CN114841475A - Water resource optimization allocation method based on two-dimensional variable random simulation - Google Patents

Water resource optimization allocation method based on two-dimensional variable random simulation Download PDF

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CN114841475A
CN114841475A CN202210768736.8A CN202210768736A CN114841475A CN 114841475 A CN114841475 A CN 114841475A CN 202210768736 A CN202210768736 A CN 202210768736A CN 114841475 A CN114841475 A CN 114841475A
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water
distribution
value
sequence
user
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陈述
李清清
雷彩秀
鄢波
刘建峰
喻志强
宋雅静
董玲燕
余姚果
宋基权
何飞飞
冯宇
李匆
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Changjiang River Scientific Research Institute Changjiang Water Resources Commission
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Abstract

The application relates to a water resource optimal allocation method based on two-dimensional variable random simulation, which comprises the following specific steps of: determining two main hydrological random variables in a water resource optimization allocation problem; adopting a Copula function to construct an edge distribution function and a joint distribution function of two variable actual measurement sequences; adopting a Monte Carlo two-dimensional random simulation method, and obtaining the length of the parameter value closest to the actually measured sequence through the evaluation and optimization of the simulation sequenceNThe two-dimensional variable of (a) is modeled as a sequence,
Figure DEST_PATH_IMAGE001
(ii) a Constructing a proper water quantity pre-distribution model, and solving through an artificial intelligence algorithmSolving to obtain water resource allocation results of each water user under each two-dimensional variable analog value; for each water userNAnd carrying out statistical analysis on the distribution results, selecting the result with the largest value probability as the optimal water resource distribution target of the water user, and combining to obtain an optimal water resource distribution scheme. The invention provides a solution for the problem of optimal allocation of regional water resources under the condition of bivariate joint randomness.

Description

Water resource optimization allocation method based on two-dimensional variable random simulation
Technical Field
The application relates to the field of efficient utilization of water resources, in particular to a water resource optimization allocation method based on two-dimensional variable random simulation.
Background
Although the total amount of water resources in China is rich and ranked sixth globally, the average occupied amount of water resources is small, which is only about 25% of the average water resource level in the world, and the method is one of countries with water shortage in the world. In addition, the problems of low water resource utilization rate, uneven water resource amount space-time distribution, serious water pollution, climate change and the like aggravate the water resource shortage problem of China. In order to solve the contradiction between water resource supply and demand and fully and effectively utilize limited water resources, the development of water resource optimization configuration is one of effective ways. The water resource optimal allocation means that in a specific basin or region, the water resources and related resources are uniformly allocated through engineering and non-engineering measures by taking a sustainable development strategy as guidance and utilizing a system analysis theory and an optimization technology, and scientific and reasonable allocation is performed on time, space and different beneficiaries.
However, there is a great deal of uncertainty in the water resource system, and the optimal allocation scheme of water resources by using the deterministic method may cause a great risk. Therefore, scholars at home and abroad widely adopt stochastic programming methods such as two-stage stochastic programming, multi-stage stochastic programming, opportunity constraint programming and related opportunity programming to solve the problem of stochastic uncertainty in the water resource allocation problem. However, the conventional stochastic programming method can only deal with the problem of two or more independent stochastic variables, and is difficult to adapt to the uncertain problem of two stochastic variables with correlation. In addition, in most stochastic programming models, the continuous random variable is generally reduced to several discrete intervals, resulting in partial information loss of the random variable.
Disclosure of Invention
The embodiment of the application aims to provide a water resource optimal allocation method based on two-dimensional variable random simulation, a pre-allocation water quantity model is constructed, and a solution is provided for the problem of regional water resource optimal allocation under bivariate joint randomness.
In order to achieve the above purpose, the present application provides the following technical solutions:
the embodiment of the application provides a water resource optimal allocation method based on two-dimensional variable random simulation, which comprises the following specific steps:
step 1, analyzing a water resource optimization allocation problem to be solved, and finding out two most main hydrological random variables in the problem;
step 2, constructing the joint distribution of the two hydrological variables by adopting a Copula function and combining the long sequence measured values of the hydrological variables;
step 3, adopting a Monte Carlo two-dimensional random simulation method, and evaluating and optimizing through a simulation sequence to obtain a parameter value which is closest to the actually measured sequenceHas a length ofNOf a two-dimensional variable simulation sequence, wherein
Figure 856012DEST_PATH_IMAGE001
；
Step 4, constructing a proper water resource pre-distribution model, and solving through an artificial intelligence algorithm to obtain water resource distribution results of each water user under each two-dimensional variable analog value;
step 5, for each water userNAnd (4) performing statistical analysis on the distribution results, selecting the result with the maximum value probability as the optimal water resource distribution target of the water user, and combining to obtain an optimal water resource distribution scheme.
In the step 2, the joint distribution of the two hydrological variables is constructed by the following steps,
fitting two measured sequences of hydrologic variables by using 8 distribution functions including Gamma, Gumbel, Logistic, Weibull, Box-Cox Cole and Green, Peason III, Generalized Gamma and Generalized Inverse Gaussian, and determining the edge distribution function of each measured sequence of the variables
Figure 983368DEST_PATH_IMAGE002
And
Figure 24136DEST_PATH_IMAGE003
and obtaining a distribution function
Figure 527930DEST_PATH_IMAGE004
And
Figure 501702DEST_PATH_IMAGE005
respectively is
Figure 331118DEST_PATH_IMAGE006
And
Figure 328024DEST_PATH_IMAGE007
；
② 4 single-parameter two-dimensional Archimedes Copula functions of Gumbel-Hougaard Copula, Clayton Copula, Ali-Mikhail-Haq Copula and Frank Copula are adopted, and parameter estimation and simulation are carried outDetermining optimized Copula function type and parameters by effect combination inspection and goodness-of-fit evaluation to obtain a combined distribution function of two measured hydrologic variable sequences
Figure 838771DEST_PATH_IMAGE008
And joint distribution function parameter values
Figure 932629DEST_PATH_IMAGE009
。
In the step 3, a two-dimensional variable simulation sequence is constructed by the following steps,
according to a joint distribution function
Figure 932946DEST_PATH_IMAGE008
The random number is generated by adopting a two-dimensional joint distribution random number generation methodMHas a length ofNThe analog sequence of (a) is,
Figure 694446DEST_PATH_IMAGE010
，
Figure 540042DEST_PATH_IMAGE011
i.e. each analog sequence containsNA two-dimensional variable analog value
Figure 753986DEST_PATH_IMAGE012
；
Secondly, determining the edge distribution function of the simulation sequence of two variables by adopting the same edge distribution function type and combined distribution function type as the actually measured sequence aiming at each simulation sequence
Figure 128466DEST_PATH_IMAGE013
And
Figure 99964DEST_PATH_IMAGE014
and simulating a sequence joint distribution function
Figure 952514DEST_PATH_IMAGE015
To obtain a distribution function
Figure 286543DEST_PATH_IMAGE013
And
Figure 363084DEST_PATH_IMAGE014
value of (2)
Figure 821878DEST_PATH_IMAGE016
、
Figure 274856DEST_PATH_IMAGE017
And simulation sequence joint distribution function
Figure 197813DEST_PATH_IMAGE015
Value of (2)
Figure 241992DEST_PATH_IMAGE018
；
Thirdly, calculating the deviation square sum of the parameter value of the distribution function of each simulation sequence and the parameter value of the distribution function of the measured sequence by adopting the following formulaRSelectingRThe smallest analog sequence is used as Monte Carlo two-dimensional random analog sequenceNA two-dimensional variable analog value;
Figure 453662DEST_PATH_IMAGE019
（1）
the water resource allocation result under each two-dimensional random analog value is obtained in the step 4, and the method comprises the following steps,
firstly, model construction, combining a two-stage random planning model, introducing water quantity pre-distribution coefficients, considering water shortage punishment caused by not meeting a water distribution target, and constructing the following water resource pre-distribution model by taking the maximum economic benefit of a water resource system as a target:
Figure 444752DEST_PATH_IMAGE020
（2）
in the formula (I), the compound is shown in the specification,frepresenting the water supply benefit of the system;Irepresenting the total number of users;
Figure 425477DEST_PATH_IMAGE021
water user for indicationiAt maximum water demand;
Figure 312662DEST_PATH_IMAGE022
water user for indicationiThe water quantity pre-distribution coefficient is a decision variable of the model;
Figure 808365DEST_PATH_IMAGE023
water user for indicationiPre-distributing water amount;
Figure 540829DEST_PATH_IMAGE024
water user for indicationiThe water supply efficiency of (1);
Figure 438378DEST_PATH_IMAGE025
water user for indicationiThe water shortage (d) is the difference between the pre-distributed water quantity and the actual distributed water quantity;
Figure 230884DEST_PATH_IMAGE026
water user for indicationiThe water shortage penalty factor of;
Figure 417146DEST_PATH_IMAGE027
indicating the system available water supply;
Figure 750038DEST_PATH_IMAGE028
water user for indicationiMinimum water requirement of (c);A i representing pre-allocation coefficientsZ i The range of the value of (a) is, A i set to {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1 };
solving a model, wherein parameters related to the upper and lower water demand limits, the water supply benefits and the water shortage punishment coefficients of the water consumers in the model are obtained through statistical analysis of historical data; the water supply amount of the system in the model is determined by a two-dimensional variable analog value according to the water supply amount obtained in the step 3NAnd aiming at each two-dimensional variable analog value, calculating the available water supply of the system, then introducing the available water supply into a water pre-distribution model, and solving by adopting an artificial intelligence algorithm to obtain the water pre-distribution coefficient of each water user under each two-dimensional variable analog value.
In the step 5, an optimal water resource allocation scheme is determined by the following steps,
value and frequency analysis, and after the model optimization in the step 4, each user can obtain the value and frequency analysisNThe value of each water pre-distribution coefficient is one of 11 discrete values, namely the value range is {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}, and the value range is for each water userNThe individual water pre-distribution coefficient is subjected to statistical analysis, and the value frequency of the water pre-distribution coefficient is calculated by adopting the following formula:
Figure 970935DEST_PATH_IMAGE029
（3）
in the formula (I), the compound is shown in the specification,
Figure 996660DEST_PATH_IMAGE030
water user for indicationiThe water amount pre-distribution coefficient isjThe value frequency of each discrete value;
Figure 201376DEST_PATH_IMAGE031
water user for indicationiThe water amount pre-distribution coefficient isjFrequency of values of the discrete values;
determining a distribution scheme, namely selecting a discrete value with the maximum value frequency as an optimal water pre-distribution coefficient for each water user, and multiplying the discrete value by the maximum water demand to obtain an optimal water resource distribution target of the water user; and combining the optimal allocation targets of all the water consumers to obtain an optimal water resource allocation scheme.
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention couples the Copula function and Monte Carlo random simulation, and can more properly describe the random information of the hydrological variables in the changing environment.
(2) The invention constructs a pre-distribution water quantity model and provides a solution for the problem of regional water resource optimization distribution under bivariate joint randomness.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
FIG. 1 is a flow chart of a water resource optimization allocation method based on two-dimensional variable random simulation.
FIG. 2 is a flow chart for constructing a joint distribution of two random variables.
FIG. 3 is a flow chart of a two-dimensional variable random simulation sequence construction.
Detailed Description
The technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
The terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
As shown in fig. 1, an embodiment of the present application provides a water resource optimization allocation method based on two-dimensional variable stochastic simulation, including the following specific steps:
step 1, analyzing a water resource optimization allocation problem to be solved, and finding out two most main hydrological random variables in the problem;
step 2, constructing the joint distribution of the two hydrological variables by adopting a Copula function and combining the long sequence measured values of the hydrological variables;
step 3, adopting a Monte Carlo two-dimensional random simulation method, and evaluating and optimizing through a simulation sequence to obtain the length of a parameter value closest to the length of an actual measurement sequence asNOf a two-dimensional variable simulation sequence, wherein
Figure 529503DEST_PATH_IMAGE032
；
Step 4, constructing a proper water resource pre-distribution model, and solving through an artificial intelligence algorithm to obtain water resource distribution results of each water user under each two-dimensional variable analog value;
step 5, for each water userNAnd carrying out statistical analysis on the distribution results, selecting the result with the largest value probability as the optimal water resource distribution target of the water user, and combining to obtain an optimal water resource distribution scheme.
In the step 2, the joint distribution of the two hydrological variables is constructed by the following steps,
fitting two measured sequences of hydrological variables by using 8 distribution functions including Gamma, Gumbel, Logistic, Weibull, Box-Cox Cole and Green, Peason III, Generalized Gamma and Generalized Inverse Gaussian to determine the edge distribution function of each measured sequence of the variables
Figure 932803DEST_PATH_IMAGE002
And
Figure 332691DEST_PATH_IMAGE003
and obtaining a distribution function
Figure 24704DEST_PATH_IMAGE004
And
Figure 902661DEST_PATH_IMAGE005
respectively is
Figure 301413DEST_PATH_IMAGE006
And
Figure 606623DEST_PATH_IMAGE007
；
② Gumbel-Houga is adoptedDetermining optimized Copula function types and parameters by using 4 single-parameter two-dimensional Archimedes Copula functions of ard Copula, Clayton Copula, Ali-Mikhail-Haq Copula and Frank Copula, and obtaining a joint distribution function of two measured sequences of hydrological variables through parameter estimation, fitting effect inspection and goodness-of-fit evaluation
Figure 51511DEST_PATH_IMAGE008
And joint distribution function parameter values
Figure 733159DEST_PATH_IMAGE009
。
In the step 3, a two-dimensional variable simulation sequence is constructed by the following steps,
according to a joint distribution function
Figure 314313DEST_PATH_IMAGE008
The random number is generated by adopting a two-dimensional joint distribution random number generation methodMHas a length ofNThe analog sequence of (a) is,
Figure 321583DEST_PATH_IMAGE010
，
Figure 722609DEST_PATH_IMAGE011
i.e. each analog sequence containsNA two-dimensional variable analog value
Figure 473527DEST_PATH_IMAGE012
；
Secondly, determining the edge distribution function of the simulation sequence of two variables by adopting the same edge distribution function type and combined distribution function type as the actually measured sequence aiming at each simulation sequence
Figure 846871DEST_PATH_IMAGE013
And
Figure 821780DEST_PATH_IMAGE014
and simulating a sequence joint distribution function
Figure 913364DEST_PATH_IMAGE015
To obtain a distribution function
Figure 999132DEST_PATH_IMAGE013
And
Figure 289299DEST_PATH_IMAGE014
value of (2)
Figure 310475DEST_PATH_IMAGE016
、
Figure 358197DEST_PATH_IMAGE017
And simulation sequence joint distribution function
Figure 185339DEST_PATH_IMAGE015
Value of (2)
Figure 798854DEST_PATH_IMAGE018
；
Thirdly, calculating the deviation square sum of the parameter value of the distribution function of each simulation sequence and the parameter value of the distribution function of the measured sequence by adopting the following formulaRSelectingRThe smallest analog sequence is used as Monte Carlo two-dimensional random analog sequenceNA two-dimensional variable analog value;
Figure 849986DEST_PATH_IMAGE019
（1）
the water resource allocation result under each two-dimensional random analog value is obtained in the step 4, and the method comprises the following steps,
firstly, model construction, combining a two-stage random planning model, introducing water quantity pre-distribution coefficients, considering water shortage punishment caused by not meeting a water distribution target, and constructing the following water resource pre-distribution model by taking the maximum economic benefit of a water resource system as a target:
Figure 990198DEST_PATH_IMAGE020
（2）
in the formula (I), the compound is shown in the specification,frepresenting the water supply benefit (element) of the system;Irepresenting the total number of users;
Figure 621031DEST_PATH_IMAGE021
water user for indicationiAt maximum water demand (m) 3 ）；
Figure 354632DEST_PATH_IMAGE022
Water user for indicationiWater amount pre-distribution coefficient (element/m) 3 ) Is a decision variable of the model;
Figure 514349DEST_PATH_IMAGE023
water user for indicationiPre-distribution water quantity (m) 3 ）；
Figure 130138DEST_PATH_IMAGE024
Water user for indicationiWater supply efficiency (Yuan/m) 3 ）；
Figure 299082DEST_PATH_IMAGE025
Water user for indicationiWater shortage (m) 3 ) Namely the difference value between the pre-distributed water quantity and the actual distributed water quantity;
Figure 683927DEST_PATH_IMAGE026
indicating water useriWater shortage punishment coefficient (Yuan/m) 3 ）；
Figure 545704DEST_PATH_IMAGE027
Indicating the system available water supply (m) 3 ）；
Figure 320893DEST_PATH_IMAGE028
Water user for indicationiMinimum water requirement (m) 3 ）；A i Representing pre-allocation coefficientsZ i The value range of (A) is, A i set to {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1 }.
Solving a model, wherein parameters related to the upper and lower water demand limits, the water supply benefits and the water shortage punishment coefficients of the water consumers in the model are obtained through statistical analysis of historical data; system in model for providingThe water quantity is determined by a two-dimensional variable analog value and is obtained according to the step 3NAnd aiming at each two-dimensional variable analog value, calculating the available water supply of the system, then introducing the available water supply into a water pre-distribution model, and solving by adopting an artificial intelligence algorithm to obtain the water pre-distribution coefficient of each water user under each two-dimensional variable analog value.
In the step 5, an optimal water resource allocation scheme is determined by the following steps,
value and frequency analysis, and after the model optimization in the step 4, each user can obtain the value and frequency analysisNThe value of each water pre-distribution coefficient is one of 11 discrete values, namely the value range is {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}, and the value range is for each water userNThe individual water pre-distribution coefficient is subjected to statistical analysis, and the value frequency of the water pre-distribution coefficient is calculated by adopting the following formula:
Figure 824687DEST_PATH_IMAGE029
（3）
in the formula (I), the compound is shown in the specification,
Figure 329617DEST_PATH_IMAGE030
water user for indicationiThe water amount pre-distribution coefficient isjThe value frequency of each discrete value;
Figure 362295DEST_PATH_IMAGE031
water user for indicationiThe water amount pre-distribution coefficient isjFrequency of values of the discrete values;
determining a distribution scheme, namely selecting a discrete value with the maximum value frequency as an optimal water pre-distribution coefficient for each water user, and multiplying the discrete value by the maximum water demand to obtain an optimal water resource distribution target of the water user; and combining the optimal allocation targets of all the water consumers to obtain an optimal water resource allocation scheme.
Example (b):
irrigation water sources of an irrigation area are mainly 2 large-scale reservoirs which can be divided into 8 irrigation subareas, and 3 main crops of medium rice, rape and cotton are planted in each subarea. In order to efficiently utilize the water resources in the irrigation areas, managers in the irrigation areas need to make a reasonable water resource distribution scheme to distribute the available water supply of the two reservoirs to the 3 main crops in each sub-area.
Step 1, two most main random variables in the problem are found.
In the water resource allocation system, the most main random variable is annual inflow of 2 reservoirs which are respectively marked as I 1 And I 2 Collecting and finishing I 1 And I 2 The long sequence of measured data.
And 2, constructing the joint distribution of the two random variables.
Determining edge distribution of random variable
8 commonly used distribution functions (Gamma, Gumbel, Logistic, Weibull, Box-Cox Cole and Green, Peason III, Generalized Gamma, and Generalized Inverse Gaussian) were used for I pair 1 And I 2 Fitting the measured data of the long sequence to obtain I 1 The optimal fitting probability distribution type is Gamma distribution, and the position parameter and the scale parameter of the distribution function are respectively
Figure 624780DEST_PATH_IMAGE033
And
Figure 932265DEST_PATH_IMAGE034
；I 2 the optimal fitting probability distribution type is Gamma distribution, and the position parameter and the scale parameter of the distribution function are respectively
Figure 494965DEST_PATH_IMAGE035
And
Figure 495282DEST_PATH_IMAGE036
。
② determination of joint distribution of random variables
4 single-parameter two-dimensional Archimedes Copula functions of Gumbel-Hougaard Copula, Clayton Copula, Ali-Mikhail-Haq Copula and Frank Copula are adopted to pair I 1 And I 2 Fitting, evaluating and checking the measured data of the long sequence. The result shows that the Frank Copula function has the best fitting effect, and the Copula reference thereofNumber is
Figure 510642DEST_PATH_IMAGE037
。
And 3, randomly simulating to generate a two-dimensional variable simulation sequence.
According to I 1 And I 2 The measured sequence joint distribution function adopts a two-dimensional joint distribution random number generation method to obtain the numberM=10000, lengthNA two-dimensional variable analog sequence of = 1000.
② for each two-dimensional variable simulation sequence, it can be decomposed into I whose length is 1000 1 And I 2 And (5) simulating a sequence. Respectively fitting I by using Gamma distribution function 1 And I 2 Simulating the sequence to obtain I 1 And I 2 Simulating sequence edge distribution fitting parameters; frank Copula function was then used to fit I 1 And I 2 And simulating the sequence to obtain the joint distribution parameters of the simulated sequence.
Calculating the deviation square sum of the distribution function parameter value of each simulation sequence and the distribution function parameter value of the actual measurement sequence for 10000 two-dimensional variable simulation sequences by formula 1RAnd selectRAnd the minimum simulation sequence is used as the optimal two-dimensional variable simulation sequence. Wherein, I 1 The values of the edge distribution function parameters of the simulation sequence are respectively
Figure 356238DEST_PATH_IMAGE038
And
Figure 711127DEST_PATH_IMAGE039
；I 2 the values of the edge distribution function parameters of the simulation sequence are respectively
Figure 820029DEST_PATH_IMAGE040
And
Figure 853844DEST_PATH_IMAGE041
(ii) a The value of the parameter of the simulated sequence joint distribution function is
Figure 768710DEST_PATH_IMAGE042
。
Step 4, constructing a proper water quantity pre-distribution model
The present example requires a reasonable allocation of reservoir available water to 3 major crops in 8 sub-divisions taking into account the joint random uncertainty of 2 reservoir inflow rates. Based on a formula 2, the following water pre-distribution model is constructed according to the actual situation of the irrigation area:
Figure 774844DEST_PATH_IMAGE043
（4）
in the formula (I), the compound is shown in the specification,
Figure 116963DEST_PATH_IMAGE044
representation sub-regionmInner cropnMaximum water demand (m) 3 ）；
Figure 360776DEST_PATH_IMAGE045
Is a sub-regionmInner cropnThe water quantity pre-distribution coefficient is a decision variable;
Figure 548175DEST_PATH_IMAGE046
representation sub-regionmInner cropnIrrigation efficiency (Yuan/m) 3 ）；
Figure 408815DEST_PATH_IMAGE047
Representation sub-regionmInner cropnWater shortage (m) under certain circumstances 3 ）；
Figure 921836DEST_PATH_IMAGE048
Representation sub-regionmInner cropnWater shortage punishment coefficient (Yuan/m) 3 ). The objective function needs to satisfy the following constraints:
(ii) Water supply amount constraint
Figure 399085DEST_PATH_IMAGE049
（5）
In the formula (I), the compound is shown in the specification,
Figure 124595DEST_PATH_IMAGE050
indicating the available water supply (m) of the irrigation area 3 ）；
Figure 370900DEST_PATH_IMAGE051
And
Figure 54822DEST_PATH_IMAGE052
respectively representing the water suppliable amounts (m) of the reservoir 1 and the reservoir 2 3 ) The water intake quantity can be determined by the annual inflow quantity value of the reservoir through water quantity balance.
② water demand restriction
Figure 753788DEST_PATH_IMAGE053
（6）
In the formula (I), the compound is shown in the specification,
Figure 548569DEST_PATH_IMAGE054
representation sub-regionmInner cropnMinimum water requirement (m) 3 ）。
③ variable constraint
Figure 383801DEST_PATH_IMAGE055
（7）
In the formula (I), the compound is shown in the specification,Arepresentation sub-regionmInner cropnThe water amount pre-distribution coefficient of the water,A={0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}。
according to the optimal two-dimensional variable simulation sequence determined in the step 3, the available water supply amount of the reservoir 1 and the available water supply amount of the reservoir 2 are calculated respectively for each two-dimensional variable simulation value, and then the available water supply amount is brought into a water pre-distribution model to be solved by adopting an artificial intelligence algorithm, so that the water pre-distribution coefficient of each water user under each two-dimensional variable simulation value is obtained.
Step 5, determining an optimal water resource allocation scheme
Based on equation 3, the sub-regions are calculated separatelymInner cropnThe pre-distribution coefficient of water amount (as shown in table 1) takes the value frequency. For each crop, selecting the discrete value with the maximum value frequency as the optimal water pre-distribution coefficient, wherein the result is shown in table 1; according to the optimal water quantityThe distribution coefficient can calculate the optimal water distribution amount of each crop.
Figure 504203DEST_PATH_IMAGE056
From the above, it can be known that the Copula function and monte carlo random simulation are coupled in the embodiment of the application, so that the random information of the hydrological variable in the changing environment can be more appropriately described; a pre-distribution water quantity model is constructed, and a solution is provided for the problem of regional water resource optimization distribution under bivariate joint randomness.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (5)

1. A water resource optimization allocation method based on two-dimensional variable random simulation is characterized by comprising the following specific steps:
step 1, analyzing a water resource optimization allocation problem to be solved, and finding out two most main hydrological random variables in the problem;
step 2, constructing the joint distribution of the two hydrological variables by adopting a Copula function and combining the long sequence measured values of the hydrological variables;
step 3, adopting a Monte Carlo two-dimensional random simulation method, and evaluating and optimizing through a simulation sequence to obtain the length of a parameter value closest to the length of an actual measurement sequence asNOf a two-dimensional variable simulation sequence, wherein
Figure 859161DEST_PATH_IMAGE001
；
Step 4, constructing a proper water resource pre-distribution model, and solving through an artificial intelligence algorithm to obtain water resource distribution results of each water user under each two-dimensional variable analog value;
step 5, for each water userNAnd carrying out statistical analysis on the distribution results, selecting the result with the largest value probability as the optimal water resource distribution target of the water user, and combining to obtain an optimal water resource distribution scheme.
2. The water resource optimal allocation method based on two-dimensional variable stochastic simulation according to claim 1, characterized in that: in the step 2, the joint distribution of the two hydrological variables is constructed by the following steps,
fitting two measured sequences of hydrologic variables by using 8 distribution functions including Gamma, Gumbel, Logistic, Weibull, Box-Cox Cole and Green, Peason III, Generalized Gamma and Generalized Inverse Gaussian, and determining the edge distribution function of each measured sequence of the variables
Figure 842161DEST_PATH_IMAGE002
And
Figure 175053DEST_PATH_IMAGE003
and obtaining a distribution function
Figure 661529DEST_PATH_IMAGE004
And
Figure 687254DEST_PATH_IMAGE005
respectively is
Figure 891970DEST_PATH_IMAGE006
And
Figure 28553DEST_PATH_IMAGE007
；
secondly, determining optimized Copula function types and parameters by using 4 single-parameter two-dimensional Archimedes Copula functions of Gumbel-Hougaard Copula, Clayton Copula, Ali-Mikhail-Haq Copula and Frank Copula, and obtaining a combined distribution function of two measured sequences of hydrologic variables through parameter estimation, fitting effect test and goodness-of-fit evaluation
Figure 838378DEST_PATH_IMAGE008
And joint distribution function parameter values
Figure 35004DEST_PATH_IMAGE009
。
3. The water resource optimal allocation method based on two-dimensional variable stochastic simulation according to claim 2, characterized in that: in the step 3, a two-dimensional variable simulation sequence is constructed by the following steps,
according to a joint distribution function
Figure 461437DEST_PATH_IMAGE010
The random number is generated by adopting a two-dimensional joint distribution random number generation methodMHas a length ofNThe analog sequence of (a) is,
Figure 198449DEST_PATH_IMAGE011
，
Figure 647798DEST_PATH_IMAGE012
i.e. each analog sequence containsNA two-dimensional variable analog value
Figure 484167DEST_PATH_IMAGE013
；
Secondly, determining the edge distribution function of the simulation sequence of two variables by adopting the same edge distribution function type and combined distribution function type as the actually measured sequence aiming at each simulation sequence
Figure 460214DEST_PATH_IMAGE014
And
Figure 938600DEST_PATH_IMAGE015
and simulating a sequence joint distribution function
Figure 254174DEST_PATH_IMAGE016
To obtainDistribution function
Figure 995865DEST_PATH_IMAGE014
And
Figure 396891DEST_PATH_IMAGE015
value of (2)
Figure 678968DEST_PATH_IMAGE017
、
Figure 380207DEST_PATH_IMAGE018
And simulation sequence joint distribution function
Figure 558379DEST_PATH_IMAGE016
Value of (2)
Figure 712280DEST_PATH_IMAGE019
；
Thirdly, calculating the deviation square sum of the parameter value of the distribution function of each simulation sequence and the parameter value of the distribution function of the measured sequence by adopting the following formulaRSelectingRThe smallest analog sequence is used as Monte Carlo two-dimensional random analog sequenceNA two-dimensional variable analog value;
Figure 532468DEST_PATH_IMAGE020
（1）。
4. the water resource optimal allocation method based on two-dimensional variable stochastic simulation according to claim 3, characterized in that: the water resource allocation result under each two-dimensional random analog value is obtained in the step 4, and the method comprises the following steps,
firstly, model construction, combining a two-stage random planning model, introducing water quantity pre-distribution coefficients, considering water shortage punishment caused by not meeting a water distribution target, and constructing the following water resource pre-distribution model by taking the maximum economic benefit of a water resource system as a target:
Figure 619373DEST_PATH_IMAGE021
（2）
in the formula (I), the compound is shown in the specification,frepresenting the water supply benefit of the system;Irepresenting the total number of users;
Figure 968446DEST_PATH_IMAGE022
water user for indicationiAt maximum water demand;
Figure 344064DEST_PATH_IMAGE023
water user for indicationiThe water quantity pre-distribution coefficient is a decision variable of the model;
Figure 967943DEST_PATH_IMAGE024
water user for indicationiPre-distributing water amount;
Figure 112616DEST_PATH_IMAGE025
water user for indicationiThe water supply efficiency of (1);
Figure 163749DEST_PATH_IMAGE026
water user for indicationiThe water shortage (d) is the difference between the pre-distributed water quantity and the actual distributed water quantity;
Figure 823401DEST_PATH_IMAGE027
water user for indicationiThe water shortage penalty factor of;
Figure 985392DEST_PATH_IMAGE028
indicating the water supply available to the system;
Figure 250151DEST_PATH_IMAGE029
water user for indicationiMinimum water requirement of (c);A i representing pre-allocation coefficientsZ i The value range of (A) is, A i set to {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1 };
solving a model, wherein parameters related to the upper and lower water demand limits, the water supply benefits and the water shortage punishment coefficients of the water consumers in the model are obtained through statistical analysis of historical data; the water supply amount of the system in the model is determined by a two-dimensional variable analog value according to the water supply amount obtained in the step 3NAnd aiming at each two-dimensional variable analog value, calculating the available water supply of the system, then introducing the available water supply into a water pre-distribution model, and solving by adopting an artificial intelligence algorithm to obtain the water pre-distribution coefficient of each water user under each two-dimensional variable analog value.
5. The water resource optimal allocation method based on two-dimensional variable stochastic simulation according to claim 4, characterized in that: in the step 5, an optimal water resource allocation scheme is determined by the following steps,
value and frequency analysis, and after the model optimization in the step 4, each user can obtain the value and frequency analysisNThe value of each water pre-distribution coefficient is one of 11 discrete values, namely the value range is {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}, and the value range is for each water userNThe individual water pre-distribution coefficient is subjected to statistical analysis, and the value frequency of the water pre-distribution coefficient is calculated by adopting the following formula:
Figure 675447DEST_PATH_IMAGE030
（3）
in the formula (I), the compound is shown in the specification,
Figure 25657DEST_PATH_IMAGE031
water user for indicationiThe water amount pre-distribution coefficient isjThe value frequency of each discrete value;
Figure 460181DEST_PATH_IMAGE032
water user for indicationiThe water amount pre-distribution coefficient isjFrequency of values of the discrete values;
determining a distribution scheme, namely selecting a discrete value with the maximum value frequency as an optimal water pre-distribution coefficient for each water user, and multiplying the discrete value by the maximum water demand to obtain an optimal water resource distribution target of the water user; and combining the optimal allocation targets of all the water consumers to obtain an optimal water resource allocation scheme.
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