A comprehensive water quality assessment method

Abstract

The present invention belongs to the technical field of water quality assessment, and specifically designs a comprehensive water quality assessment method based on multidimensional Gaussian distribution of water quality indicators and a Bayesian method. The multidimensional Gaussian distribution model of multiple water quality indicators is established to effectively quantify the relationship between different water quality indicators. The principal component analysis method is used to help determine the weight of each water quality indicator, thereby ensuring the objectivity and accuracy of the overall evaluation. The causal relationship and dependency relationship between water quality indicators are captured through a Bayesian network model, while effectively handling uncertainty. A confidence estimate for an evaluation result is provided through probabilistic inference, thereby making the evaluation result more credible and providing an effective reference for water environment management planning.

Description

Technical Field

[0001] The invention belongs to the technical field of water quality assessment, and specifically designs a comprehensive water quality assessment method based on multi-dimensional Gaussian distribution of water quality indicators and a Bayesian method. Background Art

[0002] Water environment refers to the space where water is formed, distributed and transformed in nature, which directly or indirectly affects human life and development. As the basic work of water environment governance, the accuracy of water quality evaluation is crucial to the formulation of scientific governance plans. Among the existing water quality assessment methods, the single factor evaluation method is the simplest and most feasible, but it cannot scientifically and effectively evaluate the comprehensive water quality of water bodies, nor can it effectively compare various types of water bodies. Therefore, some methods apply DS evidence theory to water quality evaluation. This method can comprehensively evaluate water quality data to a certain extent to improve the accuracy and objectivity of the evaluation. However, the allocation of basic reliability of DS evidence theory is usually obtained by the experience of experts or testers, and the weights of multiple indicators are mostly processed by equal weight method, excess standard method, etc., which makes the results relatively subjective; and the fusion method of regional water quality or water quality data within a time period adopts the mean method, which has the problem of information loss; therefore, there are problems such as large differences in evaluation results and insufficient comprehensive ability. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the technical problems that the water quality index processing of the water quality comprehensive assessment method in the prior art is relatively subjective and the fusion of water quality data has information loss resulting in inaccurate water quality assessment results, thereby providing a comprehensive water quality assessment method.

[0004] A comprehensive water quality assessment method comprises the following steps:

[0005] Step S1: Establishing a multidimensional Gaussian distribution model of multiple water quality indicators;

[0006] Step S2: Determine the weight and prior probability for each water quality indicator;

[0007] Step S3: Based on the prior probability and weight, a Bayesian network is constructed with water quality indicators as nodes;

[0008] Step S4: Obtain water quality test data and use the Bayesian network to obtain a comprehensive assessment result of the water quality.

[0009] Furthermore, the step S1 includes the following steps:

[0010] Step S1.1: obtaining original data, wherein the original data includes multiple sections, each section includes multiple water quality data, and each water quality data includes multiple water quality indicators;

[0011] Step S1.2: define that the joint distribution of the water quality indicators obeys a multidimensional Gaussian distribution, and establish a multidimensional Gaussian distribution model of the water quality indicators;

[0012] Step S1.3: Calculate the mean value of each water quality indicator and calculate the covariance matrix between each water quality indicator;

[0013] Step S1.4: Calculate the reliability support of each water quality indicator for the water quality assessment level based on the covariance matrix.

[0014] Furthermore, in step S2, the contribution rate and load coefficient are obtained by principal component analysis, thereby determining the weight of each water quality index.

[0015] Furthermore, the step S3 includes the following steps:

[0016] Step S3.1: Determine the mean vector of each node according to the mean vector in the multidimensional Gaussian distribution model;

[0017] Step S3.2: Determine the covariance matrix between each node according to the covariance matrix in the multidimensional Gaussian distribution model;

[0018] Step S3.3: Define the probability distribution of each node as Gaussian distribution. Complete the construction of the Bayesian network.

[0019] Further, the step S4 includes the following steps:

[0020] Step S4.1: Based on the Bayesian network, calculate the posterior probability of each water quality indicator in the water quality detection data;

[0021] Step S4.2: The posterior probability of each water quality indicator is integrated to calculate the comprehensive water quality evaluation result of the water quality detection data.

[0022] Furthermore, in step S4.2, a weighted average method is used to calculate a comprehensive evaluation score based on the posterior probability of each water quality indicator as a comprehensive water quality assessment result.

[0023] Furthermore, in step S4.2, the expected utility theory is used to calculate a comprehensive evaluation score based on the posterior probability of each water quality indicator as a comprehensive water quality assessment result.

[0024] Beneficial effects: The present invention provides a comprehensive water quality assessment method, which effectively quantifies the relationship between different water quality indicators by establishing a multidimensional Gaussian distribution model of multiple water quality indicators; helps determine the weight of each water quality indicator through principal component analysis, thereby ensuring the objectivity and accuracy of the overall evaluation; and captures the causal and dependency relationships between water quality indicators through a Bayesian network model, while effectively handling uncertainty, and provides a confidence estimate for the evaluation results through probabilistic inference, so that the evaluation results have a higher degree of credibility, providing an effective reference for water environment management planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0026] Figure 1 The figure is a schematic block diagram of the main process of the evaluation method of the present invention. DETAILED DESCRIPTION

[0027] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present application, so the present application is not limited by the specific embodiments disclosed below.

[0028] Reference Figure 1 As shown, this embodiment provides a method for comprehensive water quality assessment, comprising the following steps:

[0029] Step S1: Establishing a multidimensional Gaussian distribution model of multiple water quality indicators;

[0030] Step S2: Determine the weight and prior probability for each water quality indicator;

[0031] Step S3: Based on the prior probability and weight, a Bayesian network is constructed with water quality indicators as nodes;

[0032] Step S4: Obtain water quality test data and use the Bayesian network to obtain a comprehensive assessment result of the water quality.

[0033] This embodiment provides a comprehensive water quality assessment method, which effectively quantifies the relationship between different water quality indicators by establishing a multidimensional Gaussian distribution model of multiple water quality indicators; helps determine the weight of each water quality indicator through principal component analysis, thereby ensuring the objectivity and accuracy of the overall evaluation; and captures the causal and dependency relationships between water quality indicators through a Bayesian network model, while effectively handling uncertainty, and provides a confidence estimate for the evaluation results through probabilistic inference, so that the evaluation results have a higher degree of credibility, providing an effective reference for water environment management planning.

[0034] Specifically, the step S1 includes the following steps:

[0035] Step S1.1: obtaining original data, wherein the original data includes multiple sections, each section includes multiple water quality data, and each water quality data includes multiple water quality indicators;

[0036] The original data contains Section Articles The water quality data of water quality indicators are as follows:

[0037] ;

[0038] ;

[0039] Suppose there are N water quality levels, the water quality assessment level set is expressed as follows:

[0040] ;

[0041] in, Indicates Water quality assessment levels, including Better than the assessment grade .

[0042] Step S1.2: Define that the joint distribution of the water quality indicators obeys multidimensional Gaussian distribution, and establish a multidimensional Gaussian distribution model of water quality indicators:

[0043] ;

[0044] in, is a given mean and the covariance matrix Under the condition of The probability density function of is a three-dimensional data matrix of size × × ; Is the size of × × The mean vector of water quality indexes at each section and each time point represents the mean value of water quality indexes at each section and each time point. The vector of water quality indexes can be obtained by tensor For example, for the Section data, the water quality index vector can be expressed as For the The time point water quality index, the water quality index vector can be expressed as .

[0045] Step S1.3: Calculate the mean value of each water quality indicator and calculate the covariance matrix between each water quality indicator;

[0046] Defined as The average values ​​of water quality indicators are:

[0047] ;

[0048] Defined as Water quality indicators and Elements of the covariance matrix between water quality indicators:

[0049] ;

[0050] Step S1.4: Calculate the reliability support of each water quality indicator for the water quality assessment level based on the covariance matrix.

[0051] like , then the basic level division is adopted; in this embodiment, the basic level division laws and regulations, industry standards divide the environmental monitoring requirements. Otherwise, the following method is adopted to calculate each confidence support.

[0052] Defined as Water quality indicators and water quality assessment levels Credibility support:

[0053] ;

[0054] in, Indicates water quality index The corresponding reliability level.

[0055] Assumptions Represented as a solution Medium evaluation index Water quality assessment level The set of confidence support is expressed as follows:

[0056] ;

[0057] in , .

[0058] Through reliability-supported calculations, the effectiveness of each water quality indicator at each water quality assessment level can be accurately assessed, ensuring the consistency of the assessment results, thereby improving the credibility of the research or assessment.

[0059] Specifically, in step S2, the covariance matrix is ​​decomposed by the principal component analysis method to obtain eigenvalues ​​and eigenvectors, and then the first few principal components with larger explanatory variability are selected according to the size of the eigenvalues, and the load coefficient of each water quality index on the selected principal component and the contribution rate of each principal component are calculated to determine the weight of each water quality index.

[0060] Indicates The normalized weight of each water quality index is:

[0061] ;

[0062] in, is the number of principal components in principal component analysis, For the The contribution rate of the principal components, For the The principal component The load coefficient of each indicator. After normalization of the weight set, we get The weight set of evaluation indicators is expressed as , and satisfy:

[0063] ;

[0064] In this embodiment, the construction of the Bayesian network requires the determination of the prior probability, which describes the probability distribution of each node when no evidence is observed. The process of determining the prior probability combines domain knowledge, historical data, expert judgment, and other relevant information. Domain experts or relevant researchers understand the characteristics of water quality indicators and can set prior probabilities; if there is historical monitoring data, statistical analysis methods can be used to estimate prior probabilities, such as maximum likelihood estimation or Bayesian estimation; when there is no historical data or professional knowledge, prior probabilities can be set subjectively; other information sources can also be considered, such as literature, data from similar regions, etc. Through comprehensive consideration of this information, the determined prior probability will be used as the initial probability distribution of nodes in the Bayesian network.

[0065] Specifically, step S3 includes the following steps:

[0066] Step S3.1: Determine the mean vector of each node according to the mean vector in the multidimensional Gaussian distribution model;

[0067] For each node , according to the mean vector in the multidimensional Gaussian distribution model , set the mean vector of the node.

[0068] Step S3.2: Determine the covariance matrix between each node according to the covariance matrix in the multidimensional Gaussian distribution model;

[0069] For each node , according to the covariance matrix in the multidimensional Gaussian distribution model , determine the covariance matrix between nodes.

[0070] Covariance matrix setting: For each node , according to the covariance matrix in the multidimensional Gaussian distribution model , determine the covariance matrix between nodes. Considering the conditional independence in the Bayesian network, the covariance between nodes can usually be set to zero, that is, assuming that there is no direct connection between nodes.

[0071] Step S3.3: Define the probability distribution of each node as Gaussian distribution. Complete the construction of the Bayesian network.

[0072] Assume Water quality indicators The parent node set of , the set of water quality indicators it contains is expressed as , then its conditional probability distribution is:

[0073] ;

[0074] in, represents a Gaussian distribution, No. Water quality indicators The mean vector of A collection of parent nodes The mean vector of A collection of parent nodes The value of For the Water quality indicators and its parent node set The covariance matrix between A collection of parent nodes The covariance matrix between For a given set of parent nodes Under the conditions Water quality indicators The conditional covariance matrix of .

[0075] As a further improvement of this embodiment, the Bayesian network needs to be verified and optimized, and the steps are as follows:

[0076] Step S3.4.1: Parameter adjustment: Adjust the parameters in the Bayesian network to make the network better fit the actual data. This involves adjusting parameters such as mean and covariance, as well as adjusting the conditional probability distribution.

[0077] Step S3.4.2: Model evaluation: Use actual data to evaluate the Bayesian network model to assess the model's fit and predictive performance. Common evaluation indicators include log-likelihood function, model marginal likelihood, (Akaike Information Criterion), (Bayesian Information Criterion), etc.

[0078] The log-likelihood function calculation formula is as follows:

[0079] ;

[0080] in, is the sample data, yes The parent node set of is the number of sample data.

[0081] and The calculation formulas are:

[0082] ;

[0083] ;

[0084] in, is the number of model parameters, is the number of sample data.

[0085] Step S3.4.3: Structural optimization: According to the model evaluation results, the Bayesian network structure is optimized. The optimization process includes adding or deleting nodes, adjusting the connection relationship between nodes, etc. The structural optimization algorithm can adopt heuristic search, Bayesian model averaging and other methods.

[0086] Step S3.4.4: Repeat the iterations: Perform the above steps multiple times until satisfactory model performance and structure are achieved.

[0087] Specifically, step S4 includes the following steps:

[0088] Step S4.1: Based on the Bayesian network, calculate the posterior probability of each water quality indicator in the water quality detection data;

[0089] Set up The measured value of water quality index is .

[0090] For each water quality indicator , its posterior probability distribution is expressed as:

[0091] ;

[0092] Step S4.2: The posterior probability of each water quality indicator is integrated to calculate the comprehensive water quality evaluation result of the water quality detection data.

[0093] in, Water quality index The conditional probability distribution of Water quality index According to the structure of the Bayesian network, the conditional probability distribution of each node can be used for calculation.

[0094] The posterior probability distribution of each water quality indicator is combined to obtain a comprehensive assessment of water quality. This can be done in various ways, for example, by calculating a weighted average or using decision theory for a comprehensive evaluation.

[0095] In some embodiments of the present invention, in step S4.2, a weighted average method is used to calculate a comprehensive evaluation score based on the posterior probability of each water quality indicator as a comprehensive water quality assessment result.

[0096] Using weighted average: Assume that given the evidence Next, water quality indicators The posterior probability distribution of , the comprehensive evaluation result can be expressed as:

[0097] ;

[0098] in, is the comprehensive evaluation score, The weight of each water quality indicator.

[0099] In some other embodiments of the present invention, in step S4.2, the expected utility theory is used to calculate the comprehensive evaluation score based on the posterior probability of each water quality indicator as the comprehensive water quality evaluation result.

[0100] Assume that water quality levels, the utility function is ,in represents the water quality level, then the expected utility can be expressed as:

[0101] ;

[0102] in, Indicates The water quality index Water quality level, Indicates that given evidence x, the water quality index Water quality level The posterior probability of . Then the expected utility of each water quality indicator is combined to obtain an overall comprehensive evaluation. This can be done by a simple summation, that is, the weighted summation of the expected utility of each water quality indicator is obtained to obtain the comprehensive expected utility:

[0103] ;

[0104] in, is the comprehensive evaluation score, For the The expected utility of a water quality indicator is The weight of each water quality indicator.

[0105] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be construed as limiting the scope of the patent application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent application shall be subject to the attached claims.

Claims

1. A method for comprehensive water quality assessment, characterized in that: The following steps are involved: Step S1: Establish a multidimensional Gaussian distribution model for multiple water quality indicators: ； in, is a given mean and the covariance matrix Under the condition of The probability density function of is a three-dimensional data matrix with size × × ; Is the size of × × The mean vector of water quality index at each section and at each time point represents the mean value of water quality index at each section and at each time point. The vector of water quality index is obtained by tensor It is represented by different dimensions in Step S2: Determine the weight and prior probability for each water quality indicator; In step S2, the contribution rate and load coefficient are obtained by principal component analysis, thereby determining the weight of each water quality index; Step S3: Based on the prior probability and weight, a Bayesian network is constructed with water quality indicators as nodes; The step S3 comprises the following steps: Step S3.1: Determine the mean vector of each node according to the mean vector in the multidimensional Gaussian distribution model; Step S3.2: Determine the covariance matrix between each node according to the covariance matrix in the multidimensional Gaussian distribution model; Step S3.3: define the probability distribution of each node as Gaussian distribution, and complete the construction of the Bayesian network; Step S4: Obtain water quality test data and use the Bayesian network to obtain a comprehensive assessment result of the water quality.

2. A comprehensive water quality assessment method according to claim 1, characterized in that: The step S1 comprises the following steps: Step S1.1: obtaining original data, wherein the original data includes multiple sections, each section includes multiple water quality data, and each water quality data includes multiple water quality indicators; Step S1.2: define that the joint distribution of the water quality indicators obeys a multidimensional Gaussian distribution, and establish a multidimensional Gaussian distribution model of the water quality indicators; Step S1.3: Calculate the mean value of each water quality indicator and calculate the covariance matrix between each water quality indicator; Step S1.4: Calculate the reliability support of each water quality indicator for the water quality assessment level based on the covariance matrix; If the value of the covariance matrix is ​​not zero, calculate the confidence support of each water quality indicator for the water quality assessment level: ； in, Indicates water quality index The corresponding confidence level is Represents a given mean and the covariance matrix Under the condition of The probability density function of .

3. A comprehensive water quality assessment method according to claim 1, characterized in that: The step S4 comprises the following steps: Step S4.1: Based on the Bayesian network, calculate the posterior probability of each water quality indicator in the water quality detection data; Step S4.2: The posterior probability of each water quality indicator is integrated to calculate the comprehensive water quality evaluation result of the water quality detection data.

4. A comprehensive water quality assessment method according to claim 3, characterized in that: In step S4.2, a weighted average method is used to calculate a comprehensive evaluation score based on the posterior probability of each water quality indicator as a comprehensive water quality assessment result.

5. A comprehensive water quality assessment method according to claim 3, characterized in that: In step S4.2, the expected utility theory is used to calculate the comprehensive evaluation score based on the posterior probability of each water quality indicator as the comprehensive water quality evaluation result.

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