Rainfall flood similarity discrimination method based on kernel mapping

Abstract

A rainfall flood similarity discrimination method based on kernel mapping comprises the following steps: step 1, summarizing flood peaks, flood volumes, flood processes and rainfall distribution situations of main control points of main and branch flows in a research drainage basin in each typical flood process, and constructing a typical flood sample library of the drainage basin; step 2, constructing empirical kernel mapping of the flood sequence; step 3, performing empirical loss analysis on the flood sample; and 4, analyzing the rainfall flood similarity. According to the method, the rainfall flood similarity is judged through the nuclear density technology, the internal relation of hydrological data is fully mined, and a new thought is provided for rainfall flood similarity judgment.

Description

Technical Field

[0001] The invention relates to the technical field of flood control safety design of water conservancy projects, and in particular to a rainfall-flood similarity discrimination method based on kernel mapping. Background Art

[0002] The joint dispatching of reservoir groups has become an important means of comprehensive dispatching for flood control and disaster reduction in the basin. At present, there is still a lot of room for development in the ability to judge the water and rainfall conditions in the future. The formation of rainstorm floods is a gradual evolutionary process. Different water and rainfall development processes often have certain correlations and similarities. These similar characteristics may recur in historical rainfall and flood processes. Therefore, by using the rainfall and flood similarity analysis method to study historical rainfall and flood data, find out the flood processes with similar causes and magnitudes in history, appropriately extend the water and rainfall forecast period, and quickly diagnose the current water and rainfall development trend, it can provide a certain reference basis for flood control and disaster reduction dispatching in the basin.

[0003] Domestic and foreign scholars have conducted some analytical research on rainfall and flood similarity, mainly including similarity algorithms such as principal component analysis and cluster analysis, as well as summarizing and analyzing flood similarity based on the physical causes of rainstorms and floods in the basin. These analytical methods are all based on statistical theory and methods, and the mining of the internal connections of hydrological data is still insufficient.

[0004] Therefore, it is necessary to design a rainfall-flood similarity discrimination method based on kernel mapping to overcome the above problems. Summary of the invention

[0005] In order to avoid the above problems, a rainfall and flood similarity discrimination method based on kernel mapping is provided. The kernel density technology is used to discriminate rainfall and flood similarity, which fully explores the intrinsic connection of hydrological data and provides a new idea for rainfall and flood similarity discrimination.

[0006] The present invention provides a method for distinguishing rainfall and flood similarity based on kernel mapping, comprising the following steps:

[0007] Step 1: Summarize the flood peaks, flood volumes, flood processes and rainfall distribution of the main control points of the main and tributary rivers in the basin during each typical flood process, and construct a typical flood sample library in the basin;

[0008] Step 2, construct the empirical kernel map of the flood sequence;

[0009] Step 3, empirical loss analysis of flood samples;

[0010] Step 4: Analyze the similarity of rainfall and flood.

[0011] Preferably, in step 1, from the perspective of flood prevention, a typical flood sample library X that can characterize the study basin is constructed as follows:

[0012]

[0013] Where M represents the total number of stations, and N represents the total number of flood samples at a single station.

[0014] Preferably, step 2 specifically includes:

[0015] 2.1 The flood sequence values ​​of each control station of the main and tributary rivers are {x i} i＝1,…,N , its kernel matrix is ​​as follows:

[0016] K N×N ={φ(x i )φ(x j ) i＝1,…,N；j＝1,…,N};

[0017] In the formula, φ(x i ),φ(x j ) is x i 、x j In the mapping of kernel space, i and j are the serial numbers of the variables in the kernel space;

[0018] 2.2 The kernel map of the flood sequence is constructed using the Gaussian kernel density function as follows:

[0019]

[0020] Where, σ is the kernel density variance of flood samples;

[0021] 2.3 The empirical kernel mapping equation is as follows:

[0022]

[0023] In the formula, Λ R×R K N×N The eigenvalue diagonal matrix of is the matrix consisting of eigenvectors corresponding to eigenvalues.

[0024] Preferably, step 3 specifically includes:

[0025] 3.1 Classify and label the flood samples. If there is missing data, the missing data is defined as unlabeled samples X U ; The flood series consisting of labeled samples and unlabeled samples are mapped into m kernel spaces, and the label Y of the unlabeled samples U The determination method is as follows:

[0026]

[0027] Where, f(x)=sign([φ(x),1]w) is the basic classifier, and w is the weight coefficient of the basic classifier;

[0028] 3.2 Construct an empirical loss for unlabeled samples to train the model. In the iterative optimization process of the model, make full use of the collaborative work between multiple cores, pseudo-label the unlabeled samples according to the discrimination results of the basic classifier on the unlabeled samples, and construct a pseudo empirical loss R pel as follows:

[0029] R pel =(X U’ wxya U’ ) t (X U’ wxya U’ );

[0030] Among them, X U' is an unlabeled sample with pseudo labels, Y U’ is its corresponding pseudo label, and t is the gradient descent parameter;

[0031] 3.3 For all unlabeled samples, their similarity is calculated by their adjacent samples, which is defined by the following formula: s(X U ,X L ) = exp(-γ||X U -X L || 2 );

[0032] In the formula, γ is a scalar factor that controls the degree of similarity measurement of samples, X L To mark the sample.

[0033] Preferably, step 4 specifically includes:

[0034] 4.1 Define the rainfall-flood similarity objective function as follows:

[0035]

[0036] Among them, X L+U is the set of labeled samples and unlabeled samples, Y L is the label of the labeled sample, S is the similarity matrix between the unlabeled sample and the labeled sample; m is the number of kernel spaces; c1, c2, c3 and λ are weight parameters, all of which are positive real numbers; the optimal value of w is obtained by minimizing this objective function, using the Lagrangian method;

[0037] 4.2 Define the rainfall-flood similarity discriminant as:

[0038]

[0039] φl (x) and w l Respectively represent the values ​​of the weight coefficients of the kernel mapping and the basic classifier in the lth kernel space;

[0040] The larger the F(x) value, the higher the similarity.

[0041] Compared with the prior art, the present invention has the following beneficial effects: the present invention uses kernel density technology to determine the similarity of rainfall and floods. Compared with traditional statistical methods, it can more fully explore the intrinsic connection of hydrological data, more accurately identify the similarity of rainfall and floods, and provide technical support for the optimal scheduling of river basin reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The present invention is a flowchart of a method for distinguishing rainfall and flood similarity based on kernel mapping according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to facilitate ordinary technicians in the field to understand and implement the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the implementation examples described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0044] like Figure 1 As shown, this embodiment provides a method for determining rainfall and flood similarity based on kernel mapping, comprising the following steps:

[0045] Step 1: Summarize the flood peaks, flood volumes, flood processes and rainfall distribution of the main control points of the main and tributary rivers in the study basin during each typical flood process, and construct a typical flood sample library X that can characterize the study basin from the perspective of flood control disadvantage, as shown in the following formula:

[0046]

[0047] Where M represents the total number of stations, and N represents the total number of flood samples at a single station.

[0048] Step 2, construct the empirical kernel map of the flood sequence;

[0049] 2.1 The flood sequence values ​​of each control station of the main and tributary rivers are {x i} i＝1,…,N , its kernel matrix is ​​as follows:

[0050] K N×N ={φ(x i )φ(x j ) i＝1,…,N；j＝1,…,N};

[0051] In the formula, φ(x i ),φ(x j ) is xi 、x j In the mapping of kernel space, i and j are the serial numbers of the variables in the kernel space;

[0052] 2.2 The kernel map of the flood sequence is constructed using the Gaussian kernel density function as follows:

[0053]

[0054] Where, σ is the kernel density variance of flood samples;

[0055] 2.3 The empirical kernel mapping equation is as follows:

[0056]

[0057] In the formula, Λ R×R K N×N The eigenvalue diagonal matrix of is the matrix consisting of eigenvectors corresponding to eigenvalues.

[0058] Step 3, empirical loss analysis of flood samples;

[0059] 3.1 Classify and label the flood samples. If there is missing data, the missing data is defined as unlabeled samples X U ; The flood series consisting of labeled samples and unlabeled samples are mapped into m kernel spaces, and the label Y of the unlabeled samples U The determination method is as follows:

[0060]

[0061] Where, f(x)=sign([φ(x),1]w) is the basic classifier, and w is the weight coefficient of the basic classifier;

[0062] 3.2 Construct an empirical loss for unlabeled samples to train the model. In the iterative optimization process of the model, make full use of the collaborative work between multiple cores, pseudo-label the unlabeled samples according to the discrimination results of the basic classifier on the unlabeled samples, and construct a pseudo empirical loss R pel as follows:

[0063] R pel =(X U’ wxya U’ ) t (X U’ wxya U’ );

[0064] Among them, X U' is an unlabeled sample with pseudo labels, Y U’ is its corresponding pseudo label, and t is the gradient descent parameter;

[0065] 3.3 For all unlabeled samples, their similarity is calculated by their adjacent samples, which is defined by the following formula: s(X U ,X L ) = exp(-γ||X U -X L || 2 );

[0066] In the formula, γ is a scalar factor that controls the degree of similarity measurement of samples, X L To mark the sample.

[0067] Step 4, analyzing rainfall and flood similarity;

[0068] 4.1 Define the rainfall-flood similarity objective function as follows:

[0069]

[0070] Among them, X L+U is the set of labeled samples and unlabeled samples, Y L is the label of the labeled sample, S is the similarity matrix between the unlabeled sample and the labeled sample; m is the number of kernel spaces; c1, c2, c3 and λ are weight parameters, all of which are positive real numbers; the optimal value of w is obtained by minimizing this objective function, using the Lagrangian method;

[0071] 4.2 Define the rainfall-flood similarity discriminant as:

[0072]

[0073] φ l (x) and w l Respectively represent the values ​​of the weight coefficients of the kernel mapping and the basic classifier in the lth kernel space;

[0074] The larger the F(x) value, the higher the similarity.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for distinguishing rainfall and flood similarity based on kernel mapping, characterized in that: The steps include: Step 1: Summarize the flood peaks, flood volumes, flood processes and rainfall distribution of the main control points of the main and tributary rivers in the basin during each typical flood process, and construct a typical flood sample library in the basin; Step 2, construct the empirical kernel map of the flood sequence; Step 3, empirical loss analysis of flood samples; Step 4: Analyze the similarity of rainfall and flood.

2. The method for distinguishing rainfall and flood similarity based on kernel mapping as claimed in claim 1, characterized in that: In step 1, from the perspective of flood control disadvantage, a typical flood sample library X that can characterize the study basin is constructed as follows: Where M represents the total number of stations, and N represents the total number of flood samples at a single station.

3. The method for determining rainfall and flood similarity based on kernel mapping as claimed in claim 2, characterized in that: Step 2 specifically includes: 2.1 Taking the flood sample of a certain station as an example, the flood sequence value is {x i } i＝1,…,N , its kernel matrix is ​​as follows: K N×N ={φ(x i )φ(x j ) i＝1,…,N；j＝1,…,N }; In the formula, φ(x i ),φ(x j ) is x i 、x j In the mapping of kernel space, i and j are the serial numbers of the variables in the kernel space; 2.2 The kernel map of the flood sequence is constructed using the Gaussian kernel density function as follows: Where, σ is the kernel density variance of flood samples; 2.3 The empirical kernel mapping equation is as follows: In the formula, Λ R×R K N×N The eigenvalue diagonal matrix of is the matrix consisting of eigenvectors corresponding to eigenvalues.

4. The method for distinguishing rainfall and flood similarity based on kernel mapping as claimed in claim 3, characterized in that: Step 3 specifically includes: 3.1 Classify and label the flood samples. If there is missing data, the missing data is defined as unlabeled samples X U ; The flood series consisting of labeled samples and unlabeled samples are mapped into m kernel spaces, and the label Y of the unlabeled samples U The determination method is as follows: Where, f(x)=sign([φ(x),1]w) is the basic classifier, and w is the weight coefficient of the basic classifier; 3.2 Construct an empirical loss for unlabeled samples to train the model. In the iterative optimization process of the model, make full use of the collaborative work between multiple cores, pseudo-label the unlabeled samples according to the discrimination results of the basic classifier on the unlabeled samples, and construct a pseudo empirical loss R pel as follows: R pel =(X U’ w-Y U’ ) t (X U’ w-Y U’ ); Among them, X U′ is an unlabeled sample with pseudo labels, Y U’ is its corresponding pseudo label, and t is the gradient descent parameter; 3.3 For all unlabeled samples, their similarity is calculated by their adjacent samples, which is defined by the following formula: s(X U ,X L ) = exp(-γ||X U -X L || 2 ); In the formula, γ is a scalar factor that controls the degree of similarity measurement of samples, X L To mark the sample.

5. The method for determining rainfall and flood similarity based on kernel mapping as claimed in claim 4, characterized in that: Step 4 specifically includes: 4.1 The objective function of rainfall-flood similarity is defined as follows: Among them, X L+U is the set of labeled samples and unlabeled samples, Y L is the label of the labeled sample, S is the similarity matrix between the unlabeled sample and the labeled sample; m is the number of kernel spaces; c1, c2, c3 and λ are weight parameters, all of which are positive real numbers; the optimal value of w is obtained by minimizing this objective function, using the Lagrangian method; 4.2 Define the rainfall-flood similarity discriminant as: φ l (x) and w l Respectively represent the values ​​of the weight coefficients of the kernel mapping and the basic classifier in the lth kernel space; The larger the F(x) value, the higher the similarity.

Images