CN107808237A - A kind of parallel reservoir group Real time Flood risk Analytic Calculation Method - Google Patents

Abstract

The invention discloses a real-time flood control risk analysis and calculation method for a group of parallel reservoirs. The method comprises the following steps: (1) establishing a mathematical expression of an uncertainty factor, and obtaining a marginal distribution function of the uncertainty factor; (2) Based on the Copula function, the joint probability density distribution function of multi-dimensional uncertain factors is solved; (3) The real-time flood control dispatch risk model of the reservoir group is established, and the flood control dispatch risk of the reservoir group is analyzed at each time; (4) The real-time flood control dispatch risk calculation of the reservoir group is calculated. The present invention considers the influence of the correlation between uncertain factors on the risk of real-time flood control dispatching of reservoir groups, and obtains the analytic calculation formula of real-time flood control dispatching risk of reservoir groups at each time, which has high calculation efficiency, is easy to implement, and has strong universality sex.

Description

A Real-time Flood Control Risk Analysis and Calculation Method for Parallel Reservoir Groups

technical field

The invention belongs to reservoir flood control scheduling risk assessment, in particular to a real-time flood control risk analysis and calculation method for parallel reservoir groups.

Background technique

Real-time flood control scheduling of reservoir groups is one of the important technical means for flood control and disaster reduction in river basins. It can improve the efficiency of flood control projects with a small investment. However, there are many uncertain factors in the real-time flood control dispatching process of the existing reservoir groups, including the uncertainty of the inflow flow process of the reservoir group, the uncertainty of the outflow process of the reservoir group, and the uncertainty of the interval flood forecast process. These uncertain factors lead to the uncertainty of the combined flow process of downstream public flood control points, which has a certain impact on flood control decision-making and has certain risks. Therefore, the risk assessment of real-time flood control operation of reservoir groups has important academic significance and practical value. Quantitative calculations.

At present, the existing risk assessment methods for real-time flood control operation of reservoir groups mainly have the following shortcomings: (1) It is difficult to obtain the joint probability density distribution function of multi-dimensional uncertain factors; (2) The random simulation method is used to calculate the risk of real-time flood control operation of reservoir groups, The calculation efficiency is not high, and the versatility is not enough, and different systems need to be re-modeled.

Contents of the invention

Purpose of the invention: Aiming at the deficiencies of the above-mentioned prior art, the present invention provides a real-time flood control risk analysis calculation method for parallel reservoir groups to evaluate the risk problems caused by uncertain factors in the real-time flood control analysis of parallel reservoir groups.

Technical solution: a real-time flood control risk analysis and calculation method for parallel reservoir groups, including the following steps:

(1) Establish the mathematical expression of the uncertainty factor, and solve the marginal distribution function of the uncertainty factor;

(2) Based on the Copula function, solve the joint probability density distribution function of multidimensional uncertainty factors;

(3) Establish a real-time flood control dispatch risk model for reservoir groups, and analyze the flood control dispatch risks of reservoir groups at each time;

(4) Calculation of real-time flood control dispatch risk of reservoir group.

Further, the uncertain factors in step (1) include the inflow flow of the reservoir group, the outflow flow of the reservoir group and the uncertainty of interval flood forecast.

Further, said step (2) includes the following steps:

(2.1) Define H(q ₁ (t), q ₂ (t), q ₃ (t)) as the joint probability of the outflow stochastic process of reservoir 1, the outflow stochastic process of reservoir 2, and the interval flood outflow stochastic process The distribution function, the calculation formula is as follows:

H(q ₁ (t),q ₂ (t),q ₃ (t))＝C(F(q ₁ (t)),F(q ₂ (t)),F(q ₃ (t))) (1)

In the formula, q ₁ (t) is the stochastic process of the outflow flow of reservoir 1 at time t; q ₂ (t) is the stochastic process of outflow flow of reservoir 2 at time t; q ₃ (t) is the flow rate of the downstream flood control section at time t Interval flood stochastic process; F(q ₁ (t)), F(q ₂ (t)), F(q ₃ (t)) are uncertain factors respectively - the outflow stochastic process q ₁ (t) of reservoir 1 , the marginal distribution function of the reservoir 2 outflow random process q ₂ (t), and the interval flood random process q ₃ (t); C is the Copula function;

(2.2) Define h(q ₁ (t), q ₂ (t), q ₃ (t)) as the joint probability density function of the outflow stochastic process of reservoir 1, the outflow stochastic process of reservoir 2, and the interval flood stochastic process ,Calculated as follows:

In the formula, f(q _i (t)) is the probability density function of uncertainty factor q _i (t), i=1, 2, 3, c(F(q ₁ (t)), F(q ₂ ( t)), F(q ₃ (t)) is the probability density function of Copula function C(F(q ₁ (t)), F(q ₂ (t)), F(q ₃ (t)).

Furthermore, the Copula function described in step (2) includes 3 calculation formulas, the expressions are as follows:

Among them, α(t) is the parameter of Copula function;

Further, the specific steps of the step (3) are as follows:

Define the real-time flood control dispatch risk Risk(t) of the reservoir group as the probability that the combined flow process of the public flood control points exceeds the safe flow threshold of the flood control section at time t, and connect the uncertain factors in step (1) through the Copula function to obtain the real-time flood control of the reservoir group The calculation formula of scheduling risk Risk(t) is:

In the formula, Risk(t) represents the real-time flood control scheduling risk of reservoir group system at time t; Q(t) represents the combined flow process of public flood control points at time t; Q _C (t) represents the safe flow threshold of flood control control section at time t, which can be Safe discharge of public flood control points; Ω ₀ ={q ₁ (t)+q ₂ (t)+q ₃ (t)>Q _C (t)}, Ω ₁ is the integral conversion interval corresponding to Ω ₀ .

Further, said step (4) includes the following steps:

(4.1) Obtain the operation data of the reservoir group and real-time forecast inflow mean process and error distribution, interval flood forecast mean process and error distribution;

(4.2) Carry out reservoir flood regulation calculation according to the reservoir flood control regulation rules, and calculate the stochastic process of reservoir outflow flow;

(4.3) Select the Copula function as the uncertainty factor—the joint probability of the outflow stochastic process q ₁ (t) of reservoir 1, the outflow stochastic process q ₂ (t) of reservoir 2, and the interval flood stochastic process q ₃ (t) Distribution function.

(4.4) According to the selected Copula function, calculate the real-time flood control dispatch risk of the reservoir group at each time.

Beneficial effects: Compared with the prior art, the present invention has remarkable effects in that: 1. Considering the impact of the correlation between uncertain factors on the risk of real-time flood control dispatching of reservoir groups, the risk assessment method for real-time flood control dispatching of reservoir groups takes more factors into account Comprehensive; 2. The analytic calculation formula of the real-time flood control dispatching risk of reservoir groups is established through the Copula function; 3. The analytic calculation method has high calculation efficiency, is easy to implement, and has strong versatility.

Description of drawings

Fig. 1 is the flowchart of the inventive method;

Fig. 2 is the schematic diagram of parallel reservoir group system of the present invention;

Fig. 3 is a schematic flow chart of the calculation steps of the present invention.

Detailed ways

In order to further illustrate the technical solutions disclosed in the present invention, a detailed description will be given below in conjunction with the drawings and specific embodiments of the specification.

The present invention comprehensively considers the uncertainty of the inflow flow process of the reservoir group, the uncertainty of the outflow process of the reservoir group, and the uncertainty of the interval flood forecast process, and considers the correlation between uncertain factors, and establishes it through the Copula function theory Based on the joint probability density distribution function of the above uncertain factors, the definition of the real-time flood control dispatch risk of the reservoir group is proposed, and the analytical calculation formula of the real-time flood control dispatch risk of the reservoir group is obtained at each time.

As shown in Figure 1, a real-time flood control risk analysis calculation method for parallel reservoirs includes the following steps:

Step 1: Propose the mathematical expression of the uncertainty factor, and solve the marginal distribution function of the uncertainty factor:

(1.1) Define Q _i (t) as the stochastic process of the inflow flow of reservoir i at time t, and the calculation formula is as follows:

in, is the mean value of the stochastic process of the inflow flow of reservoir i at time t; ξ _i (t) is the forecast error of inflow flow of reservoir i at time t, and ξ _i (t) obeys the normal distribution, that is, distribution parameter is the mean square error of the inflow flow forecast error of reservoir i, which can be obtained by the hydrological forecast model. Then the stochastic process q _i (t) of the inflow flow of reservoir i at time t also obeys the normal distribution, namely

Then, q ₃ (t) is defined as the interval flood random process of the downstream flood control section at time t, and the calculation formula is as follows:

in, is the mean value of the random process of the interval flood at time t, that is, the deterministic hydrological forecast result; ξ ₃ (t) is the error of the interval flood forecast at time t, and ξ ₃ (t) obeys the normal distribution, namely distribution parameter is the mean square error of the interval flood forecast error, which can be obtained from the hydrological forecast model. Then the interval flood stochastic process q ₃ (t) of the downstream flood control section at time t also obeys the normal distribution, namely

(1.2) Define q _i (t) as the stochastic process of outflow flow of reservoir i at time t, and the calculation formula is as follows:

in, is the mean value of the stochastic process of outflow flow of reservoir i at time t; η _i (t) is the error of outflow flow of reservoir i at time t, and η _i (t) obeys normal distribution, that is Then the stochastic process q _i (t) of the outflow flow of reservoir i at time t also obeys the normal distribution, namely distribution parameter is the mean square error of the outflow flow error of reservoir i, and the calculation steps are as follows:

1) According to the stochastic process of the inflow flow of reservoir i and the interval flood stochastic process The distribution of , here the Latin hypercube sampling is preferred to generate M groups of samples of the inbound flow process and a sample of the interval flood process

2) According to the flood control dispatching rules of reservoir i, the reservoir flood regulation calculation is carried out through the principle of water balance, and the outflow flow process sample of reservoir i is calculated

3) According to the sample of the outflow flow process of reservoir i, the distribution of the stochastic process of outflow flow of reservoir i at each time is fitted

Step 2: Based on the Copula function, solve the joint probability density distribution function of multidimensional uncertainty factors:

Define H(q ₁ (t), q ₂ (t), q ₃ (t)) as uncertainty factors - the outflow stochastic process q _{1 (t) of reservoir 1, the outflow stochastic process q 2 (} t) of reservoir 2 ), and the joint probability distribution function of the interval flood stochastic process q ₃ (t), according to the Copula function theory, the following formula is used to calculate:

H(q ₁ (t),q ₂ (t),q ₃ (t))＝C(F(q ₁ (t)),F(q ₂ (t)),F(q ₃ (t))) (9)

Among them, F(q ₁ (t)), F(q ₂ (t)), and F(q ₃ (t)) are the stochastic process q ₁ (t) of the outflow of reservoir 1 and the outflow of reservoir 2 respectively. The marginal distribution functions of flow random process q ₂ (t) and interval flood random process q ₃ (t), C is Copula function.

The Copula functions used in this example include the following three types:

Wherein, α(t) is a parameter of the Copula function, and the maximum likelihood method is preferably used in this embodiment to estimate the parameters of the Copula function.

Taking partial derivatives on both sides of Equation (9), the uncertain factors are obtained—the stochastic process q ₁ (t) of outflow from reservoir 1, the stochastic process q ₂ (t) of outflow from reservoir 2, and the stochastic process q ₃ (t) of interval flood )’s joint probability density function is as follows:

Among them, f(q _i (t)) is the probability density function of uncertainty factor q _i (t), i=1,2,3;

h(q ₁ (t), q ₂ (t), q ₃ (t)) is the random process q ₁ (t) of the outflow of reservoir 1, the stochastic process q ₂ (t) of the outflow of reservoir 2, and the joint probability density function of interval flood stochastic process q ₃ (t);

c(F(q ₁ (t)), F(q ₂ (t)), F(q ₃ (t)) is the Copula function C(F(q ₁ (t)), F(q ₂ (t)) , the probability density function of F(q ₃ (t)).

In this embodiment, the K-S test method is used to test the three Copula functions in formula (10) respectively, and the spare Copula functions of the uncertainty factors are screened, and then the OLS criterion is used in this embodiment to evaluate the goodness of fit of the spare Copula functions , so that the Copula function with the best fitting degree is selected as the joint probability distribution of uncertainty factors, and the OLS value of each Copula function is calculated by the following formula:

in, is the uncertainty factor - the empirical cumulative probability value of the outflow stochastic process q ₁ (t) of reservoir 1, the outflow stochastic process q ₂ (t) of reservoir 2, and the interval flood stochastic process q ₃ (t); Uncertainty factors—theoretical cumulative probability values of outflow stochastic process q ₁ (t) of reservoir 1, outflow stochastic process q ₂ (t) of reservoir 2, and interval flood stochastic process q ₃ (t).

Step 3: Establish a real-time flood control dispatch risk model of the reservoir group, and analyze the flood control dispatch risk of the reservoir group at each time.

Define real-time flood control scheduling risk of reservoir group as the probability Risk(t) that the combined flow process of public flood control points exceeds the safe flow threshold of flood control section, which means that there is a probability of Risk(t) at time t that the combined flow process of public flood control points will exceed the safe flow rate of flood control section The traffic threshold provides decision makers with risk information for risk decision-making. Substituting Equation (11) into Equation (1), the analytical calculation formula of Risk(t) for real-time flood control dispatching of reservoir groups at each time is obtained:

Among them, Q _C (t) represents the safe flow threshold of the flood control section at time t, which can be taken as the safe discharge of public flood control points; Ω ₀ ={q ₁ (t)+q ₂ (t)+q ₃ (t)＞Q _C (t)}, Ω ₁ is the integral conversion interval corresponding to Ω ₀ .

Step 4: Calculation of the real-time flood control dispatch risk of the reservoir group.

Carry out the application of the real-time flood control dispatching risk model of the reservoir group. In this embodiment, the recursive algorithm is used to calculate the real-time flood control dispatching risk of the reservoir group at each time. The algorithm flow is shown in Figure 3, which mainly includes the following solution steps:

(1) Obtain the operation data of the reservoir group, including the flood control regulation of the reservoir, the water level storage capacity curve, the discharge capacity curve, the starting water level, the design flood level, the check flood level and the reservoir crest elevation and other characteristic values;

(2) The process of obtaining the real-time forecast inflow mean value of the reservoir group Mean Process of Interval Flood Forecasting Inbound flow forecast error ξ _i (t), i=1,2, interval flood forecast error ξ ₃ (t);

(3) According to the distribution of the stochastic process of the inflow flow of the reservoir group and the random process of the interval flood, Latin hypercube sampling is used in this embodiment to generate M groups of samples of the inflow flow process and a sample of the interval flood process

(4) According to the flood control dispatching rules of reservoir i, the reservoir flood regulation calculation is carried out through the principle of water balance, and the outflow flow process sample of reservoir i is calculated

(5) According to formula (8), calculate the distribution parameters of the stochastic process of outflow flow of reservoir i and

(6) Select an alternate Copula function, and carry out the K-S test;

(7) Calculate the OLS value of this Copula function according to formula (12), compare the OLS values of each backup Copula function, and select the Copula function with the smallest OLS value as the uncertainty factor—the outflow stochastic process q ₁ (t) of reservoir 1 , the joint probability distribution function of the outflow stochastic process q ₂ (t) of reservoir 2, and the interval flood stochastic process q ₃ (t);

(8) According to the selected Copula function and formula (13), set the safety flow threshold Q _C (t) of the public flood control point, and calculate the real-time flood control dispatch risk of the reservoir group at each time.

Claims (6)

1. A real-time flood control risk analysis method for parallel reservoir groups, characterized in that: comprising the following steps: (1) Establish the mathematical expression of the uncertainty factor, and solve the marginal distribution function of the uncertainty factor; (2) Based on the Copula function, solve the joint probability density distribution function of multidimensional uncertainty factors; (3) Establish a real-time flood control dispatch risk model for reservoir groups, and analyze the flood control dispatch risks of reservoir groups at each time; (4) Calculation of real-time flood control dispatch risk of reservoir group. 2. A method for analyzing and calculating real-time flood control risks of parallel reservoir groups according to claim 1, characterized in that: the uncertainty factors described in step (1) include the inflow flow of the reservoir group, the outflow flow of the reservoir group and the interval Uncertainty in Flood Forecasting. 3. a kind of parallel reservoir group real-time flood control risk analysis calculation method according to claim 1, is characterized in that: described step (2) comprises the steps: (2.1) Define H(q ₁ (t), q ₂ (t), q ₃ (t)) as the joint probability of the outflow stochastic process of reservoir 1, the outflow stochastic process of reservoir 2, and the interval flood outflow stochastic process The distribution function, the calculation formula is as follows: H(q ₁ (t),q ₂ (t),q ₃ (t))＝C(F(q ₁ (t)),F(q ₂ (t)),F(q ₃ (t))) (1) In the formula, q ₁ (t) is the stochastic process of the outflow flow of reservoir 1 at time t; q ₂ (t) is the stochastic process of outflow flow of reservoir 2 at time t; q ₃ (t) is the flow rate of the downstream flood control section at time t Interval flood stochastic process; F(q ₁ (t)), F(q ₂ (t)), F(q ₃ (t)) are uncertain factors respectively - the outflow stochastic process q ₁ (t) of reservoir 1 , the marginal distribution function of the reservoir 2 outflow random process q ₂ (t), and the interval flood random process q ₃ (t); C is the Copula function; (2.2) Define h(q ₁ (t), q ₂ (t), q ₃ (t)) as the joint probability density function of the outflow stochastic process of reservoir 1, the outflow stochastic process of reservoir 2, and the interval flood stochastic process ,Calculated as follows: In the formula, f(q _i (t)) is the probability density function of uncertainty factor q _i (t), i=1, 2, 3, c(F(q ₁ (t)), F(q ₂ ( t)), F(q ₃ (t)) is the probability density function of Copula function C(F(q ₁ (t)), F(q ₂ (t)), F(q ₃ (t)). 4. a kind of parallel reservoir group real-time flood control risk analysis calculation method according to claim 1, is characterized in that: the Copula function described in step (2) comprises 3 kinds of calculation formulas, and expression is as follows: Among them, α(t) is the parameter of Copula function. 5. a kind of parallel reservoir group real-time flood control risk analysis calculation method according to claim 1, is characterized in that: described step (3) concrete steps are as follows: Define the real-time flood control dispatch risk Risk(t) of the reservoir group as the probability that the combined flow process of the public flood control points exceeds the safe flow threshold of the flood control section at time t, and connect the uncertain factors in step (1) through the Copula function to obtain the real-time flood control of the reservoir group The calculation formula of scheduling risk Risk(t) is: In the formula, Risk(t) represents the real-time flood control scheduling risk of reservoir group system at time t; Q(t) represents the combined flow process of public flood control points at time t; Q _C (t) represents the safe flow threshold of flood control control section at time t, which can be Safe discharge of public flood control points; Ω ₀ ={q ₁ (t)+q ₂ (t)+q ₃ (t)>Q _C (t)}, Ω ₁ is the integral conversion interval corresponding to Ω ₀ . 6. a kind of parallel reservoir group real-time flood control risk analysis calculation method according to claim 1, is characterized in that: described step (4) comprises the following steps: (4.1) Obtain the operation data of the reservoir group and real-time forecast inflow mean process and error distribution, interval flood forecast mean process and error distribution; (4.2) Carry out reservoir flood regulation calculation according to the reservoir flood control regulation rules, and calculate the stochastic process of reservoir outflow flow; (4.3) Select the Copula function as the uncertainty factor—the joint probability of the outflow stochastic process q ₁ (t) of reservoir 1, the outflow stochastic process q ₂ (t) of reservoir 2, and the interval flood stochastic process q ₃ (t) Distribution function. (4.4) According to the selected Copula function, calculate the real-time flood control dispatch risk of the reservoir group at each time.