阅读说明：本技术 基于熵决策法的动态临界雨量计算方法 (Entropy decision method based dynamic critical rainfall calculation method ) 是由 林凯荣 梁汝豪 兰甜 陈海燕 于 2019-07-12 设计创作，主要内容包括：本发明涉及一种基于熵决策法的动态临界雨量计算方法；S1.收集整理流域多场洪水的实测累积雨量和对应洪峰流量数据,将其以前期土壤湿润程度和历时划分为多个样本系列；S2.对收集到的样本系列进行边缘分布拟合,用K-S检验选出拟合效果最好的分布；S3.利用Frank Copula函数构造联合分布,得到不同前期土壤湿润程度及不同历时条件下累积雨量和对应洪峰流量的联合概率分布；S4.将联合概率分布及相应参数分别代入贝叶斯效用函数和期望效用-熵风险函数公式,分别考虑主观因素、客观因素及主客观因素同时影响的情况,通过使效用函数和风险最小化得到不同前期土壤湿润程度及不同历时条件下的临界雨量值。本发明用风险决策方法解决了山洪灾害预警指标的确定问题。(The invention relates to a dynamic critical rainfall calculation method based on an entropy decision method; s1, collecting and settling actually-measured accumulated rainfall and corresponding flood peak flow data of multi-field flood of a drainage basin, and dividing the actually-measured accumulated rainfall and the corresponding flood peak flow data into a plurality of sample series according to the soil wetting degree and duration of a previous period; s2, performing edge distribution fitting on the collected sample series, and selecting the distribution with the best fitting effect by using K-S inspection; s3, constructing combined distribution by using a Frank Copula function to obtain combined probability distribution of accumulated rainfall and corresponding flood peak flow under different early-stage soil wetting degrees and different duration conditions; and S4, substituting the joint probability distribution and corresponding parameters into a Bayes utility function and an expected utility-entropy risk function formula respectively, considering the conditions that subjective factors, objective factors and subjective and objective factors are simultaneously influenced, and minimizing the utility function and the risk to obtain critical rain values under different soil wetting degrees in the early stage and different duration conditions. The invention solves the problem of determining the mountain torrent disaster early warning index by using a risk decision method.)

1. A dynamic critical rainfall calculation method based on an entropy decision method is characterized by comprising the following steps:

s1, collecting and settling actually-measured accumulated rainfall and corresponding flood peak flow data of multi-field flood of a drainage basin, and dividing the actually-measured accumulated rainfall and the corresponding flood peak flow data into a plurality of sample series according to the soil wetting degree and duration of a previous period;

s2, performing edge distribution fitting on the collected sample series, and selecting the distribution with the best fitting effect by using K-S inspection;

s3, constructing combined distribution by using a Frank Copula function to obtain combined probability distribution of accumulated rainfall and corresponding flood peak flow under different early-stage soil wetting degrees and different duration conditions;

and S4, substituting the joint probability distribution and corresponding parameters into a Bayes utility function and an expected utility-entropy risk function formula respectively, considering the conditions that subjective factors, objective factors and subjective and objective factors are simultaneously influenced, and minimizing the utility function and the risk to obtain critical rain values under different soil wetting degrees in the early stage and different duration conditions.

2. An entropy decision-making method-based dynamic critical rainfall calculation method according to claim 1, wherein the step S2 specifically comprises:

s21, selecting exponential distribution, lognormal distribution and Weibull distribution to perform edge distribution fitting on the accumulated rainfall v and the corresponding flood peak flow q sample series under different early-stage soil wetting degrees and different duration conditions, wherein the function expressions of the exponential distribution, the lognormal distribution and the Weibull distribution are respectively as follows:

in the formula, x is a random variable, and lambda is a proportional parameter of exponential distribution;

wherein x is a random variable, and μ and σ are the mean and standard deviation, respectively, of y ═ ln (x);

in the formula, x is a random variable, alpha is a scale parameter, beta is a shape parameter, and gamma is a position parameter;

s22, judging whether the sample obeys a certain distribution by using a K-S inspection method, comparing P values of the three distributions, wherein the larger the P value is, the better the fitting effect is, and finally selecting the distribution with the best fitting effect as the optimal edge distribution of the sample series.

3. An entropy decision-making method-based dynamic critical rainfall calculation method according to claim 2, wherein the step S3 specifically comprises:

s31, selecting Frank Copula function to construct joint distribution; it is defined as follows:

in the formula, F (X, Y) is a joint distribution function of random variables (X, Y) at (X, Y), C is a Copula function, and theta is a parameter of the Copula function and can be obtained by calculating a Kendall correlation coefficient tau; the formula for τ is as follows:

the joint cumulative distribution function F (x, y) of the random variables v and q may be defined as:

F(x,y)＝C(F(x),G(y))＝C(u,v)

wherein F (X, Y) is a joint distribution function of the random variable (X, Y) at (X, Y), and C is a Copula function; the joint density function is shown below:

f(x,y)＝c[F(x),G(y)]f(x)g(y)

wherein C is the density function of C, f (X) and g (Y) are the probability density functions of random variables X and Y, respectively;

s32, obtaining a Kendall correlation coefficient tau through the sample series, obtaining a parameter theta through the formula in a reverse mode, and obtaining combined distribution by combining edge distribution of two random variables v and q.

4. An entropy decision-making method-based dynamic critical rainfall calculation method according to claim 3, wherein the step S4 specifically comprises:

s41, the expectation utility-entropy decision model can combine the objective risk of implementing the action with the subjective preference of a decision maker, and the expression is as follows:

in the formula, mean_a∈A{|E[(u(X(a,θ))]| } ≠ 0, Ha (θ) represents the entropy of action a corresponding to state θ; x (a, θ) represents the result for state θ when action a is taken, and consists of four parts: x₁₁-accurately issuing an alarm, Q ≧ Q and V ≧ V_T；X₁₂Missing report, Q ≧ Q and V < V_T)；X₂₁-false positive, Q < Q and V ≧ V_TAnd X₂₂-no alarm is issued, Q < Q and V < V_T；λ∈[0,1]The 'weighing coefficient' reflects the balance between the subjective expected utility and the objective uncertainty of the behavior of the decision maker; when λ is 0, only the subjective preference of the decision maker is considered, and it is expected that the utility will have a greater impact; when λ is 1, then the desired utility of the decision maker is not considered, only entropy, i.e. the influence of objective uncertainty, is considered; however, in actual decision making, both subjective expectation and objective risk of a decision maker need to be considered, and it is assumed that λ is 0.5 and is considered as two factors; when action a is taken to make the function obtain the minimum value, namely the risk is minimum, action a is the optimal action scheme, and V is at the moment_TThe optimal critical rainfall is obtained;

s42, calculating the critical rainfall only considering the subjective preference of the decision maker by using a Bayesian utility function, wherein the critical rainfall is defined as follows:

wherein q is a flow rate value, m³S; q is the critical flow value of the river critical section, m³S; v is the cumulative rain value, mm; v_TCritical rain value, mm; t is the duration of the storm; a. b, C, C₀A ', b ', c ' are defined parameters;

critical rainfall V for different soil moisture degrees in earlier stage and different rainfall duration_TCan be determined by minimizing the expected utility loss function, i.e. finding the V that minimizes the expected utility loss function_TValue V_TThe value is the evaluated value, and the specific formula is shown as follows：

Where f (q, V | T) is the joint probability density of the cumulative rainfall and corresponding peak flows, U (q, V | V)_TT) is the utility function value;

s43, only considering the critical rainfall when objective uncertainty is calculated by utilizing entropy, and if two continuous random variables X and Y exist, the joint entropy and the conditional entropy can be respectively shown as the following formulas:

wherein f (X, Y) is the joint probability density of random variables X and Y;

in the formula, f (X | Y) is a conditional probability density, namely the probability density of the value of X when Y takes any fixed value; the properties according to the conditional probability density can be given as:

the conditional entropy in the calculation of the critical rainfall can be expressed as the following form, wherein v is the accumulated rainfall, and q is the peak flow corresponding to the accumulated rainfall:

Technical Field

The invention relates to the field of mountain torrent disaster early warning and forecasting, in particular to a dynamic critical rainfall calculation method based on an entropy decision method.

Background

The mountain torrent disaster refers to the sudden strong and destructive mountain area flood caused by short-time rainstorm. In recent years, with the rapid development of economy and society and the aggravation of extreme weather in China, mountain torrent disasters become one of the most serious natural disasters in China. According to statistics, the direct economic loss caused by mountain torrent disasters in China accounts for about 70% of the national flood disaster loss, and the casualties account for about 80%. Most areas of China belong to monsoon climate, rainfall periods are concentrated, and in addition, mountainous areas of China are wide, water loss and soil erosion are serious, so that mountain torrent disasters are frequent, serious casualties and property loss are caused, and the economic and social development of the mountainous areas is also hindered.

The mountain torrent disaster has the characteristics of strong burst and large destructive power, and the problems of few monitoring sites, shortage of hydrological and meteorological data and the like in a mountain area make the mountain torrent disaster difficult to effectively early warn and prevent. The problem can be effectively solved by a method for determining the mountain torrent disaster early warning index. The method is an important link for preventing and controlling the mountain torrent disasters, and whether the mountain torrent disasters occur can be determined only by comparing the early warning indexes with the forecast data before the mountain torrent arrives. The current commonly used early warning index is critical rainfall. The critical rainfall refers to the occurrence of mountain torrents disasters in a drainage basin when the rainfall reaches a certain magnitude, and is the critical rainfall. When the rainfall reaches the critical rainfall, runoff is formed on the ground surface, so that the flow of a certain section of the river exceeds the critical flow, and the flood submerges the farmlands on two sides of the river, thereby causing certain social and economic losses. For medium and small watershed, torrential flood is strong in outburst, and accurate critical rainfall can enable people to predict arrival of torrential flood, so that flood alarm is issued in advance, evacuation transfer work is carried out, and loss caused by torrential flood is reduced to the maximum extent. If the critical rainfall is too small, the personnel can be transferred prematurely, which results in increased transfer cost and confusion of social order. If the critical rainfall is too large, the mountain torrent disaster occurs and the materials of the masses are not transferred, which causes serious loss. Therefore, the accurate and feasible dynamic critical rainfall is calculated by a scientific method, the personnel property loss in the mountain area can be reduced to the maximum extent, the technical support is provided for the evaluation, early warning, prevention and control and decision deployment work of the mountain torrent disasters, and the method has great significance for the early warning and forecast of the mountain torrent disasters and the work of disaster prevention and reduction.

Disclosure of Invention

The invention aims to overcome the defect that the critical rainfall calculation is inaccurate in the prior art, and provides a dynamic critical rainfall calculation method based on an entropy decision-making method.

In order to solve the technical problems, the invention adopts the technical scheme that: a dynamic critical rainfall calculation method based on an entropy decision method comprises the following steps:

s1, collecting and arranging actually-measured accumulated rainfall and corresponding flood peak flow data of multi-field flood of a drainage basin, and dividing the actually-measured accumulated rainfall and the corresponding flood peak flow data into a plurality of sample series according to the soil wetting degree and duration of the former period.

The rainfall runoff data of the multi-field actual measurement flood in the drainage basin is collected and sorted, and the correlation between the critical rainfall and the soil moistening degree in the early stage is considered, the conventional method is to divide the rainfall runoff data according to the soil moistening degrees (AMCI, AMCI II and AMCI III) in the early stage, and then subdivide the rainfall runoff data according to different durations (3h, 6h, 12h and 24h) under the condition of each early stage soil moistening degree. If the collected rainfall runoff data is less, the data is divided according to the soil moisture degree in the early stage to generate a very short data sequence, and accurate edge distribution is difficult to select. Therefore, rainfall data of each flood needs to be input into a hydrological model, flow series under different early soil wetting degree conditions are simulated, and then are subdivided according to different durations to obtain a plurality of groups of sample series of accumulated rainfall v and corresponding flood peak flow q.

And S2, performing edge distribution fitting on the collected sample series, and selecting the distribution with the best fitting effect by using K-S inspection.

Further, the invention selects exponential distribution, lognormal distribution and Weibull distribution to fit the cumulative rainfall v and the corresponding flood peak flow q sample series, and selects the distribution with the best fitting effect by K-S test, and the specific calculation steps are as follows:

s21, selecting exponential distribution, lognormal distribution and Weibull distribution to perform edge distribution fitting on the accumulated rainfall v and the corresponding flood peak flow q sample series under different early-stage soil wetting degrees and different duration conditions, and meanwhile, solving parameters corresponding to all distributions. The function expressions of the exponential distribution, the lognormal distribution and the Weibull distribution are respectively as follows:

in the formula, x is a random variable, and lambda is a proportional parameter of exponential distribution;

wherein x is a random variable, and μ and σ are the mean and standard deviation, respectively, of y ═ ln (x);

in the formula, x is a random variable, alpha is a scale parameter, beta is a shape parameter, and gamma is a position parameter;

the fitting of the three edge distributions can be achieved with the functions expfit, logfit and wblfit, respectively, in MATLAB software.

S22, judging whether the sample obeys a certain distribution by using a K-S test method, and comparing P values of the three distributions, wherein the P value is a statistic used for measuring significance level in the K-S test method. In the present invention it is assumed that the sample obeys the theoretical distribution function f (x), and if at the significance level (α ═ 0.05) the P value is less than 0.05, the original assumption is rejected, the sample does not obey the given distribution function f (x). Otherwise, the original assumption is accepted, and the larger the P value is, the better the fitting effect is. And finally, selecting the distribution with the best fitting effect as the optimal edge distribution of the sample series. The K-S test can be implemented using the function kstest in MATLAB software.

And S3, constructing combined distribution by using a Frank Copula function to obtain combined probability distribution of accumulated rainfall and corresponding flood peak flow under different early-stage soil wetting degrees and different duration conditions.

Further, step S3 specifically includes the following steps:

s31, selecting a Frank Copula function to construct joint distribution, wherein the joint distribution is defined as follows:

in the formula, F (X, Y) is a joint distribution function of the random variable (X, Y) at (X, Y), C is a Copula function, θ is a parameter of the Copula function, and can be calculated by a Kendall correlation coefficient τ, and the calculation formula of τ is as follows:

the joint cumulative distribution function F (x, y) of the random variables v and q may be defined as:

F(x,y)＝C(F(x),G(y))＝C(u,v)

wherein F (X, Y) is a joint distribution function of the random variable (X, Y) at (X, Y), and C is a Copula function; the joint density function is shown below:

f(x,y)＝c[F(x),G(y)]f(x)g(y)

wherein C is the density function of C, f (X) and g (Y) are the probability density functions of random variables X and Y, respectively;

kendall correlation coefficient tau is obtained through a sample series, a parameter theta can be obtained through the formula in a reverse mode, and then the joint distribution can be obtained through combining the edge distribution of two random variables v and q.

In MATLAB software, Kendall correlation coefficient tau can be calculated by a function corr, parameters of a Copula function can be calculated by a function Copula param, and joint probability distribution of the Copula function can be calculated by a function Copula and df.

And S4, substituting the joint probability distribution and corresponding parameters into a Bayes utility function and an expected utility-entropy risk function formula respectively, considering the conditions that subjective factors, objective factors and subjective and objective factors are simultaneously influenced, and minimizing the utility function and the risk to obtain critical rain values under different soil wetting degrees in the early stage and different duration conditions.

Further, the step S4 specifically includes:

s41, the utility-entropy decision model is expected to combine the objective risk of performing an action with the subjective preference of the decision maker. The function expression is as follows:

in the formula, mean_a∈A{|E[(u(X(a,θ))]| } ≠ 0, Ha (θ) represents the entropy of action a corresponding to state θ; x (a, θ) represents the result for state θ when action a is taken, and consists of four parts: x₁₁(accurately give an alarm, Q is greater than or equal to Q and V is greater than or equal to V)_T)、X₁₂(missing report, Q is more than or equal to Q and V is less than V_T)、X₂₁(false alarm, Q is less than Q and V is more than or equal to V)_T) And X₂₂(No alarm is issued accurately, Q < Q and V < V)_T)；λ∈[0,1]The "trade-off coefficient" reflects the trade-off between the subjective expected utility and the objective uncertainty of the decision maker's behavior. When λ is 0, only the subjective preference of the decision maker is considered, and it is expected that the utility will have a greater impact; when λ is 1, then the desired utility of the decision maker is not considered, only the entropy, i.e. the influence of the objective uncertainty, is considered. However, in actual decision making, both subjective expectation and objective risk of a decision maker need to be considered, so that a case where λ is 0.5 is assumed as both factors is considered. When action a is taken to make the function obtain the minimum value, namely the risk is minimum, action a is the optimal action scheme, and V is at the moment_TThe optimal critical rainfall is obtained;

s42, calculating the critical rainfall only considering the subjective preference of the decision maker by using a Bayesian utility function, wherein the critical rainfall is defined as follows:

wherein q is a flow rate value, m³S; q is the critical flow value of the river critical section, m³S; v is the cumulative rain value, mm; v_TCritical rain value, mm; t is duration of heavy rain (3h, 6h, 12h, 24 h); parameter a is 10 × 10⁶，b＝200，c＝0.025，C₀＝10×10³，a’＝5×10⁶，b’＝800，c’＝0.03；

Critical rainfall V for different soil wetting degrees in the early stages (AMCI, AMCII) and different rainfall durations (3, 6, 12, 24 hours)_TCan be determined by minimizing the expected utility loss function, i.e. finding the V that minimizes the expected utility loss function_TValue V_TThis value is the evaluated value; the specific formula is as follows:

where f (q, V | T) is the joint probability density of the cumulative rainfall and corresponding peak flows, U (q, V | V)_TT) is the utility function value;

s43, only considering the critical rainfall when objective uncertainty is calculated by utilizing entropy, and if two continuous random variables X and Y exist, the joint entropy and the conditional entropy can be respectively shown as the following formulas:

wherein f (X, Y) is the joint probability density of random variables X and Y;

in the formula, f (X | Y) is a conditional probability density, namely the probability density of the value of X when Y takes any fixed value; the properties according to the conditional probability density can be given as:

the conditional entropy in the calculation of the critical rainfall can be expressed as the following form, wherein v is the accumulated rainfall, and q is the peak flow corresponding to the accumulated rainfall:

entropy decision methods are classical methods in the field of investment decision making, and can combine objective risk of performing an action with subjective preferences of the decision maker. When a mountain flood arrives, it is a risk action for a decision maker whether to issue a flood alarm. When taking action, the subjective judgment of a decision maker and the uncertainty of an objective event jointly determine the risk of the action, the smaller the risk is, the better the risk is, the critical rainfall at the minimum risk can be obtained by adopting the method, and the decision maker can make the minimum risk by comparing the actual rainfall with the critical rainfall when facing the coming mountain torrents. Therefore, the method for determining the critical rainfall has strong rationality and accuracy, and has a great prospect in the future research of mountain torrent disaster early warning and forecasting. The method solves the problem of determining the mountain torrent disaster early warning index by using a risk decision method, not only considers the influence of subjective preference of a decision maker, but also considers the uncertainty of objective state, fully embodies the characteristics of risk action, and has the advantages of lower calculation complexity, clear and definite structure and reasonable and accurate calculation result, thereby being widely applied to mountain torrent disaster early warning and forecasting work.

Compared with the prior art, the beneficial effects are: according to the dynamic critical rainfall calculation method based on the entropy decision method, dynamic critical rainfall under different early soil humidity conditions is calculated by introducing the entropy decision method in the risk decision field, so that personnel and property losses caused by torrential mountain torrents can be reduced to the maximum extent, scientific basis is provided for evaluation, early warning, prevention and control and decision deployment of the mountain torrents, and the method has great significance for early warning and forecast of the mountain torrents and disaster prevention and reduction.

Drawings

FIG. 1 is an overall flow chart of the method of the present invention.

Fig. 2 is a schematic diagram of three time periods (points) for calculating the accumulated rainfall v and the corresponding peak flow q according to the present invention.

Fig. 3 is a scatter diagram of a series of samples of accumulated rainfall v and corresponding flood peak flow q at different early soil wetting degrees and different durations.

Fig. 4 is a comparison graph of the fitting effect of the edge distribution of the cumulative rainfall v and the corresponding flood peak flow q sample series according to the present invention.

FIG. 5 is a graph of combined probability density over different durations under early soil wetting conditions in accordance with the present invention.

FIG. 6 is a graph showing the joint probability distribution of different durations under the soil wetting condition at the early stage of the present invention.

Fig. 7 is a diagram of a result of a critical rainfall calculation obtained by an entropy decision method according to the present invention.

Fig. 8 is a diagram illustrating evaluation of critical rainfall application effect by the entropy decision method of the present invention.

Detailed Description

The drawings are for illustration purposes only and are not to be construed as limiting the invention; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the invention.