Rainwater runoff microplastic removal rate prediction method and system based on physical constraint mixed ann

Abstract

This invention discloses a method and system for predicting microplastic removal rates in rainwater runoff based on a physically constrained hybrid neural network (ANN). The prediction method includes: acquiring an experimental sample set of microplastic removal by a microplastic adsorbent and preprocessing the sample set; constructing a hybrid neural network prediction model and training it using the preprocessed sample set; inputting the parameters to be predicted into the trained hybrid neural network prediction model to output the corresponding predicted microplastic removal rate, which can be used for process condition optimization and material application evaluation. This invention offers high prediction accuracy and strong generalization, accurately describing nonlinear adsorption behavior under multi-factor coupling. It is suitable for rapid prediction, parameter optimization, and engineering control of microplastic adsorption processes in complex water bodies such as rainwater runoff and surface water, and has promising application prospects.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of environmental functional materials, stormwater runoff pollution control, and artificial intelligence modeling. More specifically, it relates to a method and system for predicting the removal rate of microplastics in stormwater runoff based on physically constrained hybrid ANNs. Background Technology

[0002] With the rapid increase in plastic production, microplastic pollution (plastic particles or fragments with a diameter of less than 5 mm) has become a major environmental problem of global concern. It has been reported that sources of microplastics in the aquatic environment include wastewater treatment plants, atmospheric deposition, agricultural activities, and urban stormwater runoff. Urban stormwater runoff has been identified as the primary source of microplastics, with concentrations up to six times higher than those in wastewater treatment plant effluents. Studies show that Gumi City in South Korea receives approximately 287 billion microplastic particles annually through stormwater runoff, far exceeding the contribution from wastewater treatment plants; in the Valno estuary region of Germany and the Baltic Sea basin, stormwater systems contribute over 40% and 60% of microplastics, respectively; and the main source of MPs pollution in Lake Geneva, Switzerland, is stormwater runoff, with an annual load of approximately 8.9 tons. Microplastics (MPs) have been detected in stormwater runoff in Sweden, Mexico, Australia, and several Chinese cities, including Beijing, Wuhan, and Hong Kong. Global MP concentrations range from 0.38 to 197,000 particles per L, with polyethylene (PE), polypropylene (PP), and polyethylene terephthalate (PET) being the most common types. These findings indicate that urban stormwater runoff is the primary pathway for microplastics to enter water bodies, making the prevention of microplastic migration from urban stormwater runoff to water bodies an urgent problem to be solved.

[0003] Metal-organic frameworks (MOFs) are framework structures formed by the coordination of metal ions and organic linkers. In recent years, MOF materials have developed rapidly, and in 2025, the Nobel Prize in Chemistry was awarded for their pioneering contributions to porous structure design and functional materialization, further promoting the exploration of MOF applications in the environmental field. Due to their ultra-high specific surface area, tunable pore structure, and abundant chemical functional sites, MOFs have shown great potential in microplastic removal, providing new ideas for the development of highly efficient adsorption materials. However, MOF materials, due to their powdery form, are difficult to recover and separate, fragile, and sensitive to moisture and acids, making them unstable in aqueous media, which limits their practical applications. To address these issues, the availability of MOFs can be improved by loading them onto stable supports, and their water stability can be enhanced through special wettability modifications. Quartz sand is an inexpensive natural filter media, favored for its wide availability, high mechanical strength, and ease of modification. It can not only serve as a support for MOFs, but its roughness and wettability can also be modified to improve the adsorption of microplastics. The successfully constructed superhydrophobic quartz sand can be used not only as an adsorbent in the laboratory, but also as a filler in green facilities such as constructed wetlands, bioretention facilities, and rain gardens to enhance the removal of microplastics from rainwater runoff.

[0004] The adsorption process of this type of adsorbent for microplastics has the following unique characteristics: (1) Adsorption characteristics of multilayer aggregation: In the low concentration range, microplastics mainly undergo monolayer adsorption with the adsorbent surface through hydrophobic interactions and van der Waals forces, which can be described by the classical Langmuir isotherm; however, in the high concentration range, the adsorbed microplastic particles act as secondary adsorption sites, and multilayer stacking adsorption is triggered by the hydrophobic aggregation effect. The classical isotherm model cannot capture this behavior, resulting in significant deviations in model prediction.

[0005] (2) Nonlinearity of multi-factor coupling: The microplastic removal efficiency is affected by the interaction of multiple factors such as adsorbent dosage, initial concentration of microplastics, solution pH, contact time, and temperature, which are difficult to accurately characterize using traditional empirical formulas and linear regression methods.

[0006] In existing technologies, artificial neural networks (ANNs) have been applied to prediction and optimization in the field of water treatment. For example, ANNs have been used to predict the microplastic removal performance (R²) of coagulants. 2The efficiency of MOF adsorption of heavy metals can reach 0.99. The BP artificial neural network has also been used to predict the efficiency of MOF adsorption of heavy metals. The Sparrow Search Algorithm (SSA), as a swarm intelligence optimization algorithm, has been used to optimize the initial weights and biases of the BP neural network to overcome the problem that the conventional BP network is prone to getting trapped in local optima. However, the above-mentioned existing technologies have the following fundamental defects: (1) Pure data-driven models lack physical constraints: Existing ANN models rely entirely on data fitting and do not contain any physical laws of the adsorption process. They may produce prediction results that violate thermodynamic laws (such as negative adsorption amount, ΔG of spontaneous adsorption being positive when the temperature rises, etc.), and have poor generalization ability in the sparse training data range. (2) The network architecture is not designed for the special mechanism of particulate adsorption: Existing ANNs regard the entire concentration range as a unified adsorption process and cannot distinguish between the two different mechanisms of monolayer adsorption and multilayer aggregation adsorption, resulting in a sharp drop in prediction accuracy in the high concentration range (the region dominated by aggregation adsorption).

[0007] Therefore, there is an urgent need to develop an intelligent prediction method that integrates adsorption physics mechanisms and data-driven approaches, adapts to the multilayer aggregation and adsorption characteristics of particulate microplastics, and possesses uncertainty quantification capabilities and cross-system transfer learning functions. Summary of the Invention

[0008] The purpose of this invention is to overcome the problems of existing pure data-driven models that lack physical constraints, cannot distinguish the hydrophobic aggregation and adsorption behavior of particulate microplastics, lack uncertainty quantification and cross-system migration capabilities. It provides a method and system for predicting the removal rate of microplastics in rainwater runoff based on physically constrained hybrid ANNs, which can achieve high-precision prediction of the removal efficiency of PP, PE and PET microplastics by MOF-based superhydrophobic quartz sand under different operating conditions, and reveal the contribution law of key influencing factors.

[0009] As a first aspect of the present invention, a method for predicting microplastic removal rates in rainwater runoff based on physically constrained hybrid ANNs is provided, comprising the following steps: Step S1: Obtain an experimental sample set of microplastic removal by the microplastic adsorbent, and preprocess the sample set to obtain a preprocessed sample set; wherein the sample set includes input indicators and output indicators, the input indicators include at least the adsorbent dosage, initial concentration of microplastics, pH of the microplastic solution, adsorption time, and adsorption temperature, and the output indicator is the microplastic removal rate; Step S2: Construct a physical constraint hybrid neural network prediction model, and train the physical constraint hybrid neural network prediction model based on the preprocessed experimental sample set to obtain the trained physical constraint hybrid neural network prediction model; Step S3: Input the parameters to be predicted into the trained physical constraint hybrid neural network prediction model for prediction, and output the corresponding microplastic removal rate prediction value for process condition optimization and material application evaluation.

[0010] Furthermore, the input metrics also include microplastic characteristic factors, which include density, average particle size, and water contact angle.

[0011] Further, the preprocessing of the removal experimental sample set to obtain a preprocessed removal experimental sample set includes: The experimental sample set to be removed is subjected to consistency checks, missing value imputation, and outlier identification. The minimum-maximum normalization method was used to scale each index in the experimental sample set to the [0, 1] interval; The normalized sample set for removing samples was divided into a training set, a validation set, and a test set.

[0012] Further, step S1 includes: For the target removal experimental sample set where the initial microplastic concentration is in the high-concentration range after preprocessing, a conditional generative adversarial network (GAN) is used to augment the data of the target removal experimental sample set. Specifically, the generator and discriminator are trained using input metrics from the target removal experimental sample set, enabling the generator to generate a synthetic sample set with a distribution consistent with the target removal experimental sample set. A physical feasibility filter is introduced during the generation process to automatically remove synthetic samples that violate the following physical constraints: Microplastic removal rate η constraint: 0% ≤ η ≤ 100%; Monotonicity constraint: Under otherwise constant conditions, increasing the adsorbent dosage should not lead to a decrease in the microplastic removal rate; Thermodynamic constraints: For spontaneous adsorption processes, the change in Gibbs free energy as the adsorption temperature increases. It should be a negative value.

[0013] Further, prior to step S2, the following steps are included: A mechanism discrimination subnetwork is constructed, which is a shallow fully connected network. The input is a concatenated vector composed of the preprocessed removal experimental sample set, the synthetic sample set, and the microplastic feature factors. The output is the single-layer adsorption mechanism weight coefficients. α And the weighting coefficient of the multilayer aggregation adsorption mechanism 1- α Among them, the weighting coefficient of the monolayer adsorption mechanism α This indicates the dominance of the monolayer adsorption mechanism under the current input conditions; the weighting coefficient for the multilayer aggregation adsorption mechanism is 1- αThis indicates the degree to which the multilayer aggregation and adsorption mechanism dominates under the current input conditions. α ∈ [0, 1].

[0014] Further, step S2 includes: The physical constraint hybrid neural network prediction model includes a physical channel, an aggregation correction channel, a residual compensation channel, and a fusion layer. The physical channel outputs a first microplastic removal rate prediction value based on the training set. The aggregation correction channel can output a second microplastic removal rate prediction value based on the training set. The residual compensation channel can be based on the predicted value of the first microplastic removal rate. and the second predicted value of microplastic removal rate Output the third predicted value of microplastic removal rate The fusion layer can be based on the predicted value of the first microplastic removal rate. The second predicted value of microplastic removal rate The predicted value of the third microplastic removal rate The weighting coefficient of the monolayer adsorption mechanism and the weighting coefficient of the multilayer aggregation adsorption mechanism Calculate the final predicted microplastic removal rate. Wherein, the predicted final microplastic removal rate is... The calculation formula is as follows: ; Among them, when When the value approaches 1, the physical channel dominates the prediction; when When the value approaches 0, the aggregation correction channel dominates the prediction; the residual compensation channel always provides correction. Based on the training set and the final microplastic removal rate prediction output by the fusion layer Constructing a loss function that includes data fitting Quasi-second-order dynamic residual constraints Monotonicity constraint Thermodynamic consistency constraints and boundary constraints Composite loss function The composite loss function is used to train the physical constraint hybrid neural network prediction model to obtain the trained physical constraint hybrid neural network prediction model; wherein, the composite loss function is used to train the physical constraint hybrid neural network prediction model to obtain the trained physical constraint hybrid neural network prediction model. The calculation formula is as follows: ; in, 、 、 、 These are the weight hyperparameters for each constraint.

[0015] Furthermore, it also includes: (1) The Sips isotherm equation is used as the core of the physical channel: ; in, Representing the The adsorption capacity at adsorption equilibrium under each experimental condition. Represents the maximum adsorption capacity. This represents the concentration of microplastics at adsorption equilibrium. This represents the adsorption constant corresponding to the physical channel. A constant representing the heterogeneity of the adsorbent; Then the predicted value of the first microplastic removal rate The calculation formula is as follows: ; in, For the training set, the first Adsorbent dosage under each experimental condition For the training set, the first Initial concentration of microplastics under experimental conditions; (2) The aggregation correction channel is a BP neural network model optimized using the Sparrow Search Algorithm (SSA), specifically: 2.1 A BP neural network model based on a multilayer feedforward neural network was constructed; the input layer was set with 8 neurons, corresponding to: adsorbent dosage, initial concentration of microplastics, pH of microplastic solution, adsorption time, adsorption temperature, density, average particle size and water contact angle; the output layer was set with 1 neuron, corresponding to the microplastic removal rate. 2.2 Set 1 to 3 hidden layers, with 1 to 20 neurons per layer, as the BP neural network model to be optimized; the hidden layers use one or more combinations of the logsig, tansig, or purelin functions, and the output layer uses the purelin function; the minimum root mean square error (RMSE) and the coefficient of determination (R²) are used as the optimization parameters. 2 With the goal of maximizing the number of hidden layers, neurons, and activation functions, different combinations of these parameters are screened to determine the optimal BP neural network model. 2.3 The initial weights and biases of the BP neural network model are encoded using the Sparrow Search Algorithm (SSA), and the optimal initial parameters are searched using a group optimization method to obtain the BP neural network model optimized by the Sparrow Search Algorithm (SSA). 2.4 The BP neural network model optimized by the Sparrow Search Algorithm (SSA) is trained using the training set. The parameters of the BP neural network model optimized by the SSA are adjusted using the validation set to prevent overfitting. The generalization ability of the BP neural network model optimized by the SSA is evaluated using the test set. During the training process of the BP neural network model optimized by the SSA, the predicted value of the second microplastic removal rate can be output. ; (3) The residual compensation channel is a lightweight residual network, and the input is the predicted value of the first microplastic removal rate. The first residual characteristic between the experimental value and the corresponding microplastic removal rate, and the second predicted value of microplastic removal rate. The second residual feature between the experimental value of the corresponding microplastic removal rate is used to capture the unknown interaction effects that the physical channel and the aggregation correction channel failed to characterize; The lightweight residual network has two neurons in its input layer, corresponding to the first and second residual features respectively; six neurons in its hidden layer to prevent overfitting, with ReLU as the activation function; and one neuron in its output layer, corresponding to the predicted value of the third microplastic removal rate. The activation function of the output layer is Linear.

[0016] Furthermore, it also includes: (1) The data fitting loss Predicted final microplastic removal rate Mean square error between the experimental values ​​of microplastic removal rate and the actual value: ; in, N The number of experimental samples removed from the training set. Represents the first in the training set Experimental conditions, For the first Predicted final microplastic removal rate values ​​for each experimental condition For the first Experimental values ​​of microplastic removal rate corresponding to each experimental condition; (2) The quasi-second-order dynamic residual constraint The calculation formula is as follows: ; ; in, M The set of dynamic samples in the training set. For the first dynamic sample set One dynamic sample, The adsorption capacity of the adsorbent for microplastics as a function of time. The function, This represents the adsorption capacity at adsorption equilibrium. for Adsorption capacity at time, The quasi-second-order kinetic rate constant; this quasi-second-order kinetic residual constraint Ensure that the model's time-dimensional predictions conform to the laws of adsorption kinetics; (3) The monotonicity constraint Based on automatic differentiation: ; in, For the training set, the first The amount of adsorbent added corresponding to each experimental condition; this monotonic constraint Ensure that, all other things being equal, increasing the amount of adsorbent added does not lead to a decrease in the predicted final microplastic removal rate; (4) The thermodynamic consistency constraint The calculation formula is as follows: ; in, For the change of Gibbs free energy, R is the gas constant, and T is the absolute temperature; For allocation coefficients; , This represents the adsorption capacity at adsorption equilibrium. This represents the concentration of microplastics at adsorption equilibrium; this thermodynamic consistency constraint Ensure the Gibbs free energy change of the spontaneous adsorption process It is a negative value; (5) The boundary constraints The calculation formula is as follows: ; Among them, the boundary constraint Ensure that the final predicted microplastic removal rate is within the range of [0%, 100%].

[0017] Furthermore, the initial weights and biases of the BP neural network model are encoded using the Sparrow Search Algorithm (SSA), and the optimal initial parameters are searched using a swarm optimization method. This results in a BP neural network model optimized by the SSA algorithm, comprising: First, establish a sparrow population and encode each individual as a set of initial weights and bias parameters for the model to be optimized. The initial position of the population is calculated by formula (1.1): (1.1); in, This is the initial position of the population. , population The lower and upper boundaries of a dimensional variable. It is a random number; Second, the BP neural network model with the smallest root mean square error (RMSE) and coefficient of determination (R²) on the training set is selected. 2 The maximum is a dual optimization objective. A fitness function is constructed, and the discoverers, followers, and vigilants are divided based on the fitness results. Their position updates are calculated by formulas (1.2), (1.3), and (1.4), respectively: (1.2); in, For the first During the nth iteration The first sparrow Dimensional position; For the first During the nth iteration The first sparrow Dimensional position; It is a uniformly random number; This represents the maximum number of iterations. This is a warning value. This is a safety threshold; For the newly added sparrows; Let be a matrix consisting of unit row vectors 1; when Sparrows conduct a global search for food; if Add random items The discoverers roam randomly in search of food according to a normal distribution; (1.3); in, For the first The worst position of the discoverer in the next iteration; For the first The optimal position of the discoverer in the next iteration; For random elements; For the population size of sparrows; when Followers with poor fitness search in the opposite direction to the worst global position; when Then, followers with better fitness will move closer to the optimal discoverer; (1.4); in, For the first The global optimal position at the next iteration; It is a step size control parameter that follows a normal distribution; It is a random number; This represents the current fitness value of the sparrow. This is the worst fitness value globally at present. This is the current globally optimal fitness value; A minimal constant to ensure the denominator is not zero; when The vigilant moves closer to the optimal position globally; when The vigilant is far from the optimal position in the overall situation.

[0018] As a second aspect of the present invention, a rainwater runoff microplastic removal rate prediction system based on physically constrained hybrid ANNs is provided, comprising: The acquisition module is used to acquire an experimental sample set of microplastic removal by microplastic adsorbent and preprocess the removal experimental sample set to obtain a preprocessed removal experimental sample set; wherein, the removal experimental sample set includes input indicators and output indicators, the input indicators include at least the adsorbent dosage, initial concentration of microplastics, pH of microplastic solution, adsorption time and adsorption temperature, and the output indicator is the microplastic removal rate; The training module is used to construct a physical constraint hybrid neural network prediction model and train the physical constraint hybrid neural network prediction model based on the preprocessed experimental sample set to obtain the trained physical constraint hybrid neural network prediction model. The prediction module is used to input the parameters to be predicted into the trained physical constraint hybrid neural network prediction model for prediction, and output the corresponding microplastic removal rate prediction value for process condition optimization and material application evaluation.

[0019] Compared with existing technologies, the present invention provides a method and system for predicting microplastic removal rates in rainwater runoff based on physically constrained hybrid ANNs, which has the following advantages: (1) High prediction accuracy: In view of the shortcomings of pure data-driven models that lack physical constraints and cannot distinguish the dual mechanisms of multilayer hydrophobic aggregation of particulate microplastics, this invention constructs a hybrid architecture of physical constraints + data residual correction. The Sips isotherm model outputs the basic removal rate, and the BP neural network optimized by the sparrow search algorithm learns the nonlinear residuals caused by multilayer aggregation. The dual mechanisms are adaptively fused through the mechanism discrimination sub-network. (2) Applicable to multi-factor coupling system: The present invention uses adsorbent dosage, initial concentration of microplastics, solution pH, contact time and temperature as input variables, which can simultaneously characterize the comprehensive influence of multiple operating conditions and their interaction on microplastic removal rate. It breaks through the defects of the limited applicability of existing empirical formulas or single-factor fitting methods, and is suitable for rapid prediction of removal efficiency and parameter optimization under complex working conditions (such as complex environments such as actual rainwater runoff). (3) Strong interpretability: After introducing SHAP analysis, it can not only give prediction results, but also explain the positive and negative contributions and relative importance of each factor, providing a theoretical basis for the optimization of adsorption process; (4) High engineering application value: This invention can be used for process parameter optimization in microplastic treatment, screening of functional filter media, operation and control of bioretention facilities, and rapid evaluation of the performance of new adsorption materials. It has good engineering application value and promotion prospects. Attached Figure Description

[0020] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the following detailed description to explain the invention, but do not constitute a limitation thereof.

[0021] Figure 1 The flowchart of a method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANN provided by the present invention.

[0022] Figure 2 The diagram shows the structure of the SSA-BP neural network model provided by this invention.

[0023] Figure 3 This is a comparison chart of the root mean square error of the model under the hidden layer activation function.

[0024] Figure 4 The image shows the optimization results of the model under different hidden layer numbers and neuron numbers.

[0025] Figure 5 This is a comparison chart showing the fitting between the predicted and experimental removal rates of polypropylene.

[0026] Figure 6 This is a comparison chart showing the fitted relationship between the predicted and experimental removal rates of polyethylene.

[0027] Figure 7 This is a comparison chart showing the fitted relationship between the predicted and experimental removal rates of polyethylene terephthalate (PET).

[0028] Figure 8 A local dependency analysis graph for ranking variable importance based on SHAP.

[0029] Figure 9 This is a graph showing the importance ranking of global variables based on SHAP. Detailed Implementation

[0030] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a method and system for predicting microplastic removal rates in rainwater runoff based on physically constrained hybrid ANNs proposed according to the present invention. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0031] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of the invention described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0032] This embodiment provides a method for predicting microplastic removal rates in rainwater runoff based on physically constrained hybrid ANNs, such as... Figure 1 As shown, the method for predicting microplastic removal rates in rainwater runoff based on physically constrained hybrid ANNs includes the following steps: Step S1: Obtain an experimental sample set of microplastic removal by the microplastic adsorbent, and preprocess the sample set to obtain a preprocessed sample set; wherein the sample set includes input indicators and output indicators, the input indicators include at least the adsorbent dosage, initial concentration of microplastics, pH of the microplastic solution, adsorption time, and adsorption temperature, and the output indicator is the microplastic removal rate; It should be noted that the microplastic adsorbent is MOF-based superhydrophobic quartz sand. The microplastic is preferably one or more of PP, PE, and PET.

[0033] Preferably, the input indicators further include microplastic characteristic factors, which include density, average particle size, and water contact angle.

[0034] Preferably, the preprocessing of the removal experimental sample set to obtain a preprocessed removal experimental sample set includes: The experimental sample set to be removed is subjected to consistency checks, missing value imputation, and outlier identification. The minimum-maximum normalization method was used to scale each index in the experimental sample set to the [0, 1] interval; The normalized sample set was divided into training, validation and test sets in a ratio of 70%:15%:15%.

[0035] In this embodiment of the invention, a sample set for removal experiments was obtained: MOF-based superhydrophobic quartz sand was used as the microplastic removal material, and polypropylene, polyethylene, and polyethylene terephthalate were used as target pollutants. Batch desorption experiments were conducted focusing on five process variables: adsorbent dosage, initial microplastic concentration, solution pH, adsorption time, and adsorption temperature. The initial microplastic concentration was (20–500 mg / L), adsorbent dosage was (0.1–2.0 g / L), solution pH was (3–11), adsorption time was (0–120 min), and adsorption temperature was (25–45℃). ， Simultaneously, physical characteristic parameters of three types of microplastics were recorded; the output variable was the microplastic removal rate (%), and three types of microplastic datasets were established. All experiments were conducted in a constant-temperature shaker at 150 rpm with a reaction volume of 20 mL. After the reaction, the mixture was passed through a 100 μm sieve, and the fluorescence intensity of the supernatant was measured using a fluorescence spectrophotometer to calculate the microplastic concentration and removal rate. Each experiment was performed in triplicate with a blank control. After removing outliers, 180 valid datasets were constructed for each of PP, PE, and PET, for a total of 540 datasets.

[0036] In this embodiment of the invention, data preprocessing and sample partitioning are performed as follows: First, the original data undergoes a consistency check to remove duplicate records, and missing items and obvious outliers are verified. For data obtained from repeated experiments, the average or median value can be used as the representative value for that working condition to reduce the impact of random fluctuations on the modeling results. Subsequently, the min-max normalization method is used to perform dimensionless processing on the input and output variables. After normalization, each variable is mapped to the interval between 0 and 1, which can reduce the interference of different dimensions and orders of magnitude differences on neural network training. After normalization, the sample data is divided into a training set, a validation set, and a test set in a ratio of 70%:15%:15%. The training set is used for model parameter learning, the validation set is used to adjust the network structure and suppress overfitting, and the test set is used to evaluate the model's generalization ability and final prediction accuracy.

[0037] Preferably, step S1 includes: For the target removal experimental sample set with an initial microplastic concentration in the high concentration range (greater than 250 mg / L) after preprocessing, a Conditional Generative Adversarial Network (CGAN) is used to augment the data of the target removal experimental sample set to address the problem of data sparsity in the high concentration range. Specifically, the generator and discriminator are trained using the input indicators from the target removal experimental sample set, enabling the generator to generate a synthetic sample set with a distribution consistent with the target removal experimental sample set. A physical feasibility filter is introduced during the generation process to automatically remove synthetic samples that violate the following physical constraints: Microplastic removal rate η constraint: 0% ≤ η ≤ 100%; Monotonicity constraint: Under otherwise constant conditions, increasing the adsorbent dosage should not lead to a decrease in the microplastic removal rate; Thermodynamic constraints: For spontaneous adsorption processes, the change in Gibbs free energy as the adsorption temperature increases. It should be a negative value.

[0038] Preferably, before step S2, the following steps are included: A mechanism gate network (MGN) is constructed, which is a shallow fully connected network. The input is a concatenated vector composed of the preprocessed removal experimental sample set, the synthetic sample set, and the microplastic feature factors. The output is the single-layer adsorption mechanism weight coefficients. α And the weighting coefficient of the multilayer aggregation adsorption mechanism 1- α Among them, the weighting coefficient of the monolayer adsorption mechanism α This indicates the dominance of the monolayer adsorption mechanism under the current input conditions; the weighting coefficient for the multilayer aggregation adsorption mechanism is 1- α This indicates the degree to which the multilayer aggregation and adsorption mechanism dominates under the current input conditions. α ∈[0, 1].

[0039] It should be noted that, based on the deviation analysis of the adsorption isotherms in the experimental data, the critical conversion concentration between monolayer adsorption and multilayer aggregate adsorption is determined; the critical conversion concentration is defined as the equilibrium concentration corresponding to the first time the fitting residual of the classical Sips isotherm model exceeds a preset threshold.

[0040] Step S2: Construct a physical constraint hybrid neural network prediction model, and train the physical constraint hybrid neural network prediction model based on the preprocessed experimental sample set to obtain the trained physical constraint hybrid neural network prediction model; Preferably, step S2 includes: The physical constraint hybrid neural network prediction model includes a physical channel, an aggregation correction channel, a residual compensation channel, and a fusion layer. The physical channel outputs a first microplastic removal rate prediction value based on the training set. The aggregation correction channel can output a second microplastic removal rate prediction value based on the training set. The residual compensation channel can be based on the predicted value of the first microplastic removal rate. and the second predicted value of microplastic removal rate Output the third predicted value of microplastic removal rate The fusion layer can be based on the predicted value of the first microplastic removal rate. The second predicted value of microplastic removal rate The predicted value of the third microplastic removal rate The weighting coefficient of the monolayer adsorption mechanism and the weighting coefficient of the multilayer aggregation adsorption mechanism Calculate the final predicted microplastic removal rate. Wherein, the predicted final microplastic removal rate is... The calculation formula is as follows: ; Among them, when When the concentration approaches 1 (low concentration range), the physical channel dominates the prediction; when When the concentration approaches 0 (high concentration range), the aggregation correction channel dominates the prediction; the residual compensation channel always provides correction. Based on the training set and the final microplastic removal rate prediction output by the fusion layer Constructing a loss function that includes data fitting Quasi-second-order dynamic residual constraints Monotonicity constraint Thermodynamic consistency constraints and boundary constraints Composite loss function The composite loss function is used to train the physical constraint hybrid neural network prediction model to obtain the trained physical constraint hybrid neural network prediction model; wherein, the composite loss function is used to train the physical constraint hybrid neural network prediction model to obtain the trained physical constraint hybrid neural network prediction model. The calculation formula is as follows: ; in, 、 、 、 These are the weight hyperparameters for each constraint, which are automatically adjusted based on the performance of the validation set. For example, =0.2, =0.3, =0.25, =0.25.

[0041] In this embodiment of the invention, the physical channel uses a parameter generation network to dynamically generate Sips isotherm equation parameters, enabling adaptive operation of the physical channel parameters; the aggregation correction channel uses a BP neural network model optimized by the sparrow search algorithm to predict the additional adsorption amount caused by multi-layer aggregation effect; and the residual compensation channel uses a lightweight fully connected network to capture unknown interaction effects.

[0042] Specifically, it also includes: (1) The Sips isotherm equation is used as the core of the physical channel: ; in, Representing the The adsorption capacity at adsorption equilibrium under each experimental condition. Represents the maximum adsorption capacity. This represents the concentration of microplastics at adsorption equilibrium. This represents the adsorption constant corresponding to the physical channel. A constant representing the heterogeneity of the adsorbent; Then the predicted value of the first microplastic removal rate The calculation formula is as follows: ; in, For the training set, the first Adsorbent dosage under each experimental condition For the training set, the first Initial concentration of microplastics under experimental conditions; It should be noted that the parameters of the Sips isotherm equation... , , Instead of using fixed values, a parameter generation network dynamically generates parameters based on the current pH of the microplastic solution and the adsorption temperature T, allowing the physical channel parameters to adapt to changes in environmental conditions. The parameter generation network (PGN) is a two-layer fully connected network with inputs of [pH, T] and outputs of […]. , , ].

[0043] (2) The aggregation correction channel is a BP neural network model optimized using the Sparrow Search Algorithm (SSA), specifically: 2.1 As Figure 2As shown, a BP neural network model based on a multilayer feedforward neural network is constructed. The input layer has 8 neurons, corresponding to: adsorbent dosage, initial concentration of microplastics, pH of microplastic solution, adsorption time, adsorption temperature, density (not shown in the figure), average particle size (not shown in the figure), and water contact angle (not shown in the figure). The output layer has 1 neuron, corresponding to the microplastic removal rate. 2.2 To obtain the optimal network structure suitable for different microplastic systems, 1 to 3 hidden layers were set, with 1 to 20 neurons per layer, as the BP neural network model to be optimized. The hidden layers used one or more combinations of logsig, tansig, or purelin functions, and the output layer used the purelin function. The minimum root mean square error (RMSE) and the coefficient of determination (R²) were used as the optimization parameters. 2 With the goal of maximizing the number of hidden layers, neurons, and activation functions, different combinations of these parameters are screened to determine the optimal BP neural network model. In embodiments of the present invention, such as Figure 3 As shown, among the three commonly used activation functions—logsig, tansig, and purelin—the model exhibits significantly lower root mean square error (RMSE) on both the training and validation sets when tansig is used as the hidden layer activation function. This indicates that tansig can more accurately fit the nonlinear behavior of MOF-based superhydrophobic quartz sand adsorbing microplastics. Based on this comparison, this invention preferentially selects tansig as the hidden layer activation function for the BP neural network model of PP, PE, and PET microplastics.

[0044] In embodiments of the present invention, such as Figure 4 As shown, with minimizing RMSE as the optimization objective, the optimal network structure was determined by iteratively optimizing combinations of 1-3 hidden layers and 1-20 neurons. The optimal network structure for the polypropylene system was found to be 2 hidden layers and 15 neurons, with a minimum root mean square error (RMSE) of 1.1909; for the polyethylene system, it was 3 hidden layers and 17 neurons, with a RMSE of 1.6161; and for the polyethylene terephthalate system, it was 2 hidden layers and 17 neurons, with a RMSE of 1.8244. This demonstrates that the present invention can establish highly adaptable prediction models for different types of microplastics.

[0045] In this embodiment of the invention, neurons The calculation can be expressed as: (1); in, , , , These represent the activation function, weights, input, and bias, respectively. This is the number of input variables. The model's weight iterative update formula is shown in equation (2), where E is the error function, calculated by equation (3): (2); (3); in, For the updated weights, The weights before the update. This means that the updated value will overwrite the previous value. The error function E represents the weights. The gradient. N The number of experimental samples removed from the training set. Represents the first in the training set Experimental conditions, For the first The predicted values ​​of the second microplastic removal rate corresponding to each experimental condition. For the first Experimental values ​​of microplastic removal rate corresponding to each experimental condition; 2.3 To overcome the problems of convergence instability and easy getting trapped in local optima caused by random assignment of initial weights and biases in conventional BP neural network models, the Sparrow Search Algorithm (SSA) is used to encode the initial weights and biases of the BP neural network model, and the optimal initial parameters are searched using a group optimization method to obtain the BP neural network model optimized by the Sparrow Search Algorithm (i.e., the SSA-BP neural network model). Specifically, it also includes: encoding the initial weights and biases of the BP neural network model using the Sparrow Search Algorithm (SSA), and searching for the optimal initial parameters using a population optimization method, to obtain the BP neural network model optimized by the Sparrow Search Algorithm (SSA), which includes: First, establish a sparrow population and encode each individual as a set of initial weights and bias parameters for the model to be optimized. The initial position of the population is calculated by formula (1.1): (1.1); in, This is the initial position of the population. , population The lower and upper boundaries of a dimensional variable. It is a random number; Second, the BP neural network model with the smallest root mean square error (RMSE) and coefficient of determination (R²) on the training set is selected. 2The maximum is a dual optimization objective. A fitness function is constructed, and the discoverers, followers, and vigilants are divided based on the fitness results. Their position updates are calculated by formulas (1.2), (1.3), and (1.4), respectively: (1.2); in, For the first During the nth iteration The first sparrow Dimensional position; For the first During the nth iteration The first sparrow Dimensional position; , is a uniform random number, and is a constant used to control the convergence speed; This represents the maximum number of iterations. This is the warning value; , which is the safety threshold; The newly added sparrow is a random term that follows a normal distribution, used to escape local optima; Let be a matrix consisting of unit row vectors 1; when Sparrows conduct a global search for food; if Add random items The discoverers roam randomly in search of food according to a normal distribution; (1.3); in, For the first The worst position of the discoverer in the next iteration; For the first The optimal position of the discoverer in the next iteration; A matrix with random elements, taking values ​​of 1 or -1, controlling the direction of movement; For the population size of sparrows; when Followers with poor fitness search in the opposite direction to the worst global position; when Then, followers with better fitness will move closer to the optimal discoverer; (1.4); in, For the first The global optimal position at the next iteration; It is a step size control parameter that follows a normal distribution; , which is a random number, controls the direction of movement of the vigilant; This represents the current fitness value of the sparrow. This is the worst fitness value globally at present. This is the current globally optimal fitness value; A minimal constant to ensure the denominator is not zero; when The vigilant moves closer to the optimal position globally; when The vigilant is far from the optimal position in the overall situation.

[0046] In this embodiment of the invention, population size m =30, maximum number of iterations The proportion of discoverers is 20%, the proportion of vigilants is 10%, and other parameters are set to the default settings of the existing SSA algorithm.

[0047] 2.4 The BP neural network model optimized by the Sparrow Search Algorithm (SSA) is trained using the training set. The parameters of the BP neural network model optimized by the SSA are adjusted using the validation set to prevent overfitting. The generalization ability of the BP neural network model optimized by the SSA is evaluated using the test set. During the training process of the BP neural network model optimized by the SSA, the input variables in the training set are linearly combined with the weights and biases of each layer and then nonlinearly mapped into the activation function, enabling the output of the predicted value of the second microplastic removal rate. ; In this embodiment of the invention, the training parameters of the BP neural network model optimized by the Sparrow Search Algorithm (SSA) are: learning rate of 0.001, number of iterations of 8000, batch size of 32, Adam optimizer, and early stopping strategy (training stops if the validation set loss does not decrease for 50 consecutive iterations); training results: RMSE of the hybrid network training set = 0.85%, R 2 =0.992; Validation set RMSE=1.12%, R 2 =0.988, a prediction result that does not violate physical constraints.

[0048] In this embodiment of the invention, the prediction results and model verification are performed by inputting the data in the test set into the BP neural network model optimized by the Sparrow Search Algorithm (SSA), outputting the corresponding predicted value of microplastic removal rate, and comparing and verifying it with the experimental value (true value).

[0049] like Figure 5 The figure shown is a comparison of the predicted and experimental values ​​of microplastic removal rate of polypropylene (PP). Figure 5 The distribution of data points in the test set and the ideal prediction line for y = x are annotated. The data points are closely distributed near the diagonal of y = x, indicating a high degree of consistency between the model predictions and experimental values. The coefficient of determination R0 for the PP system on the test set is shown. 2 The result of 0.9922 indicates that the model has extremely high accuracy and reliability in predicting the removal rate of polypropylene.

[0050] like Figure 6The figure shown is a comparison of the predicted and experimental values ​​of microplastic removal rate of polyethylene (PE). Figure 6 The form of expression and Figure 5 Consistent. The coefficient of determination R of the test set for the PE system. 2 The value reached 0.9989, the highest among the three microplastics, indicating that the model fits the polyethylene removal rate most effectively. This may be related to the fact that PE, as the most typical hydrophobic microplastic, exhibits the strongest regularity in its adsorption behavior on the surface of superhydrophobic quartz sand.

[0051] like Figure 7 The figure shown is a comparison of the predicted and experimental values ​​for microplastic removal rate of polyethylene terephthalate (PET). The coefficient of determination R0 for the test set of the PET system is also shown. 2 It reaches 0.9965. Compared to PP and PE, PET's R... 2 The result was slightly lower, which may be related to the higher density of PET (1.38 g / cm³) and the weaker hydrophobicity of its surface, which makes its adsorption behavior more complex due to the interaction of multiple factors. However, the model can still achieve high-precision prediction.

[0052] comprehensive Figure 5 , Figure 6 and Figure 7 As a result, the prediction model based on a physically constrained hybrid neural network constructed in this invention shows that the R-value of the removal rate of microplastics of PP, PE and PET is... 2 The results reached 0.9922, 0.9989 and 0.9965 respectively, verifying the effectiveness of the hybrid architecture in integrating physical mechanism constraints and data-driven learning, and demonstrating its ability to accurately describe nonlinear adsorption behavior under multi-factor coupling.

[0053] In this embodiment of the invention, model interpretation analysis is performed as follows: To improve the interpretability of the model, the SHAP (Shapley Additive Explanations) method is used to interpret the optimal SSA-BP neural network model. Based on the model's prediction results, the marginal contribution of each input variable to the predicted value of a single sample and the overall model output is calculated, thereby obtaining the ranking of variable importance and their direction of influence. Figure 8 As shown, with increasing initial microplastic concentration, the SHAP value gradually turns negative, indicating that increased concentration reduces the removal rate. With increasing adsorbent dosage, the SHAP value gradually turns positive, indicating that increasing the dosage is beneficial for improving the removal rate. When the pH rises to the slightly alkaline range, the SHAP value changes from positive to negative, indicating that the interfacial state of the material surface under alkaline conditions is unfavorable for microplastic removal. The positive contribution from increased adsorption time is mainly reflected in the early stage, and the marginal effect weakens thereafter. The SHAP value corresponding to adsorption temperature is close to zero, indicating that under the conditions of this study, adsorption temperature has a weak impact on the model output. Figure 9As shown in the analysis, the initial concentration of microplastics and the amount of adsorbent added have the most significant impact on the predicted removal rate, followed by pH and adsorption time, while adsorption temperature has the least impact. These results can provide a basis for subsequent material design, process control, and mechanism analysis.

[0054] (3) The residual compensation channel is a lightweight residual network, and the input is the predicted value of the first microplastic removal rate. The first residual characteristic between the experimental value and the corresponding microplastic removal rate, and the second predicted value of microplastic removal rate. The second residual feature between the experimental value of the corresponding microplastic removal rate is used to capture the unknown interaction effects that the physical channel and the aggregation correction channel failed to characterize; The lightweight residual network has two neurons in its input layer, corresponding to the first and second residual features respectively; six neurons in its hidden layer to prevent overfitting, with ReLU as the activation function; and one neuron in its output layer, corresponding to the predicted value of the third microplastic removal rate. The activation function of the output layer is Linear.

[0055] Specifically, it also includes: (1) The data fitting loss Predicted final microplastic removal rate Mean square error between the experimental values ​​of microplastic removal rate and the actual value: ; in, N The number of experimental samples removed from the training set. Represents the first in the training set Experimental conditions, For the first Predicted final microplastic removal rate values ​​for each experimental condition For the first Experimental values ​​of microplastic removal rate corresponding to each experimental condition; (2) The quasi-second-order dynamic residual constraint The calculation formula is as follows: ; ; in, M The set of dynamic samples in the training set. For the first dynamic sample set One dynamic sample, The adsorption capacity of the adsorbent for microplastics as a function of time. The function, This represents the adsorption capacity at adsorption equilibrium. for Adsorption capacity at time, The quasi-second-order kinetic rate constant; this quasi-second-order kinetic residual constraint Ensure that the model's time-dimensional predictions conform to the laws of adsorption kinetics; (3) The monotonicity constraint Based on automatic differentiation: ; in, For the training set, the first The amount of adsorbent added corresponding to each experimental condition; this monotonic constraint Ensure that, all other things being equal, increasing the amount of adsorbent added does not lead to a decrease in the predicted final microplastic removal rate; (4) The thermodynamic consistency constraint The calculation formula is as follows: ; in, The value represents the Gibbs free energy change (kJ / mol). R is the gas constant (8.314 J / (mol·K)) and T is the absolute temperature; For allocation coefficients; , This represents the adsorption capacity at adsorption equilibrium. This represents the concentration of microplastics at adsorption equilibrium; this thermodynamic consistency constraint Ensure the Gibbs free energy change of the spontaneous adsorption process It is a negative value; (5) The boundary constraints The calculation formula is as follows: ; Among them, the boundary constraint Ensure that the final predicted microplastic removal rate is within the range of [0%, 100%].

[0056] Step S3: Input the parameters to be predicted into the trained physical constraint hybrid neural network prediction model for prediction, and output the corresponding microplastic removal rate prediction value for process condition optimization and material application evaluation.

[0057] As another embodiment of the present invention, a rainwater runoff microplastic removal rate prediction system based on physically constrained hybrid ANN is provided, wherein the rainwater runoff microplastic removal rate prediction system based on physically constrained hybrid ANN includes: The acquisition module is used to acquire an experimental sample set of microplastic removal by microplastic adsorbent and preprocess the removal experimental sample set to obtain a preprocessed removal experimental sample set; wherein, the removal experimental sample set includes input indicators and output indicators, the input indicators include at least the adsorbent dosage, initial concentration of microplastics, pH of microplastic solution, adsorption time and adsorption temperature, and the output indicator is the microplastic removal rate; The training module is used to construct a physical constraint hybrid neural network prediction model and train the physical constraint hybrid neural network prediction model based on the preprocessed experimental sample set to obtain the trained physical constraint hybrid neural network prediction model. The prediction module is used to input the parameters to be predicted into the trained physical constraint hybrid neural network prediction model for prediction, and output the corresponding microplastic removal rate prediction value for process condition optimization and material application evaluation.

[0058] In this embodiment of the invention, the rainwater runoff microplastic removal rate prediction system based on physical constraint hybrid ANN runs in a deep learning framework environment that supports automatic differentiation, and the partial derivatives in the composite loss function are calculated by automatic differentiation.

[0059] The present invention also provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of any of the methods described above.

[0060] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described above.

[0061] This invention provides a method for predicting microplastic removal rates in rainwater runoff based on a physically constrained hybrid ANN. Using MOF-based superhydrophobic quartz sand as the adsorbent, and focusing on three typical microplastics in rainwater runoff—polypropylene (PP), polyethylene (PE), and polyethylene terephthalate (PET)—the method selects initial microplastic concentration, adsorbent dosage, microplastic solution pH, adsorption time, and adsorption temperature as input variables, and microplastic removal rate as the output variable. Addressing the shortcomings of purely data-driven models, which lack physical constraints and cannot distinguish between the dual mechanisms of multilayer hydrophobic aggregation of particulate microplastics, this invention constructs a hybrid architecture combining physical constraints and data residual correction. A Sips isotherm model outputs the basic removal rate, while a BP neural network optimized using a sparrow search algorithm learns the nonlinear residuals caused by multilayer aggregation. A mechanism discriminant subnetwork enables adaptive fusion of the two mechanisms. Thermodynamic consistency and monotonicity physical constraint terms are embedded in the fitness function to ensure that the prediction results conform to the basic laws of adsorption. Combined with SHAP interpretability analysis, the contribution ranking and direction of key influencing factors are analyzed. The method of this invention has high prediction accuracy and strong generalization, and the coefficient of determination R for the removal rate of PP, PE and PET is high. 2 The values ​​can reach 0.9922, 0.9989, and 0.9965 respectively, which can accurately describe the nonlinear adsorption behavior under multi-factor coupling. It makes up for the shortcomings of conventional linear regression or empirical models in reflecting the interaction between multiple factors. It is suitable for rapid prediction, parameter optimization and engineering control of microplastic adsorption processes in complex water bodies such as rainwater runoff and surface water, and has good application prospects.

[0062] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting microplastic removal rates in rainwater runoff based on physically constrained hybrid ANNs, characterized in that, The method for predicting microplastic removal rates in rainwater runoff based on physically constrained hybrid ANNs includes the following steps: Step S1: Obtain an experimental sample set of microplastic removal by the microplastic adsorbent, and preprocess the sample set to obtain a preprocessed sample set; wherein the sample set includes input indicators and output indicators, the input indicators include at least the adsorbent dosage, initial concentration of microplastics, pH of the microplastic solution, adsorption time, and adsorption temperature, and the output indicator is the microplastic removal rate; Step S2: Construct a physical constraint hybrid neural network prediction model, and train the physical constraint hybrid neural network prediction model based on the preprocessed experimental sample set to obtain the trained physical constraint hybrid neural network prediction model; Step S3: Input the parameters to be predicted into the trained physical constraint hybrid neural network prediction model for prediction, and output the corresponding microplastic removal rate prediction value for process condition optimization and material application evaluation.

2. The method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANNs according to claim 1, characterized in that, The input metrics also include microplastic characteristic factors, which include density, average particle size, and water contact angle.

3. The method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANNs according to claim 2, characterized in that, The preprocessing of the removal experiment sample set to obtain the preprocessed removal experiment sample set includes: The experimental sample set to be removed is subjected to consistency checks, missing value imputation, and outlier identification. The minimum-maximum normalization method was used to scale each index in the experimental sample set to the [0, 1] interval; The normalized sample set for removing samples was divided into a training set, a validation set, and a test set.

4. The method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANNs according to claim 3, characterized in that, Step S1 includes: For the target removal experimental sample set where the initial microplastic concentration is in the high-concentration range after preprocessing, a conditional generative adversarial network (GAN) is used to augment the data of the target removal experimental sample set. Specifically, the generator and discriminator are trained using input metrics from the target removal experimental sample set, enabling the generator to generate a synthetic sample set with a distribution consistent with the target removal experimental sample set. A physical feasibility filter is introduced during the generation process to automatically remove synthetic samples that violate the following physical constraints: Microplastic removal rate η constraint: 0% ≤ η ≤ 100%; Monotonicity constraint: Under otherwise constant conditions, increasing the adsorbent dosage should not lead to a decrease in the microplastic removal rate; Thermodynamic constraints: For spontaneous adsorption processes, the change in Gibbs free energy as the adsorption temperature increases. It should be a negative value.

5. The method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANNs according to claim 4, characterized in that, Prior to step S2, the following is included: A mechanism discrimination subnetwork is constructed, which is a shallow fully connected network. The input is a concatenated vector composed of the preprocessed removal experimental sample set, the synthetic sample set, and the microplastic feature factors. The output is the single-layer adsorption mechanism weight coefficients. α And the weighting coefficient of the multilayer aggregation adsorption mechanism 1- α Among them, the weighting coefficient of the monolayer adsorption mechanism α This indicates the dominance of the monolayer adsorption mechanism under the current input conditions; the weighting coefficient for the multilayer aggregation adsorption mechanism is 1- α This indicates the degree of dominance of the multilayer aggregation and adsorption mechanism under the current input conditions. α ∈ [0, 1].

6. The method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANNs according to claim 5, characterized in that, Step S2 includes: The physical constraint hybrid neural network prediction model includes a physical channel, an aggregation correction channel, a residual compensation channel, and a fusion layer. The physical channel outputs a first microplastic removal rate prediction value based on the training set. The aggregation correction channel can output a second microplastic removal rate prediction value based on the training set. The residual compensation channel can be based on the predicted value of the first microplastic removal rate. and the second predicted value of microplastic removal rate Output the third predicted value of microplastic removal rate The fusion layer can be based on the predicted value of the first microplastic removal rate. The second predicted value of microplastic removal rate The predicted value of the third microplastic removal rate The weighting coefficient of the monolayer adsorption mechanism and the weighting coefficient of the multilayer aggregation adsorption mechanism Calculate the final predicted microplastic removal rate. Wherein, the predicted final microplastic removal rate is... The calculation formula is as follows: ； Among them, when When the value approaches 1, the physical channel dominates the prediction; when When the value approaches 0, the aggregation correction channel dominates the prediction; the residual compensation channel always provides correction. Based on the training set and the final microplastic removal rate prediction output by the fusion layer Constructing a loss function that includes data fitting Quasi-second-order dynamic residual constraints Monotonicity constraint Thermodynamic consistency constraints and boundary constraints Composite loss function The composite loss function is used to train the physical constraint hybrid neural network prediction model to obtain the trained physical constraint hybrid neural network prediction model; wherein, the composite loss function is used to train the physical constraint hybrid neural network prediction model to obtain the trained physical constraint hybrid neural network prediction model. The calculation formula is as follows: ； in, 、 、 、 These are the weight hyperparameters for each constraint.

7. The method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANNs according to claim 6, characterized in that, Also includes: (1) The Sips isotherm equation is used as the core of the physical channel: ； in, Representing the The adsorption capacity at adsorption equilibrium under each experimental condition. Represents the maximum adsorption capacity. This represents the concentration of microplastics at adsorption equilibrium. This represents the adsorption constant corresponding to the physical channel. A constant representing the heterogeneity of the adsorbent; Then the predicted value of the first microplastic removal rate The calculation formula is as follows: ； in, For the training set, the first Adsorbent dosage under each experimental condition For the training set, the first Initial concentration of microplastics under experimental conditions; (2) The aggregation correction channel is a BP neural network model optimized using the Sparrow Search Algorithm (SSA), specifically: 2.1 A BP neural network model based on a multilayer feedforward neural network was constructed; the input layer was set with 8 neurons, corresponding to: adsorbent dosage, initial concentration of microplastics, pH of microplastic solution, adsorption time, adsorption temperature, density, average particle size and water contact angle; the output layer was set with 1 neuron, corresponding to the microplastic removal rate. 2.2 Set 1 to 3 hidden layers, with 1 to 20 neurons per layer, as the BP neural network model to be optimized; the hidden layers use one or more combinations of the logsig, tansig, or purelin functions, and the output layer uses the purelin function; the minimum root mean square error (RMSE) and the coefficient of determination (R²) are used as the optimization parameters. 2 With the goal of maximizing the number of hidden layers, neurons, and activation functions, different combinations of these factors are screened to determine the optimal BP neural network model. 2.3 The initial weights and biases of the BP neural network model are encoded using the Sparrow Search Algorithm (SSA), and the optimal initial parameters are searched using a group optimization method to obtain the BP neural network model optimized by the Sparrow Search Algorithm (SSA). 2.4 The BP neural network model optimized by the Sparrow Search Algorithm (SSA) is trained using the training set. The parameters of the BP neural network model optimized by the SSA are adjusted using the validation set to prevent overfitting. The generalization ability of the BP neural network model optimized by the SSA is evaluated using the test set. During the training process of the BP neural network model optimized by the SSA, the predicted value of the second microplastic removal rate can be output. ; (3) The residual compensation channel is a lightweight residual network, and the input is the predicted value of the first microplastic removal rate. The first residual characteristic between the experimental value and the corresponding microplastic removal rate, and the second predicted value of microplastic removal rate. The second residual feature between the experimental value of the corresponding microplastic removal rate is used to capture the unknown interaction effects that the physical channel and the aggregation correction channel failed to characterize; The lightweight residual network has two neurons in its input layer, corresponding to the first and second residual features respectively; six neurons in its hidden layer to prevent overfitting, with ReLU as the activation function; and one neuron in its output layer, corresponding to the predicted value of the third microplastic removal rate. The activation function of the output layer is Linear.

8. The method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANNs according to claim 6, characterized in that, Also includes: (1) The data fitting loss Predicted final microplastic removal rate Mean square error between the experimental values ​​of microplastic removal rate and the actual value: ； in, N The number of experimental samples removed from the training set. Represents the first in the training set Experimental conditions, For the first Predicted final microplastic removal rate values ​​for each experimental condition For the first Experimental values ​​of microplastic removal rate corresponding to each experimental condition; (2) The quasi-second-order dynamic residual constraint The calculation formula is as follows: ； ； in, M The set of dynamic samples in the training set. For the first dynamic sample set One dynamic sample, The adsorption capacity of the adsorbent for microplastics as a function of time. The function, This represents the adsorption capacity at adsorption equilibrium. for Adsorption capacity at time, The quasi-second-order kinetic rate constant; this quasi-second-order kinetic residual constraint Ensure that the model's time-dimensional predictions conform to the laws of adsorption kinetics; (3) The monotonicity constraint Based on automatic differentiation: ； in, For the training set, the first The amount of adsorbent added corresponding to each experimental condition; this monotonic constraint Ensure that, all other things being equal, increasing the amount of adsorbent added does not lead to a decrease in the predicted final microplastic removal rate; (4) The thermodynamic consistency constraint The calculation formula is as follows: ； in, For the change of Gibbs free energy, R is the gas constant, and T is the absolute temperature; For allocation coefficients; , This represents the adsorption capacity at adsorption equilibrium. This represents the concentration of microplastics at adsorption equilibrium; this thermodynamic consistency constraint Ensure the Gibbs free energy change of the spontaneous adsorption process It is a negative value; (5) The boundary constraints The calculation formula is as follows: ； Among them, the boundary constraint Ensure that the final predicted microplastic removal rate is within the range of [0%, 100%].

9. The method for predicting microplastic removal rate in rainwater runoff based on physically constrained hybrid ANNs according to claim 7, characterized in that, The initial weights and biases of the BP neural network model are encoded using the Sparrow Search Algorithm (SSA), and the optimal initial parameters are searched using a swarm optimization method. The resulting BP neural network model optimized by the SSA includes: First, establish a sparrow population and encode each individual as a set of initial weights and bias parameters for the model to be optimized. The initial position of the population is calculated by formula (1.1): (1.1)； in, This is the initial position of the population. , population The lower and upper boundaries of a dimensional variable. It is a random number; Second, the BP neural network model with the smallest root mean square error (RMSE) and coefficient of determination (R²) on the training set is selected. 2 The maximum is a dual optimization objective. A fitness function is constructed, and the discoverers, followers, and vigilants are divided based on the fitness results. Their position updates are calculated by formulas (1.2), (1.3), and (1.4), respectively: (1.2)； in, For the first During the nth iteration The first sparrow Dimensional position; For the first During the nth iteration The first sparrow Dimensional position; It is a uniformly random number; This represents the maximum number of iterations. This is a warning value. This is a safety threshold; For the newly added sparrows; Let be a matrix consisting of unit row vectors 1; when Sparrows conduct a global search for food; if Add random items The discoverers roam randomly in search of food according to a normal distribution; (1.3)； in, For the first The worst position of the discoverer in the next iteration; For the first The optimal position of the discoverer in the next iteration; For random elements; For the population size of sparrows; when Followers with poor fitness will reverse their search to the worst possible position globally; when Then, followers with better fitness will move closer to the optimal discoverer; (1.4)； in, For the first The global optimal position at the next iteration; It is a step size control parameter that follows a normal distribution; It is a random number; This represents the current fitness value of the sparrow. This is the worst fitness value globally at present. This is the current globally optimal fitness value; A minimal constant to ensure the denominator is not zero; when The vigilant moves closer to the optimal position globally; when The vigilant is far from the optimal position in the overall situation.

10. A rainwater runoff microplastic removal rate prediction system based on physically constrained hybrid ANN, used to implement the rainwater runoff microplastic removal rate prediction method based on physically constrained hybrid ANN as described in any one of claims 1-9, characterized in that, The rainwater runoff microplastic removal rate prediction system based on physically constrained hybrid ANN includes: The acquisition module is used to acquire an experimental sample set of microplastic removal by microplastic adsorbent and preprocess the removal experimental sample set to obtain a preprocessed removal experimental sample set; wherein, the removal experimental sample set includes input indicators and output indicators, the input indicators include at least the adsorbent dosage, initial concentration of microplastics, pH of microplastic solution, adsorption time and adsorption temperature, and the output indicator is the microplastic removal rate; The training module is used to construct a physical constraint hybrid neural network prediction model and train the physical constraint hybrid neural network prediction model based on the preprocessed experimental sample set to obtain the trained physical constraint hybrid neural network prediction model. The prediction module is used to input the parameters to be predicted into the trained physical constraint hybrid neural network prediction model for prediction, and output the corresponding microplastic removal rate prediction value for process condition optimization and material application evaluation.

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