floods which are selected in each examination period and subjected to special value processing in the next examination period is l1，…，lm，lm+1，…，lM(ii) a The length of an actual measurement period of actual measurement flood is n, the number of floods which are selected in the actual measurement period and subjected to special large value processing in a later examination period is l, the number of non-large floods in the actual measurement period is n-l, the number of large floods in the examination period is h-k-l, the total number of floods is g-n + k-l, wherein l is less than or equal to k, l is less than or equal to n,
assuming that the minimum value of the actually measured flood series and the historical flood series is S0Maximum value of SmaxThen, S0＜S1＜…＜Sm＜Sm+1＜…＜SM＜Smax, wherein ,S0＝0，Smax＝+∞；
In order to ensure that the water-soluble organic acid,
then the process of the first step is carried out,
in the formula ,
is the mth flood threshold SmThe probability of the occurrence of the event is,
is a minimum value S0The probability of the occurrence of the event is,
is a maximum value SmaxThe probability of occurrence;
then it is determined that,
then, the mth flood threshold SmProbability of occurrence
The calculation formula of (2) is as follows:
when the ith flood sample xi∈[SM，Smax) Then, the empirical frequency correction formula for the ith flood in the historical flood series is:
when the ith flood sample xi∈[Sm+1，SM) Then, the empirical frequency correction formula for the ith flood in the historical flood series is:
in the formula ,
for the Mth flood threshold SMProbability of occurrence, i.e.
Correction factor
When the ith flood sample xi∈[Sm，Sm+1) Then, the empirical frequency correction formula for the ith flood in the historical flood series is:
in the formula ,
is the m +1 th flood threshold Sm+1Probability of occurrence, correction factor
When the ith flood sample xi∈[S1，Sm) Then, the empirical frequency correction formula for the ith flood in the historical flood series is:
in the formula ,
is the mth flood threshold SmProbability of occurrence, correction factor
When the ith flood sample xi∈[S0，S1) In time, the empirical frequency correction formula for the ith flood in the actual measurement flood series is as follows:
in the formula ,
is the 1 st flood threshold S1Probability of occurrence, correction factor
Further, the method for establishing an optimized line fitting method based on the SCE-UA algorithm and calculating the optimal value of the statistical parameter of the optimal flood frequency distribution includes:
arranging the measured flood series and the historical flood series into x from big to small(1)≥x(2)≥…≥x(g)Calculating each flood sample x according to the non-continuous sequence flood sample empirical frequency correction formula(i)Corresponding empirical frequency P(i)(i 1, 2, …, g), each sample point (P) is plotted on a probability chart paper(i)，x(i)) Taking the position as a drawing point position;
and optimizing a flood frequency distribution curve with the best fitting effect by using an SCE-UA algorithm according to the optimal flood frequency distribution, the objective function, the drawing point position and the constraint condition, and taking the corresponding parameter value as the optimal value of the flood frequency distribution statistical parameter.
Further, the objective function is a sum of absolute deviation values, that is, a sum of absolute deviation values of differences between the flood frequency distribution curve corresponding to the parameter estimation value and the ordinate of the plotted point position, and the calculation formula is as follows:
wherein S (theta) is an objective function value; θ is an optimization variable, including: the expected value Ex, the variation coefficient Cv and the ratio Cs/Cv of the variation coefficient to the skewness coefficient; x is the number ofiActual measurement flood samples and historical flood samples; f-1(Pi(ii) a Theta) is a given frequency PiThe corresponding design value is the longitudinal coordinate value of the position of a drawing point on the flood frequency curve; g is the flood sample volume.
Further, the design flood in the appointed recurrence period is calculated according to the optimal flood frequency distribution and the optimal value of the statistical parameter, and the calculation formula is as follows:
xP＝Ex×(1+ΦP×Cv)；
wherein ,
in the formula ,xPFor flood design, T is the recurrence period, P is the design frequency, phiPIs a dispersion coefficient and is a Gamma function.
Further, the recurring period is 10 years, 20 years, 30 years, 50 years, 100 years, 200 years, 300 years, 500 years, 1000 years, 2000 years, 3000 years, 5000 years or 10000 years.
The invention has the beneficial effects that: according to the non-continuous sequence flood frequency analysis method considering the historical flood, the non-continuous sequence flood sample experience frequency correction formula under the conditions of single examination period and multiple examination periods is deduced according to the uncertainty of the historical flood in each examination period in the historical flood data and the incompleteness of the adjustable historical flood information, and the full probability formula and the Bayesian formula are taken as theoretical bases, so that the optimized line-fitting method based on the SCE-UA algorithm is established, the accuracy and the reliability of the non-continuous sequence flood frequency analysis calculation result are effectively improved, the method has the advantages of high reliability, high calculation efficiency and strong applicability, a more reliable and reasonable design flood basis is provided for water conservancy and hydropower engineering planning design, construction, operation scheduling and the like, and the method has a better application prospect.
Drawings
Fig. 1 is a schematic flow chart of a non-sequential flood frequency analysis method considering historical flood according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a series of non-sequential flood samples during a single examination period according to an embodiment of the present invention;
fig. 3 is a schematic composition diagram of a multiple-examination-period non-sequential flood sample series according to an embodiment of the present invention.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the embodiments and the accompanying drawings.
The invention aims to solve the problem of low accuracy of non-continuous sequence flood frequency analysis in the prior art, and provides a non-continuous sequence flood frequency analysis method considering historical flood, and the technical scheme is summarized as follows: collecting and organizing flood data of a hydrological station of a research basin, wherein the flood data comprise actually-measured flood data and historical flood data, and determining an examination period of each historical flood in the historical flood data and a corresponding flood threshold; determining optimal flood frequency distribution according to the fitting degree of the actually measured flood data and a plurality of flood frequency distribution line types and by combining and researching the law of the flood frequency distribution line type in the region of the drainage basin; initially estimating statistical parameters of the optimal flood frequency distribution by adopting a linear moment method considering historical flood, and determining the value range of the statistical parameters by combining with a parameter area distribution rule; determining an empirical frequency correction formula of the non-sequential flood sample, establishing an optimization line fitting method based on an SCE-UA algorithm, and calculating the optimal value of the statistical parameter of the optimal flood frequency distribution; and calculating the design flood in the appointed recurrence period according to the optimal flood frequency distribution and the optimal value of the statistical parameter.
The method determines the optimal flood frequency distribution from the plurality of flood frequency distribution line types according to the fitting degree of the actually measured flood data and the plurality of flood frequency distribution line types and by combining the study on the law of the flood frequency distribution line types in the region of the drainage basin, and has better applicability. According to uncertainty of occurrence of historical flood in each examination period in historical flood data and imperfection of inquired historical flood information, a total probability formula and a Bayesian formula are used as theoretical bases, and a mathematical induction method is adopted to deduce probability of occurrence of flood threshold corresponding to each examination period; and measuring the effect of the unexplored historical flood information in the experience frequency of the flood sample by adopting a flood information quantity comparison method, and deducing a non-continuous sequence flood sample experience frequency correction formula under the conditions of single-examination period and multiple-examination period. And establishing an optimization adaptive line based on the SCE-UA algorithm according to the non-continuous sequence flood sample empirical frequency correction formula to obtain a statistical parameter optimal value of optimal flood frequency distribution, and then calculating the design flood in the appointed recurrence period, thereby realizing the efficient and accurate calculation of the non-continuous sequence flood frequency analysis.
Examples
The existing non-sequential flood frequency analysis method considering historical flood has the following problems: the traditional non-sequential flood sample empirical frequency formula is derived strictly according to a mathematical theory, and the uncertainty of the occurrence of the historical flood in each examination period in the historical flood data and the incompleteness of the inquired historical flood information are ignored; the traditional non-continuous sequence flood sample empirical frequency formula is adopted to carry out non-continuous sequence flood frequency analysis, and the designed flood result has larger uncertainty and certain defects in practical application.
In view of the above disadvantages of the prior art, an embodiment of the present invention provides a non-sequential flood frequency analysis method considering historical flood, as shown in fig. 1, including the following steps:
step S1, collecting and organizing flood data of a hydrological station in a research basin, wherein the flood data comprise actually-measured flood data and historical flood data, and determining an examination period of each historical flood in the historical flood data and a corresponding flood threshold;
specifically, the measured flood data is obtained by extracting annual maximum peak flow or total flood amount in a specified time period from measured flow data in past years by adopting an annual maximum method, and the extracted annual maximum peak flow or total flood amount is used as a flood characteristic series; wherein the total flood amount can be selected from maximum annual flood amount of 1 day, maximum annual flood amount of 3 days, maximum annual flood amount of 7 days and the like.
According to the flood calculation Specification for design of Water conservancy and hydropower engineering (SL 44-2006), the series length of the actually measured flood data is generally more than 30 years; if the actual measurement flood series length of a certain hydrological station is less than 30 years, an interpolation extension method can be adopted, and the data of longer water level, rainstorm, flow and the like are utilized to establish the synchronous correlation relationship, so that the interpolation extension is carried out on the correlation relationship, and the actual measurement flood data of the long series are obtained.
The historical flood data can be historical survey flood, ancient flood and the like; the historical survey flood is mainly obtained by on-site survey, literature reference, inscription cultural relics and the like, and the examination period is generally 100-200 years; ancient floods are mainly estimated by applying a principle method of quaternary geology, chronology and hydrology on the basis of obtaining flood advection sediments, and the examination period of the ancient floods is generally 1000-2000 years. After the peak flow or the magnitude of the period flood of the historical flood is determined, the examination period in which each historical flood is located and the corresponding flood threshold value need to be further investigated and examined, and the ranking of each historical flood in the examination period is determined.
Step S2, determining the optimal flood frequency distribution according to the fitting degree of the actually measured flood data and a plurality of flood frequency distribution line types and by combining with the law of the flood frequency distribution line type of the region where the research basin is located;
specifically, the method for determining the fitting degree of the actually measured flood data and the flood frequency distribution line type comprises the following steps:
step S21, estimating an expected value and a standard deviation of the actually measured flood series by adopting a Ksdensity nuclear density estimation method;
step S22, assuming that the actually measured flood series obeys a certain flood frequency distribution line type, calculating the expected value series of the numerical order statistics, wherein the calculation method of the expected value series of the numerical order statistics comprises the following steps:
assuming that the probability density function and the probability distribution function of the flood random variable X are f (X) and F (X), respectively, if the simple random sample of the flood random variable X is (X)1，X2，…，Xn) Defining a numerical order statistic X(m)Take (x)1，x2，…，xn) The m-th item value after the middle is arranged from big to small, then the m-th X(m)Expected value of E (X)(m)) The calculation formula is as follows:
wherein n is the length of the actually measured flood series, and x (F) is the inverse function of the probability distribution function F (x);
step S23, calculating the maximum value of the absolute value of the difference value of the actual measurement flood series and the expected value series of the numerical order statistics based on a Kolmogorov-Smirnov (KS) test method, wherein the smaller the maximum value is, the better the fitting degree of the actual measurement flood data and the flood frequency distribution line is.
Among them, the selection of the flood frequency distribution line type is one of the basic problems of the flood frequency analysis. Due to different flood causes, different countries or regions select the most suitable flood frequency distribution line type according to the actual conditions of local storm flood. The flood calculation specification of the water conservancy and hydropower engineering design in China recommends P-III type distribution as a flood frequency distribution line type. At present, about 20 distribution lines are available for use in flood frequency analysis and calculation at home and abroad, and mainly include: pearson type III (P-III) distribution, logarithmic Pearson type III (LP-III) distribution, Generalized Extreme Value (GEV) distribution, Generalized Logic (GL) distribution, two/three parameter lognormal (LN2/LN3) distribution, two/three parameter Pareto (Pareto2/Pareto3) distribution, extreme I/II/III (EV1/EV2/EV3) distribution, Critzky-Menkel (K-M) distribution, Gumbel distribution, and the like.
When the optimal flood frequency distribution is P-III type distribution, the calculation formulas of the probability density function f (X) and the probability distribution function F (X) are respectively as follows, assuming that the researched flood random variable X obeys the P-III type distribution and is recorded as X to (X; a, alpha, beta):
in the formula, a is a position parameter, namely the minimum value of a flood random variable X, alpha is a shape parameter, and beta is a scale parameter;
step S3, primarily estimating statistical parameters of the optimal flood frequency distribution by adopting a linear moment method considering historical flood, and determining the value range of the statistical parameters by combining with the regional distribution rule of the parameters;
specifically, the flood frequency distribution statistical parameters include an expected value Ex, a variation coefficient Cv and a skewness coefficient Cs, and the mathematical relationship among the position parameter a, the shape parameter α and the scale parameter β is as follows:
The linear moment method is a parameter estimation method with good unbiasedness and effectiveness, which is proposed by Hoskeg in 1990, and is widely applied to foreign flood frequency analysis and calculation; see in particular "Regional Frequency Analysis: an applied Approach Based on L-Moments (Hosking J R M, Wallis J R. London: Cambridge University Press, 1997). Assuming that a flood random variable X obeys P-III type distribution, considering that the calculation process of a linear moment method of historical flood can be provided according to a P-III distribution linear moment method with historical flood according to Chenyuan Fang and the like; other flood frequency distribution profiles may be calculated with reference to similar steps; the detailed calculation process is specifically shown in the research on the P-III distribution linear moment method with historical flood (Chenyuanfang, precious in sand, Chenjiangchi, etc. proceedings of river and sea university, 2001, 29 (4): 76-80).
Assuming that the flood random variable X obeys P-III type distribution, according to the flood cause and statistical rules, the probability of occurrence of the maximum value and the minimum value of the flood variable is very small, and the probability of occurrence of the intermediate value is relatively large, namely, the P-III type probability density curve should present bell-shaped characteristics, namely 0 < Cs < 2. Generally, the minimum value of the actually measured flood series is often greater than zero, and negative values cannot occur, so that the value of the left endpoint a of the P-III type probability density curve should satisfy: since a is EX (1-2Cv/Cs) is not less than 0, Cs is not less than 2 Cv. In addition, the minimum value x in the measured flood seriesminShould be equal to or greater than the minimum value a, i.e. x, in the flood population distributionminA ≧ EX (1-2Cs/Cv), thus
Therefore, the ratio Cs/Cv of the parameters Cs and Cv of the P-III type distribution should satisfy:
the errors of the statistical parameters Ex, Cv and Cs initially estimated by the linear moment method considering the historical flood are considered to be increased in sequence. For P-III type distribution, the value range of the flood frequency distribution statistical parameter should satisfy the following relationship:
Ex∈[Ex0×0.3，Ex0×1.7]；
Cv∈[Cv0×0.4，Cv0×1.6]；
Cs∈[Cs0×0.5，Cs0×1.5]，Cs∈[0，2]；
in the formula, the expected value Ex0, the variation coefficient Cv0 and the skewness coefficient Cs0 are initially estimated flood frequency distribution statistical parameters, and xminIs the minimum value in the measured flood series.
Step S4, determining an empirical frequency correction formula of the non-sequential flood sample, establishing an optimized line fitting method based on an SCE-UA algorithm, and calculating the optimal value of the statistical parameter of the optimal flood frequency distribution;
specifically, according to uncertainty of historical flood occurrence in each examination period in historical flood data and imperfection of inquired historical flood information, an empirical frequency correction formula of historical flood samples and actually-measured flood samples under the condition of single examination period and multiple examination periods, namely a non-sequential flood sample empirical frequency correction formula, is deduced by taking a full probability formula and a Bayesian formula as theoretical bases.
Establishing an optimization adaptive line based on an SCE-UA algorithm, realizing automatic and rapid parameter optimization, and obtaining a statistical parameter optimal value of optimal flood frequency distribution; the optimization variables are Ex, Cv and Cs/Cv, the objective function is the sum of absolute deviation values, the constraint condition is the value range of statistical parameters, the drawing point position is calculated by the non-continuous sequence flood sample empirical frequency correction formula, and the optimization algorithm is the SCE-UA algorithm.
The following describes in detail the derivation method of the empirical frequency correction formula of the non-continuous flood sample:
firstly, a single examination period non-continuous sequence flood sample experience frequency correction formula:
the measured flood series and the historical flood series are combined to form a non-continuous flood series, the number of the historical flood examination periods is only 1, the examination period length is N (including the years of the historical period and the measured period), and the corresponding flood threshold value is S1(generally lower than minimum historical floods), which is largeAt flood threshold S1The number of floods is k; the length of an actual measurement period of actually measured flood is n, and the number of floods which are selected to be subjected to special value processing in an examination period in the actual measurement period is l; then, the number of non-flood in the actual measurement period is n-l, the number of flood in the examination period is h-k-l, the total number of flood is g-n + k-l, wherein l is less than or equal to k, and l is less than or equal to n;
firstly, a mathematical induction method is adopted to deduce the probability of flood threshold value occurrence corresponding to each examination period. Assuming that the minimum value of the actually measured flood series and the historical flood series is S0Maximum value of SmaxThen S is0＜S1＜Smax, wherein ,S0＝0，Smax＝+∞。
In order to ensure that the water-soluble organic acid,
then the process of the first step is carried out,
in the formula ,
is the mth flood threshold SmThe probability of the occurrence of the event is,
is a minimum value S0The probability of the occurrence of the event is,
is a maximum value SmaxThe probability of occurrence;
then it is determined that,
thus, the 1 st flood threshold S1Probability of occurrence
The calculation formula of (2) is as follows:
then, according to uncertainty of occurrence of the historical flood in each examination period in the historical flood data and imperfection of the inquired historical flood information, a full probability formula and a Bayes formula are used as theoretical bases, and an experience frequency correction formula of the non-sequential flood sample in the single examination period is deduced, and is called a Weight formula for short; the calculation process is briefly described as follows:
(1) when the ith flood sample xi∈[S1，Smax) In the historical flood series (N is the historical flood examination period, and k extra floods are in total) the empirical frequency correction formula of the ith flood is as follows:
(2) when the ith flood sample xi∈[S0，S1) In the actual measurement flood series (n is an actual measurement period of the actual measurement flood, n-l floods are in total in the actual measurement period, and the number of the floods which are selected in the current period and subjected to extreme value processing in the later examination period is l), the empirical frequency correction formula of the ith flood is as follows:
in the formula ,
is flood threshold S1Probability of occurrence, i.e.
Correction factor
The composition of the non-sequential flood sample series in the single examination period is shown in FIG. 2.
Secondly, a frequency correction formula of the experience of the non-continuous sequence flood samples in multiple examination periods is shown:
combining the actual measurement flood series and the historical flood series into a non-continuous flood series, wherein the number of the historical flood examination periods is M, and N is respectively1，…，Nm，Nm+1，…，NMThe corresponding flood threshold values are respectively S1，…，Sm，Sm+1，…，SMThe number of floods greater than each flood threshold is k1，…，km，km+1，…，kMThe number of floods which are selected in each examination period and subjected to special value processing in the next examination period is l1，…，lm，lm+1，…，lM(ii) a The length of an actual measurement period of actual measurement flood is n, the number of floods which are selected in the actual measurement period and subjected to special large value processing in a later examination period is l, the number of non-large floods in the actual measurement period is n-l, the number of large floods in the examination period is h-k-l, the total number of floods is g-n + k-l, wherein l is less than or equal to k, l is less than or equal to n,
firstly, a mathematical induction method is adopted to deduce the probability of flood threshold value occurrence corresponding to each examination period. Assuming that the minimum value of the actually measured flood series and the historical flood series is S0Maximum value of SmaxThen, S0＜S1＜…＜Sm＜Sm+1＜…＜SM＜Smax, wherein ,S0＝0，Smax＝+∞；
In order to ensure that the water-soluble organic acid,
then the process of the first step is carried out,
in the formula ,
is the mth flood threshold SmThe probability of the occurrence of the event is,
is a minimum value S0The probability of the occurrence of the event is,
is a maximum value SmaxThe probability of occurrence;
then it is determined that,
then, the mth flood threshold SmProbability of occurrence
The calculation formula of (2) is as follows:
then, according to uncertainty of occurrence of historical flood in each examination period in historical flood data and imperfection of inquired historical flood information, a full probability formula and a Bayes formula are used as theoretical bases, and an empirical frequency correction formula, called a Weight formula for short, of the multiple examination period non-continuous sequence flood samples is deduced; the calculation process is briefly described as follows:
(1) when the ith flood sample xi∈[SM，Smax) Time, historical flood series (N)MThe M examination period is kMThe number of flood which is selected in the current period and is subjected to special big value treatment in the later examination period is lM0) the empirical frequency correction formula for the ith flood is:
(2) when the ith flood sample xi∈[Sm+1，SM) Time, historical flood series (N)m+1The m +1 test period is km+1The number of flood which is selected in the current period and is subjected to special big value treatment in the later examination period is lm+1) The empirical frequency correction formula of the ith flood is as follows:
in the formula ,
for the Mth flood threshold SMProbability of occurrence, i.e.
Correction factor
(3) When the ith flood sample xi∈[Sm，Sm+1) Time, historical flood series (N)mThe m examination period is kmThe number of flood which is selected in the current period and is subjected to special big value treatment in the later examination period is lm) The empirical frequency correction formula of the ith flood is as follows:
in the formula ,
is the m +1 th flood threshold Sm+1Probability of occurrence, correction factor
(4) When the ith flood sample xi∈[S1，Sm) Time, historical flood series (N)1Is the 1 st examination period with a total of k1The number of flood which is selected in the current period and is subjected to special big value treatment in the later examination period is l1) The empirical frequency correction formula of the ith flood is as follows:
in the formula ,
is the mth flood threshold SmProbability of occurrence, correction factor
(5) When the ith flood sample xi∈[S0，S1) In the actual measurement flood series (n is an actual measurement period of the actual measurement flood, n-l floods are in total in the actual measurement period, and the number of the floods which are selected in the current period and subjected to extreme value processing in the later examination period is l), the empirical frequency correction formula of the ith flood is as follows:
in the formula ,
is the 1 st flood threshold S1Probability of occurrence, correction factor
The composition of the non-sequential flood sample series in multiple test periods is shown in FIG. 3.
According to the non-continuous sequence flood sample empirical frequency correction formula, an optimization line fitting method based on the SCE-UA algorithm is established, and the method for calculating the optimal value of the statistical parameter of the optimal flood frequency distribution comprises the following steps:
arranging the measured flood series and the historical flood series into x from big to small(1)≥x(2)≥…≥x(g)Calculating each flood sample x according to the non-continuous sequence flood sample empirical frequency correction formula(i)Corresponding empirical frequency P(i)(i 1, 2, …, g), each sample point (P) was plotted on a probability chart paper(i)，x(i)) Taking the position as a drawing point position;
and optimizing a flood frequency distribution curve with the best fitting effect by using an SCE-UA algorithm according to the optimal flood frequency distribution, the objective function, the drawing point position and the constraint condition, and taking the corresponding parameter value as the optimal value of the flood frequency distribution statistical parameter.
Specifically, the objective function is a sum of absolute deviation values, that is, a sum of absolute deviation values of differences between a flood frequency distribution curve corresponding to the parameter estimation value and a ordinate of the plotted point position, and a calculation formula of the sum of absolute deviation values is as follows:
wherein S (theta) is an objective function value; θ is an optimization variable, including: the expected value Ex, the variation coefficient Cv and the ratio Cs/Cv of the variation coefficient to the skewness coefficient; x is the number ofiActual measurement flood samples and historical flood samples; f-1(Pi(ii) a Theta) is a given frequency PiThe corresponding design value is the longitudinal coordinate value of the position of a drawing point on the flood frequency curve; g is the flood sample volume.
In the embodiment of the invention, the SCE-UA algorithm is preferably adopted to carry out parameter solution on three optimization variables (including an expected value Ex, a variation coefficient Cv and a ratio Cs/Cv of the variation coefficient to a skewing coefficient). The SCE-UA (smoothed Complex Evolution University of Arizona) algorithm combines the advantages of random search, a traditional composite method, biological competition optimization and elimination, is an Evolution algorithm which can effectively solve the nonlinear global optimization problems of Complex high-dimensional parameters, multiple extreme values and the like, has the advantages of high calculation efficiency, high convergence speed, good solving stability and the like, and is widely applied to parameter rate centering of nonlinear Complex hydrological prediction methods.
Step S5, calculating the design flood of the appointed recurrence period according to the optimal flood frequency distribution and the optimal value of the statistical parameter, wherein the calculation formula is as follows:
xP＝Ex×(1+ΦP×Cv)；
wherein ,
in the formula ,xPFor flood design, T is the recurrence period, P is the design frequency, phiPIs a dispersion coefficient and is a Gamma function.
Specifically, the design flood refers to floods of various design standards specified by hydraulic and hydroelectric engineering planning design, construction, operation scheduling and the like, and is a design value for ensuring the flood control capacity of the reservoir and the safety of the dam. The recurring period is typically selected to be 10 years, 20 years, 30 years, 50 years, 100 years, 200 years, 300 years, 500 years, 1000 years, 2000 years, 3000 years, 5000 years, or 10000 years.
Claims (10)
1. A non-sequential flood frequency analysis method considering historical flood is characterized by comprising the following steps:
step 1, collecting and organizing flood data of a hydrological station of a research basin, wherein the flood data comprise actually-measured flood data and historical flood data, and determining an examination period of each historical flood in the historical flood data and a corresponding flood threshold;
step 2, determining optimal flood frequency distribution according to the fitting degree of the actually measured flood data and a plurality of flood frequency distribution line types and by combining and researching the law of the flood frequency distribution line types in the region of the drainage basin;
step 3, initially estimating statistical parameters of the optimal flood frequency distribution by adopting a linear moment method considering historical flood, and determining the value range of the statistical parameters by combining with the regional distribution rule of the parameters;
step 4, determining an empirical frequency correction formula of the non-continuous flood sample, establishing an optimized line fitting method based on an SCE-UA algorithm, and calculating the optimal value of the statistical parameter of the optimal flood frequency distribution;
and 5, calculating the design flood in the appointed recurrence period according to the optimal flood frequency distribution and the optimal value of the statistical parameter.
2. The method of claim 1, wherein the step of determining the fitness of the measured flood data to the flood frequency profile comprises:
estimating expected values and standard deviations of actually measured flood series by adopting a Ksdensity nuclear density estimation method;
supposing that the actually measured flood series obeys a certain flood frequency distribution line type, calculating an expected value series of numerical order statistics;
and calculating the maximum value of the absolute value of the difference value of the actually measured flood series and the expected value series of the numerical order statistics based on a Kolmogorov-Similov test method, wherein the smaller the maximum value is, the better the fitting degree of the actually measured flood data and the flood frequency distribution line is.
3. The method of non-sequential flood frequency analysis considering historical floods of claim 2, wherein the method of calculating the series of expected values of the numerical order statistic comprises:
assuming that the probability density function and the probability distribution function of the flood random variable X are f (X) and F (X), respectively, if the simple random sample of the flood random variable X is (X)1，X2，…，Xn) Defining a numerical order statistic X(m)Take (x)1，x2，…，xn) The m-th item value after the middle is arranged from big to small, then the m-th X(m)Expected value of E (X)(m)) The calculation formula is as follows:
wherein n is the measured flood series length, and x (F) is the inverse function of the probability distribution curve F (x).
4. The method of claim 1, wherein when the optimal flood frequency distribution is P-III distribution, the random variable X of the flood under study is assumed to obey P-III distribution and is denoted as X to (X; a, α, β), and the probability density function f (X) and the probability distribution function F (X) are calculated by the following formula:
in the formula, a is a position parameter, namely the minimum value of a flood random variable X, alpha is a shape parameter, and beta is a scale parameter;
the flood frequency distribution statistical parameters comprise expected values Ex, variation coefficients Cv and skewness coefficients Cs, and the mathematical relations among the position parameters a, the shape parameters alpha and the scale parameters beta are as follows:
5. The method of claim 4, wherein the range of the flood frequency distribution statistical parameter is such that:
Ex∈[Ex0×0.3，Ex0×1.7]；
Cv∈[Cv0×0.4，Cv0×1.6]；
Cs∈[Cs0×0.5，Cs0×1.5]，Cs∈[0，2]；
in the formula, the expected value Ex0, the variation coefficient Cv0 and the skewness coefficient Cs0 are initially estimated flood frequency distribution statistical parameters, and xminIs the minimum value in the measured flood series.
6. The method of non-sequential flood frequency analysis considering historical floods according to claim 4, wherein said method of empirically determining frequency correction equations for non-sequential flood samples comprises:
combining the actual measurement flood series and the historical flood series into a non-continuous flood series, wherein the number of the historical flood examination periods is M, and N is respectively1，…，Nm，Nm+1，…，NMThe corresponding flood threshold values are respectively S1，…，Sm，Sm+1，…，SMThe number of floods greater than each flood threshold is k1，…，km，km+1，…，kMThe number of floods which are selected in each examination period and subjected to special value processing in the next examination period is l1，…，lm，lm+1，…，lM(ii) a The length of an actual measurement period of actual measurement flood is n, the number of floods which are selected in the actual measurement period and subjected to special large value processing in a later examination period is l, the number of non-large floods in the actual measurement period is n-l, the number of large floods in the examination period is h-k-l, the total number of floods is g-n + k-l, wherein l is less than or equal to k, l is less than or equal to n,
assuming that the minimum value of the actually measured flood series and the historical flood series is S0Maximum value of SmaxThen, S0＜S1＜…＜Sm＜Sm+1＜…＜SM＜Smax, wherein ,S0＝0，Smax＝+∞；
In order to ensure that the water-soluble organic acid,
then the process of the first step is carried out,
in the formula ,
is the mth flood threshold SmThe probability of the occurrence of the event is,
is a minimum value S0The probability of the occurrence of the event is,
is a maximum value SmaxThe probability of occurrence;
then it is determined that,
then, the mth flood threshold SmProbability of occurrence
The calculation formula of (2) is as follows:
when the ith flood sample xi∈[SM，Smax) Then, the empirical frequency correction formula for the ith flood in the historical flood series is:
when the ith flood sample xi∈[Sm+1，SM) Then, the empirical frequency correction formula for the ith flood in the historical flood series is:
in the formula ,
for the Mth flood threshold SMProbability of occurrence, i.e.
Correction factor
When the ith flood sample xi∈[Sm，Sm+1) Then, the empirical frequency correction formula for the ith flood in the historical flood series is:
in the formula ,
is the m +1 th flood threshold Sm+1Probability of occurrence, correction factor
When the ith flood sample xi∈[S1，Sm) Then, the empirical frequency correction formula for the ith flood in the historical flood series is:
in the formula ,
is the mth flood threshold SmProbability of occurrence, correction factor
When the ith flood sample xi∈[S0，S1) In time, the empirical frequency correction formula for the ith flood in the actual measurement flood series is as follows:
in the formula ,
is the 1 st flood threshold S1Probability of occurrence, correction factor
7. The method of claim 4, wherein the method for establishing an optimized adaptive method based on the SCE-UA algorithm comprises the following steps:
arranging the measured flood series and the historical flood series into x from big to small(1)≥x(2)≥…≥x(g)Calculating each flood sample x according to the non-continuous sequence flood sample empirical frequency correction formula(i)Corresponding empirical frequency P(i)(i 1, 2, …, g), each sample point (P) is plotted on a probability chart paper(i)，x(i)) Taking the position as a drawing point position;
and optimizing a flood frequency distribution curve with the best fitting effect by using an SCE-UA algorithm according to the optimal flood frequency distribution, the objective function, the drawing point position and the constraint condition, and taking the corresponding parameter value as the optimal value of the flood frequency distribution statistical parameter.
8. The method of claim 7, wherein the objective function is a sum of absolute deviations, i.e. an absolute sum of differences between the vertical coordinates of the positions of the plotted points and the flood frequency distribution curve corresponding to the estimated values of the parameters, and is calculated by:
wherein S (theta) is an objective function value; θ is an optimization variable, including: the expected value Ex, the variation coefficient Cv and the ratio Cs/Cv of the variation coefficient to the skewness coefficient; x is the number ofiActual measurement flood samples and historical flood samples; f-1(Pi(ii) a Theta) is a given frequency PiThe corresponding design value is the longitudinal coordinate value of the position of a drawing point on the flood frequency curve; g is the flood sample volume.
9. The method of claim 4, wherein the designed flood for the designated recurrence period is calculated according to the optimal flood frequency distribution and the optimal values of the statistical parameters, and the calculation formula is as follows:
xP＝Ex×(1+ΦP×Cv)；
wherein ,
in the formula ,xPFor flood design, T is the recurrence period, P is the design frequency, phiPIs a dispersion coefficient and is a Gamma function.
10. The method of non-sequential flood frequency analysis considering historical floods of claim 9, wherein said recurrence period is 10 years, 20 years, 30 years, 50 years, 100 years, 200 years, 300 years, 500 years, 1000 years, 2000 years, 3000 years, 5000 years, or 10000 years.
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