CN117522012A - Runoff scene generation method based on seasonal period characteristics - Google Patents
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Abstract
A runoff scene generation method based on seasonal characteristics comprises the following steps: step 1, obtaining N k Runoff time sequence data of each season of the year divided into T time periodsStep 2, obtaining the cumulative distribution function cdf of each season j The method comprises the steps of carrying out a first treatment on the surface of the Step 3, expanding the original runoff time sequence data interval to be an extreme interval; step 4, the original runoff time sequence data is processedMapping to extreme intervals to obtainStep 5, obtaining the cumulative distribution function cdf of each period of each season j,t The method comprises the steps of carrying out a first treatment on the surface of the Step 6, selecting LHS sampling times N; step 7, LHS sampling inverse transformation; step 8, quantifying the fluctuation amplitude sigma of each season of the original data j The method comprises the steps of carrying out a first treatment on the surface of the And 9, recombining the sampled data to obtain a random simulation result. The time sequence scene generated by the method is more similar to the original scene in terms of upper and lower limit intervals and scene fluctuation amplitude, can improve the simulation effect of scene simulation and the rationality of further scene extraction, and has important popularization and use values for the method research of formulating the optimal operation strategy of the reservoir or new energy.
Description
Technical Field
The invention relates to the technical field of scene generation, in particular to a runoff scene generation method based on seasonal characteristics.
Background
Scene analysis is needed in the fields of reservoir dispatching optimization operation, grid dispatching system optimization operation and the like, and the optimization typical scene generation technology has important popularization and use values for method research for making the system optimal operation strategy. At present, methods such as Monte Carlo (Monte Carlo simulation) and Latin hypercube (Latin hypercube sampling, LHS) are widely applied in scene generation technology, and compared with random sampling in a conventional Monte Carlo method, LHS sampling is more robust, sampling space covered by the LHS is wider and calculation efficiency is higher under the same sampling scale. However, the LHS sampling method has higher correlation among random variables, and the current methods for data recombination include genetic algorithm, column pair algorithm, gram-Schmidt orthogonalization method, cholesky decomposition method and the like. The method only ranks the data internally aiming at the correlation among the reduced sampling matrixes, and does not consider the time sequence process and fluctuation condition of the original scene.
Therefore, it is necessary to design a runoff scene generating method based on seasonal characteristics to overcome the above-mentioned problems.
Disclosure of Invention
In order to avoid the problems, the runoff scene generation method based on seasonal characteristics is provided, the generated time sequence scene is more similar to an original scene from the upper limit interval, the lower limit interval and the scene fluctuation range, the simulation effect of scene simulation and the rationality of further scene extraction can be improved, and the method has important popularization and use values for the method research of formulating the optimal operation strategy of the reservoir or new energy.
The invention provides a runoff scene generation method based on seasonal characteristics, which comprises the following steps:
step 1, obtaining N k Runoff time sequence data of each season of the year divided into T time periodsJ=1, 2,3,4, which is a season identification, and corresponds to spring, summer, autumn and winter; k=1, 2, [ N ] N k ，N k Is the total number of scenes; t=1, 2, the terms T and T, T is the total time period number;
step 2, for the runoff time sequence dataPerforming distribution fitting to obtain a cumulative distribution function cdf of each season j ；
Step 3, setting a percentile point alpha in each season, and calculating the runoff quantity corresponding to the upper alpha component point and the lower alpha component point by adopting a reverse operation (inverse cumulative distribution function, ICDF) methodAnd will->As a runoff extreme section;
step 4, the original runoff time sequence data is processedMapping to extreme interval, the formula isWherein (1)>Is the time sequence data of the original runoff,the maximum value and the minimum value of the original runoff data; obtaining mapping result, which is new runoff time sequence data
Step 5, for new runoff time sequence dataPerforming distribution fitting to obtain cumulative distribution function cdf of each period of each season j,t ；
Step 6, selecting proper LHS sampling times N, and accumulating a distribution function cdf of each period of each season j,t At [0,1]Equally dividing the probability interval into N sub-intervals, and recording the midpoint of each probability sub-interval as the probability value for inverse transformation sampling(n＝1,2,···,N)；
Step 7, cumulative distribution function cdf of each period of each season j,t At the position ofPerforming LHS sampling inverse operation to obtain sampling result, which is marked as +.> Obtaining LHS sampling result matrix x of NxT j ；
Step 8, quantifying the fluctuation amplitude sigma of each season of the original data j ；
Step 9, according to the fluctuation range sigma of each season j Sampling the LHS result matrix x j And carrying out random transformation data recombination to obtain a random simulation result reflecting the fluctuation characteristics of the original data.
Preferably, the method for performing the distribution fitting in the step 2 and the step 5 is a kernel density estimation method, a Weibull distribution or a Normal distribution, and when the actual distribution fitting is performed, a hypothesis test method (chi-square test, KS test) is used to compare the fitting effect of the kernel density estimation method (kernel density estimation) and a parameter estimation method (for example, weibull distribution and Normal distribution) on the raw data of runoffs in each season, and a better fitting method is selected.
Preferably, the value interval of the percentile alpha in the step 3 is [95%, 100%).
Preferably, mapping is performed in a normalized manner in step 4.
Preferably, the amplitude sigma of the seasonal fluctuations of the raw data is quantized in step 8 j The method of (1) is as follows: firstly, the original runoff time sequence data is mappedMapping to LHS sample times [1, N ]]Within the interval, get->For mapping result, the formula is +.>Then, calculate the fluctuation of time period before and after each season +.>The formula isAnd calculates the fluctuation of the time period before and after each season +.>Standard deviation sigma of j The fluctuation range of each season is obtained.
Preferably, step 9 comprises the following sub-steps:
9.1 generating compliance mean value 0 and standard deviation sigma for different seasons j Normal random number matrix m of (2) j Matrix m j Is N× (T-1), where m j All the data in (a) are rounded up,
9.2sampling LHS result matrix x j And carrying out random exchange on each row in the row to obtain a random simulation result reflecting the fluctuation characteristic of the original data, wherein the formula is expressed as follows:
wherein,sampling the result matrix x for LHS j Inner nth row and nth column sample data; />For m under j seasons j Random numbers of nth row and nth column in matrix, ">The size change of the number of lines n is limited to the interval [1, N ]]An inner part; />And (5) simulating the extreme runoff scene in the j seasons.
Compared with the prior art, the invention has the following beneficial effects: the method is mainly applied to rationally describing possible uncertainty by using time sequence runoff data or other data with seasonal characteristics, and a scene generation method based on Latin hypercube (Latin hypercube sampling, LHS) probability distribution inverse transformation of seasonal division is adopted for time sequence data to generate a time sequence scene under extreme conditions. And obtaining a cumulative distribution function by adopting two different methods of parameter estimation, hypothesis test and non-parameter estimation (nuclear density estimation), and generating a time sequence scene by an inverse transformation method. The innovation provides that the fluctuation quantitative evaluation is carried out on different seasonal time sequence scenes and the method is used for simulating seasonal fluctuation characteristics during data recombination. The scene generation method for simulating the seasonal fluctuation characteristics can enable the generated time sequence scene to be more similar to the original scene from the upper limit interval, the lower limit interval and the scene fluctuation range, and can improve the simulation effect of scene simulation and the rationality of further scene extraction. Has important popularization and use values for the research of the method for making the optimal operation strategy of the reservoir or the new energy.
Drawings
FIG. 1 is a flow chart of a method for generating a runoff scenario based on seasonal characteristics according to a preferred embodiment of the present invention;
FIG. 2 is a diagram of historical runoff timing data according to a preferred embodiment of the present invention;
FIG. 3 is a graph showing the fitting result of the historical runoff amount distribution in each season according to a preferred embodiment of the present invention;
FIG. 4 is a diagram illustrating the result of the historical traffic map according to a preferred embodiment of the present invention;
FIG. 5 is a schematic diagram of the inverse LHS sample transform result in accordance with a preferred embodiment of the present invention;
FIG. 6 is a schematic diagram of a wave random simulation process according to a preferred embodiment of the present invention;
FIG. 7 is a schematic diagram of the result of random simulation of a runoff extreme scene according to a preferred embodiment of the present invention.
Detailed Description
As shown in fig. 1, the runoff scene generating method based on seasonal characteristics provided in this embodiment includes the following steps:
step 1, obtaining N k Runoff time sequence data of each season of the year divided into T time periodsJ=1, 2,3,4, which is a season identification, and corresponds to spring, summer, autumn and winter; k=1, 2, [ N ] N k ，N k Is the total number of scenes; t=1, 2, the terms T and T, T is the total time period number;
step 2, for the runoff time sequence dataPerforming distribution fitting to obtain a cumulative distribution function cdf of each season j ；
Step 3, setting a percentile point alpha in each season, and calculating the runoff quantity corresponding to the upper alpha component point and the lower alpha component point by adopting a reverse operation (inverse cumulative distribution function, ICDF) methodAnd will->As a runoff extreme section;
step 4, the original runoff time sequence data is processedNormalized mapping to extreme intervals, the formula isWherein (1)>Is the time sequence data of the original runoff,the maximum value and the minimum value of the original runoff data; obtaining mapping result, which is new runoff time sequence data
Step 5, for new runoff time sequence dataPerforming distribution fitting to obtain cumulative distribution function cdf of each period of each season j,t ；
Step 6, selecting proper LHS sampling times N, and accumulating a distribution function cdf of each period of each season j,t At [0,1]Equally dividing the probability interval into N sub-intervals, and recording the midpoint of each probability sub-interval as the probability value for inverse transformation sampling(n＝1,2,···,N)；
Step 7, cumulative distribution function cdf of each period of each season j,t At the position ofPerforming LHS sampling inverse operation to obtain sampling result, which is marked as +.> Obtaining LHS sampling result matrix x of NxT j ；
Step 8, quantifying the fluctuation amplitude sigma of each season of the original data j The method comprises the steps of carrying out a first treatment on the surface of the Firstly, the original runoff time sequence data is mappedMapping to LHS sample times [1, N ]]Within the interval, get->For the mapping result, the formula isThen, calculate the fluctuation of time period before and after each season +.>The formula isAnd calculates the fluctuation of the time period before and after each season +.>Standard deviation sigma of j The fluctuation range of each season is obtained;
step 9, according to the fluctuation range sigma of each season j Sampling the LHS result matrix x j Carrying out random transformation data recombination to obtain a random simulation result reflecting the fluctuation characteristics of the original data; comprises the following stepsThe sub-steps are as follows:
9.1 generating compliance mean value 0 and standard deviation sigma for different seasons j Normal random number matrix m of (2) j Matrix m j Is N× (T-1), where m j All data in (2) are rounded;
9.2 sampling result matrix x for LHS j And carrying out random exchange on each row in the row to obtain a random simulation result reflecting the fluctuation characteristic of the original data, wherein the formula is expressed as follows:
wherein,sampling the result matrix x for LHS j Inner nth row and nth column sample data; />For m under j seasons j Random numbers of nth row and nth column in matrix, ">The size change of the number of lines n is limited to the interval [1, N ]]An inner part; />And (5) simulating the extreme runoff scene in the j seasons.
Preferably, the method for performing the distribution fitting in the step 2 and the step 5 is a kernel density estimation method, a Weibull distribution or a Normal distribution, and when the actual distribution fitting is performed, a hypothesis test method (chi-square test, KS test) is used to compare the fitting effect of the kernel density estimation method (kernel density estimation) and a parameter estimation method (for example, weibull distribution and Normal distribution) on the raw data of runoffs in each season, and a better fitting method is selected.
The runoff scene based on seasonal period characteristics is generated by using the time sequence data of a certain hydrologic station and a certain 20-year runoff amount ten-day scale, and the method comprises the following steps:
step 1, season division. In the present exampleUsing time sequence data of a certain hydrologic station in a certain 20-year runoff amount in ten-day scale, dividing the original data according to time stamps corresponding to seasons to obtain a value of a kth scene in a jth season at a t moment, and marking the value as(j=1, 2,3,4, season identification, spring, summer, autumn, winter; k=1, 2, & N k The method comprises the steps of carrying out a first treatment on the surface of the t=1, 2, T; (wherein T and N k Respectively representing the number of time periods and the number of scenes, in this example Tfetch 9,N k 20, i.e. 20 pieces of runoff time sequence scene of 9 ten days in each season). The historical runoff data are shown in the following table 1, the flow units (m/s), and the historical runoff time sequence diagram is shown in fig. 1.
Table 1 20 year runoff ten-day scale timing data
And 2, comparing the fitting method. Performing distribution fitting on historical runoff data by using Kernel density estimation (Kernel) method, weibull distribution and Normal distribution, wherein the function expression of Kernel density estimation is as follows Representing an estimate of the cumulative distribution function F (x)And h represents window width, n represents sample capacity, and K (·) represents kernel function. There are many kinds of kernel functions, which in this example select Gaussian kernel with the expression +.>The fitting results are shown in fig. 3. Chi-square statistics are core indicators of chi-square tests, and the smaller the chi-square statistics are, the smaller the deviation between sample data and theoretical distribution is. The chi-square statistic result pair is shown in table 2.
TABLE 2 chi-square statistics comparison
As can be seen from the chi-square statistic comparison, the fitting effect of using the kernel density estimation method in this example is better than the Weibull distribution and the Normal distribution, so the kernel density estimation method is selected as the preferred fitting method.
Step 3, acquiring a cumulative distribution function cdf of each season j Carrying out distribution fitting on the raw runoff data of each season by using a Kernel fitting method to obtain a cumulative distribution function cdf of each season j The results are shown in Table 3.
TABLE 3 estimation of core Density to obtain the cumulative distribution function estimate cdf for each season j
And 4, expanding an original data interval. Based on the obtained cumulative distribution function cdf j In this embodiment, the dividing point α=99.9% is selected, and the new upper and lower limit data of each season is calculated by performing the inverse operation (ICDF), and recorded asWherein (1)>Corresponding to the lower alpha positionThe point diameter flow; />Corresponds to the alpha split site diameter flow rate and willThe extreme interval is marked; extreme runoff interval +.>Interval with original runoffIs shown in table 4.
TABLE 4 comparison of extreme runoff intervals with original runoff intervals
By comparing extreme runoff intervalsInterval with original runoffIt is understood that, in the present embodiment, when the quantile α=99.9% is selected, the runoff data interval is enlarged by about 18% on average in each season after the original data interval enlarging method is used.
And 5, mapping the original runoff data to an extreme interval. Expanding the original runoff data interval to an extreme interval in a mapping mode by a normalization mapping mode, wherein the formula is that Wherein (1)>For the original runoff time sequence data, < > a->The maximum value and the minimum value of the original runoff data; obtaining mapping result, which is new radial flow time sequence data-> The schematic diagram is shown in fig. 4.
Step 6, obtaining the cumulative distribution function cdf of each period j,t Radial flow data mapped to extreme intervals using a nuclear density estimation methodCarrying out distribution fitting on the data of each period of each season to obtain a cumulative distribution function cdf of each period of each season j,t 。
And 7, determining the LHS sampling times N. In this embodiment, the sampling number n=100 is selected, and then each period of each season will accumulate [0,1 ] of the distribution function according to the LHS sampling number N]The probability interval is divided into 100 sub-intervals, and the midpoint of each probability sub-interval is recorded as the probability value for inverse transformation sampling(n＝1,2,···,N)。
Step 8, inverse LHS sampling transformation. The cumulative distribution function of each period of each season is respectively in the probability valuePerforming inverse operation to obtain sampling result, which is marked as +.> Obtaining LHS sampling result matrix x of NxT j The method comprises the steps of carrying out a first treatment on the surface of the The sampling result is shown in fig. 5.
Step 9, quantifying the fluctuation amplitude sigma of each season of the original data j . First, original data is mapped to LHS sampling times [1, N ] by means of normalized mapping]Within the interval, the formula isWherein->Is normalized result. Calculating fluctuation of time period before and after each season>As the calculation basis of the amplitude of the analog data fluctuation, the formula is that Then calculate every season +.>Standard deviation sigma of j And as the magnitude of its fluctuation; every season in this embodiment +.>Standard deviation sigma of j The calculation results are shown in Table 5.
TABLE 5 seasons of the yearStandard deviation sigma of j
Step 10, reorganizing the sampled data. According to the quantized fluctuation amplitude result sigma of each season j Generating a compliance mean value of 0 and a standard deviation of sigma for different seasons j Normal random number matrix m of (2) j Matrix m j Is N× (T-1), m j All data in (1) are rounded and then the result matrix x is sampled by LHS j (matrix x j Is of a rank size of N x T) to obtain a random simulation result reflecting the fluctuation characteristics of the original data by performing random exchange of each row in the rank, the formula can be expressed as,wherein (1)>Sampling the result matrix x for LHS j Inner nth row and nth column sample data; />For m under the season j Random numbers of nth row and nth column in matrix, ">The size change of the number of lines n is limited to the interval [1, N ]]An inner part; />And (5) simulating the extreme runoff scene in the j seasons. The wave random simulation process is shown in fig. 6, the extreme runoff scene simulation result is shown in fig. 7, and the whole flow of the embodiment of the invention is shown in fig. 1.
The method is mainly applied to rationally describing possible uncertainty by using time sequence runoff data or other data with seasonal characteristics, and a scene generation method based on Latin hypercube (Latin hypercube sampling, LHS) probability distribution inverse transformation of seasonal division is adopted for time sequence data to generate a time sequence scene under extreme or non-extreme conditions. And obtaining a cumulative distribution function by adopting two different methods of parameter estimation, hypothesis test and non-parameter estimation (nuclear density estimation), and generating a time sequence scene by an inverse transformation method. The innovation provides that the fluctuation quantitative evaluation is carried out on different seasonal time sequence scenes and the method is used for simulating seasonal fluctuation characteristics during data recombination. The scene generation method for simulating the seasonal fluctuation characteristics can enable the generated time sequence scene to be more similar to the original scene from the upper limit interval, the lower limit interval and the scene fluctuation range, and can improve the simulation effect of scene simulation and the rationality of further scene extraction. Has important popularization and use values for the research of the method for making the optimal operation strategy of the reservoir or the new energy.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (6)
1. The runoff scene generation method based on the seasonal period characteristics is characterized by comprising the following steps of:
step 1, obtaining N k Runoff time sequence data of each season of the year divided into T time periodsJ=1, 2,3,4, which is a season identification, and corresponds to spring, summer, autumn and winter; k=1, 2, [ N ] N k ，N k Is the total number of scenes; t=1, 2, the terms T and T, T is the total time period number;
step 2, for the runoff time sequence dataPerforming distribution fitting to obtain a cumulative distribution function cdf of each season j ；
Step 3, setting a percentile alpha in each season,calculating the runoff corresponding to the upper alpha split point and the lower alpha split point by adopting an inverse operation methodAnd will->As a runoff extreme section;
step 4, the original runoff time sequence data is processedMapping to the extreme interval to obtain new runoff time sequence data
Step 5, for new runoff time sequence dataPerforming distribution fitting to obtain cumulative distribution function cdf of each period of each season j,t ；
Step 6, selecting proper LHS sampling times N, and accumulating a distribution function cdf of each period of each season j,t At [0,1]Equally dividing the probability interval into N sub-intervals, and recording the midpoint of each probability sub-interval as the probability value for inverse transformation sampling
Step 7, cumulative distribution function cdf of each period of each season j,t At the position ofPerforming LHS sampling inverse operation to obtain sampling result, which is marked as +.>Obtaining LHS sampling result matrix x of NxT j ；
Step 8, quantifying the fluctuation amplitude sigma of each season of the original data j ；
Step 9, according to the fluctuation range sigma of each season j Sampling the LHS result matrix x j And carrying out random transformation data recombination to obtain a random simulation result reflecting the fluctuation characteristics of the original data.
2. A runoff scene generating method based on seasonal characteristics as defined in claim 1, wherein: the method for performing distribution fitting in the step 2 and the step 5 is a nuclear density estimation method, a Weibull distribution or a Normal distribution.
3. A runoff scene generating method based on seasonal characteristics as defined in claim 1, wherein: and 3, the value interval of the percentile alpha in the step 3 is [95%, 100%).
4. A runoff scene generating method based on seasonal characteristics as defined in claim 1, wherein: and 4, mapping in a normalization mode.
5. A runoff scene generating method based on seasonal characteristics as defined in claim 1, wherein: step 8, quantifying the fluctuation amplitude sigma of each season of the original data j The method of (1) is as follows: firstly, the original runoff time sequence data is mappedMapping to LHS sample times [1, N ]]Within the interval, get->Then, calculate the fluctuation of time period before and after each season +.>The formula is->And calculates the fluctuation of the time period before and after each season +.>Standard deviation sigma of j The fluctuation range of each season is obtained.
6. A runoff scene generating method based on seasonal characteristics as defined in claim 1, wherein: step 9 comprises the following sub-steps:
9.1 generating compliance mean value 0 and standard deviation sigma for different seasons j Normal random number matrix m of (2) j Matrix m j Is N× (T-1), where m j All data in (2) are rounded;
9.2 sampling result matrix x for LHS j And carrying out random exchange on each row in the row to obtain a random simulation result reflecting the fluctuation characteristic of the original data, wherein the formula is expressed as follows:
wherein,sampling the result matrix x for LHS j Inner nth row and nth column sample data; />For m under j seasons j Random numbers of nth row and nth column in matrix, ">The size change of the number of lines n is limited to the interval [1, N ]]An inner part; />And (5) simulating the extreme runoff scene in the j seasons.
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