Atmospheric microplastics tracing method based on cluster analysis and factor analysis

Abstract

The application belongs to the technical field of environmental monitoring and data analysis, and discloses an atmospheric micro-plastic source tracing method based on cluster analysis and factor analysis, which comprises the following steps: S1, pre-processing the abundance data of sample micro-plastics, and using a cluster analysis algorithm to obtain the pre-processed abundance data and perform cluster analysis to obtain a cluster distribution table; S2, using a factor analysis model on the pre-processed abundance data to analyze a plurality of potential factors that play a leading role in the overall data variability, and obtaining factor correlation distribution information by calculating a factor correlation matrix; S3, cross-analysis and mutual verification are performed according to the cluster distribution table and the factor correlation distribution information, and the quantitative contribution rate of each source and its spatio-temporal distribution characteristics are output. Through the data-driven multivariate statistical method, the application realizes objective, accurate and quantifiable analysis of the source of atmospheric micro-plastics.

Description

Technical Field

[0001] This invention relates to the field of environmental monitoring and data analysis technology, and in particular to a method for tracing the source of atmospheric microplastics based on cluster analysis and factor analysis. Background Technology

[0002] Atmospheric microplastics (plastic particles, fibers, or fragments with a diameter of less than 5 mm) have become a global emerging environmental pollutant. They can migrate long distances and remain suspended in the atmosphere for extended periods, and can adsorb toxic substances such as heavy metals and persistent organic pollutants, posing a potential threat to ecosystems and human health. Accurately tracing the source of atmospheric microplastics is a crucial prerequisite for developing effective pollution control strategies and assessing environmental health risks.

[0003] However, most existing traceability technologies rely on simple physical morphological observation (such as microscopic classification) or qualitative analysis of single polymer components (such as Fourier transform infrared spectroscopy), which have the following technical shortcomings in practical applications:

[0004] (1) Insufficient statistical correlation mining: Traditional methods usually classify and analyze microplastics in isolation according to morphology (such as fibers, fragments, films) or polymer type (such as polyethylene PE, polypropylene PP, polyethylene terephthalate PET), which makes it difficult to reveal the potential intrinsic statistical correlations between different types of microplastics. For example, microplastics with multiple polymer components and morphologies may be released simultaneously from the same emission source (such as synthetic textile washing). The abundance of these microplastics in environmental samples should show synchronous changes, but traditional methods lack the ability to effectively mine such cross-dimensional correlations.

[0005] (2) Weak ability to process multiple variables: The spatiotemporal distribution of atmospheric microplastics is affected by a variety of complex factors, including meteorological conditions (wind speed, wind direction, precipitation, atmospheric stability), topography, and intensity of human activities. Existing technologies often rely on experience for manual classification. When faced with massive and multidimensional monitoring data, it is difficult to perform systematic quantitative processing, resulting in highly subjective tracing results and an inability to effectively capture the interactions between multiple variables.

[0006] (3) Lack of quantitative traceability indicators: Most existing technologies are limited to qualitative descriptions of potential sources and lack objective mathematical models to quantitatively analyze the relative contribution rates of different sources. Due to the lack of quantitative indicators such as factor loading, cluster distance, and contribution rate, the repeatability and comparability of the entire traceability process are poor, and the accuracy and reliability are difficult to guarantee. Summary of the Invention

[0007] To address the shortcomings of existing technologies for tracing atmospheric microplastics, such as insufficient statistical correlation mining, weak multivariate comprehensive processing capabilities, and lack of quantitative traceability indicators, this invention proposes an atmospheric microplastics traceability method based on cluster analysis and factor analysis.

[0008] This invention is achieved through the following technical solution, including the following steps:

[0009] S1. The abundance data of different types of microplastics in multiple environmental samples are preprocessed, and a clustering analysis algorithm is used to classify them into several groups with similar spatiotemporal behavior characteristics based on the similarity of the abundance change patterns of each microplastic type in all samples. The preprocessed abundance data is obtained and clustering analysis is performed to obtain a clustering assignment table.

[0010] S2. Apply factor analysis model to the preprocessed abundance data obtained in step S1 to identify several potential factors that play a dominant role in the overall data variability, and obtain factor correlation distribution information by calculating the factor correlation matrix.

[0011] S3. Based on the clustering assignment table obtained in step S1 and the factor correlation matrix obtained in step S2, obtain the factor correlation assignment information, perform cross-analysis and mutual verification, assign a clear environmental source physical meaning to each parsed potential factor, and finally output the quantitative contribution rate of each source and its spatiotemporal distribution characteristics.

[0012] As a further preferred option, the specific steps of step S1 are as follows:

[0013] S11. Perform a logarithmic transformation on the original abundance data and standardize it using the Z-score method to obtain the standardized data matrix Z, as shown below:

[0014] ;

[0015] In the formula, rows represent different types of microplastics, with a total of p types; columns represent different microplastic samples, with a total of n; and the elements in the matrix... This represents the normalized abundance of the p-th microplastic in the n-th sample;

[0016] S12. Based on the standardized data matrix Z, calculate the pairwise similarity between all microplastic species and construct the similarity matrix D as follows:

[0017] ;

[0018] In the formula, d ij This represents the similarity between the i-th and j-th microplastics;

[0019] S13. Based on the similarity matrix D, an agglomerative hierarchical clustering algorithm is used, with the average chain distance between groups as the inter-class distance metric. The calculation formula is as follows:

[0020] ;

[0021] In the formula, d avg (G,H) represents the average chain distance between clusters G and H; G and H represent any two clusters; |G| and |H| represent the number of microplastic species in clusters G and H, respectively;

[0022] S14. Using the elbow rule, calculate the within-group sum of squares (WSS) for different numbers of clusters, plot a scree plot, and select the number of inflection points on the curve as the optimal number of clusters K. 佳 ;

[0023] S15. Based on the optimal clustering number K 佳 Cut and partition K from the clustering dendrogram 佳 A clear group is identified, and a clustering assignment table is output.

[0024] As a further preferred option, the specific steps of step S2 are as follows:

[0025] S21. Using the standardized data matrix Z as input, construct a factor analysis model based on principal component analysis, and perform factor decomposition to obtain Q factors, as shown in the following formula:

[0026] ;

[0027] In the formula, x p y represents the normalized abundance of the p-th microplastic; Q This represents the Qth principal component combination extracted; The coefficient representing the correlation of the Qth principal component combination with the pth microplastic;

[0028] S22. Based on the Q factors obtained in step S21, calculate the correlation coefficient matrix R between all factors and microplastic types, and solve for the eigenvalues ​​of this matrix and their corresponding unit eigenvectors to construct the initial factor correlation matrix A, as shown in the following formula:

[0029] ;

[0030] In the formula, This represents the initial correlation between the Q-th factor and the p-th microplastic; Represents the eigenvalues ​​of the Q-th correlation coefficient matrix R; The correlation coefficient of the Qth principal component combination on the pth microplastic is obtained by solving the unit eigenvector of the Qth correlation coefficient matrix R. get;

[0031] S23. Based on the eigenvalues ​​obtained in step S22, calculate the variance contribution rate and cumulative variance contribution rate of each factor, and take the number of factors Q corresponding to the cumulative variance contribution rate being greater than 85% as the number of potential source factors q that need to be retained.

[0032] S24. Based on the number of potential source factors q to be retained obtained in step S23, simplify the initial factor correlation matrix A and perform an orthogonal rotation using the variance maximization method to obtain the final factor correlation matrix B, as shown in the following formula:

[0033] ;

[0034] In the formula, b pq This represents the contribution weight of the p-th microplastic to the q-th factor;

[0035] S25. Based on the final factor correlation matrix B obtained in step S24, extract the elements that are greater than the set threshold as high-load microplastic types. Combining the physicochemical properties of high-load microplastics with common sense in environmental science, scientifically infer and name the environmental pollution sources represented by each factor.

[0036] As a further preferred option, the specific steps of step S3 are as follows:

[0037] S31. Compare and analyze the clustering assignment table obtained in step S1 with the factor correlation assignment information obtained in step S2. If most or all microplastic species in a certain cluster group show high loading on the same factor, the results are mutually corroborating, indicating that the microplastic combination represented by the group originates from the same pollution source named in step S25.

[0038] S32. Based on factor naming and cross-validation results, summarize the characteristic microplastic biomarker combinations corresponding to each potential pollution source; at the same time, using the factor correlation matrix calculated during factor analysis, draw a time series diagram of the contribution value of each potential factor changing over time.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] (1) The source tracing method proposed in this invention introduces cluster analysis, which objectively groups microplastic species based entirely on the statistical characteristics of the data itself, avoiding the subjective bias of traditional methods that rely on manual experience for classification. This method can effectively reveal microplastic combinations with similar spatiotemporal variation patterns, providing a solid data foundation for the "homogeneous" hypothesis.

[0041] (2) The source tracing method proposed in this invention introduces factor analysis, which can quantitatively analyze multiple independent potential pollution sources from complex data and accurately calculate the contribution rate (i.e., factor loading) of each source to each microplastic. Through variance maximization rotation, the abstract mathematical factors are given clear physical or chemical meanings, which greatly improves the reliability and environmental interpretability of the source tracing conclusions.

[0042] (3) The source tracing method proposed in this invention innovatively cross-compares and verifies the results of cluster analysis and factor analysis. This dual evidence chain analysis framework effectively avoids the misjudgment or one-sidedness that may be caused by a single statistical method, making the final source inference more rigorous and accurate.

[0043] (4) The source tracing method proposed in this invention can present complex multidimensional source tracing information in a clear and concise manner by outputting various visualization results such as factor loading spectrum, pollution source contribution time series graph, and spatial distribution map. This provides an intuitive and effective scientific basis for environmental managers to understand the composition of pollution sources, identify key emission periods and regions, and formulate precise pollution prevention and control strategies.

[0044] (5) The traceability method proposed in this invention can systematically process multi-dimensional atmospheric microplastic data, objectively identify the intrinsic relationship between microplastic types, and quantitatively analyze the technical methods of different sources, so as to comprehensively improve the accuracy and reliability of traceability. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the overall process of the traceability method of the present invention. Detailed Implementation

[0046] The advantages and features of the present invention will be illustrated and explained by the following non-limiting description of preferred embodiments, which are given by way of example only with reference to the accompanying drawings.

[0047] like Figure 1 As shown, this invention proposes a method for tracing the origin of atmospheric microplastics based on cluster analysis and factor analysis. The core of this method lies in: firstly, objectively grouping microplastic species through cluster analysis to identify combinations of microplastics with similar behavioral patterns; then, quantitatively analyzing the potential sources and contributions of dominant data variability through factor analysis; and finally, cross-validating and comprehensively evaluating the results of the two analyses to achieve accurate, objective, and quantifiable traceability. The specific steps of the atmospheric microplastic traceability method based on cluster analysis and factor analysis proposed in this invention are as follows:

[0048] S1. The abundance data of different types of microplastics in multiple environmental samples are preprocessed, and a clustering analysis algorithm is used to classify them into several groups with similar spatiotemporal behavior characteristics based on the similarity of the abundance change patterns of each microplastic type in all samples. The preprocessed abundance data is obtained and clustering analysis is performed to obtain a clustering assignment table.

[0049] S11. Perform a logarithmic transformation on the original abundance data and standardize it using the Z-score method to obtain the standardized data matrix Z, as shown below:

[0050]

[0051] In the formula, rows represent different types of microplastics, with a total of p types. Columns represent different microplastic samples, with a total of n samples. The elements in the matrix... This represents the normalized abundance of the p-th microplastic in the n-th sample.

[0052] First, the original abundance data is logarithmically transformed to stabilize its variance and make the data distribution closer to a normal distribution. Then, the Z-score standardization method is used to make the transformed data dimensionless, eliminating the dimensional differences in the absolute abundance values ​​between different microplastic species and generating a standardized data matrix Z.

[0053] S12. Based on the standardized data matrix Z, calculate the pairwise similarity between all microplastic species and construct a similarity matrix D, as follows:

[0054]

[0055] In the formula, d ij This represents the similarity between the i-th and j-th microplastics; the smaller the value, the more similar their abundance variation patterns.

[0056] In some embodiments, the pairwise similarity between microplastic species is measured using Euclidean distance. The similarity matrix D in these embodiments is also called the distance matrix D. The formula for calculating the Euclidean distance between microplastics is as follows:

[0057]

[0058] In the formula, d ij This represents the Euclidean distance between the i-th and j-th microplastics, and also the similarity between them; a smaller value indicates a more similar abundance variation pattern. ik and z jk Let represent the normalized abundance of the i-th and j-th microplastics in the k-th sample, respectively. Based on the calculation results, construct the distance matrix D between microplastic species.

[0059] In some embodiments, Pearson correlation coefficient or cosine similarity can also be used to measure the pairwise similarity between microplastic species.

[0060] S13. Based on the similarity matrix D obtained in step S12, agglomerative hierarchical clustering algorithm is used, with the average chain distance between groups as the inter-class distance metric. The calculation formula is as follows:

[0061]

[0062] In the formula, d avg (G,H) represents the average chain distance between clusters G and H; G and H represent any two clusters; |G| and |H| represent the number of microplastic species in clusters G and H, respectively; d ij The similarity between the i-th and j-th microplastics is represented by step S12.

[0063] S14. Using the elbow rule, calculate the within-group sum of squares (WSS) for different numbers of clusters, plot a scree plot, and select the number of inflection points on the curve as the optimal number of clusters K. 佳 The formula for calculating WSS is as follows:

[0064]

[0065] In the formula, C k This represents the Cth cluster; K represents the number of clusters. Let be the row vector formed by the normalized abundance of the i-th microplastic in all samples; Let K be the centroid of cluster C (i.e., the mean of all microplastic vectors within the cluster). The value of K corresponding to the inflection point of the curve (i.e., the "elbow") is chosen as the optimal number of clusters, K. 佳 .

[0066] S15. The optimal clustering number K obtained in step S14 佳 Cut and partition K from the clustering dendrogram 佳 A clear group is generated, and a clustering assignment table is output to clearly identify the group to which each microplastic belongs.

[0067] S2. The preprocessed abundance data obtained in step S1 is analyzed using a factor analysis model to identify several potential factors that play a dominant role in the overall data variability. The factor correlation matrix is ​​calculated to obtain the factor correlation allocation information and quantitatively characterize the contribution of each potential factor to the variability of different microplastic species.

[0068] S21. Using the standardized data matrix Z obtained in step S11 as input, construct a factor analysis model based on principal component analysis (PCA) and perform factor decomposition to obtain Q principal component combinations, i.e., Q factors, as shown in the following formula:

[0069]

[0070] In the formula, x p Let y represent the original variable for the p-th microplastic, i.e., the standardized abundance; Q This represents the Qth principal component combination extracted; The coefficient representing the correlation of the Qth principal component combination with the pth microplastic is obtained from the PCA model and satisfies the unit length constraint. Furthermore, the principal component combinations are uncorrelated with each other, meaning that for any i ≠ j, y i With y j The covariance is zero. y1 has the largest variance among all linear combinations of the original variables; y2 has the second largest variance among linear combinations uncorrelated with y1; and so on. Q It has the smallest variance.

[0071] This invention employs the PCA model as the core of the factor analysis model, aiming to find a set of uncorrelated comprehensive variables (principal components) to explain the variance of the original data to the greatest extent possible. In this step, the Q factors represent several sets composed of p types of microplastics, each factor consisting of at least one type of microplastic, and each factor contains a different type of microplastic.

[0072] S22. Based on the Q factors obtained in step S21, calculate the correlation coefficient matrix R between all factors and microplastic types, and solve for the eigenvalues ​​of this matrix and their corresponding unit eigenvectors to construct the initial factor correlation matrix A, as shown in the following formula:

[0073]

[0074] In the formula, The elements in the initial factor correlation matrix A represent the initial correlation of the Q-th factor with the p-th microplastic. Represents the eigenvalues ​​of the Q-th correlation coefficient matrix R; The correlation coefficient of the Qth principal component combination on the pth microplastic is obtained by solving the unit eigenvector of the Qth correlation coefficient matrix R. The formula is: .

[0075] Since the purpose of factor analysis is to explain the main variations of the original variables using a few latent factors, usually only the first q (q < Q) factors with larger eigenvalues are retained. Select the first q eigenvalues and the corresponding eigenvectors to obtain a simplified factor correlation matrix A (q×p) containing q factors. The simplified factor correlation matrix A (q×p) is as follows:

[0076]

[0077] In the formula, q represents the number of retained factors.

[0078] S23. According to the eigenvalues obtained in step S22, calculate the variance contribution rate and cumulative variance contribution rate of each factor. Take the number of factors Q corresponding to when the cumulative variance contribution rate is greater than 85% as the number q of latent source factors to be retained. The formula is as follows:

[0079]

[0080] In the formula, represents the i-th eigenvalue; Q represents the number of factors, that is, the number of principal component groups; q is the current cumulative number of factors. When the cumulative variance contribution rate is greater than 85%, q is the number of latent source factors to be retained.

[0081] S24. Simplify the initial factor correlation matrix A according to the number q of latent source factors to be retained obtained in step S23 and perform varimax orthogonal rotation to obtain the final factor correlation matrix B. The formula is as follows:

[0082]

[0083] In the formula, b pq represents the contribution weight of the p-th microplastic to the q-th factor, that is, the factor correlation. The larger this value, the greater the influence of this type of microplastic on the variability of this factor.

[0084] The purpose of rotation is to simplify the factor structure so that each original variable has a high loading on only one factor as much as possible, thereby enhancing the interpretability of the factors. During the rotation process, it is necessary to maximize the difference in the squared loadings on different factors. Taking two factors (q = 2) as an example, let the rotated factor correlation matrix be B, and the elements and represent the correlations of the i-th microplastic on factor 1 and factor 2 respectively. Define the communality , which represents the total variance explained by the two factors for the i-th microplastic. The goal of orthogonal rotation is to maximize the following formula:

[0085]

[0086] In the formula, p is the total number of microplastic types; and are the correlations of the i-th microplastic on Factor 1 and Factor 2 respectively; is the communality of the i-th microplastic; and represent the variances of the squares of the correlations on Factor 1 and Factor 2 respectively. Maximizing G is equivalent to making the correlations on each factor polarize as much as possible towards 0 or 1.

[0087] When the number of extracted factors q is greater than 2, pairwise rotation of the factors is required. For all possible factor pairs (j, i) (j < i, there are pairs), the above two-dimensional rotation is performed in turn. After one round of rotation, the next round of rotation is repeated until G is basically unchanged or the specified number of iterations is reached. The final factor correlation matrix B is obtained after rotation.

[0088] S25. From the final factor correlation matrix B obtained in step S24, extract the elements greater than the set threshold as the types of high-load microplastics. Combining the physical and chemical properties (such as polymer type, density, common uses) of high-load microplastics and environmental science common sense, make a scientific inference and naming for the sources of environmental pollution represented by each factor, such as "textile emission factor", "tire wear factor", etc.

[0089] S3. Obtain the factor correlation allocation information from the clustering allocation table obtained in step S1 and the factor correlation matrix obtained in step S2, conduct cross-analysis and mutual verification, give a clear physical meaning of the environmental source for each resolved potential factor, and finally output the quantitative contribution rate and its spatio-temporal distribution characteristics of each source.

[0090] S31. Compare and analyze the clustering allocation table obtained in step S1 and the factor correlation allocation information obtained in step S2; if most or all of the microplastic types in a certain clustering group show high load on the same factor, the results are mutually corroborated, indicating that the microplastic combination represented by this group commonly originates from the same pollution source named in step S25. This cross-validation mechanism significantly improves the reliability of source inference.

[0091] S32. Based on the factor naming and cross-validation results, summarize the characteristic microplastic marker combinations corresponding to each potential pollution source; at the same time, use the factor correlation matrix calculated in the factor analysis process to draw a time series graph of the contribution values of each potential factor changing with time, or a spatial distribution graph at different sampling points, so as to visually display the spatio-temporal evolution law of each pollution source. Finally, form a complete source tracing conclusion report including qualitative source inference and quantitative contribution analysis, and it can be presented in various visualization forms such as radar charts and stacked bar charts, providing an intuitive basis for environmental management decisions.

[0092] In addition to the embodiments described above, the present invention can also have many other implementations. For example:

[0093] (1) In step S1, for abundance data containing a large number of zero values ​​(such as some rare species), the central log-ratio (CLR) transformation can be used instead of the simple logarithmic transformation to better handle the component data. The similarity measure can also be Pearson correlation coefficient or cosine similarity instead of Euclidean distance, depending on the characteristics of the data.

[0094] (2) In step S2, the factor analysis model is not limited to PCA. For example, the positive definite matrix factorization (PMF model) model can be used. This model can combine the uncertainty information of the data to make stricter non-negative constraints, and sometimes it can obtain a source spectrum with a clearer physical interpretation and improve the accuracy of source resolution.

[0095] (3) After obtaining the factor correlation matrix, in order to assess the robustness of the results, the bootstrap method can be used to resample the factor analysis process multiple times, thereby calculating the uncertainty range (such as confidence interval) of factor correlation and contribution rate.

[0096] (4) In the comprehensive analysis in step S3, meteorological data (such as wind speed, wind direction, temperature, humidity and atmospheric stability) monitored simultaneously can be further introduced and subjected to potential source contribution function (PSCF) analysis or correlation analysis with factor scores to explore the driving mechanism of meteorological conditions on vertical transport and diffusion of microplastics in greater depth.

[0097] The following example, using the source analysis of microplastics in the atmosphere at different heights of a high-rise building on a campus, illustrates the application process and effectiveness of the method of this invention.

[0098] Source analysis of atmospheric microplastics in high-rise buildings on campus

[0099] 1. Data Acquisition and Preprocessing

[0100] This embodiment selected a university building in a certain province as the sampling point. To study the vertical distribution characteristics of microplastics, three synchronous sampling points were set up on the 1st-floor balcony (1.6 meters high), the 11th-floor balcony (33 meters high), and the 21st-floor balcony (66 meters high). An MH-1200 high-flow-rate air sampler (flow rate set to 100 liters / minute) was used in conjunction with a quartz fiber filter membrane (0.45 micrometers pore size) for active atmospheric sampling. The sampling time covered four typical time periods of the day: morning peak (8:00-10:00), midday (13:00-15:00), evening peak (17:00-19:00), and nighttime (21:00-23:00) to capture the intraday dynamic changes in microplastic concentration.

[0101] After sampling, the filter membrane underwent pretreatment steps including ultrasonic dissociation and concentration with anhydrous ethanol. Laser-diffraction infrared spectroscopy (LDIR) was then used for automatic identification and counting of microplastics. The instrument was set to automatic particle analysis mode, with a spectral matching threshold set to greater than 0.65, and a particle size range of 20 to 500 micrometers. Based on the "polymer type-morphology" classification system, 15 major microplastic species were identified, including polyethylene (PE), polypropylene (PP), polyethylene terephthalate (PET), polyvinyl chloride (PVC), polyurethane (PU), rubber, and polytetrafluoroethylene (PTFE). The particle count of each microplastic was counted for each sample (3 heights × 4 time periods = 12 samples), constructing an original abundance data matrix (15 microplastics × 12 samples).

[0102] Subsequently, following the method described in step S11, the original abundance data matrix is ​​first transformed using a common logarithmic transformation to base 10 to stabilize the variance. Next, all data are Z-score standardized to obtain a standardized data matrix Z, which is used for subsequent analysis.

[0103] 2. Cluster analysis

[0104] Based on the standardized data matrix Z, the Euclidean distances between each pair of the 15 microplastics were calculated according to step S12, constructing a distance matrix D. Agglomerated hierarchical clustering analysis was performed according to step S13, with the inter-cluster distance using the average inter-group chain distance. Based on the elbow rule in step S14, the optimal number of clusters, K=3, was determined. The clustering analysis divided the 15 microplastics into three significantly different groups (labeled Cluster A, B, and C), where microplastics within each group were considered to have highly similar spatiotemporal abundance variation patterns. Specifically, the clustering assignments are as follows: Group A includes PET, PP, PVC, and PU; Group B includes Rubber and PTFE; and Group C mainly includes PE and other types.

[0105] 3. Factor analysis

[0106] Following step S21, principal component analysis is performed on the standardized matrix Z. The correlation coefficient matrix and its eigenvalues ​​are calculated (step S22). According to step S23, the cumulative variance contribution rate is calculated, and it is found that the cumulative variance contribution rate of the first 4 principal components has reached 92.7% (exceeding the 85% threshold). Therefore, the number of potential source factors k=4 is determined.

[0107] Following step S24, the initial factor loading matrix is ​​subjected to a variance-maximizing orthogonal rotation to obtain the rotated factor correlation matrix B. This matrix quantitatively reflects the degree to which each factor explains the variability of different microplastic types. Analysis of the correlation matrix shows that Rubber, PU, ​​and PVC have high loadings on factor 1 (0.89, 0.75, and 0.68, respectively); PET and PP have high loadings on factor 2 (0.81 and 0.79, respectively); PE has a high loading on factor 3 (0.85); and PTFE has a high loading on factor 4 (0.93).

[0108] Following step S25, and combining knowledge of common environmental sources of high-load microplastics, four factors are named: Factor 1 shows high loading on Rubber, PU, ​​and PVC, materials associated with tire wear, shoe soles, and sealants, hence named "Source of Wear and Tear in Transportation and Building Materials." Factor 2 shows high loading on PET and PP, two polymers being major components of clothing fibers, packaging bags, and bottle caps, highly relevant to daily consumption activities on campus, hence named "Source of Daily Consumption on Campus." Factor 3 dominates the variation in PE; PE has low density, is widely used in packaging films, and is easily transported long distances by wind, hence named "Source of Long-Distance Transportation / Packaging Materials." Factor 4 almost uniquely explains the variation in PTFE; PTFE is commonly used in waterproof coatings and sealing materials for building exteriors, hence named "Source of Aging in High-Rise Buildings."

[0109] 4. Comprehensive judgment and visual output

[0110] Perform cross-validation according to step S31: compare the cluster analysis results with the factor analysis results. In group A (PET, PP, PVC, PU), PET and PP dominate with factor 2, while PVC and PU dominate with factor 1. This indicates that although these microplastics have similar overall spatiotemporal variation patterns (and are therefore clustered together), their dominant sources may differ, demonstrating that cross-validation can reveal deeper differences in origin and avoid simply grouping microplastics from different sources into one category. In group B (Rubber, PTFE), the two microplastics dominate with factors 1 and 4 respectively, indicating that their origins are independent. The clustering results reflect that they may be influenced by some common environmental processes, but their core sources are different.

[0111] Following step S32, a spatiotemporal distribution analysis was conducted: using the factor score matrix obtained from factor analysis, the contribution value of each factor at different sampling times and altitudes could be calculated. Analysis of these scores revealed that Factor 1 (traffic / building material source) had a significantly higher contribution value during the morning and evening peak traffic periods at a height of 1.6 meters, with a morning peak value of 1.82 and a peak value of 2.31 during the evening peak, perfectly consistent with the characteristics of ground traffic emissions. Factor 2 (daily campus consumption source) contributed at all altitudes throughout the day, but peaked at 33 meters (1.54) during midday (13:00-15:00), indicating that it was carried to higher altitudes by daytime thermal convection. Factor 4 (building aging source) contributed most significantly in the morning at a height of 66 meters (score 1.63), directly demonstrating that the aging and peeling of high-rise building materials is a significant source of microplastics (especially PTFE) in the upper atmosphere. At night, the contribution values ​​of all factors were at relatively low levels.

[0112] Conclusion: Based on the above analysis, this invention successfully quantified the sources of atmospheric microplastics in the high-rise building area of ​​the campus into four main contributing sources, and clarified the characteristic markers of each (e.g., PET / PP as a marker of "daily consumption source"; PTFE as a marker of "building aging source") and their spatiotemporal contribution patterns. The final source tracing report reveals the complex characteristics of atmospheric microplastics in this area being affected by "ground traffic emissions," "daily campus activities," "long-distance transport," and "building aging itself," and identifies a dynamic cycle pattern of "ground emissions—heated rise—nighttime deposition," providing a scientific basis for targeted prevention and control.

[0113] In addition to the above embodiments, the present invention may have other implementation methods. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. A method for tracing the origin of atmospheric microplastics based on cluster analysis and factor analysis, characterized in that: Includes the following steps: S1. The abundance data of different types of microplastics in multiple environmental samples are preprocessed, and a clustering analysis algorithm is used to classify them into several groups with similar spatiotemporal behavior characteristics based on the similarity of the abundance change patterns of each microplastic type in all samples. The preprocessed abundance data is obtained and clustering analysis is performed to obtain a clustering assignment table. S2. Apply factor analysis model to the preprocessed abundance data obtained in step S1 to identify several potential factors that play a dominant role in the overall data variability, and obtain factor correlation distribution information by calculating the factor correlation matrix. S3. Based on the clustering assignment table obtained in step S1 and the factor correlation matrix obtained in step S2, obtain the factor correlation assignment information, perform cross-analysis and mutual verification, assign a clear environmental source physical meaning to each parsed potential factor, and finally output the quantitative contribution rate of each source and its spatiotemporal distribution characteristics.

2. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 1, characterized in that: The specific steps of step S1 are as follows: S11. Perform a logarithmic transformation on the original abundance data and standardize it using the Z-score method to obtain the standardized data matrix Z, as shown below: ； In the formula, rows represent different types of microplastics, with a total of p types; columns represent different microplastic samples, with a total of n; and the elements in the matrix... This represents the normalized abundance of the p-th microplastic in the n-th sample; S12. Based on the standardized data matrix Z, calculate the pairwise similarity between all microplastic species and construct the similarity matrix D as follows: ； In the formula, d ij This represents the similarity between the i-th and j-th microplastics; S13. Based on the similarity matrix D, an agglomerative hierarchical clustering algorithm is used, with the average chain distance between groups as the inter-class distance metric. The calculation formula is as follows: ； In the formula, d avg (G,H) represents the average chain distance between clusters G and H; G and H represent any two clusters; |G| and |H| represent the number of microplastic species in clusters G and H, respectively; S14. Using the elbow rule, calculate the within-group sum of squares (WSS) for different numbers of clusters, plot a scree plot, and select the number of inflection points on the curve as the optimal number of clusters K. 佳 ; S15. Based on the optimal clustering number K 佳 Cut and partition K from the clustering dendrogram 佳 A clear group is identified, and a clustering assignment table is output.

3. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 2, characterized in that: The specific steps of step S2 are as follows: S21. Using the standardized data matrix Z as input, construct a factor analysis model based on principal component analysis, and perform factor decomposition to obtain Q factors, as shown in the following formula: ； In the formula, x p y represents the normalized abundance of the p-th microplastic; Q This represents the Qth principal component combination extracted; The coefficient representing the correlation of the Qth principal component combination with the pth microplastic; S22. Based on the Q factors obtained in step S21, calculate the correlation coefficient matrix R between all factors and microplastic types, and solve for the eigenvalues ​​of this matrix and their corresponding unit eigenvectors to construct the initial factor correlation matrix A, as shown in the following formula: ； In the formula, This represents the initial correlation between the Q-th factor and the p-th microplastic; Represents the eigenvalues ​​of the Q-th correlation coefficient matrix R; The correlation coefficient of the Qth principal component combination on the pth microplastic is obtained by solving the unit eigenvector of the Qth correlation coefficient matrix R. get; S23. Based on the eigenvalues ​​obtained in step S22, calculate the variance contribution rate and cumulative variance contribution rate of each factor, and take the number of factors Q corresponding to the cumulative variance contribution rate being greater than 85% as the number of potential source factors q that need to be retained. S24. Based on the number of potential source factors q to be retained obtained in step S23, simplify the initial factor correlation matrix A and perform an orthogonal rotation using the variance maximization method to obtain the final factor correlation matrix B, as shown in the following formula: ； In the formula, b pq This represents the contribution weight of the p-th microplastic to the q-th factor; S25. Based on the final factor correlation matrix B obtained in step S24, extract the elements that are greater than the set threshold as high-load microplastic types. Combining the physicochemical properties of high-load microplastics with common sense in environmental science, scientifically infer and name the environmental pollution sources represented by each factor.

4. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 3, characterized in that: The specific steps of step S3 are as follows: S31. Compare and analyze the clustering assignment table obtained in step S1 with the factor correlation assignment information obtained in step S2. If most or all microplastic species in a certain cluster group show high loading on the same factor, the results are mutually corroborating, indicating that the microplastic combination represented by the group originates from the same pollution source named in step S25. S32. Based on factor naming and cross-validation results, summarize the characteristic microplastic biomarker combinations corresponding to each potential pollution source; at the same time, using the factor correlation matrix calculated during factor analysis, draw a time series plot of the contribution value of each potential factor changing over time.

5. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 4, characterized in that: In step S12, Euclidean distance is used as a measure of the pairwise similarity between microplastic species, and the calculation formula is as follows: ； In the formula, d ij z represents the Euclidean distance between the i-th and j-th microplastics; ik and z jk Let represent the normalized abundance of the i-th and j-th microplastics in the k-th sample, respectively.

6. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 4, characterized in that: The formula for calculating the sum of squares within a group (WSS) in step S14 is as follows: ； In the formula, C k This represents the Cth cluster; K represents the number of clusters. Let be the row vector formed by the normalized abundance of the i-th microplastic in all samples; Let C be the centroid of cluster C.

7. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 4, characterized in that: The formula for calculating the cumulative variance contribution in step S23 is as follows: ； In the formula, Let represent the i-th eigenvalue; Q represents the number of factors; q is the current cumulative number of factors. When the cumulative variance contribution rate is greater than 85%, q is the number of potential source factors that need to be retained.

8. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 4, characterized in that: In step S12, Pearson correlation coefficient or cosine similarity is used as a measure of the similarity between pairs of microplastic species.

9. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 4, characterized in that: In step S11, for abundance data containing a large number of zero values, the central log-log ratio (CLR) transformation is used instead of the logarithmic transformation.

10. The atmospheric microplastics tracing method based on cluster analysis and factor analysis according to claim 4, characterized in that: In step S21, the factor analysis model uses a positive definite matrix factor decomposition model instead of the principal component analysis model.

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