Source apportionment uncertainty analysis method and system based on PMF model

Abstract

The uncertainty analysis method for source analysis based on the PMF model disclosed in the present invention comprises the following steps: using a data acquisition module to obtain pollutant concentration data in a receptor sample and constructing a concentration data matrix; constructing a receptor sample uncertainty data matrix; importing the concentration data matrix and the uncertainty data matrix into the PMF model and running the model; calculating the determination coefficient, and evaluating the goodness of fit between the measured value and the predicted value through the determination coefficient; obtaining uncertainty interval results by running BS and DISP; changing model parameters, repeatedly running the PMF model, quantifying the uncertainty of the PMF model, optimizing the model settings, and obtaining an optimal source analysis scheme; performing a rotation operation according to the optimal source analysis scheme to obtain the optimal contribution rate of each factor for source analysis; the uncertainty analysis technology used in the present invention can be used for error estimation, and missing values ​​and outliers can be reasonably handled, which is helpful to improve the scientificity and stability of the PMF model and greatly improve the reliability of the PMF source analysis results.

Description

Technical Field

[0001] The present invention relates to the research field of source analysis of environmental pollutants, and in particular to a source analysis uncertainty analysis method and system based on a PMF model. Background Art

[0002] The PMF model is a commonly used pollutant source analysis method. It is a multivariate factor analysis tool that decomposes the sample content data matrix input into two matrices: factor contribution (G) and factor component spectrum (F). The multilinear multiple iteration (ME) algorithm is used to identify the number of factors and factor contributions. The PMF model can not only give the pollution source category, but also derive the exact contribution rate of the pollution source. In recent years, it has been widely used in pollutant source analysis research. However, there are few reports on the application of the PMF model to uncertainty analysis of surface water pollutant source analysis results.

[0003] Although the PMF model is widely used in the source analysis of pollutants in environmental media such as atmosphere, water and soil, the uncertainty of the model remains controversial.

[0004] First, sample data errors may lead to misjudgment of model results; second, the selection of model structure and its parameters will also affect the reliability of the model structure; and, different pollutants have different physical and chemical properties, and their migration and diffusion behaviors are also different, resulting in uneven distribution of pollutants in the environmental medium, which cannot strictly meet the receptor model's assumption that pollutants between receptors and sources are in mass balance, affecting the credibility of the model results. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, provide a source parsing uncertainty analysis method and system based on the PMF model, and propose goodness of fit analysis, bootstrap method (BS), substitution method (DISP) and rotation operation methods to perform error estimation in view of the randomness, fuzziness and uncertainty of the source parsing results of the PMF model, and reasonably handle missing values ​​and outliers, which is helpful to improve the scientificity and stability of the PMF model and greatly improve the reliability of the PMF source parsing results. The PMF model here is a positive definite matrix factor decomposition model.

[0006] The first object of the present invention is to provide a source parsing uncertainty analysis method based on the PMF model.

[0007] The second object of the present invention is to provide a source parsing uncertainty analysis system based on the PMF model.

[0008] The first object of the present invention is achieved by the following technical solutions:

[0009] The uncertainty analysis method of source apportionment based on the PMF model includes the following steps:

[0010] The data acquisition module is used to obtain the pollutant concentration data in the receptor sample and construct a concentration data matrix;

[0011] Construct the uncertainty data matrix of receptor samples;

[0012] Import the concentration data matrix and uncertainty data matrix into the PMF model and run it to obtain the pollution source contribution rate results of the basic operation;

[0013] The coefficient of determination was calculated to assess the goodness of fit between the measured and predicted values;

[0014] By running BS and DISP, uncertainty interval results are obtained, and the PMF model is evaluated by the uncertainty interval results;

[0015] Change model parameters, evaluate the pollution source contribution rate results of basic operation, quantify PMF model uncertainty, optimize model settings, and obtain the best source apportionment solution;

[0016] The rotation operation is performed according to the optimal source analysis scheme to obtain the optimal contribution rate of each factor in source analysis.

[0017] Furthermore, the concentration data matrix includes date, pollutant type name, and concentration, and the concentration data matrix is ​​constructed with the pollutant type name as a column and the date as a row.

[0018] Further, the calculation of the receptor sample uncertainty data matrix is ​​specifically as follows: setting the receptor sample type uncertainty to include sampling error and analysis error;

[0019] If the concentration of the monitored item is less than or equal to the method detection limit MDL of the element measuring instrument, the uncertainty Unc is calculated as follows:

[0020]

[0021] If the concentration of the monitored item is greater than the method detection limit MDL of the element measuring instrument, the uncertainty Unc is calculated as follows:

[0022]

[0023] Among them, EF is the percentage of uncertainty in the measurement result, and concentration is the concentration of the monitored item.

[0024] Furthermore, the concentration data matrix and the uncertainty data matrix are imported into the PMF model and run to obtain the pollution source contribution rate results of the basic operation, specifically: the "missing value indicator" is set to "-999", and the species are replaced with the MDL median to obtain the pollution source contribution rate results of the basic operation.

[0025] Furthermore, before running the PMF model, the concentration data and uncertainty data are analyzed, and it is determined whether some species are excluded or weighted downward according to the analysis results;

[0026] The analysis is as follows: the species category is set according to the signal-to-noise ratio, the species correlation is evaluated through the concentration scatter plot, the initial starting point is randomly selected, and the number of factors is set before iterative calculation:

[0027]

[0028] In the formula, p is the number of factors; i is the i-th sample; j is the j-th element; X ij is an i×j matrix consisting of the concentrations of j elements in i samples; G ik is the contribution of factor k to each sample i; F kj is the species distribution for each source; E ij is the residual matrix; G ik and F kj The value of is constrained to be positive;

[0029] The solution of the iterative calculation formula is obtained by using the uncertainty Unc and the non-negative matrix element G ik 、F kj As a constraint, design the objective function Q to minimize the objective function:

[0030]

[0031] Where m is the number of samples and n is the number of elements.

[0032] Furthermore, the determination coefficient is calculated, and the goodness of fit between the measured value and the predicted value is evaluated by the determination coefficient, specifically: the goodness of fit is tested by evaluating the value of the determination coefficient:

[0033]

[0034] Where: is the predicted value of site i; y i is the measurement value of site i; is the average measurement value of site i; n is the number of sites, R 2 is the coefficient of determination;

[0035] The measured value is the actual value detected by sampling and instrumentation;

[0036] The calculation formula for the predicted value is as follows:

[0037]

[0038] Among them, G ik 、F kjis a non-negative matrix element, and p is the number of factors.

[0039] Furthermore, the uncertainty interval results are obtained by running BS and DISP, specifically: BS operation is to continuously calculate the estimated value by reconstructing the sample, that is, resampling the original data and then running PMF multiple times; DISP operation is to repeatedly run PMF after perturbing each parameter value in the factor loading matrix F in turn; and then obtain the uncertainty interval results:

[0040]

[0041] Where m is the number of samples; n is the number of elements, Unc is the uncertainty, E ij is the residual matrix;

[0042] The aforementioned objective function minimization is to minimize the Q value of the basic operating result of PMF. A result with the minimized Q value is selected from each batch of operating results for subsequent uncertainty interval analysis. Each batch can be set to run 20 times, 200 times, etc.

[0043] The obtained uncertainty interval results were subsequently used to evaluate the robustness and reproducibility of the model.

[0044] Furthermore, the changing of the model parameters specifically includes: changing the number of factors and EF value.

[0045] Furthermore, the rotation operation is specifically performed as follows:

[0046] The rotation tool is used to perform rotation operations according to the peak values ​​of 0.5, -0.5, 1.0, -1.0, and -1.5 in sequence to obtain the optimal contribution rate of each factor for source analysis.

[0047] The second object of the present invention is achieved by the following technical solutions:

[0048] Source analysis uncertainty analysis system based on PMF model, including:

[0049] A data acquisition module is used to obtain the pollutant concentration data in the receptor sample at the monitoring point and to construct a concentration data matrix;

[0050] Uncertainty data matrix calculation module, used to calculate the uncertainty data matrix of the receptor sample;

[0051] PMF model, used to import the concentration data matrix and uncertainty data matrix into the PMF model and run it;

[0052] A goodness of fit evaluation module is used to calculate the coefficient of determination and evaluate the goodness of fit between the measured value and the predicted value through the coefficient of determination;

[0053] The uncertainty interval result calculation module obtains the uncertainty interval result by running BS and DISP;

[0054] Model optimization module, which changes model parameters, repeatedly runs the PMF model, quantifies PMF model uncertainty, optimizes model settings, and obtains the best source apportionment solution;

[0055] The source tracing analysis module performs rotation operations according to the optimal source analysis scheme to obtain the contribution rate of each factor with the best source analysis.

[0056] The principle of the present invention is as follows: The goodness of fit is mainly determined by the coefficient of determination (R 2 ) to evaluate, the larger R 2 The results show that the factor configuration in the PMF model has good robustness. BS analysis can be used to determine whether some sample data disproportionately affect the PMF solution. The BS error interval includes the effects of random error and rotation ambiguity. Random error is caused by errors in the process of obtaining information from the sample data. Rotation ambiguity is caused by the existence of infinite solutions that are similar to the PMF solution in many ways. In other words, for any pair of matrices, infinite variations of this pair of matrices can be produced by simple rotation. Since the PMF model has only one non-negative source contribution, it is impossible to restrict this rotation space, so BS error estimation is very necessary. The DISP method is an analytical method that can help researchers understand the selected solution in more detail. It is to obtain uncertainty estimates for each parameter in the factor loading matrix F by perturbing each parameter value in turn and repeatedly running the PMF model. Therefore, it has strong sensitivity to small changes in parameters. The DISP error interval includes the effects of rotation ambiguity, but does not include the effects of random errors in the data. After evaluating the above error estimates, rotation errors should be explored in depth. Rotation errors can be rotated by adjusting parameters and running Fpeak multiple times. The PMF model is rotated to reduce collinearity sources and obtain the optimal contribution rate of each factor for source analysis.

[0057] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0058] The technical solution of the present invention uses goodness of fit analysis, bootstrap (BS), substitution method (DISP) and rotation operation to perform uncertainty analysis on the quantitative source analysis of pollutants in the positive definite matrix factor decomposition model, that is, by running different factor number scenario schemes, perturbing the parameters in the factor load matrix and reconstructing the sample calculation estimate, the model result error is quantified, and the optimal environmental pollutant source analysis scheme is obtained, which has guiding significance for environmental pollutant control. The present invention can identify the key factors affecting the model simulation results from the parameter perspective, help compare and analyze sensitive parameters similar to the number of factors, calibrate and verify the model parameters, in order to provide a reference for selecting better, more stable and more practical positive definite matrix factor decomposition model parameters, and provide a reference for a comprehensive and objective understanding of the sources of environmental pollutants and the rational implementation of environmental protection measures. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of the uncertainty analysis method of source parsing based on the PMF model described in the present invention;

[0060] Figure 2 This is a diagram showing the PAHs source analysis results in Example 1 of the present invention;

[0061] Figure 3 This is a structural block diagram of the source parsing uncertainty analysis system based on the PMF model described in the present invention. DETAILED DESCRIPTION

[0062] The present invention is further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0063] Embodiment 1:

[0064] Source apportionment uncertainty analysis methods based on PMF models, such as Figure 1 As shown, the following steps are included:

[0065] The data acquisition module is used to obtain the pollutant concentration data in the receptor sample and construct a concentration data matrix;

[0066] Construct the uncertainty data matrix of receptor samples;

[0067] Import the concentration data matrix and uncertainty data matrix into the PMF model and run it to obtain the pollution source contribution rate results of the basic operation;

[0068] The coefficient of determination was calculated to assess the goodness of fit between the measured and predicted values;

[0069] By running BS and DISP, uncertainty interval results are obtained, and the PMF model is evaluated by the uncertainty interval results;

[0070] Change model parameters, evaluate the pollution source contribution rate results of basic operation, quantify PMF model uncertainty, optimize model settings, and obtain the best source apportionment solution;

[0071] The rotation operation is performed according to the optimal source analysis scheme to obtain the optimal contribution rate of each factor in source analysis.

[0072] The details are as follows:

[0073] Step 1: Obtain the pollutant concentration data matrix in suspended particulate matter in surface water. Here, we select the concentration data of 16 priority PAHs in suspended particulate matter in surface water, including naphthalene (Nap), acenaphthylene (Acy), acenaphthene (Ace), fluorene (Flu), phenanthrene (Phe), anthracene (Ant), fluoranthene (Fla), pyrene (Pyr), benzo(a)anthracene (BaA), benzo(b)fluoranthene (BbF), benzo(k)fluoranthene (BkF), benzo(a)pyrene (BaP), dibenzo(a,h)anthracene (DahA), indeno(1,2,3-cd)pyrene (InP), and benzo(ghi)perylene (BghiP);

[0074] Furthermore, the receptor sample may be suspended particles in surface water, but is not limited to suspended particles in surface water, and may also include environmental media such as soil, surface water, and atmosphere;

[0075] The concentration matrix has PAHs type names as columns and dates as rows. Each row has a header. Do not enter units and ensure that there are no blank cells.

[0076] Step 2: Calculate the uncertainty data matrix of the receptor sample;

[0077] The uncertainty for the sample type should include errors such as sampling and analytical errors. For some data sets, the analytical laboratory or reporting agency provides the uncertainty for each value. However, uncertainties are not always reported, and when they are not available, the uncertainty must be calculated. If the concentration is less than or equal to the method detection limit (MDL) of the instrument measuring the element, the uncertainty (Unc) is calculated using a fixed fraction of the MDL:

[0078] That is, if the concentration of the monitored item is less than or equal to the method detection limit MDL of the element measuring instrument, the uncertainty Unc is calculated as follows:

[0079]

[0080] If the concentration of the monitored item is greater than the method detection limit MDL of the element measuring instrument, the uncertainty Unc is calculated as follows:

[0081]

[0082] Among them, EF is the percentage of measurement uncertainty, concentration is the concentration of the monitoring item, and the uncertainty here is the input file "uncertainty data file".

[0083] Step 3: Import the concentration data matrix and uncertainty data matrix into the PMF model and run it;

[0084] Specify the Missing Value Indicator in the Input File box on the Data File screen. Set the Missing Value Indicator to "-999" and choose to replace species with the MDL median value.

[0085] Before running the PMF model, the concentration data and uncertainty data are analyzed, and based on the analysis results, it is decided whether some species should be excluded or down-weighted, for example, due to increased uncertainty, low signal-to-noise ratio or outliers;

[0086] The analysis is as follows: the species category is set according to the signal-to-noise (S / N) intensity, the species correlation is evaluated through the concentration scatter plot, the initial starting point is randomly selected, and the number of factors is set before iterative calculation:

[0087]

[0088] In the formula, p is the number of factors; i is the i-th sample; j is the j-th element; X ij is an i×j matrix consisting of the concentrations of j elements in i samples; G ik is the contribution of factor k to each sample i; F kj is the species distribution for each source; E ij is the residual matrix; G ikand F kj The value of is constrained to be positive;

[0089] The solution of the iterative calculation formula is obtained by the non-negative matrix element G ik 、F kj As a constraint, design the objective function Q to minimize the objective function:

[0090]

[0091] Step 4: Calculate the coefficient of determination (R 2 ) Evaluate the goodness of fit between measured and predicted values;

[0092] Specifically:

[0093]

[0094] Where: is the predicted value of site i; y i is the measurement value of site i; is the average measurement value of site i; n is the number of sites, R 2 is the coefficient of determination;

[0095] The calculation formula for the predicted value is as follows:

[0096]

[0097] Among them, G ik 、F kj is a non-negative matrix element, and p is the number of factors.

[0098] Step 5: Run BS and DISP to obtain the uncertainty interval results, specifically:

[0099]

[0100] The uncertainty here is the output result, referring to "Uncertainty analysis"

[0101] Step 6: Repeat the PMF model by changing the number of factors and EF value parameters to quantify the uncertainty of the PMF model, optimize the model settings, and obtain the best source apportionment solution.

[0102] Step 7: Rotation operation: The rotation operation is specifically as follows:

[0103] The rotation tool was used to perform rotation operations according to the peak values ​​of 0.5, -0.5, 1.0, -1.0, and -1.5 in turn to reduce collinear sources and obtain the optimal contribution rate of each factor for source analysis.

[0104] The above shows the principle of the present invention and verifies the effectiveness of the present invention. The improved environmental pollutant source analysis method improves the stability and reliability of the PMF source analysis results. The PAHs source analysis results are shown in FIG. Figure 2 Specifically, compared with the single use of PMF basic operation results, the method of the present invention can quantify the model result error by running different factor number scenarios, perturbing the parameters in the factor load matrix and reconstructing the sample calculation estimate, and obtain the optimal environmental pollutant source analysis plan, which has guiding significance for the treatment of PAHs in water bodies.

[0105] Embodiment 2:

[0106] Source apportionment uncertainty analysis system based on PMF model, such as Figure 3 As shown, including:

[0107] Data acquisition module, which is used to obtain the PAHs concentration data in the receptor samples at the monitoring points and construct a concentration data matrix;

[0108] Uncertainty data matrix construction module, used to construct the uncertainty data matrix of receptor samples;

[0109] PMF model, used to import the concentration data matrix and uncertainty data matrix into the PMF model and run it;

[0110] A goodness of fit evaluation module is used to calculate the coefficient of determination and evaluate the goodness of fit between the measured value and the predicted value through the coefficient of determination;

[0111] The uncertainty interval result calculation module obtains the uncertainty interval result by running BS and DISP;

[0112] Model optimization module, which changes model parameters, repeatedly runs the PMF model, quantifies PMF model uncertainty, optimizes model settings, and obtains the best source apportionment solution;

[0113] The source tracing analysis module performs rotation operations according to the optimal source analysis scheme to obtain the contribution rate of each factor with the best source analysis.

[0114] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. Source apportionment uncertainty analysis method based on PMF model, characterized by: The following steps are involved: The data acquisition module is used to obtain the pollutant concentration data in the receptor sample and construct a concentration data matrix; Construct the uncertainty data matrix of receptor samples; Import the concentration data matrix and uncertainty data matrix into the PMF model and run it to obtain the pollution source contribution rate results of the basic operation; The coefficient of determination was calculated to assess the goodness of fit between the measured and predicted values; By running BS and DISP, uncertainty interval results are obtained, and the PMF model is evaluated by the uncertainty interval results; Changing model parameters, specifically: changing the number of factors and EF values, evaluating the pollution source contribution rate results of basic operation, quantifying the uncertainty of PMF model, optimizing model settings, and obtaining the best source analysis solution; The rotation operation is performed according to the optimal source analysis solution, and the rotation operation is specifically: The rotation tool is used to perform rotation operations according to the peak values ​​of 0.5, -0.5, 1.0, -1.0, and -1.5 in turn to obtain the optimal contribution rate of each factor in source analysis; Get the best contribution rate of each factor for source analysis; The construction of the receptor sample uncertainty data matrix specifically includes: setting the receptor sample type uncertainty to include sampling error and analysis error; If the concentration of the monitored item is less than or equal to the method detection limit MDL of the element measuring instrument, the uncertainty Unc is calculated as follows: If the concentration of the monitored item is greater than the method detection limit MDL of the element measuring instrument, the uncertainty Unc is calculated as follows: Among them, EF is the percentage of uncertainty of the measurement result, and concentration is the concentration of the monitoring item; The determination coefficient is calculated to evaluate the goodness of fit between the measured value and the predicted value by the determination coefficient, specifically: the goodness of fit is tested by evaluating the value of the determination coefficient: Where: is the predicted value of site i; y i is the measurement value of site i; is the average measurement value of site i; n is the number of sites, R 2 is the coefficient of determination; The measured value is the actual value detected by sampling and instrumentation; The calculation formula for the predicted value is as follows: Among them, G ik 、F kj is a non-negative matrix element, and p is the number of factors; The uncertainty interval results are obtained by running BS and DISP, and the PMF model is evaluated by the uncertainty interval results, specifically: The BS operation is to continuously calculate the estimated value by reconstructing the sample, that is, resampling the original data multiple times and then running PMF; the DISP operation is to repeatedly run PMF after perturbing each parameter value in the factor loading matrix F in turn; and then obtain the uncertainty interval result: Where m is the number of samples; n is the number of elements, E ij is the residual matrix, and Unc is the uncertainty.

2. The source analysis uncertainty analysis method based on the PMF model according to claim 1 is characterized in that: The concentration data matrix includes date, pollutant type name, and concentration, and the concentration data matrix is ​​constructed with the pollutant type name as a column and the date as a row.

3. The source analysis uncertainty analysis method based on the PMF model according to claim 1 is characterized in that: The concentration data matrix and the uncertainty data matrix are imported into the PMF model and run to obtain the pollution source contribution rate results of the basic operation, specifically: the "missing value indicator" is set to "-999", and the species are replaced with the MDL median to obtain the pollution source contribution rate results of the basic operation.

4. The source analysis uncertainty analysis method based on the PMF model according to claim 3 is characterized in that: Before running the PMF model, the concentration data and uncertainty data are analyzed, and it is determined whether some species are excluded or weighted downward based on the analysis results; The analysis is as follows: the species category is set according to the signal-to-noise ratio, the species correlation is evaluated through the concentration scatter plot, the initial starting point is randomly selected, and the number of factors is set before iterative calculation: In the formula, p is the number of factors; i is the i-th sample; j is the j-th element; X ij is an i×j matrix consisting of the concentrations of j elements in i samples; G ik is the contribution of factor k to each sample i; F kj is the species distribution for each source; E ij is the residual matrix; G ik and F kj The value of is constrained to be positive; The solution of the iterative calculation formula is obtained by using the uncertainty Unc and the non-negative matrix element G ik 、F kj As a constraint, design the objective function Q to minimize the objective function: Where m is the number of samples; n is the number of elements, and Unc is the uncertainty.

5. A source analysis uncertainty analysis system based on a PMF model, applying the method described in any one of claims 1 to 4, characterized in that: include: A data acquisition module is used to obtain the pollutant concentration data in the receptor sample at the monitoring point and to construct a concentration data matrix; Uncertainty data matrix construction module, used to construct the uncertainty data matrix of receptor samples; PMF model, used to import the concentration data matrix and uncertainty data matrix into the PMF model and run it; A goodness of fit evaluation module is used to calculate the coefficient of determination and evaluate the goodness of fit between the measured value and the predicted value through the coefficient of determination; The uncertainty interval result calculation module obtains the uncertainty interval result by running BS and DISP; Model optimization module, which changes model parameters, repeatedly runs the PMF model, quantifies PMF model uncertainty, optimizes model settings, and obtains the best source apportionment solution; The source tracing analysis module performs rotation operations according to the optimal source analysis scheme to obtain the contribution rate of each factor with the best source analysis.

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