KDE-Vine Copula-based eutrophication risk assessment method for black and odorous water body

Abstract

The invention discloses a black and odorous water eutrophication risk assessment method based on KDE-Vine Copula, and the method comprises the steps: carrying out the preliminary discrimination through a black and odorous water recognition model, recognizing the feature importance through an SEaTH algorithm, constructing a multi-dimensional feature space, optimizing a preliminary recognition result according to an optimal support vector principle, and estimating the edge distribution through a radial basis function. And selecting a Copula function with an optimal fitting effect, and constructing a Vine Copula tree structure to evaluate the eutrophication risk of the black and odorous water body. Compared with an original parameter method for constructing edge distribution, the KDE is not limited to any distribution hypothesis, the random variable distribution form can be met to the maximum degree, and the fitting effect is better. On the whole, the eutrophication risk assessment model is constructed by integrating various water quality parameters, and a new way is provided for water quality condition assessment.

Description

Technical Field

[0001] The invention belongs to the field of water environment remote sensing, relates to a water eutrophication risk assessment method, and specifically relates to a black and odorous water eutrophication risk assessment method based on KDE-Vine Copula. Background Art

[0002] Water quality assessment is a basic task for the rational development, utilization and protection of water resources. It is the most important means for the government to control water ecology and water environment. It is also a comprehensive task involving multiple factors such as pollution sources and water quality parameter indicators. In recent years, the China National Environmental Monitoring Center has evaluated the degree of eutrophication of water bodies through 3,641 surface water assessment sections and the Comprehensive Nutritional Status Index (TLI), providing a basis for relevant government departments to prevent or rectify the water ecological environment.

[0003] With the acceleration of urban industrialization, the discharge of wastewater rich in organic matter is bound to pollute urban rivers, bring about secondary disasters such as eutrophication, and cause the self-purification capacity of rivers to exceed the load, thereby accelerating the deterioration of water quality and becoming one of the factors hindering the construction of water ecological civilization. Therefore, controlling the degree of eutrophication of water bodies is a necessary stage in urban river management, and water quality monitoring is an important part of urban water environment management.

[0004] Traditional monitoring methods are small in scope and low in efficiency. Satellite remote sensing water quality monitoring has the advantages of low cost and high efficiency, providing a new technical means for urban water quality monitoring. Through remote sensing technology, the formation, harm, evaluation and governance of water eutrophication have been studied at home and abroad. Li Yunmei used the analytical model method to establish a water body reflectance simulation model, and evaluated the eutrophication of water bodies by solving the optimization function to calculate the nutrient status index of the sampling point; Wang Shengrui used mathematical statistics, remote sensing quantitative inversion and quantitative interpretation, and hierarchical analysis to determine the water ecological risk of Dongting Lake, and proposed a technical route for the prevention and control of Dongting Lake water ecological risk; Jingxia used the semi-empirical regression model and the modified Carlson index method to evaluate the eutrophication degree of Miyun Reservoir water bodies; Azevedo used the cumulative probability density model to predict the eutrophication risk; Biggs proposed a function based on concentration and cumulative days to predict the eutrophication degree based on the maximum chlorophyll a regression model. From the current research situation, large-scale water quality monitoring is mainly completed through remote sensing technology, and local small waters can be evaluated by field sampling and testing. However, in current research, many scholars use a single indicator to evaluate the eutrophication degree of water bodies, and there are few multi-parameter risk assessment models, which lack a comprehensive analysis of water quality conditions. As a mathematical model that connects multivariate distributions, the Vine Copula function can better combine multiple indicators for risk probability assessment, which helps to analyze the internal correlation characteristics of high-dimensional variables. It has been applied to the evaluation of water quality nutrient status in a small area, such as Zhang Yan used the Copula function to evaluate the eutrophication status of Meihu, an artificial lake of Zhengzhou University. However, there is a lack of application of remote sensing technology combined with the VineCopula function in the risk assessment of eutrophication of large-scale water bodies such as urban areas. Summary of the invention

[0005] In view of the current situation that there are few overall indicators used for evaluation in previous studies and a lack of large-scale remote sensing monitoring, the present invention uses KDE (kernel density function estimation method) and Copula theory to provide a new black and odorous water eutrophication risk assessment method based on KDE-Vine Copula, and uses KDE to reconstruct the marginal distribution. Compared with the original parameter method to construct the marginal distribution, KDE is not limited to any distribution assumptions and can maximize the distribution form of random variables, that is, the fitting effect is better. In general, the method of the present invention integrates a variety of water quality parameters to construct a eutrophication risk assessment model, providing a new way to evaluate water quality conditions.

[0006] The objective of the present invention is achieved through the following technical solutions: A black and odorous water eutrophication risk assessment method based on KDE-Vine Copula comprises the following steps: Step 1: Remote sensing image feature optimization and black and odorous water body identification: The black and odorous water body recognition model is used to make a preliminary identification of the black and odorous water body, the SEaTH (SEparability and THresholds) algorithm is used to identify the importance of features, a multi-dimensional feature space is constructed, and the preliminary identification results are optimized by combining it with the optimal support vector theory; Step 2: Construction of edge distribution: The inversion results of water quality parameters Chl-a (chlorophyll a), TSS (suspended solids), and SD (transparency) are used as one-dimensional indicator sequences, and the KDE method is used to smooth them based on the kernel function, that is, the overall one-dimensional distribution is inferred based on the existing data samples:

[0007] In the formula, represents any sample value, For a water quality monitoring indicator, if the simulation sequence Smaller than The number is , is the sample size, express The corresponding cumulative frequency; Step 3: Selection of Vine Copula function: Based on the marginal distribution constructed in step 2, the Copula function fitting effect and applicability are judged according to the squared euclidean metric in the two-dimensional random variable state. In the high-dimensional random variable, the tree structure is used to simplify the calculation, and the optimal Copula function is determined according to the AIC (Akaike information criterio) of each edge, and then the optimal Copula joint probability distribution model is established. Step 4: Solve the joint probability distribution: The joint probability distribution is solved according to the optimal Copula joint probability distribution model established in step 3 to comprehensively analyze the eutrophication risk of water bodies.

[0008] Compared with the prior art, the present invention has the following advantages: (1) This invention combines the Vine Copula function with remote sensing technology to study and analyze the eutrophication risk of water bodies in a large area. Compared with traditional water quality monitoring, this method improves the monitoring efficiency to a certain extent and expands the monitoring scope. On the basis of the original single indicator evaluation, the eutrophication risk probability assessment based on multiple factors is helpful to further evaluate the water ecological environment and reflect the water quality status more realistically and accurately.

[0009] (2) The present invention uses KDE to improve the marginal distribution structure of the original Vine Copula function and combines it with the two-dimensional model of the Vine Copula function. This method does not require prior knowledge of the original data, is not limited to any distribution assumptions, and can maximize the distribution form of random variables. A kernel density function is established based on the radial basis function (RBF), and the kernel density function value of each sample point is weighted averaged to obtain the probability density estimate of the sample point. When the number of samples tends to infinity, the kernel density estimate probability density function is infinitely close to the true probability density distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 This is a flow chart of the black and odorous water eutrophication risk assessment method based on KDE-Vine Copula; Figure 2 is the two-dimensional joint risk probability under the combination of (Chl-a, SD), (Chl-a, TSS), and (TSS, SD); Figure 3 is the three-dimensional joint risk probability under the (Chl-a, TSS, SD) combination. DETAILED DESCRIPTION

[0011] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0012] The present invention provides a black and odorous water body eutrophication risk assessment method based on KDE-Vine Copula, which makes a preliminary judgment through a black and odorous water body recognition model, uses the SEaTH algorithm to identify the importance of features, constructs a multidimensional feature space, optimizes the preliminary recognition results according to the optimal support vector principle, estimates the marginal distribution using the radial basis function, selects the Copula function with the best fitting effect, and constructs a Vine Copula tree structure to assess the eutrophication risk of black and odorous water bodies. Figure 1 As shown, the specific steps include: Step 1: Remote sensing image feature optimization and black and odorous water body identification: The black and odorous water body recognition model is used to make a preliminary identification of the black and odorous water body. The SEaTH algorithm is used to identify the importance of features, and a multidimensional feature space is constructed. The preliminary identification results are optimized by combining it with the optimal support vector theory. The specific steps are as follows: Step 1.1: Due to the high concentration of suspended solids in black and odorous water, the overall change of its reflectivity between the green light band and the red light band is gentle, while the change of general water is more obvious. Therefore, the present invention uses the normalized ratio model BOI (Black and Odorous Water Index) to make a preliminary judgment on black and odorous water:

[0013] In the formula, is the remote sensing reflectance in the blue light band, is the remote sensing reflectance of the green light band, is the remote sensing reflectivity in the red light band.

[0014] Step 1.2: Extract the spectral mean, variance, contrast, correlation, entropy, homogeneity, dissimilarity and second moment features of remote sensing images. eigenvalues, represents the number of features, Indicates the number of bands The SEaTH algorithm is used to identify feature importance. The JM (Jeffries-Matusita) distance is usually used to measure sample separation and rank feature importance. The feature corresponding to the maximum JM distance between two categories is taken as the best feature, and the feature importance is selected according to feature importance. The best features construct a multidimensional feature space :

[0015] In the formula, represents the Bhattacharyya distance, and represents the mean of a feature of two categories, and represents the characteristic standard deviation of the two categories, represents the JM distance; Step 1.3: In the multidimensional feature space, the preliminary recognition results are used as training samples, and the support vector machine is used to identify black and odorous water bodies to obtain the final optimization results.

[0016] Step 2: Construction of edge distribution: The inversion results of water quality parameters Chl-a (chlorophyll a), TSS (suspended solids), and SD (transparency) are used as one-dimensional indicator sequences, and the KDE method is used to smooth them based on the kernel function, that is, the overall one-dimensional distribution is inferred based on the existing data samples:

[0017] In the formula, represents any sample value, For a water quality monitoring indicator, if the simulation sequence Smaller than The number is , is the sample size, express The corresponding cumulative frequency.

[0018] The kernel density estimation function expression is:

[0019] In the formula, For The estimated probability density function at is the sample size, Indicates bandwidth , Represents Gaussian kernel function.

[0020] Bandwidth is an important parameter that affects the smoothness and accuracy of the estimate. The larger the bandwidth, the smoother the function, while weakening the detailed features of some data points. The smaller the bandwidth, the better the function fitting accuracy, but it will generate noise. Therefore, in the process of kernel density estimation, the optimal bandwidth should be selected, and the expression is:

[0021] In the formula, , represents the sample standard deviation, represents the sample interquartile range.

[0022] The Gaussian kernel function expression is:

[0023] In the formula, Represents the input value, Represents the Gaussian kernel function value.

[0024] Step 3: Selection of Vine Copula function: On the basis of the marginal distribution constructed in step 2, in order to analyze the joint risk probability of water eutrophication indicators, it is necessary to construct a multivariate function model for analysis. That is, in the state of two-dimensional random variables, the Copula function fitting effect and applicability are judged according to the squared Euclidean metric. However, in high-dimensional random variables, as the variable dimension increases, it will bring about the "dimensionality disaster" and increase the complexity of the model. Usually, a tree structure is used to simplify the calculation, and the optimal Copula function is determined according to the AIC (Akaike information criterio) of each edge, and then the optimal Copula joint probability distribution model is established. The specific steps are as follows: Step 3.1: Under the two-dimensional random variable state, determine the optimal Copula function according to the principle of minimum squared Euclidean distance. The expression of squared Euclidean distance is:

[0025] In the formula, Represents the Copula sample frequency, that is, the empirical frequency, Indicates the Copula calculation frequency, that is, the calculation frequency, is the sample size.

[0026] Step 3.2, in the state of multidimensional random variables, determine the optimal Copula function according to the AIC of each edge. The AIC expression is:

[0027] In the formula, represents the number of model parameters, represents the log-likelihood function of the model.

[0028] Step 3.3, use the maximum likelihood estimation method to solve the Copula model parameters, and the joint probability density function can be expressed as:

[0029] In the formula, Indicates a water quality monitoring indicator. Indicates the parameters to be requested, , to obtain .

[0030] Step 3.4: Sum the AIC values ​​of all edges of the tree structure and select the tree structure with the minimum total AIC as the optimal function model.

[0031] Step 4: Solve the joint probability distribution: Copula functions are random variables The joint distribution of With their respective marginal distribution functions A function connected to each other, then there exists a function

[0032] satisfy , according to the optimal Copula joint probability distribution model, the joint probability distribution is solved to comprehensively analyze the eutrophication risk of water bodies. The specific steps for solving the joint probability distribution are as follows: Step 4.1: To solve the joint probability distribution, express the joint probability density function as:

[0033] In the formula, is the joint probability density, is the Copula function, is the marginal distribution function, is the edge density function.

[0034] Step 4.2: According to conditional probability, we can get:

[0035] Decompose the three-dimensional joint probability density function into:

[0036] Inferred:

[0037] Step 4.3: Combine steps 4.1 and 4.2 to obtain the joint probability density function:

[0038] Figure 2 and Figure 3 This is a black and odorous water eutrophication risk assessment result diagram based on KDE-Vine Copula of the present invention. Figure 2 (a), (b), and (c) are the two-dimensional joint risk probabilities under the combination of (Chl-a, SD), (Chl-a, TSS), and (TSS, SD), respectively. Figure 3It represents the three-dimensional joint risk probability under the combination of (Chl-a, TSS, SD). As the concentration of each parameter increases, the overall eutrophication risk probability gradually increases. When the concentrations of Chl-a, TSS, and SD are all small, the eutrophication risk probability is low. When the concentration of Chl-a or SD remains unchanged, the change in TSS concentration has a more obvious effect on the eutrophication risk probability, indicating that TSS will have a greater impact on water quality. The reason is that TSS includes many components, and different components and different concentrations will affect water quality. Eutrophication of water bodies is not limited to a certain water quality parameter, but is caused by multiple factors. If the eutrophication risk probability is to be maintained at a low level and a good water quality is to be maintained, the water quality cannot be evaluated by a single indicator. The concentration of each water quality parameter must be accurately controlled, and the concentration of TSS and its components must be monitored. Only by fully considering the impact of multiple parameters and conducting a comprehensive analysis can the evaluation results of water quality be more accurate.

Claims

1. A risk assessment method for eutrophication of black and odorous water bodies based on KDE-Vine Copula, characterized in that The method comprises the following steps: Step 1: Remote sensing image feature optimization and black and odorous water body identification: The black and odorous water body recognition model is used to make a preliminary identification of the black and odorous water body, the SEaTH algorithm is used to identify the importance of features, a multi-dimensional feature space is constructed, and the preliminary identification results are optimized by combining it with the optimal support vector theory; Step 2: Construction of edge distribution: The inversion results of Chl-a, TSS and SD water quality parameters are respectively used as one-dimensional indicator sequences, and the KDE method is used to smooth them based on the kernel function, that is, the overall one-dimensional distribution is inferred based on the existing data samples: In the formula, represents any sample value, For a water quality monitoring indicator, if the simulation sequence Smaller than The number is , is the sample size, express The corresponding cumulative frequency; Step 3: Selection of Vine Copula function: Based on the marginal distribution constructed in step 2, the Copula function fitting effect and applicability are judged according to the squared Euclidean distance in the two-dimensional random variable state. In the high-dimensional random variable, the tree structure is used to simplify the calculation, and the optimal Copula function is determined according to the AIC of each edge, and then the optimal Copula joint probability distribution model is established; Step 4: Solve the joint probability distribution: The joint probability distribution is solved according to the optimal Copula joint probability distribution model established in step 3 to comprehensively analyze the eutrophication risk of water bodies.

2. The black and odorous water eutrophication risk assessment method based on KDE-Vine Copula according to claim 1, characterized in that The specific steps of step 1 are as follows: Step 1.1: Use the normalized ratio model BOI to make a preliminary judgment on black and odorous water bodies: In the formula, is the remote sensing reflectance in the blue light band, is the remote sensing reflectance of the green light band, is the remote sensing reflectance in the red light band; Step 1.2: Extract the spectral mean, variance, contrast, correlation, information entropy, homogeneity, heterogeneity and second-order moment features of remote sensing images. eigenvalues, represents the number of features, Indicates the number of bands, , the SEaTH algorithm is used to identify the importance of features, the JM distance is used to measure the sample separation, the feature importance is sorted, and the feature corresponding to the maximum JM distance between the two categories is taken as the best feature. The best features construct a multidimensional feature space: In the formula, represents the Bhattacharyya distance, and represents the mean of a feature of two categories, and represents the characteristic standard deviation of the two categories, represents the JM distance, ; Step 1.3: In the multidimensional feature space, the preliminary recognition results are used as training samples, and the support vector machine is used to identify black and odorous water bodies to obtain the final optimization results.

3. The black and odorous water eutrophication risk assessment method based on KDE-Vine Copula according to claim 1, characterized in that In step 2, the kernel density estimation function expression is: In the formula, For The estimated probability density function at is the sample size, Indicates bandwidth , represents the Gaussian kernel function.

4. The black and odorous water eutrophication risk assessment method based on KDE-Vine Copula according to claim 1, characterized in that The specific steps of step 3 are as follows: Step 3.1: Under the two-dimensional random variable state, determine the optimal Copula function according to the principle of minimum squared Euclidean distance. The expression of squared Euclidean distance is: In the formula, Represents the Copula sample frequency, that is, the empirical frequency, Indicates the Copula calculation frequency, that is, the calculation frequency, is the sample size; Step 3.2, in the state of multidimensional random variables, determine the optimal Copula function according to the AIC of each edge. The AIC expression is: In the formula, represents the number of model parameters, represents the log-likelihood function of the model; Step 3.3, use the maximum likelihood estimation method to solve the Copula model parameters, and the joint probability density function is expressed as: In the formula, Indicates a water quality monitoring indicator. Indicates the parameters to be requested, , to obtain ; Step 3.4: Sum the AIC values ​​of all edges of the tree structure and select the tree structure with the minimum total AIC as the optimal function model.

5. The black and odorous water eutrophication risk assessment method based on KDE-Vine Copula according to claim 1, characterized in that The specific steps of step 4 are as follows: Step 4.1: To solve the joint probability distribution, express the joint probability density function as: In the formula, is the joint probability density, is the Copula function, is the marginal distribution function, is the edge density function; Step 4.2, according to conditional probability, we get: Decompose the three-dimensional joint probability density function into: Inferred: Step 4.3: Combine steps 4.1 and 4.2 to obtain the joint probability density function: 。

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