CN109271664B - Design rainstorm safety analysis method based on assumed conditions of consistency and non-consistency - Google Patents
Design rainstorm safety analysis method based on assumed conditions of consistency and non-consistency Download PDFInfo
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Abstract
The invention discloses a design rainstorm safety analysis method based on assumed conditions of consistency and non-consistency, which comprises the following steps: extracting an annual maximum value sequence from a perennial daily precipitation sequence; extracting a series of subsequences from the annual maximum value sequence by adopting a 30-year window sliding method and a 30-year window increasing method; fitting each subsequence through generalized extremum distribution and calculating a design rainstorm value sequence; calculating a trend value of a designed rainstorm sequence by adopting a linear regression method; and (4) making a difference value of the trend values of the designed rainstorm sequence under the two extraction methods, and carrying out safety analysis according to the difference value. The invention provides a new method for researching the difference of the non-uniformity and the uniformity hypothesis to the design rainstorm, compares the annual difference of the design rainstorm calculated under the two hypotheses, is favorable for evaluating the safety of the design standard, and can provide reference significance for hydraulic engineering construction, water resource and safety management, flood control and disaster reduction.
Description
Technical Field
The invention relates to the field of hydrological meteorology and hydrological statistics, in particular to a designed rainstorm safety analysis method based on assumed conditions of consistency and non-consistency.
Background
Due to the influence of global climate change, many hydrological and meteorological elements show obvious variation with time, and precipitation is one of the elements with variation. In actual hydraulic engineering construction, design rainstorm is generally calculated by a maximum annual method and a hydrological frequency curve based on consistency assumption, and typical hydrological frequency curves include generalized extreme value distribution (GEV), pearson type iii, generalized normal distribution, generalized logistic distribution and the like. Therefore, the existence of the inconsistency can cause the difference between the actually adopted design value and the expected value, and the discussion of the potential difference has important significance on the safety of the hydraulic engineering. In the related research for designing rainstorm differences under consistent and inconsistent assumptions, most of the research focuses on discussing the calculation method and the variation trend of the inconsistent rainstorm design value. To investigate the effect of non-uniformity, there are probably two approaches: (1) considering the statistical parameters of the distribution function as functions of time or other factors (such as precipitation, air temperature and other factors), although the method can discuss the change trend of historical and future design rainstorm, the type of the distribution of the function met by the parameters needs to be assumed in advance; (2) the influence of non-uniformity is weakened by adopting a fixed year window sliding method, such as a 30-year sliding window method, namely, a hydrological frequency curve is fitted to a precipitation sequence which is continuous for 30 years each time, which is different from the traditional method of directly fitting all precipitation sequences, and the method is suitable for discussing the change trend of historical design rainstorm. However, for the differences in designed rainstorms under the consistent and inconsistent assumptions, most studies consider the designed rainstorm values, which are derived based on the consistent assumptions, as fixed values, i.e. fitting the hydrological frequency curves to all available precipitation sequences, ignoring their effect as the observed years increase (precipitation sequences grow).
Disclosure of Invention
The invention aims to overcome the defects and shortcomings in the prior art, provides a design rainstorm safety analysis method based on the assumed conditions of consistency and inconsistency, provides reference for the safety of large-scale hydraulic engineering design, and further provides scientific and practical values for hydraulic engineering construction, water resource and safety management, flood control and disaster reduction.
In order to realize the purpose, the invention adopts the following technical scheme:
the design rainstorm safety analysis method based on the assumed conditions of consistency and inconsistency comprises the following steps:
s1, extracting an annual maximum value sequence X ═ X from the annual daily precipitation sequence 1 ,X 2 ,...,X i ,...,X n Is given, wherein n is the sequence length, X i Represents the maximum rainfall in the ith year in the sequence, 0<i<N, and i ∈ N + ；
S2, extracting n-29 subsequences from the annual maximum value sequence by respectively adopting a 30-year window sliding method and a 30-year window increasing method, wherein the general formula of the set of the subsequences is S ═ S { (S) } 1 ,S 2 ,...,S j ,...,S n-29 In which S is j Denotes the jth group of subsequences, 0<j<N-29, and j ∈ N + ；
S3, adopting generalized extremum distribution to fit each subsequence of the set S, and calculating the subsequence S j Designing a rainstorm value in a given reproduction period, and further solving a designed rainstorm sequence;
s4, performing trend analysis on the designed rainstorm sequence obtained in the step S3 by using a linear regression method, and calculating the annual change trend of the designed rainstorm value;
s5, extracting the subsequence S based on the 30-year window sliding method and the 30-year window increasing method respectively j The annual variation trends of the design rainstorm values under the two extraction methods are obtained according to the annual variation trend of the design rainstorm values obtained in step S4, the two trends are subtracted, and the safety of the design rainstorm values calculated under the conditions of consistency assumption and non-consistency assumption is analyzed according to the trend difference.
Preferably, in step S2, for n-29 subsequences extracted by 30-year window sliding method, each subsequence has 30 consecutive years of data, and the subsequence S extracted by 30-year window sliding method j Can be expressed as: s j ＝{X j ,X j+1 ,...,X j+29 }，0<j<N-29 and j ∈ N + ；
For n-29 sub-sequences extracted by a 30-year window-growing method, the initial sequence is the same as the initial sequence extracted by a 30-year window-sliding method, and then each sub-sequence is gradually increased by one value, so that the sub-sequence S extracted by the 30-year window-growing method j Can be expressed as: s j ＝{X 1 ,X 2 ,...,X j+29 }，0<j<N-29 and j ∈ N + 。
As a preferable embodiment, in step S2, the assumed non-conformity and conformity conditions are simulated by using a 30-year window sliding method and a 30-year window increasing method.
As a preferred technical solution, in step S3, each subsequence of the generalized extremum distribution fitting set S is adopted, a maximum likelihood method is adopted to estimate parameters of the generalized extremum distribution, and then a design rainstorm value is calculated according to a given rainstorm recurrence period, wherein each subsequence obtains the design rainstorm value in the given recurrence period, and since the subsequences are extracted respectively based on a 30-year window sliding method and a 30-year window increasing method, two groups of design rainstorm sequences are obtained in each recurrence period, and each group of sequences contains n-29 design rainstorm values.
As a preferred technical solution, in step S3, the specific process is as follows:
the generalized extreme value distribution is based on an extreme value theory, has 3 parameters in total, and is used for quantitatively designing the intensity and the frequency of the rainstorm; the generalized extremum distribution function is as follows:
wherein the content of the first and second substances,
x represents time, and μ, σ and k represent a position parameter, a scale parameter and a shape parameter, respectively;
calculating by adopting a maximum likelihood estimation method to obtain 3 parameters of the generalized extreme value distribution function, and further finishing the quantification of designing the rainstorm according to the generalized extreme value distribution function; for each subsequence S j Given a design rainstorm in T years, the quantified design rainstorm value is:
for a given recurrence period, i.e., T years of design rainstorm, set S ═ S by subsequence 1 ,S 2 ,...,S j ,...,S n-29 And subsequence S j Calculating the design rainstorm value to obtain a design rainstorm value sequence:
wherein 0<j<N-29 and j ∈ N + 。
Preferably, the step S3 is based on the 30-year window sliding method and the 30-year windowSubsequence S extracted by mouth growth method j In contrast, the generalized extremum distribution is adopted for the subsequence S j When fitting is carried out, fitting parameters obtained by calculation through a maximum likelihood estimation method are different, and the quantized design rainstorm value y j T In contrast, two different design rainstorm values can be obtained for each given recurrence period T, and two different sets of design rainstorm sequences can be obtained.
As a preferable technical solution, in step S4, a linear regression equation is used to calculate the variation trend of the design rainstorm value, where:
wherein
And
respectively representing intercept and slope, x is time, y is precipitation, x i Which represents the time of the i-th year,
arithmetic mean, y, representing the year sequence i Indicates the precipitation amount of the i-th year,
denotes y i The arithmetic mean of (a); the annual variation trend of the design rainstorm values can be determined by designing the rainstorm sequence y T The following formula is used to obtain:
wherein
Is a sequence y T The jth group of (a) design storm values,
is a sequence y T Is calculated as the arithmetic mean of the average of the values,
and designing an annual trend value of the rainstorm for the first time of T years.
As a preferable technical solution, in step S4, when trend analysis is performed on the designed rainstorm sequence, F distribution is used to check the significance of the trend, and the confidence level is 0.05.
Preferably, in step S5, the subsequence S is extracted based on the 30-year window sliding method and the 30-year window growing method, respectively j By quantified design rainstorm values
And the annual change trend of the design storm value
Two trend values can be obtained and are respectively recorded as
The difference between the two is:
wherein the content of the first and second substances,
indicating a design rainstorm value trend value based on a 30-year window sliding method,
represents a design rainstorm annual trend value based on a 30-year window growth law,
representing the difference of the two trend values;
if it is
That is, the design rainstorm value calculated based on the non-consistency assumption is smaller than the design rainstorm value calculated based on the consistency assumption, which indicates that the design rainstorm value calculated by adopting the consistency assumption is safer for engineering construction in the long run; if it is
It indicates that in the long run, it is not advantageous to design a rainstorm method using the consensus hypothesis calculation.
Compared with the prior art, the invention has the following advantages and effects:
the invention provides a new analysis method for discussing the design rainstorm safety under the assumption of non-uniformity and consistency, and the 30-year window sliding method and the 30-year window increasing method are used for respectively simulating the non-uniformity and the consistency assumption to plan the rainstorm, thereby not only representing the annual change of the non-uniformity to the design rainstorm, but also considering the influence of the extension of a precipitation sequence to the consistency assumption to plan the rainstorm, overcoming the defect that the traditional engineering design ignores the non-uniformity of the precipitation sequence, and perfecting the defect that the influence of the increase of the precipitation sequence to the design rainstorm value in the existing research. By comparing the difference of the annual change trend of the design rainstorm under two assumptions, the method is beneficial to evaluating the change of the actual standard of related infrastructure along with the increase of the service life, and evaluating the influence (namely the safety) of the change on the normal operation of the infrastructure on the basis, so that the method can provide reference significance for hydraulic engineering construction, water resource and safety management, flood control and disaster reduction.
Drawings
FIG. 1 is a flow chart of a design storm safety analysis method based on assumed conditions of consistency and inconsistency according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting.
Examples
As shown in fig. 1, the method for analyzing the safety of design rainstorm based on assumed conditions of consistency and inconsistency comprises the following steps:
s1, extracting an annual maximum value sequence X ═ X from the annual daily precipitation sequence 1 ,X 2 ,...,X i ,...,X n Is given, wherein n is the sequence length, X i Represents the maximum rainfall in the ith year in the sequence, 0<i<N, and i ∈ N + ；
S2, adopting a 30-year window sliding method and a 30-year window increasing method to simulate assumed conditions of non-consistency and consistency, respectively adopting the 30-year window sliding method and the 30-year window increasing method to extract n-29 subsequences from the annual maximum value sequence, wherein the general set formula of the subsequences is S ═ { S { (S) } 1 ,S 2 ,...,S j ,...,S n-29 In which S is j Denotes the jth group of subsequences, 0<j<N-29, and j ∈ N + ；
For n-29 groups of subsequences extracted by a 30-year window sliding method, each subsequence has 30 continuous years of data, and the subsequence S extracted by the 30-year window sliding method j Can be expressed as: s j ＝{X j ,X j+1 ,...,X j+29 }，0<j<N-29 and j ∈ N + ；
For n-29 groups of subsequences extracted by the 30-year window increasing method, the initial sequence is the same as the initial sequence extracted by the 30-year window sliding method, and then each subsequence is increased by one value, so that the subsequence S extracted by the 30-year window increasing method j Can be expressed as: s j ＝{X 1 ,X 2 ,...,X j+29 }，0<j<N-29 and j ∈ N + 。
S3, adopting generalized extremum distribution to fit each subsequence of the set S, and calculating the subsequence S j Designing a rainstorm value in a given reappearance period, and further solving a designed rainstorm sequence; the specific process is as follows:
generalized extreme value distribution (GEV) is based on an extreme value theory, has 3 parameters in total, and is used for quantitatively designing the intensity and frequency of the rainstorm; the generalized extremum distribution function is as follows:
wherein the content of the first and second substances,
x represents time, and μ, σ and k represent a position parameter, a scale parameter and a shape parameter, respectively;
calculating by adopting a maximum likelihood estimation method to obtain 3 parameters of the generalized extreme value distribution function, and further finishing the quantification of the designed rainstorm according to the generalized extreme value distribution function; for each subsequence S j Given a design rainstorm in T years, the quantified design rainstorm value is:
for a given recurrence period, i.e., T years of design rainstorm, set S ═ S by subsequence 1 ,S 2 ,...,S j ,...,S n-29 And subsequence S j Calculating the design rainstorm value to obtain a design rainstorm value sequence:
wherein 0<j<N-29 and j ∈ N + 。
S4, performing trend calculation on the designed rainstorm sequence obtained in the step S3 by using a linear regression method to obtain the annual variation trend of the designed rainstorm value; the specific process is as follows:
calculating the change trend of the designed rainstorm value by adopting linear regression, wherein the linear regression equation is as follows:
wherein
And
respectively representing intercept and slope, x is time, y is precipitation, x i Which represents the time of the i-th year,
arithmetic mean, y, representing the year sequence i Indicates the precipitation amount of the i-th year,
denotes y i The arithmetic mean of (a); the annual variation trend of the design storm values can be determined by designing the storm sequence y T The following formula is used to obtain:
wherein
Is a sequence y T The jth group of (a) design storm values,
is a sequence y T Is calculated as the arithmetic mean of the average of the values,
designing an annual trend value of rainstorm for T year; trend significance was tested using an F-distribution (i.e., F-distribution, presented in 1924 by the statistician r.a. fisher), with a confidence level of 0.05.
S5, and subsequence S extracted respectively based on 30-year window sliding method and 30-year window growing method j Obtaining the annual variation trend of the designed rainstorm value under two extraction methods according to the annual variation trend of the designed rainstorm value obtained in S4, making a difference between the two trends, and analyzing the safety of the designed rainstorm value calculated under the conditions of consistency assumption and non-consistency assumption according to the trend difference; the specific process is as follows:
subsequence S respectively extracted based on 30-year window sliding method and 30-year window growing method j Design of rainstorm values by quantification
And annual variation trend of design storm values
Two trend values can be obtained and are respectively recorded as
The difference between the two is:
wherein the content of the first and second substances,
represents a design rainstorm annual trend value based on a 30-year window sliding method,
represents a design rainstorm annual trend value based on a 30-year window growth law,
representing the difference of the two trend values;
if it is
That is, the design rainstorm value calculated based on the non-consistency assumption is smaller than the design rainstorm value calculated based on the consistency assumption, which indicates that the design rainstorm value calculated by adopting the consistency assumption is safer for engineering construction in the long run; if it is
It indicates that in the long run, it may be disadvantageous to design a rainstorm method using the consensus hypothesis calculation.
The following is a specific application example of the method of the present invention:
based on the 1961-2013-year Chinese grid daily rainfall data set, a 30-year window sliding method and a 30-year window increasing method are adopted to simulate the assumption of non-consistency and consistency, the historical evolution trend of designing rainstorm of 3825 grid points is discussed, and the difference of calculation results of the two methods in China is explored.
The specific calculation steps are as follows:
(1) extracting a annual maximum daily precipitation sequence (total 53 years from 1961 to 2013) from daily precipitation data of 3825 grid points;
(2) respectively extracting 24 subsequences from the annual maximum value sequence by adopting a 30-year window sliding method and a 30-year window growing method;
(3) and fitting each subsequence by adopting GEV distribution, estimating GEV parameters by adopting a maximum likelihood method, calculating design rainstorm values by taking 20-year-one-chance, 50-year-one-chance and 100-year-one-chance in the recurrence period as examples, and obtaining 3 design rainstorms in the recurrence period for each subsequence. Thus, based on the 30-year window sliding method and the 30-year window growing method, two sets of designed rainstorm sequences were obtained for each recurrence period, each set of sequences containing 24 values.
(4) Based on design violenceAnd 4, calculating a designed rainstorm change trend by adopting a linear regression equation in the rain value sequence. The spatial distribution of 3825 grid point trends in the country is the annual change trend values of 20-year-first, 50-year-first and 100-year-first obtained by adopting a 30-year window sliding method
A value; adopting 30-year window increasing method to obtain annual change trend values of 20-year-one, 50-year-one and 100-year-one
A value; grid points that failed the significance test (significance of 0.05) are represented by black scatter dots, and trend values (units: mm/yr, i.e., mm/year) are represented by slope.
(5) And (5) calculating the difference of the two change trends according to the formula (5), and analyzing the safety of the two methods for hydraulic engineering design.
Utilizing the difference of annual variation trend of 20-year-one, 50-year-one and 100-year-one
And the calculation result shows that the difference of the rainstorm trend has obvious spatial difference. In general, most grid point trend differences in northeast, south and northwest China
The trend calculated by the 30-year window sliding method is greater than that calculated by the 30-year window increasing method, which indicates that the designed rainstorm value calculated by the non-uniformity assumption is higher than that calculated by the uniformity scenario, and the traditional calculation method is not beneficial to large-scale hydraulic engineering design; trend difference of most grid points in northern and southwest China
Namely, the trend calculated by the 30-year window sliding method is smaller than that calculated by the 30-year window increasing method, which shows that the designed rainstorm value calculated by the non-uniformity assumption is lower than that calculated by the uniformity situation, and the traditional calculation method is safer for hydraulic engineering design.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is specific and detailed, but not to be understood as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the claims.
Claims (7)
1. The method for analyzing the safety of the design rainstorm based on the assumed conditions of consistency and non-consistency is characterized by comprising the following steps of:
s1, extracting an annual maximum value sequence X ═ X from the annual daily precipitation sequence 1 ,X 2 ,...,X i ,...,X n Where n is the sequence length, X i Represents the maximum rainfall of the ith year in the sequence, 0 < i < N, and i belongs to N + ；
S2, extracting n-29 subsequences from the annual maximum value sequence by respectively adopting a 30-year window sliding method and a 30-year window increasing method, wherein the general formula of the set of the subsequences is S ═ S 1 ,S 2 ,...,S j ,...,S n-29 In which S is j Represents the jth group of subsequences, 0 < j < N-29, and j ∈ N + ；
S3, adopting generalized extremum distribution to fit each subsequence of the set S, and calculating the subsequence S j Designing a rainstorm value in a given reappearance period, and further solving a designed rainstorm sequence;
s4, performing trend analysis on the designed rainstorm sequence obtained in the step S3 by using a linear regression method, and calculating the annual change trend of the designed rainstorm value;
s5, extracting the subsequence S based on the 30-year window sliding method and the 30-year window growing method respectively j Obtaining the annual variation trend of the designed rainstorm value under two extraction methods according to the annual variation trend of the designed rainstorm value obtained in S4, subtracting the two trends, and analyzing the safety of the designed rainstorm value calculated under the conditions of consistency assumption and non-consistency assumption according to the trend difference;
in step S2, for n-29 sub-sequences extracted by 30-year window sliding method, each sub-sequence has 30 continuous years of data, and the 30-year window sliding method extracts the sub-sequence S j Can be expressed as: s j ＝{X j ,X j+1 ,...,X j+29 0 < j < N-29 and j is equal to N + ；
For n-29 groups of subsequences extracted by the 30-year window increasing method, the initial sequence is the same as the initial sequence extracted by the 30-year window sliding method, and then each subsequence is increased by one value, so that the subsequence S extracted by the 30-year window increasing method j Can be expressed as: s j ＝{X 1 ,X 2 ,...,X j+29 0 < j < N-29 and j is equal to N + ；
In step S5, subsequences S extracted based on 30-year window sliding method and 30-year window growing method respectively j Design of rainstorm values by quantification
And annual variation trend of design storm values
Two trend values can be obtained and are respectively recorded as
The difference between the two is:
wherein the content of the first and second substances,
represents a design rainstorm value trend value based on a 30-year window sliding method,
represents a design rainstorm annual trend value based on a 30-year window growth law,
representing the difference of the two trend values;
if it is
That is, the design rainstorm value calculated based on the non-consistency assumption is smaller than the design rainstorm value calculated based on the consistency assumption, which indicates that the design rainstorm value calculated by adopting the consistency assumption is safer for engineering construction in the long run; if it is
It is shown that designing a rainstorm method using the consistency assumption calculation is disadvantageous in the long run.
2. The method for analyzing the safety of design rainstorm based on the assumed conditions of consistency and non-consistency as claimed in claim 1, wherein in step S2, the assumed conditions of non-consistency and consistency are simulated by using a 30-year window sliding method and a 30-year window increasing method.
3. The method for analyzing the safety of design rainstorm based on assumed conditions of consistency and non-consistency according to claim 1, wherein in step S3, each subsequence of the set S is fitted with the generalized extremum distribution, and parameters of the generalized extremum distribution are estimated by using a maximum likelihood method, and then the design rainstorm value is calculated for a given rainstorm recurrence period, wherein each subsequence obtains the design rainstorm value for the given recurrence period, and two sets of design rainstorm sequences are obtained for each recurrence period, each set containing n to 29 design rainstorm values, because the subsequences are extracted based on a 30-year window sliding method and a 30-year window growing method, respectively.
4. The method for analyzing the safety of the design rainstorm based on the assumed conditions of consistency and inconsistency according to claim 3, wherein the specific process in step S3 is as follows:
the generalized extreme value distribution is based on an extreme value theory, has 3 parameters in total, and is used for quantitatively designing the intensity and the frequency of the rainstorm; the generalized extremum distribution function is as follows:
wherein the content of the first and second substances,
x represents time, and mu, sigma and k represent a position parameter, a scale parameter and a shape parameter respectively;
calculating by adopting a maximum likelihood estimation method to obtain 3 parameters of the generalized extreme value distribution function, and further finishing the quantification of the designed rainstorm according to the generalized extreme value distribution function; for each subsequence S j Given a design rainstorm in T years, the quantified design rainstorm value is:
for a given recurrence period, i.e., T years of design rainstorm, set S ═ S by subsequence 1 ,S 2 ,...,S j ,...,S n-29 And subsequence S j Calculating the design rainstorm value to obtain a design rainstorm value sequence:
wherein j is more than 0 and less than N-29 and j is equal to N + 。
5. The method for analyzing the safety of design rainstorm based on the assumption of consistency and non-consistency as claimed in claim 3, wherein in step S3, the subsequence S extracted based on the 30-year window sliding method and the 30-year window growing method is used as a result of the extraction j In contrast, the subsequence S is given a generalized extremum distribution j When fitting is carried out, fitting parameters obtained by calculation by adopting a maximum likelihood estimation method are notIn the same way, the design rainstorm value of the quantification
Differently, two different design rainstorm values can be obtained for each given recurrence period T, and thus two different sets of design rainstorm sequences can be obtained.
6. The method for analyzing the safety of the design storm according to the claim 1, wherein in the step S4, the change trend of the design storm value is calculated by using the linear regression equation:
wherein
And
respectively representing intercept and slope, x is time, y is precipitation, x i Which represents the time of the i-th year,
arithmetic mean, y, representing the year sequence i Indicates the precipitation amount of the i-th year,
denotes y i The arithmetic mean of (a); the annual variation trend of the design storm values can be determined by designing the storm sequence y T The following formula is used to obtain:
wherein
Is a sequence y T The jth group of (a) design storm values,
is a sequence y T Is calculated as the arithmetic mean of the average of the values,
and designing an annual trend value of the rainstorm for the first time of T years.
7. The method for analyzing the safety of the design rainstorm based on the assumed conditions of consistency and non-consistency of the design rainstorm according to claim 6, wherein in the step S4, when the trend analysis is carried out on the design rainstorm sequence, the F distribution is adopted to check the significance of the trend, and the confidence level is 0.05.
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