Bayesian theory-based drainage basin high-quality development set evaluation method

Abstract

The invention discloses a Bayesian theory-based drainage basin high-quality development set evaluation method, which comprehensively considers a plurality of evaluation indexes, adopts the Bayesian theory to carry out weight optimization, not only considers the historical performance and data change of each index, but also can update the weight according to real-time data. According to the method, the comprehensive better performance and poor performance of the whole system can be quantitatively and comprehensively evaluated, interval evaluation instead of deterministic evaluation of the system is formed, the evaluation is more comprehensive and scientific, and a decision maker can better understand the potential and risk of basin development, so that a more reasonable and effective decision is made; and the decision quality of drainage basin management is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of data analysis and water resources management, and is particularly applicable to a collective evaluation method for high-quality development of a watershed based on Bayesian theory. Background Art

[0002] As a complex ecosystem, river basin management involves the effective management and analysis of a wide range of meteorological, hydrological, geographical and economic data. The integration and evaluation of these data are of vital importance for optimizing water resources allocation, assessing environmental impacts, supporting scientific research and formulating policies.

[0003] Existing technologies are capable of processing complex data and constructing a hierarchical multi-indicator evaluation system to comprehensively assess the high-quality development of a watershed. However, there are still challenges in how to scientifically integrate these indicators and dynamically adjust the weights to adapt to environmental and policy changes.

[0004] At present, traditional weight determination methods can be divided into subjective weighting method, objective weighting method and equal weighting method. Among them, the objective weighting method reduces the intervention of human factors and has attracted the attention of researchers. Commonly used objective weighting methods include principal component analysis and entropy weight method. The principal component analysis method evaluates the contribution of each indicator by extracting the principal components of the data to determine the weight; while the entropy weight method uses the concept of information entropy to evaluate the discreteness of the indicator. The greater the variability of the indicator, the higher its weight, which reflects the indicator's ability to distinguish. However, this method mainly relies on static data analysis and is usually unable to dynamically adapt to the impact of environmental or policy changes. At the same time, the current high-quality development assessment methods for watersheds are often not flexible enough in dealing with the uncertainty and complexity of data, and it is difficult to provide interval evaluation of the overall performance of the system, which limits its effectiveness in the evaluation of complex systems. Summary of the invention

[0005] The purpose of the present invention is to provide a collective evaluation method for high-quality development of watersheds based on Bayesian theory, so as to solve the problems in the current evaluation of high-quality development of watersheds, such as the inability to dynamically adjust weights, insufficient flexibility in data processing, and inability to achieve interval evaluation of overall performance.

[0006] To achieve the above object, the present invention adopts the following technical solutions: The method for evaluating high-quality development of a watershed based on Bayesian theory of the present invention comprises the following steps: S1. Use statistical analysis methods to evaluate the relationship between candidate indicators and high-quality development of the basin, and select indicators that are highly relevant to development goals as evaluation indicators for high-quality development of the basin; S2, after normalizing the original data of the evaluation index, calculating the difference between each normalized data and the corresponding ideal value; S3, formulate a weight adjustment strategy, and calculate the dynamic weights and comprehensive evaluation results of each evaluation indicator based on Bayesian theory.

[0007] Furthermore, the evaluation index should be a function of time.

[0008] Furthermore, in step S2, after the original data of the evaluation index are normalized, the consistency of the normalized data and the accuracy of the standardization should be checked according to the data distribution characteristics obeyed by the difference between the original data of each evaluation index and the corresponding ideal value.

[0009] Furthermore, the weight adjustment strategy includes determining k The ideal value of the indicator Assign greater weights to indicators with better performance or determine the best value. k The ideal value of the indicator is the worst value, assigning a larger weight to the indicator with worse performance.

[0010] Furthermore, the comprehensive evaluation result is the product of the weight and value of each evaluation indicator.

[0011] Furthermore, the comprehensive evaluation results are used to identify the best and worst areas for high-quality development in the river basin.

[0012] The advantage of the present invention is that by comprehensively considering multiple evaluation indicators and using Bayesian theory to optimize weights, not only the historical performance and data changes of each indicator are considered, but also the weights can be updated according to real-time data. The present invention can also quantitatively and comprehensively evaluate the overall better performance and worse performance of the entire system, forming a systematic interval evaluation rather than a deterministic evaluation, which is more comprehensive and scientific, enabling decision makers to better understand the potential and risks of basin development, thereby making more reasonable and effective decisions and improving the decision-making quality of basin management. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The present invention is a flowchart of the method.

[0014] Figure 2 The figure is a calculation flow chart of the method of the present invention.

[0015] Figure 3 The figure is a calculation flow chart of the weight adjustment strategy in the method of the present invention.

[0016] Figure 4 Schematic diagram of the comprehensive evaluation results of Example 2 of the present invention. DETAILED DESCRIPTION

[0017] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] Example 1 like Figures 1 to 3 As shown, the ensemble evaluation method for high-quality development of a watershed based on Bayesian theory of the present invention comprises the following steps: S1. Statistical analysis methods are used to evaluate the relationship between candidate indicators and high-quality development of the watershed, and indicators that are highly correlated with development goals are selected as evaluation indicators for high-quality development of the watershed.

[0019] Among them, the candidate indicators cover the economy, such as GDP growth rate, per capita income, and agricultural irrigation costs; society, such as employment rate and population growth rate; environment and water resources management, such as dissolved oxygen, total nitrogen, total phosphorus, vegetation coverage, biodiversity index, water resource utilization rate, river water level changes, groundwater recharge rate and other fields.

[0020] GDP growth rate can measure the economic development of the basin region. Per capita income can measure the living standards of residents in the basin. Agricultural irrigation costs reflect the correlation between water resources management and agricultural production. Employment rate reflects social stability in the basin. Population growth rate measures the population development trend in the basin and its impact on resource management. Vegetation coverage reflects the ecological status of the basin. Biodiversity index measures the health of the ecosystem. Water resource utilization rate reflects the efficiency of water resource use; river water level changes reflect the effectiveness of water resource scheduling and management in the basin. Groundwater recharge rate can measure the recovery rate of groundwater and ensure sustainable water resource management.

[0021] The indicator values ​​corresponding to each candidate indicator come from government databases, scientific research institutions and international organizations, ensuring the breadth and update of the data.

[0022] After collecting the candidate indicators and initial indicator data, statistical analysis methods such as correlation analysis and regression analysis are used to evaluate the relationship between the candidate indicators and the high-quality development of the watershed; indicators that are highly relevant to the development goals are selected to ensure that the selected indicators can effectively support the weight allocation strategy based on Bayesian theory.

[0023] The correlation analysis method uses the Pearson correlation coefficient to calculate the correlation between each candidate indicator and the high-quality development goals of the basin (such as economic growth, environmental protection, social welfare, etc.), and analyzes the intensity relationship between each indicator. The regression analysis method uses a multivariate linear regression or nonlinear regression model to evaluate the specific impact of each candidate indicator on the development of the basin. A regression model can be constructed to predict, such as the relationship between GDP growth rate, employment rate and water resource utilization efficiency. By organizing expert discussions and stakeholder meetings, opinions from all parties are collected to ensure that indicators covering multiple fields such as economy, society, environment and water resources management are covered. Expert consultation techniques such as the Delphi method are used to conduct multiple rounds of surveys to determine the final set of evaluation indicators.

[0024] Each evaluation index should be a function of time. Assuming that n evaluation indexes are finally selected, these evaluation indexes are marked as ,in and . No. k The time series vector of the evaluation index can contain time point, denoted as ,in and The time point can be year, month, day, hour, etc.

[0025] In addition, in addition to determining the evaluation indicators of high-quality development of the river basin through the relationship between candidate indicators and high-quality development of the river basin, it is also necessary to evaluate the completeness, consistency and accuracy of the data in the data set of the selected river basin high-quality development evaluation indicators. The consistency of the data in the data set can be determined through correlation verification, cross-source comparison, historical data comparison, etc.

[0026] For example: Completeness check uses database query completeness check tools to determine whether all expected data has been collected. If data for certain time periods or geographic areas are missing, they can be marked and supplementary data sources can be found. Consistency check uses correlation verification and cross-source comparison methods to ensure that the trends and magnitudes of data obtained from different sources (such as government databases and scientific research institutions) on the same indicator are consistent. Time series analysis tools can be used to check the continuity and consistency of data from different years or different sources. Accuracy verification uses historical data comparison methods to confirm data accuracy by comparing with historical data and verified reliable data sets. Expert consultation methods can also be used to invite field experts to evaluate the rationality of the data, especially to conduct accuracy audits when the data fluctuates abnormally.

[0027] It can also assist in data cleaning and preprocessing steps, such as using interpolation methods (such as linear interpolation and spline interpolation) to fill in missing time series data; or using multiple imputation to generate a variety of reasonable completion values ​​based on historical data of similar geographical areas.

[0028] Outlier detection uses box plot or Z-score methods to identify outliers in indicator data. For identified outliers, further checks can be performed to confirm whether they are measurement errors or extreme but reasonable observations.

[0029] Use regression analysis to identify systematic deviations in data and correct some persistent deviation problems through models. You can also apply normalization methods to convert highly deviated indicator data into a normal distribution that is more suitable for analysis.

[0030] S2, after normalizing the original data of each evaluation index, calculate the difference between each data in each evaluation index and the corresponding ideal value.

[0031] The normalization of the original data of the evaluation index should be based on the characteristics and data types of the evaluation index, and the appropriate normalization method should be selected for different index data. The optional normalization methods include the common maximum and minimum method, Z-score normalization method, etc. For example, when it is necessary to maintain the original linear proportion of the data, the maximum and minimum method (Min-Maxnormalization) is selected, and when the original data is approximately normally distributed, the Z-score normalization (Z-score normalization) is used.

[0032] The selected normalization method is applied to the raw data of each evaluation indicator to convert the raw data under the evaluation indicator into a unified measurement range, usually an interval of 0 to 1 or -1 to 1. During the normalization process, it should be ensured that the distribution characteristics and information of the raw data are not lost and the real situation of each indicator can be accurately reflected.

[0033] It should be emphasized that after the original data of the evaluation indicators are normalized, the consistency of the normalized data and the accuracy of standardization should be checked according to the data distribution characteristics obeyed by the difference between the original data and the corresponding ideal value in each evaluation indicator.

[0034] If the difference between the original data and the corresponding ideal value in the evaluation index obeys the normal distribution, semi-normal distribution or other distribution forms, the original data of the evaluation index should be normalized to check whether the difference between the normalized data and the corresponding ideal value still obeys the corresponding data distribution form to ensure that no artificial deviation is introduced. If it obeys, it means that the normalized data has high consistency and standardized accuracy. If it does not obey, the normalization method should be adjusted and the original data should be normalized again to ensure the effectiveness and relativity of all indicators in the subsequent Bayesian analysis.

[0035] Each normalized data is compared with the corresponding ideal value (denoted as , usually 1, 0 or -1, depending on the nature of the indicator) is the difference or in, For the k The difference vector between the normalized evaluation index data and the ideal value.

[0036] S3, formulate a weight adjustment strategy, and calculate the dynamic weights and comprehensive evaluation results of each evaluation indicator based on Bayesian theory.

[0037] like Figure 3 As shown, the weight adjustment strategy includes determining the k The ideal value of the indicator is the optimal value, and a larger weight is assigned to indicators with better performance This approach focuses on highlighting the basin's strengths and potential in certain key aspects, namely the potential for basin development.

[0038] Or determine the k The ideal value of the indicator Assign greater weights to indicators with poor performance , this approach focuses on identifying and improving weak links in watershed management, which is the bottom line for watershed development.

[0039] According to the selected weight adjustment strategy, the likelihood function and posterior distribution are recalculated based on Bayesian theory to obtain the latest weights of each evaluation indicator and determine the weights. Then the comprehensive evaluation result is calculated based on the latest weights of each evaluation indicator. The comprehensive evaluation result is the product of the weight and value of each evaluation indicator, which is: in, and The comprehensive evaluation index vectors are respectively the strategy schemes that assign larger weights to the indicators with better performance and the strategy schemes that assign larger weights to the indicators with worse performance. They are all functions of time and updated in time series. If a comprehensive value is needed as a global evaluation index, a suitable method needs to be used for statistics, such as the average method.

[0040] By dynamically adjusting the weights of various indicators according to different weight strategies, evaluations in different dimensions can be performed. At the same time, analyzing the comprehensive evaluation results can also identify the best and worst areas for high-quality development in the basin, providing a scientific basis for decision-making.

[0041] The calculation of the dynamic weight of each evaluation index based on Bayesian theory specifically includes the following steps: S3.1, determine the prior distribution: use a suitable random variable distribution model as the prior distribution of the weights of each evaluation index , such as average distribution, error weight, expert experience, binomial distribution, normal distribution, etc.

[0042] ① Average distribution (uniform distribution): If there is not enough information to distinguish the importance of each evaluation indicator, it can be assumed that the weights of all indicators have the same probability. In this case, a uniform distribution can be selected for each weight; uniform distribution means that every value within its range is equally likely, which is usually suitable for situations where detailed information is lacking.

[0043] ② Error weight: If necessary, make a preliminary weight setting based on the difference from the ideal. Smaller differences from the ideal are given larger weights to reflect that the performance of the indicator is closer to the ideal state. For example, use a simple weighting or inverse method to determine the preliminary weight: the larger the value, the better the effect. Use the weighting method; otherwise, use the inverse method (which means using the inverse of the indicator error to set the prior weight). ), the specific formula is: in, Is an indicator The prior weight of Is an indicator The initial weight of is the mean of the distances d from the ideal value, is a small constant to avoid division by zero.

[0044] ③ Expert experience: If there is reliable expert knowledge available for reference, the prior distribution of indicator weights can be set based on the expert’s judgment; for example, if experts believe that certain indicators are more critical to evaluating the quality of watershed development, the weights of these indicators can be set to a higher prior probability.

[0045] ④ Binomial distribution: If the importance of the evaluation indicator can be regarded as the result of a series of success / failure experiments, then the distribution of weights can be represented by a binomial distribution; in this case, the choice of parameters depends on the number of experiments and the probability of success.

[0046] ⑤ Normal distribution: For weights that are expected to vary around a certain value but have possible deviations, normal distribution can be used; normal distribution is very suitable for representing random variables in natural or social science phenomena, especially when we believe that certain indicator weights fluctuate around a certain mean value.

[0047] S3.2, Determine the likelihood function: Select an appropriate likelihood function based on the data properties (continuous or discrete), correlation and distribution characteristics of the normalized indicator. The general form is: in, are model parameters, yes The specific form of the likelihood function for the corresponding random variable depends on the chosen distribution. The relevant parameters can be determined by methods such as moment method estimation or maximum likelihood estimation. For example, for a normal distribution: ,have in, is the mean, is the standard deviation and needs to be determined by an appropriate method.

[0048] S3.3, Calculate the posterior distribution: Use Bayes' theorem to update the posterior probability of each model. The posterior probability reflects the relative probability of each indicator after observing the data: in, is the observed or ideal data time series vector. The posterior weights are updated using prior knowledge and real-time data to optimize the weight distribution to improve the adaptability and accuracy of the evaluation method.

[0049] Example 2 The application process of the ensemble evaluation method for high-quality development of a watershed based on Bayesian theory described in this invention is explained in combination with a watershed S1: Select indicators that are highly relevant to development goals as evaluation indicators for high-quality development of the watershed.

[0050] The data of high-quality development evaluation indicators of a river basin from 1990 to 2023 are collected, including three major indicators: river health, ecological environment, and economic and social development. Among them, river health includes indicator 1 annual total precipitation (unit: 100 million cubic meters) and per capita water resources (unit: cubic meter); the ecological environment includes indicator 3 habitat quality index (unit: none) and indicator 4 soil and water loss control area (unit: 10,000 square kilometers); the economy and society includes indicator 5 per capita GDP (unit: 10,000 yuan) and indicator 6 grain output (unit: 100 million jin).

[0051] The six indicators are recorded as ;No. k The time series vector of the evaluation index contains 34 time points in total. For example, for indicator 4, the area of ​​soil and water loss control, .

[0052] According to the literature, these indicators are highly relevant and very important for the evaluation of high-quality development of the Yellow River Basin. These indicators have different numerical ranges and units. The larger the value of these six indicators, the higher the evaluation of the quality of basin development; these six indicator data provide valuable data support for the implementation of the evaluation method based on the Bayesian theorem of this patent.

[0053] S2, after normalizing the original data of the evaluation index, calculate the difference between each normalized data and the corresponding ideal value.

[0054] All the data of the six indicators are normalized using the Min-Max normalization method to obtain , the range is [0,1]; k The normalized time series vector of the evaluation index is , for example, after normalization, indicator 4 becomes Checking the distribution characteristics of the data and the information is not lost during the normalization process, which can accurately reflect the true distribution of each indicator.

[0055] The normalized data were tested to check the consistency of the data and the accuracy of standardization to ensure that no artificial bias was introduced.

[0056] Assumed difference from ideal value and It obeys a half-normal distribution with a mean of 0 and a standard deviation of 1, that is, . Calculate the difference vectors of the six indicators from the ideal values ​​and get ;No. k The normalized time series vector of the difference from the ideal value of each evaluation index is For example, the time series vector of the difference between indicator 4 and the ideal is and .

[0057] S3, calculation of the weights of each indicator based on Bayesian theorem.

[0058] The average distribution and error weight are used to determine the prior distribution respectively, and two sub-schemes are formed, which are recorded as sub-scheme 1 and sub-scheme 2 respectively, to identify the impact of the prior distribution on the ensemble evaluation results.

[0059] At the same time, according to the weight adjustment strategy of the present invention, there are two corresponding extreme benefit schemes, which are recorded as extreme benefit scheme one and extreme benefit scheme two.

[0060] For the extreme benefit plan 1, the prior weight of the prior distribution of sub-plan 1 is , , the corresponding prior distribution is The prior weight of the prior distribution of sub-scheme 2 is , the corresponding prior distribution is For the extreme benefit plan 2, the prior weight of the prior distribution of sub-plan 1 is , the corresponding prior distribution is The prior weight of the prior distribution of sub-scheme 2 is , the corresponding prior distribution is .

[0061] For example, for indicator 4, the prior distributions are , , and .

[0062] According to the previous assumptions, the difference from the ideal value , then the corresponding likelihood function is For the extreme benefit plan 1, the likelihood function vector is For the second extreme benefit scenario, the likelihood function vector is Update the posterior probability of each model using Bayes' theorem.

[0063] For the extreme benefit plan 1, the posterior distribution of sub-plan 1 is The posterior distribution of sub-scheme 2 is For the extreme benefit plan 2, the posterior distribution of sub-plan 1 is The posterior distribution of sub-scheme 2 is S4, dynamic evaluation of extreme benefits based on Bayesian theory.

[0064] According to the previous calculations, the optimal values ​​of the six indicators in the extreme benefit scheme 1 are are all 1, and the relevant weight is According to the previous calculation, the worst ideal values ​​of the six indicators in the extreme benefit plan 1 are all 1, and the relevant weight is Calculate the comprehensive evaluation results: (1) For extreme benefit plan 1: The posterior distribution of sub-scheme 1 is The posterior distribution of sub-scheme 2 is (2) For the extreme benefit plan 2: The posterior distribution of sub-scheme 1 is The posterior distribution of sub-scheme 2 is If the time series is updated, the overall evaluation results can also be recalculated.

[0065] Figure 4 The results of this example are shown. This example assumes that the distance from the ideal follows a half-normal distribution with a mean of 0 and a standard deviation of 1. It was found that in the extreme benefit scenario 1 (potential evaluation), the two scenarios first decreased and then increased over time, reaching a minimum value in 2021. The difference between the two is the different methods of determining the prior weights, sub-scheme 1 is an average distribution, and sub-scheme 2 is an error weight distribution. The two scenarios have similar trends to the habitat quality index because the evaluation index is closest to the optimal ideal value, resulting in a smaller distance from the ideal value and a larger posterior weight. Without additional information, it was found from the potential evaluation that the potential for high-quality development of the basin did not change much before 2010, with a comprehensive evaluation value of around 0.9, gradually decreasing from 2010 to 2020, plummeting from 2020 to 2021, and gradually and rapidly increasing from 2021 to 2023.

[0066] In the extreme benefit scenario 2 (bottom line evaluation), the two scenarios first rise, then fall, and then rise again over time, reaching the maximum and minimum points in 2020 and 2021 respectively. The difference between the two is consistent with the potential evaluation. Compared with the potential evaluation, the trend of the bottom line evaluation is more comprehensive. Without additional information, it is found from the bottom line evaluation that the potential for high-quality development of the basin gradually increased before 2020, also dropped sharply from 2020 to 2021, and gradually rose rapidly from 2021 to 2023. In summary, the development potential of the basin gradually declined before 2020, and the development bottom line gradually increased, which may be related to the high-quality development of the basin; the sharp drop in development potential and bottom line from 2020 to 2021 may be related to epidemic prevention, and the rapid increase in development potential and bottom line after 2021 may be related to the further high-quality development of the basin. It should be emphasized that if the prior distribution, likelihood function, etc. change, the results will also change, and the comprehensive evaluation results are highly dependent on these conditions.

Claims

1. A ensemble evaluation method for high-quality development of a watershed based on Bayesian theory, characterized in that: The following steps are involved: S1. Use statistical analysis methods to evaluate the relationship between candidate indicators and high-quality development of the basin, and select indicators that are highly relevant to development goals as evaluation indicators for high-quality development of the basin; S2, after normalizing the original data of the evaluation index, calculating the difference between each normalized data and the corresponding ideal value; S3, formulate a weight adjustment strategy, and calculate the dynamic weights and comprehensive evaluation results of each evaluation indicator based on Bayesian theory.

2. According to claim 1, a method for evaluating high-quality development of a watershed based on Bayesian theory is characterized by: The evaluation index should be a function of time.

3. According to claim 1, a method for collective evaluation of high-quality development of a watershed based on Bayesian theory is characterized by: In step S2, after the original data of the evaluation index are normalized, the consistency of the normalized data and the accuracy of the standardization should be checked according to the data distribution characteristics obeyed by the difference between the original data of each evaluation index and the corresponding ideal value.

4. According to claim 1, a method for collective evaluation of high-quality development of a watershed based on Bayesian theory is characterized by: The weight adjustment strategy includes determining the k The ideal value of the indicator Assign greater weights to indicators with better performance or determine the best value. k The ideal value of the indicator is the worst value, assigning a larger weight to the indicator with worse performance.

5. According to claim 1, a method for collective evaluation of high-quality development of a watershed based on Bayesian theory is characterized by: The comprehensive evaluation result is the product of the weight and value of each evaluation indicator.

6. According to claim 1, a method for collective evaluation of high-quality development of a watershed based on Bayesian theory is characterized by: The comprehensive evaluation results are used to identify the best and worst areas for high-quality development in the basin.

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