A new method of coupling apcs-mlr with pmf for source apportionment and dynamic risk quantification

Abstract

This invention discloses a novel pollutant source apportionment and dynamic risk quantification assessment method coupling APCS-MLR and PMF, relating to the field of environmental management technology. The method includes: collecting pollutant concentration data from environmental samples, preprocessing the data to construct a data matrix; running various models to perform source apportionment based on the data matrix, extracting source apportionment feature information, and matching the pollution sources identified by each model to obtain high-confidence source matching pairs; fusing the source contribution concentrations of the two models based on the high-confidence source matching pairs to obtain a fused contribution concentration; calculating the ecological and human health risk values ​​of each pollution source based on the fused contribution concentration to obtain source-specific risk values, calculating the risk contribution rate of each pollution source, and outputting a list of high-risk sources. This invention solves the problems of insufficient accuracy and reliability of source apportionment using a single model, and addresses the issues of the disconnect between source apportionment results and risk assessment, making it difficult to identify high-risk pollution sources.

Description

Technical Field

[0001] This invention relates to the field of environmental management technology, and more specifically, to a novel pollutant source apportionment and dynamic risk quantification method coupled with APCS-MLR and PMF. Background Technology

[0002] With the acceleration of industrialization and the widespread use of chemicals, the detection frequency of new pollutants (such as perfluorinated compounds, antibiotics, microplastics, and endocrine disruptors) in environmental media is increasing year by year. These pollutants are typically characterized by low concentrations, high toxicity, complex sources, and uncertain environmental behavior, posing significant challenges to environmental monitoring, pollution source tracing, and risk assessment. Traditional pollutant source apportionment methods mainly rely on receptor models, among which the APCS-MLR model and the positive definite matrix factorization (PMF) model are widely used.

[0003] However, the APCS-MLR model has inherent flaws: it may produce negative contribution concentrations during the calculation process, which contradicts the physical reality that the contribution of pollution sources cannot be negative, resulting in unclear physical meaning of the analysis results; at the same time, the model lacks objective standards for determining the number of factors and is easily affected by subjective judgment.

[0004] The PMF model also has limitations: it is sensitive to the setting of initial values ​​and is prone to getting trapped in local optima; the selection of the number of factors depends on the changes in Q value and residual analysis, which has a certain degree of subjectivity and ambiguity; in addition, the PMF model has high requirements for data quality and sample size, and may have problems such as poor fitting effect or unstable factor identification when processing low-concentration new pollutant data.

[0005] In summary, the existing technologies mainly have the following problems: (1) Each single receptor model (APCS-MLR or PMF) has its own defects in the source apportionment process. APCS-MLR has the problem of negative contribution, and PMF has the ambiguity of factor number selection and the risk of local optimal solution. A single model is difficult to guarantee the accuracy and credibility of the source identification results; (2) There is a lack of a mechanism for systematic matching and fusion of the analysis results of the two models, and it is impossible to use the complementary advantages of the two models to improve the reliability of source apportionment; (3) The source apportionment results are separated from the risk assessment model, and it is impossible to quantify the contribution ratio of each pollution source to ecological risk and human health risk, making it difficult to identify high-risk pollution sources. Summary of the Invention

[0006] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a novel pollutant source apportionment and dynamic risk quantification assessment method that couples APCS-MLR and PMF. This method solves the problem of insufficient accuracy and reliability of source apportionment using a single model, and addresses the issue of source apportionment results being disconnected from risk assessment and the difficulty in identifying high-risk pollution sources through a source-specific risk quantification method.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] This application provides a novel pollutant source apportionment and dynamic risk quantification assessment method coupling APCS-MLR and PMF. The method includes: collecting pollutant concentration data of environmental samples and constructing a data matrix after processing; performing source apportionment using the APCS-MLR model and the PMF model respectively based on the data matrix, and extracting source apportionment feature information of each model; matching the pollution sources identified by each model based on the source apportionment feature information to obtain high-confidence source matching pairs; fusing the source contribution concentrations of the two models based on the high-confidence source matching pairs to obtain a fused contribution concentration that satisfies mass conservation; calculating the ecological risk value and human health risk value of each pollution source based on the fused contribution concentration to obtain a source-specific risk value; and calculating the risk contribution rate of each pollution source based on the source-specific risk value and outputting a list of high-risk sources.

[0009] In one embodiment, pollutant concentration data of environmental samples are collected, processed, and a data matrix is ​​constructed, including: collecting raw pollutant concentration data and method detection limits of environmental samples; preprocessing the raw concentration data to obtain concentration data; calculating the uncertainty of each pollutant in each sample based on the concentration data and method detection limits; calculating the signal-to-noise ratio and classifying pollutant information based on the concentration data and uncertainty; and constructing a data matrix for model input based on the concentration data, uncertainty, and pollutant classification information.

[0010] In one embodiment, source apportionment is performed using the APCS-MLR model, including: performing principal component analysis on the standardized concentration data, extracting principal components and obtaining factor loading matrices and factor score matrices; introducing a zero-concentration reference point and calculating absolute principal component scores based on the factor score matrices; performing multiple linear regression with concentration data as the dependent variable and absolute principal component scores as the independent variable to obtain regression coefficients; calculating the APCS-MLR source contribution concentrations based on the regression coefficients, normalizing the regression coefficients to obtain APCS-MLR source component spectral vectors, and normalizing the regression coefficients to obtain APCS-MLR source component spectral vectors for each pollution source.

[0011] In one embodiment, running a PMF model for source apportionment includes: setting the calculation weight of each component in the PMF model based on pollutant classification information; setting the number of candidate factors and performing multiple iterative calculations to determine the optimal number of factors based on the rate of change of the objective function value; and outputting the factor contribution matrix and factor spectrum matrix based on the optimal number of factors, and obtaining the PMF contribution concentration.

[0012] In one embodiment, based on source apportionment feature information, pollution sources identified by each model are matched to obtain high-confidence source matching pairs, including: constructing an APCS-MLR source vector set based on the source component spectrum in the APCS-MLR source apportionment feature information; constructing a PMF factor vector set based on the factor spectrum matrix in the PMF source apportionment feature information; calculating the cosine similarity between each pair of source vectors and factor vectors in the two vector sets to obtain a similarity matrix; performing bidirectional consistency verification based on the similarity matrix, and marking matching pairs that meet the preset similarity threshold and pass the bidirectional verification as high-confidence source matching pairs.

[0013] In one embodiment, the source contribution concentrations of the two models are fused based on high-confidence source matching pairs, including: extracting the goodness-of-fit data of each simulation based on the high-confidence source matching pairs and calculating the initial weights of the matched source-pollutant pairs; calculating the APCS confidence coefficient and PMF confidence coefficient respectively based on the APCS-MLR source contribution concentration and PMF source contribution concentration using a comprehensive criterion; and calculating the fused contribution concentration based on the initial weights, APCS confidence coefficient, and PMF confidence coefficient.

[0014] In one embodiment, the comprehensive criterion includes a nonnegativity criterion, a reasonableness criterion, and a consistency criterion.

[0015] In one embodiment, obtaining the fusion contribution concentration that satisfies mass conservation further includes: summing the fusion contribution concentrations to obtain the total fusion contribution concentration; calculating the mass closure residual based on the total fusion contribution concentration and the measured total concentration; verifying the mass closure residual; for sample-pollutant pairs that need correction, allocating the residual back to each source contribution according to the contribution ratio of each source, and performing a non-negativity test and processing on the allocated source contribution concentrations to obtain the corrected source contribution concentration that satisfies mass conservation.

[0016] In one embodiment, based on the fusion contribution concentration, the ecological risk value and human health risk value of each pollution source are calculated to obtain the source-specific risk value. This includes: acquiring ecotoxicity parameter data, including ecotoxicity parameters and health toxicity parameters; calculating the ecological risk quotient of each pollutant based on the corrected source contribution concentration and ecotoxicity parameters, and summing the values ​​for all pollutants from the same pollution source in the same sample to obtain a cumulative ecological risk index; calculating the average daily exposure dose under different exposure pathways based on the corrected source contribution concentration; and calculating the non-carcinogenic risk quotient and carcinogenic risk of each pollution source based on the average daily exposure dose and health toxicity parameters, and summing the values ​​to obtain the cumulative non-carcinogenic risk index and the cumulative carcinogenic risk index, respectively.

[0017] In one embodiment, based on source-specific risk values, the risk contribution rate of each pollution source is calculated, and a list of high-risk sources is output. This includes: calculating the ratio of each source-specific risk value to the total risk value of all corresponding sources to obtain the risk contribution rate of each source; weighting and summing the risk contribution rates of each source in conjunction with regional environmental management objectives to obtain a comprehensive risk contribution rate; and classifying risk levels according to the comprehensive risk contribution rate and a preset grading threshold, and outputting a list of high-risk sources and a risk contribution rate distribution report.

[0018] As can be seen from the above technical solutions, the embodiments of this application have the following advantages:

[0019] By employing a systematic dual-model coupling and dynamic risk quantification mechanism, a complete technical closed loop from data preprocessing to high-risk source identification is constructed. Its core advantages are: First, uncertainty calculation based on signal-to-noise ratio classification and parallel analysis of the dual models ensure the reliability of the input data quality while significantly improving the accuracy and credibility of source identification through the source fingerprint mutual verification mechanism of APCS-MLR and PMF. Second, the innovative introduction of source-pollutant pair level weighting, multi-dimensional credibility criteria, and normalized weighted fusion strategies effectively solves technical challenges in traditional methods such as negative contributions, quality non-closure, and misjudgment by a single model. Finally, by deeply integrating source apportionment results with ecological and health risk assessment models, a leap from "concentration source tracing" to "risk source tracing" is achieved. Furthermore, risk weights are dynamically adjusted based on regional protection targets, outputting a list of high-risk sources, providing a scientific, quantitative, and operable decision-making basis for precise environmental governance and priority control of pollution sources. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of a novel pollutant source apportionment and dynamic risk quantification assessment method coupled with APCS-MLR and PMF, provided for embodiments of this application.

[0022] Figure 2 A line graph of pollutant classification based on signal-to-noise ratio provided for embodiments of this application.

[0023] Figure 3 The APCS-MLR and PMF source matching similarity matrix diagram provided for the embodiments of this application.

[0024] Figure 4 A comparison chart of source contribution concentrations provided for embodiments of this application. Detailed Implementation

[0025] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0026] It should also be noted that, in this document, terms such as “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or device. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the article or device that includes the aforementioned element.

[0027] Reference Figure 1 As shown in the diagram, this invention provides a flowchart of a novel pollutant source apportionment and dynamic risk quantification assessment method coupled with APCS-MLR and PMF, comprising the following steps:

[0028] S1: Collect raw concentration data of multiple pollutants from multiple samples in the environmental medium, preprocess the data, calculate the uncertainty of each component, and construct a data matrix for model input, including:

[0029] Collect raw concentration data of multiple pollutants from multiple samples in the environmental medium and record the method detection limit (MDL) for each pollutant.

[0030] The raw concentration data is preprocessed, including data cleaning, removal of outliers (such as negative values), and imputation of missing values ​​(such as using the median) to obtain the concentration data.

[0031] Based on the concentration data and the method detection limit, the uncertainty of each pollutant in each sample is calculated, specifically as follows:

[0032] If concentration data If the method detection limit is given, the specific formula for calculating the uncertainty is as follows:

[0033]

[0034] When pollutant concentrations are below the method detection limit, the measured values ​​are unreliable and cannot be directly calculated using conventional error calculation formulas. Therefore, classical environmental statistical methods (such as the EPA PMF 5.0 User Guide) are employed to process the data, replacing values ​​below the detection limit with... The uncertainty is set to .

[0035] The statistical source for this coefficient is: if the concentration is uniformly distributed within the interval [0, MDL], then the standard deviation of the data within this interval is approximately ≈0.2887×MDL, but in practice, to cover potential variability and conservatively estimate uncertainty, the PMF model uses... This serves as an empirical value. It is greater than the theoretical standard deviation, thus absorbing the dispersion of data below the detection limit, preventing the model from over-relying on inaccurate measurements, and preserving sample information without directly discarding them.

[0036] If concentration data If the method detection limit is given, the specific formula for calculating the uncertainty is as follows:

[0037]

[0038] In the formula, Uncertainty for each contaminant in each sample. The relative deviation (usually provided by the laboratory, typically 5%–20%, determined based on the precision of the analytical method) This is concentration data.

[0039] The purpose of multiplying by 0.5 in the formula is to convert the method detection limit into a constant component of the uncertainty. The coefficient 0.5 comes from the default recommendation of the EPA PMF model: This serves as the fundamental uncertainty introduced by the detection limit. This term ensures that the uncertainty transitions smoothly as the concentration approaches the MDL, without any mathematical abrupt discontinuity. The mathematical basis for using the sum-of-squares form is the assumption that the relative error (proportional to the concentration) and the absolute error (proportional to the MDL) are independent sources of variance contribution.

[0040] Based on concentration data and uncertainty, the signal-to-noise ratio for each pollutant is obtained by calculating the ratio of concentration value to uncertainty. and according to The value is used to classify pollutants into "Strong" ( “Weak” ) and "Bad" Information on the classification of pollutants into three categories, such as Figure 2 As shown, this is used for dynamic adjustment of weights in the subsequent PMF model;

[0041] A data matrix for model input is constructed based on concentration data, uncertainty, and pollutant classification information.

[0042] S2, based on the data matrix, runs the preset APCS-MLR model and PMF model respectively for source analysis, extracts the source analysis feature information of each model as input for subsequent steps.

[0043] This includes running the preset APCS-MLR model for source parsing, including:

[0044] The concentration data were Z-score standardized to obtain a standardized concentration matrix;

[0045] The standardized concentration matrix is ​​calculated using the following formula:

[0046]

[0047] In the formula, For the standardized concentration matrix, Let j be the average value of pollutant j. Let be the standard deviation of pollutant j.

[0048] Principal component analysis was performed on the standardized concentration matrix to extract principal components with eigenvalues ​​greater than 1. The number of extracted principal components was equal to the number of APCS-MLR pollution sources. The factor loading matrix obtained from the principal component analysis was rotated using the maximum variance rotation method to obtain the rotated factor loading matrix and factor score matrix.

[0049] The factor loading matrix describes the degree of linear correlation between each pollutant and each common factor (pollution source). The element values ​​represent the magnitude of the pollutant's loading on the corresponding factor, reflecting the strength of the pollutant's influence by that factor. The factor score matrix is ​​a matrix calculated based on the factor loading matrix, with each sample's score on each factor as its elements. It is used to quantify the magnitude of each sample's influence by each factor (pollution source).

[0050] For the factor score matrix, a zero-concentration reference point is introduced. The scores of each principal component at zero concentration are calculated, and the absolute principal component scores are obtained based on the difference between the actual sample scores and the zero-concentration scores. ;

[0051] The score at zero concentration is calculated using the following formula:

[0052]

[0053] In the formula, The score at zero concentration. , which is the factor score coefficient, is a matrix output from the analysis software. It is used to linearly transform the standardized values ​​of the original variables into scores for each factor (pollution source), where m is the number of pollutants.

[0054] Using concentration data as the dependent variable and absolute principal component scores as independent variables, a regression equation is constructed, and multiple linear regression is performed to obtain the regression coefficients.

[0055] The specific calculation formula for the regression equation is as follows:

[0056]

[0057] In the formula, For constant terms, is the regression coefficient, and p is the number of principal components.

[0058] Based on the regression coefficients, the APCS-MLR source contribution concentration of each source k to pollutant j in sample i is calculated, and the regression coefficients are normalized to obtain the APCS-MLR source component spectral vector of each pollution source.

[0059] Normalization refers to dividing the regression coefficient corresponding to each pollution source by the sum of the regression coefficients of all its components to obtain the relative contribution ratio of each pollutant, so that the sum of all elements of the source component spectral vector is 1.

[0060] The specific formula for calculating the APCS-MLR source contribution concentration is as follows:

[0061]

[0062] In the formula, Contributes concentration to APCS-MLR source.

[0063] APCS-MLR source apportionment feature information is obtained based on the APCS-MLR source contribution concentration, APCS-MLR source component spectral vector, and the number of APCS-MLR pollution sources.

[0064] Furthermore, the preset PMF model is run to perform source resolution, including:

[0065] Based on pollutant classification information, the calculation weights of each component in the PMF model are set. The weight of the component with the signal-to-noise ratio classification information of "Strong" is set to 1, the weight of the component with the signal-to-noise ratio classification information of "Weak" is set to 3, and the component with the signal-to-noise ratio classification information of "Bad" is removed.

[0066] Set several candidate factor numbers. For each candidate factor number, use the PMF2 algorithm to start with multiple random initial values ​​(usually more than 20 times). By iteratively minimizing the objective function, obtain the corresponding factor contribution matrix and factor spectrum matrix. Based on the rate of change of the objective function value, i.e., observe the curve of the objective function value as the number of factors increases, select the factor number at the inflection point to determine the optimal number of factors.

[0067] Among them, the PMF2 algorithm is a classic computer program used to implement the positive definite matrix factorization (PMF) model. Its core feature is to identify the factor analysis problem as a weighted least squares problem, solve it through an iterative optimization algorithm, and apply non-negativity constraints during the solution process to ensure that the factor contributions and factor spectra decomposed are non-negative and have clear physical meaning.

[0068] The PMF2 algorithm first transforms the source analysis problem into a weighted least squares problem. Starting with a randomly generated initial factor matrix, the algorithm iteratively adjusts the factor contribution matrix and factor spectrum matrix using an optimization algorithm (such as the conjugate gradient method or alternating least squares method) to gradually reduce the objective function value until it converges to the minimum. Since the objective function may have multiple local optima, multiple random initial values ​​are used to start the iteration from different starting points, thereby increasing the probability of finding the global optimum. Finally, the solution with the smallest objective function value and the most reasonable physical meaning is selected as the optimal result for that number of factors. Throughout the iteration process, the PMF2 algorithm ensures that the elements in the factor contribution matrix and factor spectrum matrix are non-negative after each iteration through a built-in non-negativity constraint mechanism. This conforms to the physical reality that the pollution source contribution concentration and source component spectrum cannot be negative.

[0069] The objective function is calculated using the following formula:

[0070]

[0071] In the formula, The objective function value, Let n be the residual and n be the number of samples. Calculate the weights for the components defined based on the signal-to-noise ratio classification.

[0072] Based on the determined optimal number of factors, the final factor contribution matrix is ​​output. (representing the total quality contribution of the k-th source to the i-th sample) and the factor spectrum matrix (representing the characteristic content of the j-th pollutant in the k-th source), and the PMF contribution concentration of each source to each pollutant is obtained by multiplying the factor contribution matrix with the factor spectrum matrix;

[0073] The optimal number of factors is used as the number of pollution sources identified by PMF, and the PMF contribution concentration and factor spectrum matrix are combined as the source apportionment feature information of the PMF model.

[0074] Among them, the source composition spectrum refers to the relative content or characteristic proportion of various chemical components emitted by a specific pollution source, presented in vector form, reflecting the "fingerprint" characteristics of the source, and used to distinguish different pollution source types; the factor contribution matrix is ​​a matrix in the PMF model that represents the contribution of each factor (pollution source) to the total mass of each sample; the factor spectrum matrix is ​​a matrix that represents the characteristic content of each chemical component in each factor. The two are obtained through non-negative matrix decomposition and together describe the quantitative contribution and chemical composition of the pollution source; the source contribution concentration refers to the mass concentration contribution value of a specific pollution source to a certain pollutant in a certain environmental sample, that is, the concentration of the pollutant in the sample is directly caused by the emission of the source, and it is the quantitative output result of source apportionment.

[0075] It should be noted that a systematic dual-model coupling mechanism achieves a complete technical closed loop from data preprocessing to source apportionment and risk quantification. Its core advantages are as follows: First, the weight setting and uncertainty calculation based on signal-to-noise ratio classification ensure the quality and reliability of the input data to the PMF model. At the same time, the standardization processing of APCS-MLR eliminates the influence of dimensions, laying a solid foundation for subsequent analysis. Second, by running the APCS-MLR and PMF models separately and extracting their respective source apportionment feature information, the advantages of APCS-MLR in quickly fitting the total mass concentration are utilized, while the non-negative constraint characteristics of PMF ensure the physical authenticity of the source component spectra. The parallel analysis of the two models forms a source fingerprint mutual verification mechanism, effectively avoiding the risk of misjudgment caused by the algorithm defects of a single model. Finally, the number of pollution sources, contribution concentration, and source component spectra output by the two models are used as standardized feature information input to subsequent steps, providing a unified, complete, and high-confidence data foundation for source matching fusion and dynamic risk quantification. This enables the entire method to accurately identify the source of new pollutants and quantify their risk contribution, significantly improving the accuracy of source apportionment and the scientific nature of risk assessment under complex environmental conditions.

[0076] S3, based on source resolution feature information, calculate the cosine similarity between each source vector of APCS-MLR and each factor vector of PMF, match source pairs with similarity higher than a preset threshold as the same type of pollution source, and mark them as high-confidence source matching pairs, including:

[0077] Based on the source component spectra in the source analysis feature information of APCS-MLR, construct the APCS-MLR source vector set. , where each vector This represents the component spectrum value of the i-th APCS-MLR source for d pollutants;

[0078] Based on the factor spectrum matrix in the PMF source analysis feature information, construct the PMF factor vector set. , where each vector denoted as the factor spectrum value of the j-th PMF factor on d pollutants, where m and n are the number of pollution sources identified by APCS-MLR and PMF, respectively;

[0079] Based on two vector sets, the cosine similarity between each pair of APCS-MLR source vectors and PMF factor vectors is calculated to obtain a similarity matrix, such as... Figure 3 As shown;

[0080] The cosine similarity is calculated using the following formula:

[0081]

[0082] In the formula, For cosine similarity, Let i be the component spectrum value of the i-th APCS-MLR source for the k-th pollutant. Let be the factor spectrum value of the j-th PMF factor on the k-th pollutant.

[0083] Based on the similarity matrix, for each APCS-MLR source Find the PMF factor with the highest similarity. If the maximum similarity exceeds a preset threshold, each APCS-MLR source and PMF factor will be initially classified as the same type of pollution source, forming a preliminary matching pair; otherwise, it will be... Marked as a source that does not match;

[0084] A two-way consistency verification is performed on the initial matching pairs. This involves checking whether the APCS-MLR source has the maximum value and is higher than the threshold among the similarities between the PMF factor of the matching pair and all APCS-MLR sources. If the two-way verification passes, the matching pair is marked as a high-confidence source matching pair.

[0085] Among them, the high-confidence source matching refers to the fact that in the dual-model source analysis, the source identified by APCS-MLR and the factor identified by PMF are confirmed to be the same type of pollution source through cosine similarity calculation. This indicates that the source is stably identified in both independent models and has high confidence.

[0086] S4, based on high-confidence source-matching pairs, constructs initial weights by combining the goodness-of-fit data of each model for each pollutant, and introduces the APCS confidence coefficient and PMF reasonableness criterion based on multidimensional criteria to calculate the fusion contribution concentration of each pollutant, including:

[0087] Based on high-confidence source-matching pairs, goodness-of-fit data for each matched source k to each pollutant j is extracted from the results of the APCS-MLR model and the PMF model, respectively. The goodness-of-fit data includes APCS goodness-of-fit data. Goodness of fit with PMF ;

[0088] Among them, goodness-of-fit data refers to the explanatory power of the APCS-MLR model or PMF model for each source-pollutant pair, and is used to quantify the credibility of the source-pollutant pair in their respective models.

[0089] For each matched source and pollutant, if the APCS goodness of fit is less than 0, then set the APCS goodness of fit to 0; if the PMF goodness of fit is less than 0, then set the PMF goodness of fit to 0. Then calculate the initial weights of the APCS-MLR model on the source-pollutant pair and the initial weights of the PMF model.

[0090] The initial weights of the APCS-MLR model are calculated using the following formula:

[0091] .

[0092] The initial weights of the PMF model are calculated using the following formula:

[0093]

[0094] In the formula, The initial weights for the APCS-MLR model, These are the initial weights for the PMF model.

[0095] Based on the APCS-MLR source contribution concentration, the APCS confidence coefficient is calculated using a comprehensive criterion, which includes non-negativity criteria, reasonableness criteria, and consistency criteria, including:

[0096] Based on the nonnegativity criterion, if the APCS-MLR source contribution concentration exceeds 0, the APCS confidence coefficient is equal to 1, and otherwise it is 0.

[0097] Based on the reasonableness criterion, if the APCS-MLR source contribution concentration does not exceed the measured total concentration, then the APCS confidence coefficient is equal to 1; otherwise, the APCS confidence coefficient is calculated using the following formula:

[0098]

[0099] In the formula, This represents the APCS credibility coefficient. This represents the measured total concentration.

[0100] Based on the consistency criterion, the relative deviation between the APCS-MLR source contribution concentration and the PMF source contribution concentration is calculated, and the APCS confidence coefficient is obtained through calculation.

[0101] The specific formula for calculating the relative deviation is as follows:

[0102]

[0103] In the formula, This is a relative deviation. Contributes concentration to PMF source To prevent small positive numbers from being divided by zero.

[0104] The APCS credibility coefficient is calculated using the following formula:

[0105]

[0106] The minimum value among the comprehensive criteria is taken as the APCS confidence coefficient.

[0107] Based on the PMF source contribution concentration, a reasonableness criterion is applied. If the PMF source contribution concentration does not exceed the measured total concentration, the PMF confidence coefficient is 1; otherwise, it is 1. ,in, The PMF (Productability Factor) confidence coefficient;

[0108] Based on the initial weights and the APCS and PMF confidence coefficients, the fusion contribution concentration is calculated, such as... Figure 4 As shown;

[0109] The specific formula for calculating the fusion contribution concentration is as follows:

[0110]

[0111] In the formula, The fusion contribution concentration represents the best-estimated contribution of the source to the pollutant in the sample.

[0112] Among them, the APCS confidence coefficient is used to evaluate the physical rationality and reliability of the APCS contribution concentration, and the PMF confidence coefficient is used to evaluate the rationality of the PMF contribution concentration.

[0113] It should be noted that a systematic dual-model matching and fusion mechanism was used to achieve high-confidence calibration and optimization of source apportionment results. Its core advantages are: First, source matching and bidirectional consistency verification based on cosine similarity ensure that the same type of pollution source identified by APCS-MLR and PMF is stably identified in both independent models, significantly improving the accuracy and reliability of source type determination. Second, by introducing a goodness-of-fit weight allocation for source-pollutant pair levels and combining multi-dimensional criteria (non-negativity, reasonableness, and consistency) to calculate the APCS confidence coefficient and the PMF reasonableness criterion, a refined confidence assessment system was constructed, effectively solving the problem of relying solely on numerical magnitude or single-model correction in traditional methods. Finally, through a normalized weighted average fusion strategy, the initial weights and dual-model confidence coefficients were uniformly incorporated into the calculation, resulting in a fusion contribution concentration with clear physical meaning, reasonable data boundaries, and high model consistency. This provides high-quality, highly reliable input data for subsequent dynamic risk quantification assessment, significantly improving the overall scientific rigor and practicality of new pollutant source apportionment.

[0114] S5. Based on the fusion contribution concentration, calculate the residual between it and the measured total concentration, and allocate it back to each source contribution for correction in proportion to ensure that the fusion result meets the quality conservation. Based on the corrected source contribution concentrations, calculate the source-specific risk value of each pollution source to the ecological environment and human health.

[0115] Specifically, based on the fusion contribution concentration, the residual between it and the measured total concentration is calculated and proportionally allocated back to each source contribution for correction, including:

[0116] The total fusion contribution concentration is obtained by summing the fusion contribution concentrations of all matching sources.

[0117] Calculate the mass closure residual of pollutants in the sample based on the total fusion contribution concentration and the measured total concentration;

[0118] The specific formula for calculating the quality closure residual is as follows:

[0119]

[0120] In the formula, The mass closure residual reflects the degree of deviation between the sum of the source contribution concentrations after fusion and the measured total concentration. Contributes to the overall fusion concentration.

[0121] The reasonableness of the quality closure residual is checked. ,in, If the preset residual tolerance threshold is used, it is determined that the sample-contaminant pair has a significant quality non-closure and needs to be corrected.

[0122] For sample-contaminant pairs that need correction, calculate the contribution percentage of each matched source in the current sample-contaminant pair based on the fusion contribution concentration;

[0123] The specific formula for calculating the contribution percentage is as follows:

[0124]

[0125] In the formula, As for the percentage of contribution, To match the number of sources.

[0126] Based on the quality closure residual and contribution ratio, the residual is proportionally allocated back to each source contribution to obtain the corrected source contribution concentration.

[0127] The corrected source contribution concentration is calculated using the following formula:

[0128]

[0129] In the formula, To correct the source contribution concentration, this correction method ensures that the sum of the corrected source contribution concentrations equals the measured total concentration, thus satisfying the law of conservation of mass.

[0130] A nonnegativity test is performed on the corrected source contribution concentration. If there is a corrected source contribution concentration less than 0, iterative redistribution and proportional compression are performed to obtain the final corrected source contribution concentration that satisfies mass conservation.

[0131] The iterative redistribution involves setting negative values ​​to zero and redistributing their absolute values ​​according to the proportion of the remaining positive sources, repeating the iteration until the concentration of all source contributions is non-negative; the proportional compression involves setting the corrected source contribution concentration to 0 if the negative value is less than a preset threshold, and readjusting the contributions of other sources according to a preset new proportion to ensure that the sum is still equal to the measured total concentration.

[0132] It should be noted that the residual proportional allocation mechanism ensures that the sum of the source contribution concentrations after fusion is strictly consistent with the measured total concentration, satisfying the law of mass conservation. At the same time, the introduction of non-negativity quadratic test and iterative redistribution strategy effectively avoids the generation of new negative values ​​or distortions during the correction process, ensuring the physical rationality of the source contribution concentrations and the integrity of the data, and providing accurate, reliable and mass-conserving input data for subsequent risk quantification assessment.

[0133] Furthermore, based on the corrected source contribution concentrations, a source-specific risk value for each pollution source to the ecological environment and human health is calculated. This source-specific risk value includes a cumulative ecological risk index, a cumulative non-carcinogenic risk index, and a cumulative carcinogenic risk index, comprising:

[0134] Toxicity parameter data are obtained, including ecotoxicity parameters and health toxicity parameters. Ecotoxicity parameters include predicted no-effect concentration and safety factor, while health toxicity parameters include oral reference dose, skin contact reference dose, inhalation reference dose, carcinogenicity slope factor, and skin absorption factor.

[0135] Based on the corrected source contribution concentration and toxicity parameter data, the ecological risk quotient of each pollution source k to pollutant j in sample i is calculated;

[0136] The ecological risk quotient is calculated using the following formula:

[0137]

[0138] In the formula, The ecological risk quotient represents the degree of ecological risk posed by pollutant j emitted from source k alone. To predict the concentration of no effect, This is for the safety factor.

[0139] Based on the ecological risk quotient of each pollutant, and considering the toxicity mechanism of each pollutant as additive, the cumulative ecological risk index of the source is obtained by summing all pollutants in the same sample from the same pollution source.

[0140] The cumulative ecological risk index is calculated using the following formula:

[0141]

[0142] In the formula, To accumulate the ecological risk index, This represents the total number of pollutants included in the assessment.

[0143] Based on the corrected source contribution concentration, and in accordance with the US EPA standard exposure assessment model framework, the average daily exposure dose under different exposure routes, including oral ingestion, skin contact, and inhalation, was calculated.

[0144] Among them, the average daily exposure dose via oral intake route The specific calculation formula is as follows:

[0145]

[0146] Daily exposure dose via skin contact The specific calculation formula is as follows:

[0147]

[0148] Average daily exposure dose via inhalation The specific calculation formula is as follows:

[0149]

[0150] The parameters are defined as shown in Table 1:

[0151] Table 1. Parameter Meaning Table

[0152]

[0153] Based on the exposure dose and reference dose of health toxicity parameters under each exposure route, the non-carcinogenic risk quotient of each pollution source to the pollutants in the sample is calculated, and the summation is used to obtain the cumulative non-carcinogenic risk index of the source.

[0154] The specific formula for calculating the non-carcinogenic risk quotient is as follows:

[0155]

[0156] In the formula, The non-carcinogenic risk quotient represents the non-carcinogenic health risk posed by pollutant j emitted from source k through multiple pathways of exposure. This is a reference dose for oral intake. Reference dose for skin contact Inhalation reference dose.

[0157] Based on the exposure dose and carcinogenic slope factor of each route, the carcinogenic risk of each pollution source k to pollutant j in sample i is calculated, and the cumulative carcinogenic risk index is obtained by summing the risks of all pollutants from the same source in the same sample;

[0158] The carcinogenic risk The specific calculation formula is as follows:

[0159]

[0160] In the formula, , , These are carcinogenic slope factors via oral ingestion, skin contact, and inhalation.

[0161] It should be noted that by combining the corrected source contribution concentration with comprehensive toxicity parameters, the system calculates source-specific ecological and health risk values. This not only accurately quantifies the cumulative ecological risk of a single pollution source based on the principle of additive effects, but also comprehensively covers the three main exposure routes—oral, skin contact, and inhalation—according to the US EPA standard exposure assessment framework, calculating the cumulative non-carcinogenic and carcinogenic risks separately. This achieves precise source tracing and quantitative assessment from pollution source to risk effect, ensuring the scientific, standardized, and comprehensive nature of the risk assessment, while also clarifying the differences in risk contribution from each pollution source. This provides reliable technical support for subsequent precise control and risk prevention of pollution sources.

[0162] S6. Based on the source-specific risk value, calculate the risk contribution rate of each pollution source and output a list of high-risk sources, including:

[0163] The risk contribution rate of each source-specific risk value is obtained by calculating the ratio of the source-specific risk value to the total risk value of all corresponding sources.

[0164] The risk contribution rate of each source-specific risk value is weighted and summed in combination with the environmental management objectives of the study area to obtain the comprehensive risk contribution rate.

[0165] The weighting coefficients can be dynamically adjusted based on regional protection objectives (e.g., prioritizing carcinogenic risks for drinking water sources and prioritizing ecological risks for ecological protection zones). Specifically, the priority risk types are determined first based on the regional functional positioning (e.g., drinking water sources, ecological protection zones, residential areas, industrial zones, etc.). Then, using the analytic hierarchy process (AHP) or expert scoring method, combined with regional environmental management requirements, different weight values ​​are assigned to ecological risks, non-carcinogenic risks, and carcinogenic risks. For example, in drinking water sources, a carcinogenic risk weight of 0.6, a non-carcinogenic risk weight of 0.3, and an ecological risk weight of 0.1 can be set to prioritize human health. In ecological protection zones, an ecological risk weight of 0.7, a non-carcinogenic risk weight of 0.2, and a carcinogenic risk weight of 0.1 can be set to prioritize ecosystem safety.

[0166] Based on the comprehensive risk contribution rate, risk levels are classified according to preset grading thresholds, and all pollution sources are divided into high-risk sources, medium-risk sources, and low-risk sources. A list of high-risk sources and a risk contribution rate distribution report are output to guide precise environmental governance and priority control of pollution sources.

[0167] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0168] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0169] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0170] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0171] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A novel pollutant source apportionment and dynamic risk quantification method coupling APCS-MLR and PMF, characterized in that, include: Pollutant concentration data from environmental samples were collected, processed, and then used to construct a data matrix. Based on the data matrix, the APCS-MLR model and PMF model were run respectively for source resolution, and the source resolution feature information of each model was extracted. Based on source analysis feature information, the pollution sources identified by each model are matched to obtain high-confidence source matching pairs; Based on high-confidence source matching pairs, the source contribution concentrations of the two models are fused to obtain the fused contribution concentration that satisfies mass conservation. Based on the fusion contribution concentration, the ecological risk value and human health risk value of each pollution source are calculated to obtain the source-specific risk value; Based on source-specific risk values, the risk contribution rate of each pollution source is calculated, and a list of high-risk sources is output.

2. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 1, characterized in that, The pollutant concentration data from the collected environmental samples are processed to construct a data matrix, including: Raw concentration data of pollutants collected from environmental samples and the limits of detection of the methods; The raw concentration data is preprocessed to obtain the concentration data; Based on the concentration data and the method detection limit, calculate the uncertainty of each pollutant in each sample; Based on concentration data and uncertainty, the signal-to-noise ratio is calculated and pollutant classification information is determined. A data matrix for model input is constructed based on concentration data, uncertainty, and pollutant classification information.

3. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 1, characterized in that, Run the APCS-MLR model for source resolution, including: Principal component analysis was performed on the standardized concentration data to extract principal components and obtain the factor loading matrix and factor score matrix. A zero-concentration reference point is introduced, and the absolute principal component score is calculated based on the factor score matrix. Multiple linear regression was performed with concentration data as the dependent variable and absolute principal component scores as the independent variables to obtain regression coefficients. Based on the regression coefficients, the APCS-MLR source contribution concentrations are calculated, and the regression coefficients are normalized to obtain the APCS-MLR source component spectral vectors.

4. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 1, characterized in that, Run the PMF model for source resolution, including: Based on pollutant classification information, the calculation weights of each component in the PMF model are set. The number of candidate factors is set and multiple iterative calculations are performed. The optimal number of factors is determined based on the rate of change of the objective function value. Based on the optimal number of factors, the factor contribution matrix and factor spectrum matrix are output, and the PMF contribution concentration is obtained.

5. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 1, characterized in that, The process of matching pollution sources identified by each model based on source resolution feature information to obtain high-confidence source matching pairs includes: Based on the source component spectrum in the source parsing feature information of APCS-MLR, construct the APCS-MLR source vector set; Based on the factor spectrum matrix in the PMF source analysis feature information, construct the PMF factor vector set; Calculate the cosine similarity between each pair of source vectors and factor vectors in the two vector sets to obtain the similarity matrix; Based on the similarity matrix, a two-way consistency verification is performed. Matching pairs that meet the preset similarity threshold and pass the two-way verification are marked as high-confidence source matching pairs.

6. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 1, characterized in that, The source contribution concentration fused from the two models based on high-confidence source matching pairs includes: Based on high-confidence source matching pairs, extract the goodness-of-fit data for each simulation and calculate the initial weights of the matching source-pollutant pairs; Based on the APCS-MLR source contribution concentration and the PMF source contribution concentration, the APCS confidence coefficient and the PMF confidence coefficient are calculated by comprehensive criteria, respectively. The fusion contribution concentration is calculated based on the initial weights, APCS confidence coefficient, and PMF confidence coefficient.

7. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 6, characterized in that, The comprehensive criteria include nonnegativity criteria, rationality criteria, and consistency criteria.

8. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 7, characterized in that, The method for obtaining the fusion contribution concentration that satisfies mass conservation also includes: The total fusion contribution concentration is obtained by summing the fusion contribution concentrations. The mass closure residual is calculated based on the total fusion contribution concentration and the measured total concentration. The mass closure residuals are tested. For sample-pollutant pairs that need correction, the residuals are allocated back to each source contribution according to the contribution ratio of each source. The non-negativity test and processing of the allocated source contribution concentrations are then performed to obtain the corrected source contribution concentrations that satisfy mass conservation.

9. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 8, characterized in that, Based on the fusion contribution concentration, the ecological risk value and human health risk value of each pollution source are calculated to obtain the source-specific risk value, including: Obtain ecotoxicity parameter data, including ecotoxicity parameters and health toxicity parameters; Based on the corrected source contribution concentration and ecotoxicity parameters, the ecological risk quotient of each pollutant is calculated, and the cumulative ecological risk index is obtained by summing the values ​​of all pollutants from the same source in the same sample. Calculate the average daily exposure dose for different exposure pathways based on the corrected source contribution concentration; Based on the average daily exposure dose and health toxicity parameters, the non-carcinogenic risk quotient and carcinogenic risk for each pollution source are calculated, and the cumulative non-carcinogenic risk index and cumulative carcinogenic risk index are obtained by summing them separately.

10. The method for new pollutant source apportionment and dynamic risk quantification assessment coupled with APCS-MLR and PMF according to claim 1, characterized in that, The method calculates the risk contribution rate of each pollution source based on source-specific risk values ​​and outputs a list of high-risk sources, including: The risk contribution rate of each source is obtained by calculating the ratio of the source-specific risk value to the total risk value of all sources. The risk contribution rate of each source is weighted and summed in conjunction with the regional environmental management objectives to obtain the comprehensive risk contribution rate. Based on the comprehensive risk contribution rate, risk levels are classified according to preset grading thresholds, and a list of high-risk sources and a risk contribution rate distribution report are output.

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