Water pollution tracing method based on interpretable machine learning

Abstract

The invention belongs to the field of environmental protection, and discloses a water pollution tracing method based on interpretable machine learning. The interpretable machine learning technology is combined with the PMF model, the defects of the PMF model in the aspect of input index selection are overcome, a working system of regional water quality evaluation, pollution key region identification, water quality index determination and pollution source tracing analysis is constructed, the influence of each pollution source on the water quality is evaluated more scientifically, and the accuracy of an analysis result is improved. According to the method, the index selection process of the PMF model is optimized through an interpretable machine learning technology, the fitting coefficient of each index is improved from 0.40 to 0.65, the number of samples with residual absolute values larger than 3 is reduced from 40 to 8, meanwhile, different pollution sources are recognized and quantified, the source analysis precision and efficiency of the model are greatly improved, and the method is suitable for large-scale popularization and application. And the popularization and application of the PMF model in more regions are promoted, and a local environmental protection department is helped to formulate a pollution treatment scheme with stronger pertinence.

Description

Technical Field

[0001] The present invention belongs to the field of environmental protection and relates to a water pollution source tracing method based on explainable machine learning. Background Art

[0002] With the accelerated advancement of industrialization and urbanization, the impact of human activities on the natural environment has become increasingly severe, especially the pollution of surface water bodies such as rivers, which has become a key factor restricting the sustainable development of social economy. The sewage discharge caused by residents' lives and industrial and agricultural production not only affects the balance of the water ecosystem, but also threatens human drinking water safety and public health. Therefore, scientifically and effectively identifying and quantitatively analyzing the main pollution sources has become an important prerequisite and basic guarantee for promoting water environment governance.

[0003] In the field of pollution source analysis, inventory analysis, diffusion model and receptor model are the three most commonly used technologies. Among them, the inventory analysis method constructs a list of pollution source information by observing and simulating factors such as pollution source emissions, emission characteristics and their geographical distribution. Although it can obtain information over a large range and a long time span, its data lag is significant and the uncertainty of the calculation results is relatively large. Diffusion model technology simulates the hydrological process of pollutants from source to sink, but because it requires detailed pollution sources, environmental data and migration and diffusion characteristic parameters, and model calibration requires a large amount of measured data, this method is limited to a certain extent. In this context, receptor model technology has been more widely used in the field of pollution source analysis in recent years.

[0004] Among various receptor model technologies, the positive definite matrix factorization (PMF) model performs particularly well. The PMF model can directly analyze the contribution of pollution sources based on environmental monitoring data without relying on detailed emission inventory data and complex parameter calibration. In the process of quantifying pollution sources, the model also imposes positivity constraints on the data matrix, effectively avoiding the appearance of negative values ​​without physical meaning in the matrix decomposition results, thereby ensuring that both factor loadings and factor scores are highly interpretable and have clear physical meanings. In addition, compared with other receptor model technologies such as principal component-linear regression (PCA-MLR), the PMF model shows higher flexibility and adaptability. Operators can adjust the parameters of the PMF model according to the actual data situation, which not only provides an accurate one-to-one uncertainty estimate for each sample, but also allows the robustness and reliability of the model to be enhanced by optimizing the data quality through the signal-to-noise ratio. Therefore, the PMF model has stronger advantages and potential in accurately analyzing the sources of pollution.

[0005] However, the application of the PMF model also has certain limitations. Although the patent No. 2019104492258 mentions a pollution source identification method based on principal component analysis and K-means clustering, which improves the problem of the inability to accurately determine the number of pollution sources to a certain extent, the indicators of the PMF model input model still lack effective guidance, which may cause some indicators with low or no significant impact on water quality to be added to the model calculation process, reducing the overall fitting accuracy of the model, increasing the randomness and uncertainty of the model output results, and affecting the formulation and implementation of the final water quality management strategy. In this context, the use of machine learning technology, which currently has excellent performance in data analysis, is expected to optimize the implementation process of the PMF model and build a more scientific and feasible PMF model watershed water pollution source analysis system and method. Summary of the invention

[0006] The purpose of this invention is to establish a water pollution source tracing system and method based on interpretable machine learning, optimize the shortcomings of the traditional PMF model in parameter selection, and construct a more feasible watershed water pollution source analysis framework, which is easy to promote and apply in river water environment management.

[0007] The technical solution of the present invention:

[0008] A water pollution source tracing method based on interpretable machine learning, the steps are as follows:

[0009] Step 1: In order to study the water quality of the basin and analyze the source of pollution, long-term water quality monitoring data from several monitoring stations in the basin were collected and sorted into a water quality parameter data set; after checking for missing values ​​and outliers, descriptive statistical analysis was performed on the water quality parameter data set to confirm the distribution characteristics and fluctuations of each water quality parameter; then, based on the water quality monitoring data from different monitoring stations, the weights and normalized scores of different indicators were set by expert scoring, and the WQI (Water Quality Index) water quality evaluation method was used to evaluate the water quality level and identify regional differences;

[0010] Furthermore, water quality parameters include water temperature WT, dissolved oxygen DO, permanganate index COD Mn , five-day biochemical oxygen demand BOD5, ammonia nitrogen NH4 + -N, chemical oxygen demand COD Cr , volatile phenol VP, cyanide CN - , arsenic As, petroleum TPH, total phosphorus TP, copper Cu, zinc Zn, fecal Escherichia coli E.coil, electrical conductivity EC and total nitrogen TN.

[0011] Furthermore, descriptive statistical analysis included obtaining the minimum, maximum, mean, and standard deviation of water quality parameters.

[0012] Furthermore, the WQI water quality evaluation method determines the weights of water quality parameters and normalized scores based on expert scores, according to the formula:

[0013]

[0014] Among them, m is the number of water quality parameters, C k is the normalized value of the kth water quality parameter, P k is the weight of the kth water quality parameter;

[0015] Step 2: Calculate the average value of each water quality parameter at each monitoring station, use the system cluster analysis tool in SPSS26.0 software, and perform cluster analysis on the water quality data of different monitoring stations based on the Euclidean distance method of Ward link, divide the monitoring stations into different categories, and identify the spatial characteristics of pollution distribution; compare the average WQI scores of different clusters to screen out areas with more serious pollution, form a water quality parameter data set for highly polluted areas, and conduct key analysis in subsequent pollution source analysis work to improve the pertinence of pollution control and save capital investment;

[0016] Step 3: Using Python 3.12.3 software, the XGBoost model algorithm was used to check missing values ​​and outliers in the data. The water quality parameter data set obtained in step 2 was divided into a training set and a test set. The measured data of each water quality parameter was used as the feature variable, and the measured value of WQI was used as the target variable. The XGboost algorithm was used to run the data matrix to quantify the feature importance of each water quality parameter relative to the WQI value. To ensure the data training effect and avoid overfitting, 85% of the data in the water quality parameter data set was used as the training set, and 15% of the data was used as the test set. The depth of the tree gradually increased from 3, and the sampling ratio of each tree was set to 0.8.

[0017] Subsequently, the SHAP tool was introduced to explain the overall and local contributions of each water quality parameter to the change in WQI value. Based on the bee colony diagram obtained by the SHAP tool, the characteristics of the impact of each independent measured value of different water quality parameters on the prediction of WQI value were analyzed, and the impact of the concentration change of each water quality parameter on water quality prediction was analyzed. In this step, water quality parameters with an importance lower than 0.1 were deleted; the remaining water quality parameters with high importance were included in the PMF model for pollution tracing; then, the XGBoost model algorithm was used again to test the prediction effect of the screened water quality parameters on the WQI value, output relevant performance parameters, test the fitting effect, and finally determine the water quality parameters included in the PMF model calculation;

[0018] Furthermore, when building the XGBoost model, the objective function of the XGBoost model is as follows:

[0019]

[0020] Where n is the number of samples, y i is the measured value of sample i, is the prediction result of sample i, is the loss function (squared error), Ω(f k ) is a regularization term used to control the complexity of the XGBoost model;

[0021] Furthermore, the XGBoost model output performance evaluation parameters include mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), determination coefficient (R 2 ), according to the formula:

[0022]

[0023] Where n is the number of samples, y i is the measured value for each sample, is the average value of the measured value of this indicator. is the predicted value obtained using the model;

[0024] Furthermore, the SHAP tool is based on the Shapley value in game theory. It explains the output of the XGBoost model by calculating the marginal contribution of each water quality parameter and quantifies the contribution of each water quality parameter to water quality changes. In the bee colony diagram, blue indicates a positive impact on the predicted value, and red indicates a negative impact on the predicted value. The darker the color, the higher the degree. The SHAP value calculation formula is:

[0025]

[0026] in: is the SHAP value of the kth water quality parameter; N is the set of all features; S is the feature subset that does not contain water quality parameter k; f(S) is the model prediction value of subset S; f(S∪{k}) is the model prediction of the features in S plus the features

[0027] Step 4: Use principal component analysis (PCA) to reduce the dimension of the water quality parameter data set obtained in step 2 and the water quality data set screened in step 3. Determine the number of principal components based on the factor eigenvalue (greater than 1) and the scree plot. Use the number of principal components as the preset number of pollution sources in the PMF model. In the PMF model, use the two groups of water quality parameter data sets (step 2 and step 3) to construct the PMF model, and compare the R under different parameter selections. 2 , residual and other performance indicators are used to verify the degree of improvement in model performance, and the output results of the optimized PMF model are selected for pollution source identification and quantification.

[0028] Furthermore, the factor analysis tool embedded in SPSS software was used in principal component analysis, combined with the scree plot to extract components with eigenvalues ​​greater than 1, and the maximum variance method was used to perform factor rotation to ensure that the explanatory power of the factors was maximized.

[0029] Step 5: In the BASE file output by the PMF model, organize the pollution source contribution matrix and display the contribution rate of different water quality parameters to each pollution source in a tabular form; identify and name the pollution source according to the characteristic water quality parameters of each pollution source, and calculate the average contribution rate of different pollution sources. Finally, determine the priority of basin pollution control according to the contribution rate.

[0030] Furthermore, the PMF model is used to quantify the contribution of possible pollution sources to water quality indicators. Its basic formula is:

[0031]

[0032] Among them, X ik represents the monitoring concentration of the kth water quality parameter of the ith sample; g ip Indicates the contribution of the i-th sample caused by the p-th factor; f pk represents the species concentration of the pth factor on the kth water quality parameter; e ik Represents the residual amount for each sample.

[0033] The innovation of this invention lies in the combination of explainable machine learning technology with the PMF model, which solves the shortcomings of the traditional PMF model in the selection of input indicators and constructs a working system of "regional water quality evaluation-identification of key pollution areas-determination of water quality indicators-pollution source tracing and analysis". It can more scientifically evaluate the impact of various pollution sources on water quality and improve the accuracy of analysis results, thereby providing reliable support for river basin water environment management and pollution control.

[0034] Beneficial effects of the present invention:

[0035] 1. This paper optimizes the indicator selection process of the PMF model through interpretable machine learning technology, and converts the fitting coefficient (R 2 ) was increased from 0.40 to 0.65, and the number of samples with residual absolute values ​​greater than 3 was reduced from 40 to 8. At the same time, four different pollution sources were successfully identified and quantified, which greatly improved the source analysis accuracy and efficiency of the model. This can promote the promotion and application of the PMF model in more regions and help local environmental protection departments to formulate more targeted pollution control plans.

[0036] 2. The present invention combines multivariate statistical methods (cluster analysis, principal component analysis) and machine learning techniques (XGBoost algorithm, SHAP interpreter) to construct a more scientific water quality evaluation and pollution source analysis system. Based on the water quality evaluation of different monitoring points in the basin, key areas are selected for source tracing and analysis, and the contribution of different pollution sources is accurately quantified, which greatly improves the water environment protection efficiency of the basin and provides a management framework that can be used as a reference for rivers with complex pollution sources and uneven pollution distribution.

[0037] 3. The present invention quantifies the contribution of different water quality indicators to water quality through machine learning technology, which helps local governments to reasonably adjust water quality monitoring plans, select key indicators for water quality monitoring in key areas, reduce the manpower and material resources required for pollution tracing, and promote environmental protection and sustainable social and economic development. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of a water pollution tracing system and method based on explainable machine learning of the present invention.

[0039] Figure 2 It is a spatial clustering diagram of water pollution characteristics.

[0040] Figure 3 This is a ranking diagram of the importance of different water quality index characteristics.

[0041] Figure 4 It is a beeswarm diagram based on SHAP interpretation.

[0042] Figure 5 It is the fitting graph of the XGBoost model screening indicators predicting the WQI value. DETAILED DESCRIPTION

[0043] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0044] A flow chart of a water pollution source tracing method based on interpretable machine learning Figure 1 As shown, the following steps are included:

[0045] Step 1: Collect and organize water quality data, check missing values ​​and outliers, use descriptive statistics to evaluate the water quality characteristics of the river, and complete the establishment of a water quality data set. In order to establish a database with sufficient sample size, the Laixi River Basin, a first-level tributary of the Tuojiang River, was selected as the study area. From 2015 to 2019, water quality monitoring was carried out monthly at 7 points in the basin. The physical and chemical indicators included water temperature WT, dissolved oxygen DO, and permanganate index COD Mn , five-day biochemical oxygen demand BOD5, ammonia nitrogen NH4 + -N, chemical oxygen demand COD Cr , Volatile phenol VP, Cyanide CN -, arsenic As, petroleum TPH, total phosphorus TP, copper Cu, zinc Zn, fecal coliform E.coil, electrical conductivity EC, total nitrogen TN. Descriptive statistics are shown in Table 1.

[0046] Table 1 Water quality parameter statistics

[0047]

[0048]

[0049] As shown in Table 2, the indicator weights and normalized value tables required by the WQI method were constructed by consulting high-level journals, monographs and the "Surface Water Environmental Quality Standard" (GB3838-2002) at home and abroad. The higher the weight, the greater the impact on water quality, and the higher the score, the better the water quality. The water quality score of each sample point was calculated using the WQI method. From upstream to downstream, the average water quality scores of the seven stations were: 74.11 (Laixi1), 66.50 (Laixi2), 72.08 (Laixi3), 75.33 (Laixi4), 60.75 (Laixi5), 58.29 (Laixi6), and 66.26 (Laixi7). It can be seen that the water quality at Laixi4 is the best, and the water quality at Laixi6 is the worst. There are large differences in the spatial distribution of water quality in the region. It is necessary to identify key areas and carry out targeted pollution prevention and control actions.

[0050] Table 2. Weights and scores of WQI methods

[0051]

[0052] Step 2: Based on the average water quality data of the seven monitoring stations, the present invention uses the system clustering method in SPSS software to analyze and cluster the spatial characteristics of water pollution distribution. The clustering results are as follows: Figure 2 As shown. Among them, Laixi2, Laixi3, Laixi5, Laixi6, and Laixi7 are classified into one category, which are mainly urban or suburban monitoring stations in the basin, with an average WQI of 64.77; Laixi1 and Laixi4 are classified into one category, which are mainly rural area monitoring stations, with an average WQI of 74.72. It can be seen that the water quality of cluster one is significantly worse than that of cluster two. From the perspective of spatial distribution, the monitoring stations involved in cluster one are also concentrated in urban areas. Therefore, the station where cluster one is located will be selected as the key area for pollution source analysis.

[0053] Step 3: Use the XGBoost algorithm to analyze the feature importance of different water quality indicators relative to the WQI value. The data set is divided into a training set and a test set at a ratio of 85:15. The depth of the tree gradually increases from 3, and the sampling ratio of each tree is set to 0.8. The importance ranking results are shown in Figure 2. Figure 3 As shown, the top five indicators are NH4 + -N、COD Mn , DO, E.coil and BOD5, among which NH4 + -N has the greatest impact on water quality, with an importance value of 3.68. Then, the SHAP method is used to display the impact of each sample parameter on the predicted value through a beeswax diagram, such as Figure 4 As shown, most pollutant indicators (such as NH4 + -N、COD Mn , TP, etc.) have a negative SHAP value, indicating a negative impact on WQI, while the larger the SHAP value of DO is, the positive SHAP value is, indicating a positive impact on water quality. - The importance values ​​of are all lower than 0.1, which means they have a low impact on water quality, and the SHAP value scatter points are concentrated close to the central axis, indicating that water quality is not sensitive to changes in their concentrations. Therefore, these five items will not be included in the subsequent PMF model. Figure 5 As shown in the figure, in order to verify the rationality of the parameter selection results, the screened water quality indicators are continued to be used as characteristic variables, the WQI value is the target variable, and the output model performance parameters are MAE = 1.211, MSE = 4.965, RMSE = 1.822, R 2 =0.943, achieving a good prediction effect, which further illustrates that the screening parameters can replace the original water quality information and can be used in the subsequent pollution source analysis model.

[0054] Step 4: Use principal component analysis (PCA) to perform dimensionality reduction analysis on the water quality data set of all indicators, and the eigenvalues ​​of the first four components are 3.23, 1.78, 1.26, and 1.03, respectively, which cumulatively explain 79.66% of the variance variables. PCA analysis was performed on the water quality data set after indicator screening, and 4 principal components were also obtained. Therefore, according to the results of principal component analysis, the number of factors in the PMF model was set to 4, and the PMF model was run according to the original indicators and the indicators screened by machine learning. As shown in Table 3, by comparing the model output results, it was found that the number of residuals output by the PMF model after indicator screening was reduced from 40 to 8, and the average R of each index after screening was 2. 2 The above results show that the combination of XGBoost algorithm and SHAP interpreter to select key indicators and construct PMF model improves the fitting degree of PMF model, makes the output results of the model more credible, and greatly enhances the accuracy of PMF model in water pollution source analysis.

[0055] Table 3 R before and after index screening 2 contrast

[0056]

[0057]

[0058] Step 5: After the index screening, the contribution rate of each water quality index obtained by the PMF model is shown in Table 4. Factor 1 significantly affects the E. coli index, which has the highest concentration in the central area of ​​the city, mainly due to untreated domestic sewage, which is attributed to domestic sewage discharge; the significant indicators of Factor 2 are WT, COD Mn , BOD5, indicating that organic pollution and water temperature changes have a greater impact on this factor, which may be related to seasonal production activities and explained as industrial emission pollution sources; the significant indicator of Factor 3 is NH4 + -N, TP, and TN are mainly nutrient indicators, which may be related to agricultural activities such as agricultural planting, livestock and poultry, and aquaculture in the region, and are classified as agricultural activity pollution sources; while the significant indicators of Factor 4 are DO and EC, which reflect the changes in the physical and chemical properties of water bodies, such as seasonal fluctuations in ion concentrations and dissolved oxygen levels, which represent the impact of natural ecological processes on water quality. Overall, the average contribution rates of the four pollution sources of domestic sewage, industrial emissions, agricultural activities, and natural factors were 12.75%, 32.37%, 28.06%, and 26.82%, respectively. Industrial sewage discharge is the primary source of pollution in the region, followed by agricultural activities. In the future, managers can formulate more targeted water environment management measures based on the results of pollution source analysis, improve the level of pollution control, and promote water environment protection and sustainable use of water resources.

[0059] Table 4 PMF model factor contribution rate

[0060]

[0061]

Claims

1. A water pollution source tracing method based on explainable machine learning, characterized in that: Here are the steps: Step 1: In order to study the water quality of the basin and analyze the source of pollution, long-term water quality monitoring data from several monitoring stations in the basin were collected and sorted into a water quality parameter data set; after checking for missing values ​​and outliers, descriptive statistical analysis was performed on the water quality parameter data set to confirm the distribution characteristics and fluctuations of each water quality parameter; Subsequently, based on the water quality monitoring data from different monitoring stations, the weights and normalized scores of different indicators were set using expert scoring, and the WQI water quality evaluation method was used to assess the quality level of water bodies and identify regional differences; Step 2: Calculate the average value of each water quality parameter at each monitoring station, use the system cluster analysis tool in SPSS26.0 software, and perform cluster analysis on the water quality data of different monitoring stations based on the Euclidean distance method of Ward link, divide the monitoring stations into different categories, and identify the spatial characteristics of pollution distribution; Compare the average WQI scores of different clusters to screen out areas with more serious pollution, form a water quality parameter data set for highly polluted areas, and conduct key analysis in subsequent pollution source analysis to improve the pertinence of pollution control and save capital investment; Step 3: Using Python 3.12.3 software, the XGBoost model algorithm was used to check missing values ​​and outliers in the data. The water quality parameter data set obtained in step 2 was divided into a training set and a test set. The measured data of each water quality parameter was used as the feature variable, and the measured value of WQI was used as the target variable. The XGboost algorithm was used to run the data matrix to quantify the feature importance of each water quality parameter relative to the WQI value. To ensure the data training effect and avoid overfitting, 85% of the data in the water quality parameter data set was used as the training set, and 15% of the data was used as the test set. The depth of the tree gradually increased from 3, and the sampling ratio of each tree was set to 0.

8. Subsequently, the SHAP tool was introduced to explain the overall and local contributions of each water quality parameter to the change in WQI value. Based on the bee colony diagram obtained by the SHAP tool, the characteristics of the impact of each independent measured value of different water quality parameters on the prediction of WQI value were analyzed, and the impact of the concentration change of each water quality parameter on water quality prediction was analyzed. In this step, water quality parameters with an importance lower than 0.1 were deleted; the remaining water quality parameters with high importance were included in the PMF model for pollution tracing; then, the XGBoost model algorithm was used again to test the prediction effect of the screened water quality parameters on the WQI value, output relevant performance parameters, test the fitting effect, and finally determine the water quality parameters included in the PMF model calculation; Step 4: Use principal component analysis (PCA) to reduce the dimension of the water quality parameter data set obtained in step 2 and the water quality data set screened in step 3. Determine the number of principal components based on the factor eigenvalue greater than 1 and the scree plot. Use the number of principal components as the preset number of pollution sources in the PMF model. In the PMF model, use the water quality parameter data set obtained in step 2 and the water quality data set screened in step 3 to construct the PMF model, and compare the R under different parameter selections. 2 , residuals and other performance indicators to verify the degree of improvement in model performance, and select the output results of the optimized PMF model for pollution source identification and quantification; Step 5: In the BASE file output by the PMF model, organize the pollution source contribution matrix and display the contribution rate of different water quality parameters to each pollution source in a tabular form; identify and name the pollution source according to the characteristic water quality parameters of each pollution source, and calculate the average contribution rate of different pollution sources. Finally, determine the priority of basin pollution control according to the contribution rate.

2. The water pollution source tracing method based on interpretable machine learning method according to claim 1 is characterized in that: The water quality parameters include water temperature WT, dissolved oxygen DO, permanganate index COD Mn , five-day biochemical oxygen demand BOD5, ammonia nitrogen NH4 + -N, chemical oxygen demand COD Cr , volatile phenol VP, cyanide CN - , arsenic As, petroleum TPH, total phosphorus TP, copper Cu, zinc Zn, fecal Escherichia coli E.coil, electrical conductivity EC and total nitrogen TN.

3. The water pollution source tracing method based on interpretable machine learning method according to claim 1 is characterized in that: The descriptive statistical analysis includes obtaining the minimum value, maximum value, mean value and standard deviation of the water quality parameters.

4. The water pollution source tracing method based on interpretable machine learning method according to claim 1 is characterized in that: The WQI water quality evaluation method is to determine the weights of water quality parameters and normalized scores based on expert scoring, according to the formula: Among them, m is the number of water quality parameters, C k is the normalized value of the kth water quality parameter, P k is the weight of the kth water quality parameter.

5. The water pollution source tracing method based on interpretable machine learning method according to claim 1 is characterized in that: When building the XGBoost model, the objective function of the XGBoost model is as follows: Where n is the number of samples, y i is the measured value of sample i, is the prediction result of sample i, is the loss function, Ω(f k ) is a regularization term used to control the complexity of the XGBoost model; The XGBoost model output performance evaluation parameters include mean absolute error, mean square error, root mean square error, and determination coefficient, according to the formula: Where n is the number of samples, y i is the measured value for each sample, is the average value of the measured value of this indicator. is the predicted value obtained using the model.

6. The water pollution source tracing method based on interpretable machine learning method according to claim 1 is characterized in that: The SHAP tool is based on the Shapley value in game theory. It explains the output of the XGBoost model by calculating the marginal contribution of each water quality parameter and quantifies the contribution of each water quality parameter to water quality changes. The SHAP value calculation formula is: in: is the SHAP value of the kth water quality parameter; N is the set of all features; S is the feature subset that does not contain water quality parameter k; f(S) is the model prediction value of subset S; f(S∪{k}) is the model prediction of the features in S plus the features 7. The water pollution source tracing method based on interpretable machine learning method according to claim 1 is characterized in that: In principal component analysis, the factor analysis tool embedded in SPSS software was used, combined with the scree plot to extract components with eigenvalues ​​greater than 1, and the maximum variance method was used to perform factor rotation to ensure the maximum explanatory power of the factors.

8. The water pollution source tracing method based on interpretable machine learning method according to claim 1 is characterized in that: The PMF model is used to quantify the contribution of possible pollution sources to water quality indicators. The basic formula is: Among them, X ik represents the monitoring concentration of the kth water quality parameter of the ith sample; g ip Indicates the contribution of the i-th sample caused by the p-th factor; f pk represents the species concentration of the pth factor on the kth water quality parameter; e ik Represents the residual amount for each sample.

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