A Machine Learning-Based Method for Predicting the Distribution of Microplastic Pollution in Seawater

Abstract

This invention relates to the field of marine environmental monitoring and data processing technology, and discloses a machine learning-based method for predicting the distribution of microplastic pollution in seawater. The method includes: acquiring marine environmental characteristics and measured microplastic data to construct a training dataset; performing adaptive logarithmic smoothing transformation on skewed environmental characteristics, and selecting core features through significance testing to generate a standard feature matrix; smoothing and standardizing the measured microplastic data and dividing the data into subsets; using partial least squares regression to extract orthogonal latent variables and constructing a microplastic abundance prediction model; inputting the feature data into the model to generate prediction results, and sequentially performing inverse standardization, inverse exponential transformation, and non-negativity constraint processing; and combining spatial interpolation algorithms to output a spatial distribution map of microplastic abundance. This invention effectively handles the skewed distribution and multicollinearity of environmental data, ensuring that the prediction results conform to non-negativity physical laws and improving the accuracy of spatial distribution extrapolation.

Description

Technical Field

[0001] This invention relates to the field of marine environmental monitoring and data processing technology, specifically to a method for predicting the distribution of microplastic pollution in seawater based on machine learning. Background Technology

[0002] Currently, the quantitative acquisition of marine microplastic abundance mainly relies on shipboard on-site sampling and laboratory instrument detection. While these physical detection methods can provide reliable measured data, they are costly, have narrow spatiotemporal coverage, and long analysis cycles, making them unsuitable for continuous dynamic monitoring of large-scale marine areas. To extrapolate regional pollution distribution based on limited sampling data, existing technologies typically employ statistical models such as linear regression, correlation analysis, and spatial interpolation to estimate microplastic abundance.

[0003] However, the spatial distribution pattern of marine microplastics is comprehensively influenced by various environmental factors, including seawater temperature, salinity, sea surface wind field, ocean currents, and various biochemical elements. These multi-source environmental factors exhibit complex nonlinear correlations and multicollinearity. When processing such high-dimensional correlated data, traditional empirical statistical models suffer from poor stability in matrix calculations, leading to increased variance in model parameter estimation and weak generalization ability of prediction results.

[0004] At the data input level, measured parameters of the marine environment generally exhibit skewed and long-tailed distribution characteristics. Existing prediction methods lack adaptive smoothing and core feature selection mechanisms for skewed data, and excessive weighting of extreme values ​​often leads to skewed fitting directions in subsequent machine learning models. At the computational output level, conventional numerical regression algorithms lack boundary constraint mechanisms for objective physical laws, and their numerical fitting errors frequently result in negative predicted values, violating the actual physical meaning that microplastic abundance is always greater than or equal to zero.

[0005] In addition, existing distribution prediction schemes are mostly local fittings for nearshore shallow waters, and have not formed a systematic framework that integrates feature dimensionality reduction, collinearity elimination and distribution pattern correction. They cannot meet the high-precision extrapolation requirements of the spatial gradient evolution of microplastic pollution in complex deep-sea areas. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a machine learning-based method for predicting the distribution of microplastic pollution in seawater. This method solves the problems of existing methods for predicting the distribution of microplastics in seawater, which are unable to effectively handle skewed distributions and multicollinearity in environmental data, and whose prediction results are prone to negative values ​​that violate the laws of reality, resulting in insufficient accuracy in spatial distribution extrapolation.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A machine learning-based method for predicting the distribution of microplastic pollution in seawater includes the following steps: We acquired environmental characteristic data and microplastic measurement data, and removed samples with missing values ​​to construct a training dataset. The environmental feature data in the training dataset is subjected to skewness test, and an adaptive log smoothing transformation is performed on the environmental feature data whose skewness exceeds a preset threshold. The significance test results between the environmental feature data after skewness test and transformation processing and the measured data of microplastics are calculated, and the core features are selected to generate a standard feature matrix. Smoothing and standardization processes were performed on the microplastic measurement data to generate a standard target variable vector. The standard dataset, which is composed of the standard feature matrix and the standard target variable vector, was divided into a training set and a validation set. A microplastic abundance prediction model was constructed based on the training set using the partial least squares regression algorithm. The standard feature matrix from the validation set was then input into the microplastic abundance prediction model to generate the abundance prediction results. The abundance prediction results are processed by inverse standardization, inverse exponential transformation and nonnegativity constraint, and combined with spatial interpolation algorithm to output a spatial distribution map of microplastic abundance.

[0008] Further steps in acquiring environmental feature data and microplastic measured data, and removing missing value samples to construct the training dataset, specifically include: simultaneously acquiring multi-source marine environmental parameters of the target sea area as environmental feature data. These multi-source marine environmental parameters consist of longitude, latitude, sea surface temperature, sea surface salinity, sea surface wind speed, sea surface pressure, precipitation, dissolved oxygen, nitrate concentration, phosphate concentration, ocean current velocity, traffic density, and water depth. Based on the spatial coordinates of each sampling location, the environmental feature data and microplastic measured data are correlated and matched, data samples containing missing values ​​are removed, and the resulting dataset is used to generate the training dataset. This step combines multi-dimensional parameters such as marine physical and dynamic processes, biochemical characteristics, and external emissions to construct the dataset required for model training.

[0009] Furthermore, the step of performing adaptive logarithmic smoothing transformation on environmental feature data with skewness exceeding a preset threshold specifically includes: extracting the minimum value of environmental feature data with skewness exceeding the preset threshold across all samples; when the minimum value is determined to be less than zero, performing a logarithmic translation transformation on the environmental feature data with skewness exceeding the preset threshold. When the minimum value is determined to be greater than or equal to zero, a standard logarithmic transformation is performed on environmental feature data whose skewness exceeds a preset threshold. This step uses different logarithmic transformation methods based on the boundaries of environmental variable values, reducing the data range while avoiding meaningless values ​​generated by logarithmic operations.

[0010] In a preferred embodiment of the present invention, the step of calculating the significance test results between the environmental feature data after skewness test and transformation processing and the microplastic measured data, and screening core features to generate a standard feature matrix specifically includes: converting the environmental feature data after skewness test and transformation processing and the microplastic measured data into rank sequences respectively, and calculating the Spearman correlation coefficient; Construct a test statistic, call the cumulative probability function to obtain the probability value of the test statistic under the two-tailed test condition, and use the probability value as the significance test result; When the probability value is less than the confidence threshold, the associated environmental features are retained as core features. Zero-mean standardization is then performed on these core features, and the results are merged to generate a standard feature matrix. This step utilizes rank operations to evaluate the nonlinear relationships between variables and eliminates weakly correlated variables to reduce the dimensionality of the feature matrix.

[0011] Furthermore, the steps for performing smoothing and standardization on the microplastic measured data to generate a standard target variable vector specifically include: adding a constant one to the microplastic measured data and then performing a natural logarithm operation to generate a smoothed target variable vector; Extract the mean and standard deviation of the smoothed target variable vector from the entire sample set; then, use the mean and standard deviation to perform zero-mean standardization on the smoothed target variable vector to generate a standard target variable vector. This step aims to correct the right-skewed long-tailed distribution characteristics of the microplastic abundance data to reduce the heteroscedasticity of the regression residuals.

[0012] Furthermore, the step of dividing the standard dataset, which is composed of the standard feature matrix and the standard target variable vector, into a training set and a validation set specifically includes: performing a random row shuffling operation on the standard dataset while keeping the internal features of a single sample and the correlation with the target unchanged; The integer quotient of the total number of samples divided by the fold is used as the base sample size. The remainder after division is used as the number of subsets that need to be expanded. The sample size of the data subset corresponding to the number of subsets that need to be expanded is set as the base sample size plus one. The sample size of the remaining data subset is set as the base sample size, thus dividing the data into multiple sets of subsets. During the cross-validation iteration process, a subset of data is extracted as the validation set, and all remaining subsets are concatenated to form the training set. This step ensures a balanced data subset partition and prevents array out-of-bounds errors by dynamically allocating samples and calculating the remainder.

[0013] Furthermore, the specific steps for constructing a microplastic abundance prediction model based on the training set using the partial least squares regression algorithm include: Set the standard feature matrix in the training set as the initial independent variable matrix, and set the smoothed target variable vector corresponding to the training set as the initial dependent variable vector; in the feature extraction cycle, calculate the feature weight vector based on the independent variable residual matrix and dependent variable residual matrix output in the previous cycle, and extract the latent variable score vector based on the feature weight vector; The regression loading vectors of the independent variable residual matrix along the latent variable score vector dimension are calculated. Orthogonalized variance information corresponding to the regression loading vectors is extracted from the independent variable residual matrix to generate a new independent variable residual matrix for the next period. The dependent variable residual matrix is ​​updated synchronously. After a preset number of latent variable extractions, a microplastic abundance prediction model is generated. This step addresses the problem of unstable regression coefficient estimation caused by multicollinearity of environmental variables by extracting mutually orthogonal latent variables.

[0014] In a preferred embodiment of the present invention, the step of inputting the standard feature matrix from the validation set into the microplastic abundance prediction model to generate the abundance prediction result specifically includes: The model extracts all feature weight vectors and regression loading vectors from the microplastic abundance prediction model. Matrix operations are then performed on these vectors to generate a column vector of regression coefficients. Matrix multiplication is then performed between the standard feature matrix from the validation set and the column vector of regression coefficients to calculate the abundance prediction results. This step maps the parameters from the low-dimensional space back to the original feature dimension, directly deriving the prediction results through matrix operations, thus improving inference efficiency.

[0015] Furthermore, the specific steps for performing inverse standardization, inverse exponential transformation, and nonnegativity constraint processing on the abundance prediction results include: The abundance prediction results are multiplied by the standard deviation and the mean is added to generate the transitional prediction value. The natural constant is set as the base, the transitional prediction value is set as the exponent and the power operation is performed. After subtracting the constant one, the preliminary microplastic abundance prediction value is generated. When the preliminary microplastic abundance prediction value is determined to be less than zero, the preliminary microplastic abundance prediction value is forcibly assigned to zero, and the predicted microplastic abundance value is output. This step performs an inverse transformation on the prediction result to restore its actual physical magnitude, and corrects the negative value anomaly caused by fitting error through non-negativity constraints.

[0016] Furthermore, the steps of outputting a spatial distribution map of microplastic abundance using a spatial interpolation algorithm specifically include: dividing the target sea area into a two-dimensional spatial grid, and extracting the center point of each grid in the two-dimensional spatial grid as the target spatial point; Calculate the straight-line spatial distance between the specified target spatial point and each sampling location; after adding the zero constant to the straight-line spatial distance, perform the inverse distance decay exponent operation to generate the spatial influence weight; perform a weighted normalization summation operation based on the spatial influence weight and the predicted microplastic abundance value corresponding to each sampling location to generate the microplastic inferred abundance of the specified target spatial point. The microplastic abundance of all target spatial points is mapped to a color rendering layer. This color rendering layer is then aligned and merged with the geographic base map of the target sea area to generate a spatial distribution map of microplastic abundance. This step uses spatial interpolation based on the distance attenuation principle to transform the predicted data from discrete sites into a continuous layer, presenting the pollution distribution in the target sea area.

[0017] This invention provides a machine learning-based method for predicting the distribution of microplastic pollution in seawater. It offers the following advantages: 1. This invention performs an adaptive logarithmic smoothing transformation on environmental feature data with skewness exceeding a threshold, employing either a shifted logarithmic transformation or a standard logarithmic transformation based on whether the minimum value of the data sample is less than zero. Combined with the Spearman correlation coefficient, a nonparametric statistical method, to screen core features, this approach overcomes the computational obstacle caused by abnormal logarithmic operations when negative extreme values ​​exist in multi-source marine environmental variables. It also reduces the interference of extremely skewed data on model training and improves the quality of input data.

[0018] 2. This invention utilizes partial least squares regression to construct a microplastic abundance prediction model. During the feature extraction cycle, orthogonal latent variable information is extracted successively from the residual matrices of the independent and dependent variables. This step eliminates the inherent multicollinearity problem among various marine environmental parameters (such as seawater temperature, salinity, and sea surface wind speed), ensures the numerical stability of the model matrix inversion calculation, and avoids distortion in regression coefficient estimation caused by high feature correlation.

[0019] 3. This invention introduces non-negativity constraints on the initial predicted values ​​after inverse transformation, forcing predicted data less than zero to be assigned a value of zero, and adding a zero-prevention constant to the spatial interpolation algorithm to calculate the spatial influence weight. This approach corrects the defect of conventional numerical regression models that are prone to producing negative predictions, ensuring that the final output microplastic abundance extrapolation data conforms to non-negative objective physical laws, while also ensuring the reliability of the program when performing interpolation calculations from discrete sampling points to a continuous spatial grid. Attached Figure Description

[0020] Figure 1 This is a system architecture diagram of the present invention; Figure 2 This is a flowchart of the method of the present invention; Figure 3 This is a flowchart of the Spearman correlation analysis and statistical hypothesis testing of the present invention; Figure 4 This is a flowchart of the latent variable extraction and model training process for the partial least squares regression model of the present invention. Figure 5 This is a flowchart of the inverse transformation of physical state of model prediction data and spatial interpolation rendering of the present invention; Figure 6 This is a graph showing the attenuation of the spatial influence weight as a function of distance in this invention. Figure 7 This is a comparison curve of the model prediction and tracking of the present invention; Figure 8 This is a bar chart comparing the prediction errors of different test models of the present invention. Detailed Implementation

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] See attached document Figure 1 This invention provides a machine learning-based system for predicting the distribution of microplastic pollution in seawater, comprising a database construction module, a distribution transformation module, a variable selection module, a data partitioning module, a model construction module, and a distribution estimation module. In the specific workflow, the database construction module acquires environmental characteristic data and measured microplastic abundance data of the target sea area to construct an initial multidimensional feature matrix, and then transmits it to the distribution transformation module. The distribution transformation module performs smoothing mapping and standardization preprocessing on the received data to eliminate distribution skewness and dimensional differences, generate a standard dataset, and transmit it to the variable filtering module. The variable filtering module extracts core environmental feature variables based on the standard dataset and removes redundant features, then sends the dimensionality-reduced feature dataset to the data partitioning module. The data partitioning module splits the entire sample according to the cross-validation strategy and distributes the generated training set and validation set to the model building module; The model building module extracts orthogonal latent variables and derives regression coefficients based on the training set, performs matrix operations on the validation set, and transmits the generated model prediction control data to the distribution estimation module. Finally, the distribution estimation module performs inverse physical state transformation and boundary constraint processing on the model's predicted values, and performs spatial interpolation and layer rendering in conjunction with the geographic coordinates of the monitoring stations to output a continuous spatial distribution map of microplastic abundance in the target sea area, thereby completing the end-to-end data processing closed loop of the system.

[0023] See attached document Figure 2This invention provides a machine learning-based method for predicting the distribution of microplastic pollution in seawater, comprising the following steps: S10, Obtain multi-source measured data, match and remove samples, and construct a training set: Obtain measured sample data of microplastics in the target sea area, simultaneously obtain multi-source marine environmental parameters at the corresponding sampling locations, uniformly match all environmental features and target variables, remove samples with missing values, and construct a training dataset. S20, Check the skewness of environmental features and perform log smoothing transformation: Check the skewness of each environmental feature in the training dataset. When the skewness of a variable exceeds a preset threshold, perform an adaptive log smoothing transformation on the corresponding variable. When the minimum value of a variable is less than 0, a translational logarithmic transformation is used, and when the minimum value of a variable is greater than or equal to 0, a standard logarithmic transformation is used. S30, Spearman Feature Selection and Standard Input Matrix Construction: Spearman correlation analysis was used to calculate the correlation between transformed environmental variables and microplastic abundance. Based on the significance test results, core feature variables were selected. A significance threshold was set to remove weakly correlated variables with microplastic abundance, retaining core environmental variables reflecting ocean dynamic conditions, water mass structure, and nutrient cycling characteristics. For cases where correlations still exist among the retained variables, subsequent partial least squares regression models were used to reduce the impact of multicollinearity through latent variable extraction. Z-score standardization was applied to the retained core environmental variables to construct a standardized input feature matrix. S40, Smoothing the target variable and dividing the cross-validation set: Log smoothing is performed on the microplastic abundance target variable, and the dataset is divided into training set and test set using the cross-validation method. S50, Partial Least Squares Model Building, Extracting Latent Variables and Predicting: A microplastic abundance prediction model is built using the partial least squares regression algorithm. The partial least squares regression algorithm processes the covariance relationship between the input variables and the target variables and extracts latent variables during the dimensionality reduction process. After the model training is completed, the test set is input into the microplastic abundance prediction model for prediction calculation, and the microplastic abundance estimation results of the target sea area are output. S60, Inverse Transformation and Constraints for Spatial Distribution Interpolation: The microplastic abundance estimation results are subjected to inverse standardization and inverse exponential transformation. The results are first multiplied by the standard deviation of the target variable saved during the training phase and then the mean of the target variable is added. The inverse exponential transformation is then performed to restore the true microplastic abundance values. The abnormal negative values ​​generated after the inverse transformation are subjected to non-negative constraint processing. The spatial distribution prediction results of the microplastic abundance in the target sea area are output. The marine microplastic pollution distribution map is generated by combining GIS spatial interpolation technology.

[0024] Through data acquisition and feature parameter definition operations, environmental data extracted from sampling points and microplastic measurement data are integrated into a unified matrix structure. This includes the following sub-steps: S101, Obtain measured seawater microplastic sample data from the target sea area as the target variable for the prediction model. Set the total number of measured samples obtained within the target sea area to be... , A positive integer greater than 0. Construct a target variable vector based on the sampled data. Its mathematical expression is: ; In the formula, Indicates the first Measured values ​​of seawater microplastic abundance obtained from each sampling location; subscript The value range is 1 to ; superscript This represents the transpose operation of a vector.

[0025] S102 synchronously acquires multi-source marine environmental parameters based on the spatial coordinates of the sampling location. The acquired environmental parameters consist of 13 scalar features, including longitude, latitude, sea surface temperature, sea surface salinity, sea surface wind speed, sea surface air pressure, precipitation, dissolved oxygen, nitrate concentration, phosphate concentration, ocean current velocity, traffic density, and water depth.

[0026] Among the above parameters, seawater temperature, seawater salinity, ocean current velocity, and sea surface wind speed are used to characterize ocean dynamics and water mass physical processes; dissolved oxygen, nitrate concentration, and phosphate concentration are used to characterize the characteristics of marine biogeochemical cycles; water depth and traffic density are used to characterize topographic constraints and external emission intensity. Traffic density is calculated based on Automatic Identification System (AIS) data, route data, or ship passage records, and can be specifically expressed as the ratio of the number of ship trajectory points, ship track length, or number of ship passages within a preset radius and preset time window around the sampling point to the corresponding sea area.

[0027] The total dimension of the environmental parameters is set as follows: Corresponding to the above 13 indicators, The value is set to 13, where longitude and latitude are used as independent spatial coordinate feature columns to characterize the spatial location of the sampling points and are used for subsequent spatial distribution estimation and environmental data matching. This is used to construct the target variable vector. The corresponding initial matrix of multi-source marine environmental features Its expression is: ; In the formula, matrix elements Indicates the first The sampling position corresponding to the first Numerical values ​​of multiple marine environmental parameters, subscript The value range is 1 to subscript The value range is 1 to .

[0028] S103, Initial matrix of multi-source marine environmental characteristics With the target variable vector A unified matching process is performed based on sampling location. Specifically, the longitude, latitude, and sampling time of the sampling point are used as matching indices. For marine environmental data with a grid structure, nearest neighbor extraction, bilinear interpolation, or inverse distance weighted interpolation are used to obtain the environmental parameters corresponding to the sampling point. For environmental data with time resolution, data at the corresponding time of sampling is selected, or the average value within a preset time window before and after the sampling time is selected as the matching value. Rows containing samples with null values ​​for environmental features or target variables are removed, and the cleaned training dataset is output.

[0029] In a specific embodiment of the present invention, the database construction module reconstructs the acquired multi-source data to form a complete data structure that the model can read. This process specifically includes the following steps: S104, the database construction module performs a unified matching operation on multi-source data. Using the sampling location as the mapping benchmark, the target variable vector... The elements in the matrix and the initial environmental feature matrix A horizontal correlation was established between the row vectors of environmental variables corresponding to the same sampling location. By traversing the measured samples one by one, a unified matching was completed between all multi-source marine environmental characteristic data and the microplastic target variable.

[0030] S105, the database construction module performs a missing value sample removal operation. To ensure the validity of matrix operations during subsequent model training, the input feature space needs to have data integrity. The database construction module performs numerical validity determination on the matched data, specifically by traversing the initial environment feature matrix row by row. When an environment parameter with a null value is detected in a row vector, or when the corresponding target variable is detected to be null, the associated sample is determined to be incomplete data.

[0031] After the above determination occurs, the database construction module synchronously deletes the initial environment feature matrix. The line in the text, and the target variable vector. The corresponding element in the dataset. After completing the traversal and removal of all samples, the database construction module outputs the cleaned environmental feature matrix and the cleaned target variable vector, which together constitute a high-quality training dataset.

[0032] In specific embodiments of the present invention, marine environmental factors such as precipitation, ocean current velocity, and traffic density exhibit an asymmetrical long-tailed distribution in space due to the influence of seasonal changes or localized activities. When skewed data is directly used for partial least squares regression modeling, it can skew the direction of variance maximization in the model, reducing prediction accuracy.

[0033] Therefore, the distribution transformation module performs a skewness test on the cleaned training dataset to quantitatively assess the degree of skewness in the distribution of each environmental variable. This process specifically includes the following steps: S201, the distribution transformation module calculates the mean of each marine environmental variable in the training dataset. The input dataset contains the total number of measured samples obtained within the target sea area. The total dimension of the characteristics of environmental parameters For the first A multi-source marine environmental parameter is used. The distribution transformation module extracts the value of the variable in all samples and calculates its arithmetic mean according to the following formula: ; In the formula, Indicates the first The mean values ​​of multiple marine environmental parameters; This represents the total number of measured samples obtained within the target sea area; Indicates the first The sampling position corresponding to the first The values ​​of multiple marine environmental parameters; The value range is 1 to ; The value range is 1 to .

[0034] S202, the distribution transformation module constructs a skewness calculation formula based on the calculated arithmetic mean to obtain the skewness values ​​of each marine environmental variable. The specific calculation formula is as follows: ; In the formula, Indicates the first The skewness values ​​of several multi-source marine environmental parameters are calculated, with the physical meanings of the remaining symbols remaining consistent with step S201. The distribution transformation module calculates the skewness value of each environmental feature using this formula, resulting in a value derived from... The evaluation set consists of skewness values.

[0035] S203, the distribution transformation module performs threshold comparison and transformation status marking operations. The distribution transformation module is configured with preset thresholds. The preset threshold The skewness value used to classify whether a variable belongs to a skewed distribution ranges from 0.5 to 1.5; in this embodiment, 1.0 is used. The distribution transformation module converts the skewness values ​​of each marine environmental variable calculated in step S202. Extract the absolute value and then... With preset threshold Perform numerical comparison.

[0036] When the judgment is satisfied When the marine environmental variable is determined to exhibit a highly skewed distribution, the distribution transformation module marks the variable as a state to be transformed; when the determination satisfies If the marine environmental variable is determined to be close to a normal distribution, the distribution transformation module marks the variable as remaining in its original state. After marking, the distribution transformation module inputs the candidate variables marked as to be transformed into the subsequent logarithmic transformation process to reduce the interference of extreme values ​​on model training.

[0037] In a specific embodiment of the present invention, due to the influence of the marine physical environment, some environmental variables have values ​​less than zero. To meet the operational requirement that the independent variable of the logarithmic function be greater than zero and to avoid computational failure, the distribution transformation module receives the environmental variables after they have been marked with state labels and performs differentiated logarithmic smoothing mathematical transformation based on the actual value boundaries of each feature variable. This operation compresses the range space of the feature data and reduces the weight of extreme values. The process specifically includes the following steps: S204, the distribution transformation module targets the state marked as to be transformed. A multi-source marine environmental parameter, traversing the variable across all... Extract the minimum value of the variable from the values ​​in the nth sample. The minimum value of the multi-source marine environmental parameter is denoted as Its mathematical expression is: ; In the formula, This represents a function that takes the minimum value. Indicates the first The sampling position corresponding to the first The values ​​of multiple marine environmental parameters; The value range is 1 to ; The value range is 1 to .

[0038] S205, the distribution transformation module calculates the minimum value extracted. The positive or negative attribute determines the logic for adaptive logarithmic smoothing transformation. The specific branch determination method is as follows: When the judgment is satisfied At that time, the distribution transformation module performs the following operation on the first... The multi-source marine environmental parameters undergo a logarithmic translational transformation. The mathematical formula for the logarithmic translational transformation is as follows: ; In the formula, Represents the transformed th The sampling position corresponding to the first The values ​​of multiple marine environmental parameters; Represented by constants The natural logarithm function with base 0. By subtracting the corresponding minimum negative value and adding a constant 1 during the shift operation, the overall input variable within the parentheses before the transformation is always greater than or equal to 1, ensuring the validity of the logarithmic operation.

[0039] When the judgment is satisfied At that time, the distribution transformation module performs the following operation on the first... The standard logarithmic transformation of the multi-source marine environmental parameters is performed. The mathematical formula for the standard logarithmic transformation is as follows: ; In the formula, the physical meaning of each symbol is consistent with that of the translational logarithmic transformation formula. The addition of the constant 1 is used to prevent the logical dead zone where the natural logarithm calculation becomes meaningless when the environmental variable takes the value of 0.

[0040] S206, After the distribution transformation module completes the adaptive logarithmic smoothing transformation of all marine environmental variables marked as being to be transformed, the transformed values ​​will be... Update to the corresponding original position of the initial environmental feature matrix. For marine environmental variables marked as maintaining their original state, their values ​​remain unchanged. After completing the data update, the distribution transformation module outputs the environmental feature matrix with optimized distribution, and uses it as input data to the subsequent feature standardization processing flow.

[0041] See attached document Figure 3 In a specific embodiment of the present invention, a nonlinear response relationship is observed between marine environmental variables and microplastic abundance. The variable screening module employs rank-based Spearman correlation analysis for feature correlation measurement. This method is independent of the specific distribution of the data and is used to evaluate and screen environmental features that exhibit a monotonic nonlinear relationship with the target variable. The process specifically includes the following steps: S301, the variable filtering module will... The multi-source marine environmental parameter sequences and the microplastic abundance target variable sequence were converted into rank sequences. The variable selection module then processed the target variable vector. The values ​​of each sample are sorted in ascending order of magnitude to obtain the first value. The ranking of microplastic abundance at each sampling location in the sequence is denoted as follows: If samples with the same value exist in the sequence, the arithmetic mean of the ranks of these values ​​is taken as their corresponding rank. Using the same rule, the variable filtering module obtains the... The sampling position corresponding to the first The hierarchical ranking of several multi-source marine environmental parameters in the sequence is denoted as follows: .

[0042] S302, the variable selection module calculates the rank difference for each sample and performs Spearman correlation coefficient calculation based on the rank difference. The variable selection module calculates the... The Spearman correlation coefficients between the multi-source marine environmental parameters and the target variable are denoted as . Its mathematical formula is: ; In the formula, Indicates the first Spearman correlation coefficients between multiple marine environmental parameters and the target variable; This represents the total number of measured samples; Indicates the first The sampling position corresponding to the first The order of multiple marine environmental parameters; Indicates the first The rank of the target variable for microplastic abundance corresponding to each sampling location.

[0043] S303, The variable selection module processes the calculated Spearman correlation coefficient. Perform statistical hypothesis testing. To avoid program errors such as zero denominators in subsequent calculations, the variable selection module determines the Spearman correlation coefficient. Is the absolute value equal to 1? When determining... When it is determined that the environmental variable is correlated with the target variable of microplastic abundance, the statistical test process is skipped; when it is determined that... At that time, the variable selection module is constructed according to the following degrees of freedom: of The distribution test statistic is denoted as . Its mathematical formula is: ; In the formula, Indicates the relationship with the first The test statistics for the association of multiple marine environmental parameters are as follows, and the physical meanings of the other symbols are consistent with those in step S302.

[0044] S304, for In this case, the variable selection module is based on the test statistic. The internal cumulative probability function is called to obtain its probability value under a two-sided test, and this test probability value is denoted as... The variable selection module includes a confidence threshold for determining whether a correlation exists. In this embodiment, 0.05 is used as the confidence threshold. The criteria for judgment.

[0045] S305, the variable selection module performs numerical comparison and feature removal operations. The variable selection module will examine the probability values. With confidence threshold Compare. When determining... At that time, determine the first There is a statistically effective correlation between several multi-source marine environmental parameters and the target variable of microplastic abundance. The variable screening module will select the first... Several multi-source marine environmental parameters were marked as retained features; When the judgment When it is determined that the correlation between the environmental variable and the target variable is not statistically significant, the variable screening module will remove the first environmental variable. Several multi-source marine environmental parameters are marked as redundant features. After traversing and comparing all environmental features, the variable filtering module removes the corresponding data columns marked as redundant features from the environmental feature matrix, and outputs the dimensionality-reduced environmental feature subset matrix.

[0046] In a specific embodiment of the present invention, the environmental variables retained after statistical hypothesis testing (such as seawater temperature, seawater salinity, dissolved oxygen, nutrient concentration, ocean current velocity, water depth, or traffic density) possess different physical dimensions and numerical magnitudes. In multivariate regression analysis, unscaled data can lead to features with large absolute values ​​having excessive weights in matrix calculations, affecting model convergence. The variable selection module receives a dimensionality-reduced subset matrix of environmental features and performs a dimensionless standardization mathematical transformation on each feature variable to construct a model input feature space with a uniform scale. This process specifically includes the following steps: S306, the variable selection module extracts a dimensionality-reduced subset matrix of environmental features and performs zero-mean standardization (Z-score standardization) on each retained environmental variable within this matrix. Specifically, the variable selection module calculates the arithmetic mean and standard deviation of a single environmental variable across all sample data; then, it subtracts the calculated arithmetic mean from each sample value under that environmental variable and divides by the corresponding standard deviation to obtain the standardized value. Before performing Z-score standardization, the variable selection module first performs a variance check on the dimensionality-reduced subset matrix of environmental features, eliminating constant features with a standard deviation of zero. After the above processing, the standard deviation of each retained environmental variable is not zero, avoiding program anomalies such as a denominator of zero during computer division operations.

[0047] S307, through the aforementioned zero-mean standardization process, the variable selection module maps the data distribution of each environmental variable to a numerical space with a mean of 0 and a standard deviation of 1, eliminating dimensional differences between various physical parameters. The variable selection module then reorganizes the standardized values ​​of all environmental variables according to their original row and column structures to generate a standard feature matrix. Simultaneously, the module saves the skewness transformation state, minimum value, translation parameter, mean, standard deviation, and list of retained features for each retained environmental variable. These parameters are used for the homogeneous preprocessing of the validation set, test set, and grid points in the space to be predicted, ensuring consistency in data transformation rules between the model training and application phases.

[0048] In step S308, the variable selection module does not directly perform Z-score standardization on the original microplastic abundance target variable. Instead, it transmits the original target variable vector to the subsequent model building module. The model building module first performs log-smoothing on the original microplastic abundance target variable, then calculates the mean and standard deviation of the log-smoothed target variable based on the training set, and performs Z-score standardization on the log-smoothed target variable to obtain the standard target variable vector. The variable selection module then transmits the generated standard feature matrix, along with the original target variable vector required for target variable processing, to the subsequent model building module.

[0049] In a specific embodiment of the present invention, the marine microplastic abundance data exhibits a right-skewed long-tailed distribution in spatial distribution. Directly using long-tailed data for regression modeling can lead to heteroscedasticity in the model residuals, reducing the overall fitting accuracy. Before establishing the partial least squares regression model, the model building module performs a logarithmic smoothing transformation on the original values ​​of the microplastic abundance target variable to optimize the data distribution. This process specifically includes the following steps: S401, the model building module extracts the raw microplastic abundance target variable data sequence. This target variable data sequence is set to include... The first sample data, the first The raw values ​​of microplastic abundance corresponding to each sampling location are denoted as follows: The physical measurement results of microplastic abundance are non-negative, and the data range meets the following conditions. The model building module processes the target variable in the order of first log smoothing and then standardization, and saves the mean of the log smoothed target variable. and standard deviation This is used for the inverse standardization and inverse exponential transformation of subsequent prediction results.

[0050] S402, the model building module performs natural logarithmic smoothing with an additional constant on each sample value in the target variable data sequence. This is for sample data where microplastics were not detected in actual environmental sampling (i.e., To avoid computational failure when the computer executes the natural logarithm function due to the independent variable being zero, a shift transformation with an increment of 1 is used. The value of the target variable after the smooth transformation is denoted as... Its mathematical formula is: ; In the formula, Indicates the th after smooth transformation Microplastic abundance values ​​at each sampling location; Indicates the first before transformation Raw values ​​of microplastic abundance at each sampling location; Represented by constants The natural logarithm function with base 0; The value range is 1 to By uniformly adding a constant of 1 to the logarithmic independent variable, we can ensure that the input is always greater than or equal to 1, thus eliminating the logical dead zone in natural logarithm operations.

[0051] S403, the model building module completes all After calculating the logarithmic smoothing of each sample, the calculated transformed values ​​are... The vector of smoothed target variables is reorganized. The model building module calculates the mean based on the smoothed target variable vector in the training set. and standard deviation The target variable is then Z-score standardized to obtain a standard target variable vector. The model building module aligns this standard target variable vector with the standard feature matrix output from the previous process according to the sample dimensions, forming a standard dataset. This standard dataset is then transferred to the data partitioning module for subsequent cross-validation. For the validation set or the samples to be predicted, the mean of the target variable is... and standard deviation It is only used for the inverse transformation of the prediction results and is not used as model input.

[0052] In a specific embodiment of the present invention, to evaluate the generalization performance of the partial least squares regression model and alleviate overfitting, the data partitioning module uses a cross-validation mechanism to split the standard dataset. To prevent validation set information from leaking into the model training process, in each cross-validation iteration, the skewness test parameters, log-smoothing transformation parameters, feature selection results, standardized mean and standard deviation of features, and log-smoothed mean and standard deviation of the target variable are all calculated based solely on the current training set; the validation set only calls the aforementioned parameters stored in the current training set for the same transformation and does not participate in parameter calculation or feature selection.

[0053] This mechanism generates multiple sets of mutually exclusive training and validation data pairs, ensuring that every sample point can participate in model training and evaluation. In practical applications, folding... The value is typically set to 5 or 10, with the specific value pre-configured based on the total sample size. The dataset partitioning process includes the following steps: S404, The data partitioning module receives the pre-aligned included... The dataset consists of a standard feature matrix and a smoothed target variable vector. The data partitioning module, while maintaining the correspondence between feature data and target variable data within each sample, randomly shuffles the dataset along the row dimension to reduce the negative impact of the original data collection sequence or spatial ordering on the model training process.

[0054] S405, The data partitioning module extracts the folds from the cross-validation configuration parameters. And calculate the sample allocation capacity for each data subset. (Regarding the total number of samples...) Unable to be folded Given the objective situation of divisibility, the data partitioning module calculates the integer quotient of the total number of samples divided by the fold as the basic sample size, and calculates the corresponding remainder as the number of subsets that need to be added.

[0055] S406, the data partitioning module allocates capacity according to the calculated sample allocation, and physically divides the randomly shuffled standard dataset into rows sequentially. There are several data subsets. The specific allocation rule is as follows: the data partitioning module sets the sample size of the subset with the remainders obtained from the aforementioned calculation to the base sample size plus 1, and sets the sample size of the remaining data subsets to the base sample size. Through this remainder allocation logic, the data partitioning module controls the difference in sample size between all subsets to not exceed 1, maintaining the balance of the data partitioning structure and avoiding array out-of-bounds dead zones during data splitting.

[0056] S407, the data partitioning module executes the cross-validation assembly logic for the standard dataset. The current iteration index is set to... Its value ranges from 1 to In the first In the next iteration, the data partitioning module extracts the first... A subset of data was used as the validation set, and the remaining data was used as the validation set. A subset of data is concatenated along the row dimension and used as the training set. This assembly logic requires the first... In this iteration, the training and validation sets are mutually exclusive in terms of sample elements, and their combination completely covers the entire original dataset. Each sample. The data partitioning module iterates through and executes the complete process. The assembly iteration generates Set up independent training and validation data pairs and store them in the input data pool of the model building module for later use.

[0057] See attached document Figure 4 In a specific embodiment of the present invention, multicollinearity exists among various environmental characteristics (such as seawater temperature and dissolved oxygen concentration, longitude and distance from shore) in marine environmental monitoring scenarios. If such highly correlated data matrices are directly input into a traditional multiple linear regression model, it is easy to cause numerical instability in the matrix inversion process, leading to an increase in the estimated variance of the model regression coefficients and affecting the model stability.

[0058] To improve this situation, the model building module invokes partial least squares regression, which reduces collinearity interference among the original features by constructing an orthogonal latent variable space. This process specifically includes the following steps: S501, the model building module extracts the training set data corresponding to the current cross-validation iteration from the input data pool. The model building module denotes the standard feature matrix in the training set as the initial independent variable matrix. The corresponding smoothed objective variable vector is denoted as the initial dependent variable vector. The training set is configured to contain... There are samples, with a feature dimension of . .in, Used to represent the environmental feature dimension input into the partial least squares regression model after feature filtering.

[0059] S502, the model building module performs iterative initialization for latent variable extraction. The index of the currently extracted latent variable is set to... Its value starts from 1 and increases sequentially. In the th... During this extraction process, the model building module is based on the independent variable residual matrix updated in the previous round. With the residual matrix of the dependent variable Calculate the corresponding feature weight vector Those skilled in the art should understand that the calculation of this feature weight vector aims to extract the maximum variance information within the residual matrix of the independent variables while maintaining a high covariance with the residual matrix of the dependent variable. The model building module extracts the first... The score vector of each latent variable Its mathematical formula is: ; In the formula, Indicates the first The score vector of each latent variable; Indicates the first The residual matrix of independent variables before the extraction, when This matrix is ​​then the initial independent variable matrix. ; Indicates the first The corresponding feature weight vector is extracted in this step, which is derived from the residual matrix of the independent variables updated in the previous round. With the residual matrix of the dependent variable Obtained through calculation.

[0060] In S503, the model building module performs orthogonalization information stripping and residual matrix update calculations. To maintain orthogonality among the latent variables and reduce multicollinearity interference, the model building module calculates the independent variable residual matrix within the current latent variable score vector. regression loading vector on Subsequently, the model building module extracts the variance information explained by the latent variable from the current residual matrix of the independent variable, generating a new residual matrix for use in the next iteration. The mathematical formula for this information extraction is as follows: ; In the formula, This represents the residual matrix of independent variables after the update, which will be used for the next latent variable extraction. Represents the regression loading vector; This indicates that a matrix transpose operation is performed on the load vector. Using the same information stripping logic, the model building module calculates the load vector corresponding to the dependent variable and updates the dependent variable residual matrix synchronously. .

[0061] S504, The model building module determines whether the set total number of latent variables extracted has been reached. Total number of latent variables extracted The value of is limited by the environmental feature dimension input into the partial least squares regression model after feature filtering. and the number of training samples ,satisfy The specific value is pre-selected by calculating the sum of squared cross-validation prediction residuals (PRESS) for different numbers of candidate latent variables. Specifically, the model building module sets the number of candidate latent variables to 1 to... Construct corresponding partial least squares regression models and calculate the sum of squared cross-validation predicted residuals (PRESS) corresponding to the number of candidate latent variables. The number of latent variables corresponding to the minimum PRESS is denoted as... Alternatively, based on the one-standard-error rule, select the smaller number of latent variables and denote it as... And extract the total number of the finally selected latent variables. Set as or To balance model accuracy and model complexity.

[0062] During the latent variable extraction iteration process Indicates the index for extracting the current latent variable. It is a positive integer, ranging from 1 to... ;No. The second latent variable extraction corresponds to the generation of the first One latent variable. When determining At that time, the model building module will Increment by 1, and return to step S502 to extract the next latent variable; when the determination... At this point, the model building module terminates its iteration. After the above iterative operations, the model building module will exhibit collinearity. 3D environment feature matrix mapping transformed into by The low-dimensional information space consists of mutually orthogonal latent variables, and the output is a set of extracted results containing the score vectors of all latent variables, feature weight vectors, and loading vectors.

[0063] In a specific embodiment of the present invention, after completing the orthogonal extraction of the latent variable space, the model building module maps the loadings of the low-dimensional information space back to the original environmental feature dimension, generating a regression equation. Subsequently, the model building module performs numerical calculations and inverse physical state transformations on the validation set, outputting the abundance prediction results. This process specifically includes the following steps: S505, the model building module, based on the latent variable extraction result set output from the preceding steps, calculates and generates a regression coefficient vector of standard feature dimensions. Those skilled in the art should understand that by combining the feature weight vectors of the latent variables with the loading matrix through matrix operations, the partial least squares latent variable space can be transformed into a linear regression equation form. The model building module, combined with the weight data corresponding to the target dependent variable, calculates the regression coefficient vector of the standardized input space with dimension [missing value]. The regression coefficient vector is denoted as... The regression coefficient vector reflects the mapping weights of each environmental feature to the target variable after reducing collinearity interference.

[0064] S506, The model building module extracts the current iteration index from the cross-validation data pool. The corresponding validation set data. This validation set is configured to include... The model building module denotes the standard feature matrix in the validation set as: [samples]. The feature matrix and the regression coefficient vector Perform matrix multiplication to calculate the standardized prediction vector of the target variable, denoted as . The mathematical formula for this computational logic is: ; In the formula, This represents the column vector of predicted numerical values ​​of the validation set in the normalized space. The standard feature matrix of the validation set has 10 rows. The number of columns is ; For dimension is The regression coefficient column vector.

[0065] S507, the model building module performs multiple physical state inverse transformations on the calculated standardized prediction values. The model building module extracts the log-smoothed mean of the target variable calculated and stored from the training set in the current cross-validation iteration. with standard deviation For the prediction vector The first in Each prediction element The model building module sequentially performs inverse standardization and natural index translation transformation operations to obtain abundance prediction results that restore the physical dimensions. In this process, inverse standardization is used to restore the standardized predictions to the logarithmic smoothed space, and inverse exponential transformation is used to restore the predictions in the logarithmic smoothed space to the original microplastic abundance dimensions. The mathematical formula for its inverse transformation is as follows: ; In the formula, This represents the predicted microplastic abundance value after restoring the original distribution pattern. Represented by natural constant An exponential function with base 0; The value of the validation set sample index ranges from 1 to 1. Regarding the prediction results caused by model calculation errors. For out-of-bounds values ​​less than 0, the model building module corrects them to 0 to meet the non-negative boundary conditions of microplastic abundance data in environmental monitoring scenarios and eliminates the data dead zone in program execution.

[0066] S508, The model building module has completed the current step. After predicting the validation set, determine the iteration index. Has the number of folds in the cross-validation configuration parameters been reached? When judged When the model building module increments the iteration index by 1, it enters the next cross-validation iteration, recalculates the regression coefficients based on the new training set, and predicts the corresponding validation set; when the decision is made... At this point, the model building module ends its iteration loop. The model building module concatenates and aligns the true microplastic abundance values ​​of all samples collected during the cross-validation process with the corresponding predicted abundance values, outputs the model prediction control dataset, and transmits it to the performance evaluation stage.

[0067] The performance evaluation stage is based on the microplastic abundance prediction values ​​after inverse standardization, inverse exponential transformation and nonnegative constraints. At least one of the following evaluation indicators is calculated: root mean square error, mean absolute error and coefficient of determination, to evaluate the model's prediction accuracy and generalization performance.

[0068] See attached document Figure 5 In a specific embodiment of the present invention, the predicted values ​​output by the partial least squares regression model are within a transformation space that has been standardized and logarithmically smoothed. Those skilled in the art should understand that model error evaluation metrics are sensitive to data dimensions; directly using numerical values ​​within the transformation space to calculate errors makes it difficult to reflect the true deviation of microplastic abundance. To ensure that model evaluation has a consistent comparative basis, the distribution estimation module performs inverse transformation and physical boundary constraint processing on the preliminary predicted data. This process specifically includes the following steps: S601, the distribution estimation module receives the model prediction control dataset output from the preceding process. This dataset is set to contain preliminary predicted values ​​for all samples. For each sample's standardized predicted value, the distribution estimation module retrieves the target variable's arithmetic mean and standard deviation parameters saved during the data preprocessing stage. The distribution estimation module multiplies the standardized predicted value by the standard deviation and adds the arithmetic mean, performing an inverse standardization operation to generate transitional predicted values ​​in logarithmic space.

[0069] S602, the distribution estimation module performs an inverse exponential transformation operation on the destandardized transitional prediction values. Since a natural logarithmic smoothing transformation with a constant of 1 was applied to the original microplastic abundance data during the data preprocessing stage, to maintain the symmetry of the algorithm's mapping logic, the distribution estimation module uses the natural constant as the base and the calculated transitional prediction values ​​as the exponent to perform a power operation. Then, the result of the power operation is subtracted from the constant 1 to calculate the preliminary microplastic abundance prediction values ​​that restore the physical dimensions.

[0070] In step S603, the distribution estimation module performs a physical non-negativity constraint check on the restored preliminary microplastic abundance prediction values. Due to the interference of regression model fitting errors, some samples may have calculated values ​​less than 0 after inverse exponential transformation. Microplastic abundance is an objective physical measurement, and its true physical state possesses a non-negativity property. To correct for data out-of-bounds errors caused by calculation errors, the distribution estimation module screens the entire prediction data. When the preliminary microplastic abundance prediction value of a sample is determined to be less than 0, the distribution estimation module directly assigns the prediction result to 0; when the prediction value is determined to be greater than or equal to 0, the distribution estimation module retains the original calculated value. After this non-negativity constraint processing, the distribution estimation module outputs a final predicted microplastic abundance dataset that conforms to the actual physical monitoring patterns, and uses it as the benchmark input data for calculating various performance evaluation indicators.

[0071] In a specific embodiment of the present invention, the microplastic abundance data, predicted and processed using a regression model with non-negative constraints, is represented as discrete data points in geographic space. To characterize the continuous spatial distribution features of microplastics within the target sea area, the distribution estimation module performs spatial interpolation calculations and layer rendering based on the predicted data from discrete stations, converting the discrete data into a planar spatial distribution map. This process specifically includes the following steps: S604, the distribution estimation module extracts the geographic coordinates and corresponding abundance values ​​of each monitoring station from the predicted microplastic abundance dataset output by the previous steps, and constructs a spatial discrete dataset. The distribution estimation module obtains the latitude and longitude boundary range of the target sea area, and divides the sea area into a two-dimensional spatial matrix composed of multiple rectangular grids according to the preset spatial resolution parameters.

[0072] The distribution estimation module extracts the geographic coordinates of the center points of each grid in the two-dimensional spatial matrix and defines them as target spatial points to be extrapolated. For each target spatial point, the distribution estimation module simultaneously extracts multi-source marine environmental parameters of the same origin and type as those in the training phase, and preprocesses them according to the feature transformation parameters, retained feature list, and standardized parameters saved in the training phase to form a standardized input feature vector for the target spatial point. The distribution estimation module inputs this standardized input feature vector into the trained partial least squares regression model to obtain the predicted microplastic abundance value for the target spatial point.

[0073] S605, the distribution estimation module prioritizes calculating the predicted microplastic abundance values ​​for each target spatial point based on the multi-source marine environmental parameters corresponding to the target spatial point and the trained partial least squares regression model. When some environmental parameters are missing for a target spatial point, or when it is necessary to smoothly display the prediction results of discrete monitoring stations in a continuous layer, the distribution estimation module calls a spatial interpolation algorithm to calculate the extrapolated microplastic abundance values ​​for each target spatial point. Those skilled in the art should understand that the influence weight of closer monitoring stations on the target spatial point is greater than that of more distant stations.

[0074] Regarding the first The distribution estimation module calculates the relationship between the target spatial point and the i-th target spatial point in the spatial discrete dataset. Spatial distance between known monitoring stations Spatial distances can be calculated using planar Euclidean distance in a projected coordinate system or spherical distance based on latitude and longitude coordinates. When mapping at a regional scale, latitude and longitude coordinates should be converted to a unified projected coordinate system before calculating distances to ensure consistency in spatial distance dimensions.

[0075] To avoid division errors (where the denominator is zero) that occur during program execution due to the target spatial point coinciding with the coordinates of known monitoring stations, the distribution estimation module introduces a zero-division-prevention constant in the distance calculation logic. The distribution estimation module calculates the first... The known monitoring stations for the first Spatial influence weight of each target spatial point Its mathematical formula is: ; In the formula, Indicates the first The target spatial point and the first Spatial distance between known monitoring stations; To prevent division by zero, its value is set to a constant of 10. -6 This is to ensure the stability of the program's numerical calculations; The distance decay index reflects the rate at which spatial correlation decreases with distance; in practical engineering, the value is set to 2.

[0076] After calculating the spatial influence weights corresponding to all known monitoring stations, the distribution estimation module calculates the first value by weighted normalization summation. Microplastic abundance at each target spatial point Its mathematical formula is: ; In the formula, Indicates the first Microplastic abundance at a target spatial point; This represents the total number of known monitoring stations; The index of the known monitoring station, with a value ranging from 1 to... ; Indicates the first Predicted microplastic abundance values ​​for 1 known monitoring site; The spatial influence weights of the output are calculated for the preceding formula.

[0077] S606, the distribution estimation module iterates through and performs numerical calculations to generate a continuous abundance projection set covering the two-dimensional spatial matrix, and then performs layer rendering operations. The distribution estimation module establishes a dictionary mapping the microplastic abundance numerical ranges to color channel gradients.

[0078] The distribution estimation module assigns corresponding color fill values ​​to each grid in the two-dimensional spatial matrix based on the mapping dictionary, generating a color rendering layer. The module then calls a geographic information system interface to align the coordinate system of this color rendering layer with the geographic base map of the target sea area and overlays and merges them, outputting a spatial distribution map of microplastic abundance in the target sea area.

[0079] Specific application examples: In a specific application scenario of this invention, a microplastic pollution distribution prediction system is deployed to assess the spatial state of microplastic abundance in a target nearshore bay. During operation, the system receives and cleans measured microplastic abundance data from 120 discrete monitoring stations within the sea area, along with corresponding multi-source environmental parameters such as hydrodynamics and biochemical nutrients. After adaptive logarithmic smoothing and skewness elimination are performed by the distribution transformation module, and redundant variables are removed by the variable selection module, the system retains eight core environmental features, including seawater temperature, salinity, and ocean current velocity, to construct a standard matrix.

[0080] Subsequently, the partial least squares regression model extracts orthogonal latent variables and derives regression coefficients under a cross-validation mechanism, outputting preliminary predicted values. Finally, the distribution estimation module, combined with a spatial interpolation algorithm constrained by dead zone prevention, transforms the discrete prediction results into a continuous areal distribution map of the entire sea area, generating a microplastic spatial pollution gradient reflecting the true physical dimensions, providing objective data support for marine environmental governance.

[0081] In the spatial mapping derivation stage of the above specific embodiment, in order to extend the predicted station data in the validation set to the unsampled grid area, the distribution estimation module performs numerical interpolation calculations based on the distance decay law.

[0082] See attached document Figure 6 In this legend, the horizontal axis represents the spatial distance between the known monitoring station and the target spatial point. The unit is kilometers; the vertical axis represents the spatial influence weight of the calculated output. The nonlinear decreasing curve in the figure objectively maps the physical process of spatial correlation decay. Assuming a local grid simulation, it is known that there are two monitoring stations in the surrounding area (i.e., the total number of stations). The system extracts preset parameters and removes zero constants. 10 -6 Distance decay index The distribution estimation module calls the formula. The computational space influence weights correspond to Figure 6 Two coordinate mapping points on the curve: Distance to the first known station The distance is 2.0 kilometers, and its corresponding weight is... The distance to the second known station The distance is 4.0 kilometers, and its corresponding weight is... .

[0083] If the abundance is predicted at the first site 15.0 units / m 3 The second site predicts abundance. 5.0 units / m 3 The module calls the weighted normalized summation formula. Perform calculations to accurately determine the estimated abundance of microplastics at the target spatial point. 13.0 units / m 3 By traversing all target grids and repeating the above matrix and scalar calculations, the system completed the closed-loop generation of continuous microplastic abundance values ​​within the region.

[0084] To verify the effectiveness of the present invention's implementation scheme in addressing the problems of skewed distribution and multicollinearity in marine data, this embodiment sets up a comparative verification scheme based on the same sample data, using the root mean square error (RMSE) as the core evaluation index. This embodiment constructs three parallel control groups, with the baseline input being multi-source data from the aforementioned 120 stations: Control group 1 used a traditional multiple linear regression model without distribution transformation, control group 2 used a random forest nonlinear model, and the experimental group used the complete link model of this invention. (See appendix) Figure 8 In the legend, light gray bars represent the traditional linear group, medium gray bars represent the random forest group, and dark gray bars represent the model group of this invention. Test results are as follows... Figure 8 As shown: Due to the long-tailed distribution and internal collinearity of marine environmental data, the RMSE of the traditional linear group is as high as 5.68, indicating divergence error; the RMSE of the random forest group is 3.10; while the experimental group of this invention successfully suppressed the weight interference of extreme outliers and eliminated collinearity by using logarithmic smoothing mapping dimensionality reduction and physical inverse transformation. Its validation set RMSE was reduced to 2.15, showing a significant objective technical advantage in generalization prediction accuracy.

[0085] Furthermore, for the evaluation of the fitting ability of long-tailed extreme value data, refer to the appendix. Figure 7 This figure extracts and displays the abundance prediction trends of 20 consecutive samples in the validation set. In the legend, the solid black line with filled dots represents the measured microplastic abundance curve, the dashed line with hollow squares represents the predicted smooth curve of this invention, and the dotted-dash line with hollow triangles represents the traditional linear prediction curve. Observation Figure 7 The fluctuation pattern of the smooth curve shows that the dashed line representing the experimental group of the present invention closely follows the solid line of the measured value at each sample node. Especially in the right-skewed high abundance peak intervals of sample numbers 6 to 8 and 15 to 16, the model of the present invention still maintains a high degree of approximation and overlap. In contrast, the dashed line representing the traditional control group showed a significant downward deviation in the high abundance peak region. This comparative result fully demonstrates that, after undergoing adaptive distribution transformation and orthogonal latent variable extraction, the present invention compensates for the lack of fitting ability of conventional algorithms to long-tailed extreme value data, and improves the robustness and accuracy of the pollution prediction system in complex marine environmental scenarios.

Claims

1. A machine learning-based method for predicting the distribution of microplastic pollution in seawater, characterized in that, Includes the following steps: Acquire environmental characteristic data and microplastic measurement data, and remove samples with missing values ​​to construct a training dataset; The environmental feature data in the training dataset is subjected to skewness test, and the environmental feature data with skewness exceeding the preset threshold is subjected to adaptive log smoothing transformation; The significance test results between the environmental feature data after the skewness test and transformation processing and the measured microplastic data are calculated, and the core features are selected to generate a standard feature matrix; The microplastic measured data are smoothed and standardized to generate a standard target variable vector. The standard dataset, which is formed by merging the standard feature matrix and the standard target variable vector, is divided into a training set and a validation set. A microplastic abundance prediction model is constructed based on the training set using the partial least squares regression algorithm. The standard feature matrix in the validation set is then input into the microplastic abundance prediction model to generate abundance prediction results. The abundance prediction results are subjected to inverse standardization, inverse exponential transformation and nonnegative constraint processing, and combined with spatial interpolation algorithm to output a spatial distribution map of microplastic abundance.

2. The method for predicting the distribution of seawater microplastic pollution based on machine learning according to claim 1, characterized in that, The steps of acquiring environmental feature data and microplastic measurement data, and removing missing value samples to construct a training dataset specifically include: Simultaneously acquire multi-source marine environmental parameters of the target sea area as the environmental characteristic data. The multi-source marine environmental parameters consist of longitude, latitude, sea temperature, sea salinity, sea surface wind speed, sea level air pressure, precipitation, dissolved oxygen, nitrate concentration, phosphate concentration, ocean current velocity, traffic density, and water depth. Based on the spatial coordinates of each sampling location, the environmental feature data and the measured microplastic data are correlated and matched, data samples containing null values ​​are removed, and the training dataset is generated by combining them.

3. The method for predicting the distribution of seawater microplastic pollution based on machine learning according to claim 1, characterized in that, The step of performing adaptive logarithmic smoothing transformation on environmental feature data with skewness exceeding a preset threshold specifically includes: Extract the minimum value of environmental feature data whose skewness exceeds a preset threshold across all samples; When the minimum value is determined to be less than zero, a logarithmic shift transformation is performed on environmental feature data whose skewness exceeds a preset threshold. When the minimum value is determined to be greater than or equal to zero, a standard logarithmic transformation is performed on environmental feature data whose skewness exceeds a preset threshold.

4. The method for predicting the distribution of seawater microplastic pollution based on machine learning according to claim 3, characterized in that, The steps of calculating the significance test results between the environmental feature data after the skewness test and transformation processing and the measured microplastic data, and selecting core features to generate a standard feature matrix, specifically include: The environmental characteristic data after the skewness test and transformation process and the microplastic measured data are respectively converted into rank sequences, and the Spearman correlation coefficient is calculated. Construct a test statistic, call the cumulative probability function to obtain the probability value of the test statistic under the two-tailed test condition, and use the probability value as the significance test result; When the probability value is determined to be less than the confidence threshold, the associated environmental features are retained as the core features, and zero-mean standardization is performed on the core features to generate the standard feature matrix.

5. The method for predicting the distribution of seawater microplastic pollution based on machine learning according to claim 1, characterized in that, The steps for performing smoothing and standardization on the measured microplastic data to generate a standard target variable vector specifically include: After adding a constant 1 to the measured data of the microplastics, a natural logarithm operation is performed to generate a smooth target variable vector; Extract the training set and calculate the mean and standard deviation of the smoothed target variable vector; Using the mean and the standard deviation, perform zero-mean standardization on the smoothed target variable vector to generate the standard target variable vector.

6. The method for predicting the distribution of seawater microplastic pollution based on machine learning according to claim 1, characterized in that, The step of dividing the standard dataset, which is composed of the standard feature matrix and the standard target variable vector, into a training set and a validation set specifically includes: While maintaining the correlation between the internal features of a single sample and the target, a random row shuffling operation is performed on the standard dataset; The integer quotient of dividing the total number of samples by the fold is used as the base sample size, and the remainder after division is used as the number of subsets that need to be expanded. Set the number of data subset samples corresponding to the number of subsets that need to be expanded to the base sample size plus one, and set the number of remaining data subset samples to the base sample size to divide the data into multiple sets of data subsets. During the cross-validation iteration process, a subset of the data is extracted as the validation set, and all remaining subsets of the data are concatenated and combined to form the training set.

7. The method for predicting the distribution of seawater microplastic pollution based on machine learning according to claim 1, characterized in that, The steps of constructing a microplastic abundance prediction model based on the training set using the partial least squares regression algorithm specifically include: Set the standard feature matrix in the training set as the initial independent variable matrix, and set the smoothed target variable vector corresponding to the training set as the initial dependent variable vector; In the feature extraction cycle, a feature weight vector is calculated based on the independent variable residual matrix and dependent variable residual matrix output from the previous cycle, and a latent variable score vector is extracted based on the feature weight vector. Calculate the regression loading vector of the independent variable residual matrix in the dimension of the latent variable score vector; The orthogonalized variance information corresponding to the regression loading vector is extracted from the independent variable residual matrix to generate a new independent variable residual matrix for the next period. The dependent variable residual matrix is ​​updated synchronously. After reaching the preset number of latent variable extractions, the microplastic abundance prediction model is generated.

8. The method for predicting the distribution of seawater microplastic pollution based on machine learning according to claim 7, characterized in that, The steps of inputting the standard feature matrix from the validation set into the microplastic abundance prediction model to generate abundance prediction results specifically include: Extract all the feature weight vectors and regression loading vectors contained in the microplastic abundance prediction model, and perform matrix operations on all the feature weight vectors and regression loading vectors to generate a regression coefficient column vector; The abundance prediction result is generated by performing matrix multiplication between the standard feature matrix in the validation set and the regression coefficient column vector.

9. A method for predicting the distribution of microplastic pollution in seawater based on machine learning according to claim 5, characterized in that, The steps of performing inverse standardization, inverse exponential transformation, and nonnegativity constraint processing on the abundance prediction results specifically include: The abundance prediction result is multiplied by the standard deviation and then added to the mean to generate a transitional prediction value. The natural constant is set as the base, the transition prediction value is set as the exponent and a power operation is performed. After subtracting the constant one, a preliminary microplastic abundance prediction value is generated. When the preliminary microplastic abundance prediction value is determined to be less than zero, the preliminary microplastic abundance prediction value is forcibly assigned to zero, and the predicted microplastic abundance value is output.

10. A method for predicting the distribution of seawater microplastic pollution based on machine learning according to claim 8, characterized in that, The specific steps for outputting the spatial distribution map of microplastic abundance using the spatial interpolation algorithm include: The target sea area is divided into a two-dimensional spatial grid, and the center point of each grid in the two-dimensional spatial grid is extracted as the target spatial point; Calculate the spatial distance between the specified target point and each sampling location; After adding the zero constant to the spatial distance, the spatial influence weight is generated by combining it with the distance decay index. Based on the spatial influence weights and the predicted microplastic abundance values ​​corresponding to each sampling location, a weighted normalization summation operation is performed to generate the microplastic inference abundance of the specified target spatial point. The microplastic abundance of all target spatial points is mapped to a color rendering layer, and the color rendering layer is aligned and merged with the geographic base map of the target sea area to generate a spatial distribution map of the microplastic abundance.

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