Method and system for correcting hygroscopicity parameters of non-ideal mixed aerosols and medium

Abstract

The application discloses a kind of non-ideal mixed aerosol hygroscopicity parameter correction method, system and medium, belong to atmospheric measurement technical field.Its method includes: obtaining instrument observation data;Estimate instrument observation data by ZSR ideal mixing criterion, generate ZSR hygroscopicity observation parameter;According to ZSR hygroscopicity observation parameter, instrument observation data and inversion generated by instrument observation data inversion hygroscopicity observation parameter, obtain input feature data set;Input feature data set is input into the bias prediction model pre-constructed, and output non-ideal mixing bias term;Calculate the main effect value of input feature data set, and generate the empirical correction term based on key features according to main effect value;According to ZSR hygroscopicity observation parameter, pre-constructed seasonal correction coefficient, the empirical correction term based on key features, obtain hygroscopicity parameter correction result.The application can explain the deviation part, and quantitatively explain the contribution degree of each influence factor.

Description

Technical Field

[0001] This invention relates to the field of atmospheric measurement technology, and in particular to a method, system, and medium for correcting the hygroscopic parameters of non-ideal mixed aerosols. Background Technology

[0002] Hygroscopicity of aerosols characterizes the property of water vapor condensing into liquid water on the surface of particulate matter under subsaturated or saturated conditions. Hygroscopic parameters are commonly used to characterize the magnitude of aerosol hygroscopicity. Depending on the measuring instrument and data, there are various methods for calculating hygroscopic parameters. For example, hygroscopic parameters can be derived by inverting the hygroscopic growth factor observed using a hygroscopic tandem differential mobility analyzer (HTDMA); or by combining chemical composition data observed using an aerosol chemical spectrometer (ACSM) with the Zdanovski-Stokes-Robinson (ZSR) ideal mixing criterion, assuming a homogeneous internal mixing state of the aerosol particles. The ZSR ideal mixing criterion states that the hygroscopic processes of each aerosol component are completely independent, and the hygroscopic parameter characterizing the overall hygroscopicity of the aerosol is a weighted sum of the hygroscopic parameters of each component by volume fraction. An internally mixed state means that each component exists uniformly within a single aerosol particle, rather than being dispersed as independent particles. Both the ZSR ideal mixing criterion and the internal mixing assumption are ideal mixing assumptions, and are collectively referred to as the ZSR ideal mixing criterion in this invention. The mixing state of aerosols is one of the important factors affecting the hygroscopicity of aerosols. The mixing state of the components in the actual atmosphere is not a uniform internal mixing state. At the same time, the interaction between different chemical components during the hygroscopic process cannot be ignored. This makes the calculation method of hygroscopic parameters based on the ZSR ideal mixing criterion superimposed with the internal mixing assumption have significant room for improvement in terms of accuracy and applicability.

[0003] In the real atmosphere, aerosols often exhibit non-ideal mixing, leading to systematic biases in the calculation of hygroscopic parameters based on the ZSR ideal mixing criterion and the internal mixing assumption. While existing research has attempted to incorporate machine learning methods for correction, these are mostly black-box models that cannot explain the sources of bias, thus limiting the physical reliability and generalizability of the models. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, system and medium for correcting the hygroscopic parameters of non-ideal mixed aerosols. This method can correct the deviation caused by estimating the hygroscopic parameters by the ZSR ideal mixing criterion, which can not only improve the prediction accuracy, but also explain the deviation and quantitatively explain the contribution of each influencing factor.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] On the one hand, the present invention provides a method for correcting the hygroscopic parameters of non-ideal mixed aerosols, comprising:

[0007] Acquire instrumental observation data related to the hygroscopicity of non-ideal mixed aerosols within a predetermined time period;

[0008] The instrument observation data were estimated using the ZSR ideal mixing criterion to generate ZSR hygroscopicity observation parameters.

[0009] The input feature dataset is obtained by using the ZSR hygroscopicity observation parameters, instrument observation data, and inverted hygroscopicity observation parameters generated from the instrument observation data.

[0010] The input feature dataset is input into a pre-built deviation prediction model, so that the deviation prediction model predicts the hygroscopic deviation of the input feature dataset according to the seasonal category of the input feature dataset and outputs a non-ideal mixed deviation term.

[0011] Calculate the main effect value of the input feature dataset, and analyze the direct contribution of each input feature data in the input feature dataset to the non-ideal mixture bias term, as well as the interaction contribution of each input feature data and other input feature data to the non-ideal mixture bias term based on the main effect value;

[0012] Based on direct and interactive contributions, key features are extracted from the input feature dataset, and empirical correction terms based on the key features are generated.

[0013] Based on the ZSR hygroscopicity observation parameters, the pre-constructed seasonal correction coefficients, and the empirical correction terms based on key features, the hygroscopicity parameter correction results are obtained.

[0014] Optionally, the input feature dataset includes chemical component volume fraction features, chemical component interaction features, seasonal and diurnal variation features, meteorological element features, ZSR hygroscopicity observation parameters, and inverted hygroscopicity observation parameters.

[0015] Optionally, the training of the deviation prediction model includes:

[0016] Obtain the training dataset;

[0017] Based on the pre-built seasonal adaptive adjustment module, the training dataset is divided into four categories of seasonal training data according to the season;

[0018] The BOHB algorithm and elastic weight update strategy are used to optimize the hyperparameters of the bias prediction model through four types of seasonal training data, resulting in a well-trained bias prediction model.

[0019] Optionally, the seasonal adaptive adjustment module is represented as:

[0020] ;

[0021] in, This indicates a seasonal adaptive adjustment module; This represents the weight of the seasonal category s at time t; This represents the seasonal function of the input feature dataset x on the seasonal category s.

[0022] Optionally, the elastic weight update strategy is expressed as:

[0023] ;

[0024] in, This indicates the updated hyperparameters; Indicates the initial hyperparameters; This represents the hyperparameters corresponding to the instrument observation data; This represents the forgetting factor.

[0025] Optionally, the main effect values ​​of the input feature dataset are represented as follows:

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] in, This represents the predicted value of input feature data i in the input feature dataset x for the LightGBM model. The degree of contribution; This represents the input feature dataset that does not contain input feature data i; This represents the input feature dataset; Indicates the number of data points in the input feature dataset; This represents the LightGBM model prediction value when using the input feature data within the brackets; This represents the factorial operation; This represents the interaction effect value on the input feature dataset x; i and j represent the indices of the input feature dataset. This represents the main effect value of the input feature dataset x; This represents the main effect value of the input feature dataset x for each season; Represents a collection of seasons; This represents a set of seasonal characteristics.

[0031] Optionally, the seasonal correction factor is expressed as:

[0032] ;

[0033] in, Represents month variable The seasonal correction coefficients; A, B, C, D, E, and F represent seasonal modulation effect parameters.

[0034] Optionally, the hygroscopicity parameter correction result is expressed as:

[0035] ;

[0036] ;

[0037] in, This represents an empirical correction term based on key features; Represents the key feature set The predicted values ​​of the LightGBM model; Indicates the baseline value; Represents the key feature set The contribution of key feature q to the predicted values ​​of the LightGBM model; Represents the key feature set The key feature q in; This indicates the amount of data in the key feature set; This indicates the result of the hygroscopicity parameter correction; This represents the observed parameters of ZSR hygroscopicity; Represents month variable The seasonal correction factor.

[0038] Secondly, the present invention provides a hygroscopic parameter correction system for non-ideal mixed aerosols, comprising:

[0039] The data acquisition module is used to acquire instrument observation data related to the hygroscopicity of non-ideal mixed aerosols within a predetermined time period.

[0040] The criterion estimation module is used to: estimate the instrument observation data using the ZSR ideal mixing criterion and generate ZSR hygroscopicity observation parameters;

[0041] The feature generation module is used to: obtain the input feature dataset based on the ZSR hygroscopicity observation parameters, instrument observation data, and inverted hygroscopicity observation parameters generated from the instrument observation data;

[0042] The deviation prediction module is used to: input the input feature dataset into a pre-built deviation prediction model, so that the deviation prediction model predicts the hygroscopic deviation of the input feature dataset according to the seasonal category of the input feature dataset and outputs a non-ideal mixed deviation term;

[0043] The contribution analysis module is used to: calculate the main effect value of the input feature dataset, and analyze the direct contribution of each input feature data in the input feature dataset to the non-ideal mixture bias term, as well as the interaction contribution of each input feature data and other input feature data to the non-ideal mixture bias term based on the main effect value;

[0044] The correction analysis module is used to: extract key features from the input feature dataset based on direct and interactive contributions, and generate empirical correction terms based on the key features;

[0045] The calibration generation module is used to obtain the calibration results of the hygroscopic parameters based on the ZSR hygroscopicity observation parameters, the pre-constructed seasonal calibration coefficients, and the empirical calibration terms based on key features.

[0046] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the method for correcting the hygroscopic parameters of non-ideal mixed aerosols as described in the first aspect.

[0047] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0048] This invention quantifies the contribution of each index to the correction term and evaluates the synergistic or inhibitory effects of interactions between features, transforming the model from a black box into an interpretable machine learning model. While outputting high-precision predictions, it can also explain the physicochemical factors and their mechanisms of action in non-ideal mixed effects, providing theoretical support for parameterization schemes. It can clearly understand the contribution of interactions between different factors to the hygroscopicity parameter correction term, thereby linking the prediction results with actual physicochemical mechanisms. A seasonal correction coefficient is introduced to characterize the seasonal periodic changes. The model can capture and adapt well to the seasonal variation characteristics and long-term trends of aerosols, maintaining stable and reliable performance in different times and application scenarios. Attached Figure Description

[0049] Figure 1 The diagram shown is a flowchart of one embodiment of the method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to the present invention.

[0050] Figure 2 The diagram shows the SHAP value distribution of different input feature data in one embodiment of the method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to the present invention.

[0051] Figure 3 The figure shown is a schematic diagram of the time series prediction effect of the method for correcting the hygroscopic parameters of non-ideal mixed aerosols of the present invention in the second embodiment, which randomly selects 100 sets of sample data.

[0052] Figure 4 The diagram shows the empirical formula fitting effect of the method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to the present invention in the third embodiment. Detailed Implementation

[0053] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0054] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0055] Example 1

[0056] like Figure 1 As shown in the figure, this embodiment introduces a method for correcting the hygroscopic parameters of a non-ideal mixed aerosol, including the following steps:

[0057] Step 1: Acquire instrument observation data, specifically:

[0058] Instrumental observation data related to the hygroscopicity of non-ideal mixed aerosols during the predetermined time period include hygroscopic growth factor (GF) data observed by the Hygroscopic Tandem Differential Mobility Analyzer (HTDMA), chemical composition data observed by the Aerosol Chemical Speciation Monitor (ACSM), aerosol particle spectrum data observed by the Scanning Mobility Particle Sizer (SMPS), and temperature (T) and relative humidity (RH) data from meteorological stations.

[0059] The instrument observation data were subjected to quality control and data assimilation to obtain preprocessed data, which was then used to generate hygroscopicity observation parameters, namely:

[0060] Statistical methods were used to identify and remove missing and outlier values ​​from instrument observation data, specifically based on 3 Outlier detection is performed in principle. First, statistical analysis is conducted on the instrument observation data to calculate its mean. with standard deviation Secondly, it will satisfy ( Data points meeting the condition of the k-th instrument observation at time t are defined as outliers; finally, missing values ​​in the instrument observation data and the aforementioned outliers are uniformly cleaned up. Furthermore, when processing chemical component data from ACSM observations, data with concentrations of two or more components at a given time point that are 0 are considered invalid and discarded, using the following formula:

[0061] ;

[0062] in, This indicates a mismatch and needs to be removed.

[0063] Data assimilation involves matching the time series of each instrument observation data after quality control to the same timestamp, as shown in the formula:

[0064] ;

[0065] in, , Let represent the observation data of the kth instrument at time t1 and the observation data of the kth instrument at time t2, respectively.

[0066] Based on the preprocessed chemical composition data and combined with the (Zdanovski-Stokes-Robinson, ZSR) mixing criterion, the instrument observation data are estimated to generate ZSR hygroscopicity observation parameters:

[0067] Specifically, the molar concentration of the main inorganic components is obtained using an ion pairing scheme, as follows:

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] in, Indicates the molar concentration of ammonium nitrate; Indicates the molar concentration of nitrate; Indicates the molar concentration of ammonium hydrogen sulfate; Indicates the molar concentration of sulfate ions; Indicates the molar concentration of ammonium ions; Indicates the molar concentration of ammonium sulfate; Indicates the molar concentration of sulfuric acid; These represent taking the maximum value and taking the minimum value, respectively.

[0073] After obtaining the molar concentration of the main inorganic components, the volume concentration of each component can be obtained by combining the relative molecular mass and density. The volume concentrations of organic matter and black carbon in the aerosol can be directly calculated from their mass concentration and density. The ZSR hygroscopicity observation parameters of the multi-component aerosol can then be determined according to the ZSR ideal mixing criterion. , represented as:

[0074] ;

[0075] in, This represents the volume fraction of the w-th chemical component; This indicates the magnitude of the hygroscopic parameter of the w-th chemical component as determined in the laboratory.

[0076] Finally, the ZSR hygroscopicity observation parameters of the multi-component aerosol were... Inverted hygroscopic observation parameters obtained from instrument observation data at the same time By taking the difference, we obtain the true non-ideal mixed deviation term. ,Right now:

[0077] ;

[0078] The goal of this embodiment is to accurately predict and interpret the non-ideal mixing deviation term, thereby achieving precise correction of the ZSR hygroscopicity observation parameters obtained under the ZSR ideal mixing criterion from a physical mechanism perspective.

[0079] Step 2: Generate the input feature dataset, specifically:

[0080] Based on the ZSR hygroscopicity observation parameters, preprocessed data, and the inverted hygroscopicity observation parameters generated by them, the input feature dataset is obtained, which specifically includes the following five categories of features:

[0081] (1) The volume fraction characteristics of chemical components are as follows: based on the ion pairing scheme, the ion data obtained by ACSM observation are used to calculate the volume fraction of each chemical component, including nitrate (NH4NO3), sulfuric acid (H2SO4), ammonium bisulfate (NH4HSO4), ammonium sulfate ((NH4)2SO4), organic matter (Org) and black carbon (BC), as well as the total inorganic integral (Inorg) calculated from these basic components.

[0082] (2) Interaction characteristics of chemical components: constructing interaction terms for each component to characterize the interactions between them and quantifying their impact on the hygroscopic process. Specifically, this includes the ratio of organic to inorganic matter, the ratio of black carbon to organic matter, the ratio of sulfate to nitrate, the degree of ammonium salting, and the chemical diversity index (CD) calculated based on the Shannon entropy formula. This index is used to characterize the complexity of the chemical composition of aerosols and is expressed as:

[0083] ;

[0084] The CD (Distribution of Volume Fractions) maps the volume fraction distribution of each component to a scalar to measure the uncertainty or disorder of the aerosol's chemical composition. The larger the value, the more complex the chemical composition of the aerosol, the more homogeneous the mixing, and the greater the potential for and impact of non-ideal interactions between the components.

[0085] (3) Seasonal and daily variation characteristics: Considering that the aerosol characteristics change strongly over time, seasonal and daily variation characteristic data are constructed, including monthly and hourly time dimension characteristics. At the same time, considering that the seasonal and daily variations of aerosol characteristics are periodic, periodic function transformation is used to characterize the above periodic characteristics, including annual periodic sine, annual periodic cosine, daily periodic sine, and daily periodic cosine terms.

[0086] (4) Meteorological element characteristics, specifically including air temperature (T), relative humidity (RH), and temperature-humidity interaction term. Considering that anomalous aerosol behavior under extreme conditions may affect the stability of the model as outliers, high temperature and high humidity indicators based on empirical thresholds are specifically set to separately screen the aerosol behavior under these extreme conditions. The high temperature indicator is set to 1 when the air temperature is above 20°C, and 0 otherwise. The high humidity indicator is set to 1 when the relative humidity is above 80%, and 0 otherwise. The above thresholds are determined based on atmospheric chemistry and aerosol physics principles and are used to characterize the special behavior of aerosols under non-ideal mixing under extreme meteorological conditions.

[0087] (5) Hygroscopic observation parameters, specifically including ZSR hygroscopic observation parameters and inverted hygroscopic observation parameters generated from preprocessed data inversion. The inverted hygroscopic observation parameters are the observed hygroscopic growth factors.

[0088] Step 3: Construct the deviation prediction model, specifically as follows:

[0089] In this embodiment, the bias prediction model selected is the Light Gradient Boosting Machine (Light GBM) model.

[0090] In machine learning, model performance often depends on fine-tuning of hyperparameters. Traditional grid search methods are inefficient, require a large parameter space, and have high training costs.

[0091] During training, the training dataset is first acquired. Based on the pre-built seasonal adaptive adjustment module, the training dataset is divided into four seasonal training data categories. The Bayesian Optimization and HyperBand (BOHB) algorithm and elastic weight update strategy are used to optimize the hyperparameters of the bias prediction model through the four seasonal training data categories, resulting in a well-trained bias prediction model.

[0092] Based on the seasonal variation patterns of aerosols, a seasonal adaptive adjustment module is introduced. First, it identifies the key meteorological characteristic change patterns of the four seasons. Then, it trains specific sub-models for different seasons, laying the groundwork for fitting empirical formulas for different seasons in the next step. During actual prediction, the appropriate seasonal model is automatically selected based on the temporal characteristics of the input data. The seasonal adaptive adjustment module is represented as follows:

[0093] ;

[0094] in, This indicates a seasonal adaptive adjustment module; This represents the weight of the seasonal category s at time t; This represents the seasonal function of the input feature dataset x on the seasonal category s.

[0095] This embodiment selects the BOHB algorithm for hyperparameter tuning of the model, maximizing model performance while reducing training costs. First, the optimizer is initialized using a Tree-structured Parzen Estimator (TPE) sampler and a Hyperband efficient pruner. A wide-range hyperparameter search is defined, i.e., a wide-range search is performed first, followed by a fine-grained search within a narrow range. Time-series cross-validation is constructed, and an objective function is built to evaluate parameter performance. Next, the optimization process is run. The system uses Bayesian guidance to dynamically eliminate inferior parameter combinations based on early performance over a wide range, and allocates more computational resources to more promising parameter combinations. Finally, the optimal parameters are obtained based on the data convergence history, achieving the goal of maximizing model performance through hyperparameter optimization. The BOHB algorithm combines Bayesian optimization and Hyperband optimization strategies, possessing the advantages of both. It can quickly eliminate poorly performing hyperparameter configurations through the fast pruning mechanism of the Hyperband algorithm, greatly reducing unnecessary waste of computing resources. At the same time, it can rely on Bayesian optimization to model and guide based on historical results, exploring the parameter space more intelligently and quickly, ultimately achieving a dual improvement in efficiency and performance.

[0096] The specific steps for hyperparameter optimization using the BOHB algorithm are as follows:

[0097] First, considering the strong time dependence of aerosol data characteristics, we determine the optimization objective as minimizing the root mean square error of time series cross-validation. The advantage of using time series cross-validation is that it strictly adheres to using past data to predict future situations, avoiding information leakage caused by time series disorder.

[0098] The data is divided into continuous training and validation sets according to time sequence. Next, the fitting model with the current hyperparameters is used to predict the validation set, and the mean root mean square error of each fold validation set is calculated based on the actual non-ideal mixture bias term and the predicted non-ideal mixture bias term. Finally, the mean root mean square error of all folds is arithmetically averaged as the performance evaluation index of the model under this set of hyperparameter vectors.

[0099] After determining the optimization objective, the Hyperband algorithm is used to allocate computational resources preferentially to hyperparameter sets with greater potential, achieving efficient pruning. Resources are defined as the number of training iterations. ,in, Indicates the maximum number of iterations and the minimum number of iterations. As a reduction factor, it is usually taken as =3. For each resource level, the algorithm first initializes a certain number of hyperparameter vectors, where the initial number is... , This represents the maximum number of hyperparameter vector configurations evaluated at the minimum resource level. Next, the algorithm employs a round-by-round elimination mechanism. In each round of evaluation, all current hyperparameter vectors are trained and validated using the same amount of computational resources, and the best-performing vector from each round is retained (1 / 3 of the total). .

[0100] The second step is to use a Gaussian process to establish the model's hyperparameter vector. With objective function The probabilistic model between parameters not only predicts the model's performance under a given hyperparameter vector configuration but also quantifies the uncertainty of the prediction, thereby guiding subsequent exploration of the parameter space. The probabilistic model is expressed as:

[0101] ;

[0102] in, Represents a conditional probability distribution; A Gaussian process is a probability distribution defined on a function space. It is the mean function, i.e., the objective function. Expected estimate Unoptimized hyperparameters With optimization of hyperparameters The covariance matrix based on the Matérn kernel function is expressed as follows:

[0103] ;

[0104] in, This represents the hyperparameters of the Matérn kernel; , is the Euclidean distance between hyperparameter vectors. The length scale parameter can be changed. Used to control the smoothness of function changes; It is the signal variance, representing the overall fluctuation amplitude of the objective function; and It is adaptively learned from historical observation data, so the Gaussian model can adaptively capture the changing characteristics of the objective function.

[0105] The third step involves using the Gaussian process model and employing expected improvement to guide the next round of hyperparameter search. Expected improvement measures the anticipated improvement of the new hyperparameter vector relative to the known best observed values. The function expression is as follows:

[0106] ;

[0107] in, Represents the mathematical expectation; This represents the hyperparameter vector under the current optimal parameter configuration. For hyperparameters Optimize the decision-making criteria, we can do so by The decision is to either continue exploring unknown areas or to tap into known advantageous areas, thereby propelling the entire optimization process in a more favorable direction.

[0108] The fourth step is to perform multi-fidelity optimization, which is carried out in two stages:

[0109] In the first stage, a subset of data is used to evaluate the objective function for rapid screening, quickly eliminating obviously unsuitable parameters. The filtered objective function... as follows:

[0110] ;

[0111] in, The total dataset size, For one of the data subsets; express One of the data points; Indicates the measured value; This represents the model's predicted value.

[0112] In the second stage, more computational resources are allocated to more promising parameter configurations, performing in-depth optimization within the local search space, and optimizing the hyperparameters. Represented as:

[0113] ;

[0114] in, This represents the independent variable corresponding to the minimum value; This represents the error metric across the entire dataset. The neighborhood of the optimal parameters from the first stage is expressed as follows:

[0115] ;

[0116] in, This represents the optimal hyperparameters selected in the first stage; It represents a very small neighborhood.

[0117] This strategy is based on an important observation: determining the potential of a set of parameters does not necessarily require evaluation using all the data and complete training. Practical applications show that this strategy can reduce overall computation time by more than 60% while maintaining optimization quality, making it of significant practical value for processing large-scale aerosol observation data.

[0118] Fifth, to avoid overfitting and wasting computational resources, an early stopping mechanism is set during training. The stopping conditions are as follows:

[0119] ;

[0120] in, For round T, round Round validation set loss; Tolerance threshold; To ensure patience, the number of rounds is taken in this embodiment. =50. If in consecutive During the evaluation round, if the improvement of the validation set loss compared to the best loss in the historical record is consistently greater than the tolerance threshold, it is determined that the optimization space of the hyperparameter configuration is insufficient, triggering a stop.

[0121] Furthermore, to adapt to long-term changes in aerosol properties, an elastic weight update strategy is designed. This means that when the model's performance degrades beyond a threshold on new observation data, the system automatically triggers an update process, employing an elastic weight update strategy, expressed as:

[0122] ;

[0123] in, This indicates the updated hyperparameters; Indicates the initial hyperparameters; This represents the hyperparameters corresponding to the instrument observation data; This represents the forgetting factor, which controls the degree to which old knowledge is retained. The default setting is 0.7.

[0124] Step 4: The model predicts the non-ideal mixture bias term, specifically:

[0125] The input feature dataset is fed into the constructed and trained deviation prediction model, so that the deviation prediction model can predict the hygroscopic deviation of the input feature dataset according to the seasonal category of the input feature dataset and output a non-ideal mixed deviation term.

[0126] Step 5: Perform interpretability analysis on the non-ideal mixed bias term, specifically:

[0127] Interpretability analysis is performed using Shapley values. The Shapley values ​​are calculated to explain the direction and magnitude of the contribution of each feature to the prediction results. For the non-ideal mixture bias term predicted within the LightGBM model framework, Shapley Additive exPlanations (SHAP) analysis is implemented using a TreeExplainer. This explainer is based on the Tree Shapley Additive exPlanations (TreeSHAP) algorithm, which specifically optimizes the Shapley value calculation for tree models. Compared to general SHAP calculation methods, it can calculate more complex nonlinear features and efficiently handle multi-feature aerosol datasets.

[0128] The main effects (SHAP) value is a game-theoretic Shapley score, which involves adding or removing features one by one and observing the changes in the model's predictions. The specific formula for calculating the first Shapley score is as follows:

[0129] ;

[0130] in, This represents the predicted value of input feature data i in the input feature dataset x for the LightGBM model. The degree of contribution; This represents the input feature dataset that does not contain input feature data i; This represents the input feature dataset; Indicates the number of data points in the input feature dataset; This represents the LightGBM model prediction value when using the input feature data within the brackets; This represents the factorial operation; These are the predictions from the LightGBM model when only the feature subset S is used; This represents the model prediction value for the feature subset S and the input feature data i; These are weighting coefficients that ensure all features can be arranged and combined fairly.

[0131] In particular, This represents the average contribution of input feature data i in the input feature dataset x to the model's prediction, along with the positive or negative nature of the contribution. A value greater than 0 indicates a positive contribution from input feature data i to the prediction result, while a value less than 0 indicates a negative contribution. The absolute value of this value represents the absolute degree of contribution of input feature data i to the prediction result. Therefore, the model's predicted value can be considered as a linear superposition of the contributions of each feature, satisfying the additivity property.

[0132] ;

[0133] ;

[0134] in, This represents the LightGBM model prediction value for the input feature dataset x; Indicates the baseline value; This represents the contribution of input feature data i to the prediction result of input feature dataset x; This represents the input feature data i in the input feature dataset x; i represents the input feature data j in the input feature dataset x; i and j represent the indices of the input feature data.

[0135] For the correction and interpretation of hygroscopic parameters in non-ideal aerosol mixtures, the most important factor is that the Shapley value can calculate the interaction effects between characteristics, thus explaining the interaction of each characteristic. The specific formula for calculating the interaction effect is as follows:

[0136] ;

[0137] in, This represents the interaction effect value on the input feature dataset x; This represents the model prediction value for the feature subset S and the input feature data j; This represents the model prediction value of a feature subset S, input feature data i, and input feature data j; when When the value is positive, it indicates that the input feature data i and input feature data j contribute more to the model prediction when they work together than when they work alone, indicating a positive synergistic effect between them; conversely, it indicates a negative inhibitory effect between the features.

[0138] Therefore, based on the first Shapley value and interaction effect value of each input feature data, we obtain the main effect value of the input feature dataset x. Represented as:

[0139] .

[0140] The main effect value integrates the direct contribution of a feature and its interaction contribution with other features, thus reflecting the importance of the feature more comprehensively. Next, an interpretability analysis is conducted on the aerosol hygroscopicity parameter inversion model based on multiple main effect values. Specifically, this includes identifying key influencing factors through global feature importance analysis, revealing the seasonal variation characteristics of feature contributions through seasonal contribution pattern analysis, and analyzing the nonlinear response patterns of key features through feature dependencies. Specifically, the mean absolute value of the main effect values ​​of the input feature dataset x is calculated across all samples. The expression is as follows:

[0141] ;

[0142] The main effect values ​​are calculated by grouping by season. The main effect values ​​of the input feature dataset x for each season are expressed as follows:

[0143] ;

[0144] in, Represents a collection of seasons; This represents a set of seasonal characteristics, and analyzes the seasonal variation characteristics of the contribution of each characteristic.

[0145] Based on the main effect analysis, the direct contribution of each input feature data in the input feature dataset to the non-ideal mixture bias term, as well as the interactive contribution of each input feature data and other input feature data to the non-ideal mixture bias term, are analyzed. Based on the direct and interactive contributions, key features are extracted from the input feature dataset to generate empirical correction terms based on the key features.

[0146] The top 15 input features with the largest main effect values ​​are selected as key features. This means that direct and interaction contributions are sorted by magnitude, and the top 15 input features with the largest contributions are selected as key features. Figure 2 As shown in the figure, the SHAP value distribution (degree of influence) reveals that, in this embodiment, the contribution of the input feature dataset to the non-ideal mixture bias term, in descending order, is as follows: hygroscopic growth factor, inorganic volume fraction, ratio of organic to inorganic matter, annual cycle cosine term, black carbon volume fraction, sulfuric acid volume fraction, annual accumulated days, nitrate volume fraction, ratio of black carbon to organic matter, ammonium sulfate volume fraction, temperature and humidity interaction term, relative humidity, organic matter volume fraction, annual cycle sine term, and month. Therefore, these 15 input feature data are used as key features, and the key feature set composed of these 15 key features is used to calculate the empirical correction term based on the key features.

[0147] Step Six: Construct the seasonal correction factor, specifically:

[0148] Due to the significant seasonal variation in aerosol hygroscopicity parameters, a seasonal correction coefficient was constructed to correct for these parameters, thereby improving prediction accuracy under different seasonal conditions. This seasonal correction coefficient was determined by analyzing the statistical distribution characteristics of hygroscopicity parameters in historical observation data for each season and their correlation patterns with meteorological conditions and chemical composition.

[0149] The seasonal correction coefficient is constructed using the multiharmonic function form, and its mathematical expression is as follows:

[0150] ;

[0151] in, Represents month variable The seasonal correction coefficients; A, B, C, D, E, and F represent seasonal modulation effect parameters.

[0152] Step 7: Calculate the hygroscopicity parameter correction results, specifically:

[0153] Based on the ZSR hygroscopicity observation parameters, the pre-constructed seasonal correction coefficients, and the empirical correction term based on key features, the hygroscopicity parameter correction result, i.e., the hygroscopicity prediction parameter, is obtained, and the formula is:

[0154] ;

[0155] ;

[0156] in, This represents an empirical correction term based on key features; Represents the key feature set The predicted values ​​of the LightGBM model; Represents the key feature set The contribution of key feature q to the predicted values ​​of the LightGBM model; Represents the key feature set The key feature q in; This indicates the amount of data in the key feature set; This indicates the result of the hygroscopicity parameter correction; This represents the observed parameters of ZSR hygroscopicity.

[0157] Based on the Shapley value, more important factors are selected as predictors. After the model fits the parameters, the hygroscopic parameter correction results can be transformed into a simple empirical formula.

[0158] Example 2

[0159] Based on Example 1, this example presents an experimental example of a method for correcting the hygroscopic parameters of non-ideal mixed aerosols:

[0160] After constructing the training dataset, it was divided into training and test sets in a 7:3 ratio. Based on the target characteristics, we selected the eXtreme Gradient Boosting (XGBoost), LightGBM, and Categorical Boosting (CatBoost) models. Each model was trained using the training set, and the trained models were evaluated using the test set. Specifically, each model underwent a 5-fold cross-validation, and the coefficient of determination (R²), mean absolute error (MAE), root mean square error (RMSE), training time, and inference time were recorded for each fold. A scoring criterion was designed, and a comprehensive score was calculated for each model. Through multi-dimensional comprehensive evaluation, we selected the high-performing LightGBM model as the core algorithm, achieving a balance between computational accuracy and efficiency in machine learning. Experiments show that the LightGBM model has the following advantages in the task of correcting the hygroscopic parameters of non-ideal mixed aerosols: it is more efficient in processing time series data, fits data with periodic features better, and significantly improves the computational speed of interpretability analysis when combined with the SHAP value algorithm.

[0161] To facilitate a comparison of the performance of different models, a multi-dimensional comprehensive evaluation system was designed. This system comprehensively considers four key dimensions: the predictive accuracy of the included model, its generalization ability, its improvement over traditional methods (i.e., the hygroscopicity observation parameters under the ZSR ideal mixture criterion), and its computational efficiency. Through quantification and normalization, the system aims to achieve a fair comparison of different models. The specific content of this evaluation system is as follows:

[0162] Prediction accuracy is evaluated using three core metrics: R², MAE, and RMSE. Figure 3 The figure shows the time series prediction results of 100 randomly selected sample data points.

[0163] To test the model's generalization ability, i.e., its predictive ability on new data, this invention evaluates generalization ability through cross-validation stability using a 5-fold cross-validation approach. This involves uniformly dividing the dataset into five random subsets. In each round, one subset is selected as the validation set, and the other four subsets are used as the test set. R² is calculated based on the test results, resulting in five sets of results. The subscripts represent the round numbers. The mean and standard deviation of the five rounds of results are then combined and substituted into the coefficient of variation. formula:

[0164] ;

[0165] in, To cross-validate the standard deviation of each fold R²; This is the average of the R² values ​​from each fold of the cross-validation. Coefficient of variation. The smaller the value, the smaller the difference in the model's fitting performance across different training sets, indicating a more stable model and stronger generalization ability.

[0166] The improvement of quantization-included model methods compared to traditional ZSR methods The calculation formula is as follows:

[0167] ;

[0168] in, and These represent the root mean square error (RMSE) of the traditional method and the RMSE of the method including the model, respectively, under the ZSR ideal mixture assumption. The larger the value, the better the improvement of the method that includes the model compared to the traditional approach.

[0169] The computational efficiency is evaluated by combining training time and inference time, and the calculation formula is as follows:

[0170] ;

[0171] in, Score based on time. Scoring is based on training time. Score for reasoning time. Take 0.5, Take 0.5. The smaller the value, the less time the method containing the model needs to complete the task, and the faster the computation speed.

[0172] After calculating the scoring indicators for each dimension above, in order to unify the optimization objective and ensure that all indicators satisfy the condition that better model performance leads to higher scores, all indicators are normalized to the [0,1] interval using the range method. This method also eliminates interference from different units, allowing for weighted calculations of the indicators. The specific steps of the range method are as follows:

[0173] For positive indicators, use the following formula:

[0174] ;

[0175] For negative indicators, use the following formula:

[0176] ;

[0177] in, It refers to the standardized value of an indicator in a certain dimension after normalization. It refers to the magnitude of an indicator value in a certain dimension. These refer to the maximum and minimum values ​​of all candidate models in a certain dimension.

[0178] Finally, the specific formulas for calculating the scores of each dimension (Accuracy Score AS, Generalization Score GS, Improvement Score IS, and Efficiency Score ES) are as follows:

[0179] ;

[0180] ;

[0181] ;

[0182] ;

[0183] The final score (CS) is the weighted sum of the scores for each item, calculated using the following formula:

[0184] ;

[0185] in, , These represent the normalized training time and the normalized inference time, respectively.

[0186] After comprehensive consideration, we weighted the scores across four dimensions: prediction accuracy (40%), generalization ability (25%), improvement degree (20%), and computational efficiency (15%). A higher overall score (CS) indicates better performance of the method incorporating the model. After comprehensive evaluation, the method incorporating the LightGBM model achieved the highest overall score and best model performance, as shown in Table 1. Therefore, we ultimately selected the LightGBM model with the higher overall score as the core algorithm to achieve a balance between machine learning prediction accuracy and physical interpretability.

[0187] Table 1. Evaluation results of the model

[0188] Model Overall score Precision score Generalization score Improved score Efficiency Score LightGBM 0.9936 1 0.9996 0.9685 1.0000 XGBoost 0.5526 0.1021 0.9997 0.9551 0.4720 CatBoost 0.4785 0 0.9997 0.9538 0.2520

[0189] like Figure 4 As shown, the experimental results demonstrate that the empirical formula fits the non-ideal mixing effect of aerosols well and can accurately describe the relationship between observed and predicted values. This indicates that the empirical formula has a good fitting effect, simplifies the calculation process for correcting hygroscopic parameters under the ZSR ideal mixing assumption, and can quickly and accurately obtain corrected parameters in some special scenarios, reducing the cost and complexity of the analysis.

[0190] Example 3

[0191] This embodiment introduces a hygroscopic parameter correction system for non-ideal mixed aerosols, including:

[0192] The data acquisition module is used to acquire instrument observation data related to the hygroscopicity of non-ideal mixed aerosols within a predetermined time period.

[0193] The criterion estimation module is used to: estimate the instrument observation data using the ZSR ideal mixing criterion and generate ZSR hygroscopicity observation parameters;

[0194] The feature generation module is used to: obtain the input feature dataset based on the ZSR hygroscopicity observation parameters, instrument observation data, and inverted hygroscopicity observation parameters generated from the instrument observation data;

[0195] The deviation prediction module is used to: input the input feature dataset into a pre-built deviation prediction model, so that the deviation prediction model predicts the hygroscopic deviation of the input feature dataset according to the seasonal category of the input feature dataset and outputs a non-ideal mixed deviation term;

[0196] The contribution analysis module is used to: calculate the main effect value of the input feature dataset, and analyze the direct contribution of each input feature data in the input feature dataset to the non-ideal mixture bias term, as well as the interaction contribution of each input feature data and other input feature data to the non-ideal mixture bias term based on the main effect value;

[0197] The correction analysis module is used to: extract key features from the input feature dataset based on direct and interactive contributions, and generate empirical correction terms based on the key features;

[0198] The calibration generation module is used to obtain the calibration results of the hygroscopic parameters based on the ZSR hygroscopicity observation parameters, the pre-constructed seasonal calibration coefficients, and the empirical calibration terms based on key features.

[0199] The specific functions of each module described above are explained in the relevant content of the method in Embodiment 1, and will not be repeated here.

[0200] Example 4

[0201] This embodiment describes a computer-readable storage medium storing a computer program / instruction that, when executed by a processor, implements the steps of the method for correcting the hygroscopic parameters of non-ideal mixed aerosols as described in Embodiment 1 or 2.

[0202] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0203] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0204] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0205] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0206] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for correcting the hygroscopic parameters of a non-ideal mixed aerosol, characterized in that, include: Acquire instrumental observation data related to the hygroscopicity of non-ideal mixed aerosols within a predetermined time period; The instrument observation data were estimated using the ZSR ideal mixing criterion to generate ZSR hygroscopicity observation parameters. The input feature dataset is obtained by using the ZSR hygroscopicity observation parameters, instrument observation data, and inverted hygroscopicity observation parameters generated from the instrument observation data. The input feature dataset is input into a pre-built deviation prediction model, so that the deviation prediction model predicts the hygroscopic deviation of the input feature dataset according to the seasonal category of the input feature dataset and outputs a non-ideal mixed deviation term. Calculate the main effect value of the input feature dataset, and analyze the direct contribution of each input feature data in the input feature dataset to the non-ideal mixture bias term, as well as the interaction contribution of each input feature data and other input feature data to the non-ideal mixture bias term based on the main effect value; Based on direct and interactive contributions, key features are extracted from the input feature dataset, and empirical correction terms based on the key features are generated. Based on the ZSR hygroscopicity observation parameters, the pre-constructed seasonal correction coefficients, and the empirical correction terms based on key features, the hygroscopicity parameter correction results are obtained.

2. The method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to claim 1, characterized in that, The input feature dataset includes chemical component volume fraction features, chemical component interaction features, seasonal and diurnal variation features, meteorological element features, ZSR hygroscopicity observation parameters, and inverted hygroscopicity observation parameters.

3. The method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to claim 1, characterized in that, Training the bias prediction model includes: Obtain the training dataset; Based on the pre-built seasonal adaptive adjustment module, the training dataset is divided into four categories of seasonal training data according to the season; The BOHB algorithm and elastic weight update strategy are used to optimize the hyperparameters of the bias prediction model through four types of seasonal training data, resulting in a well-trained bias prediction model.

4. The method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to claim 3, characterized in that, The seasonal adaptive adjustment module is represented as follows: ； in, This indicates a seasonal adaptive adjustment module; This represents the weight of the seasonal category s at time t; This represents the seasonal function of the input feature dataset x on the seasonal category s.

5. The method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to claim 3, characterized in that, The elastic weight update strategy is expressed as follows: ； in, This indicates the updated hyperparameters; Indicates the initial hyperparameters; This represents the hyperparameters corresponding to the instrument observation data; This represents the forgetting factor.

6. The method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to claim 1, characterized in that, The main effect values ​​of the input feature dataset are expressed as follows: ； ； ； ； in, This represents the predicted value of input feature data i in the input feature dataset x for the LightGBM model. The degree of contribution; This represents the input feature dataset that does not contain input feature data i; This represents the input feature dataset; Indicates the number of data points in the input feature dataset; This represents the LightGBM model prediction value when using the input feature data within the brackets; This represents the factorial operation; This represents the interaction effect value on the input feature dataset x; i and j represent the indices of the input feature dataset. This represents the main effect value of the input feature dataset x; This represents the main effect value of the input feature dataset x for each season; Represents a collection of seasons; This represents a set of seasonal characteristics.

7. The method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to claim 1, characterized in that, The seasonal correction factor is expressed as follows: ； in, Represents month variable The seasonal correction coefficients; A, B, C, D, E, and F represent seasonal modulation effect parameters.

8. The method for correcting the hygroscopic parameters of non-ideal mixed aerosols according to claim 1, characterized in that, The correction result for the hygroscopicity parameter is expressed as follows: ； ； in, This represents an empirical correction term based on key features; Represents the key feature set The predicted values ​​of the LightGBM model; Indicates the baseline value; Represents the key feature set The contribution of key feature q to the predicted values ​​of the LightGBM model; Represents the key feature set The key feature q in; This indicates the amount of data in the key feature set; This indicates the result of the hygroscopicity parameter correction; This represents the observed parameters of ZSR hygroscopicity; Represents month variable The seasonal correction factor.

9. A system for correcting the hygroscopic parameters of a non-ideal mixed aerosol, characterized in that, include: The data acquisition module is used to acquire instrument observation data related to the hygroscopicity of non-ideal mixed aerosols within a predetermined time period. The criterion estimation module is used to: estimate the instrument observation data using the ZSR ideal mixing criterion and generate ZSR hygroscopicity observation parameters; The feature generation module is used to: obtain the input feature dataset based on the ZSR hygroscopicity observation parameters, instrument observation data, and inverted hygroscopicity observation parameters generated from the instrument observation data; The deviation prediction module is used to: input the input feature dataset into a pre-built deviation prediction model, so that the deviation prediction model predicts the hygroscopic deviation of the input feature dataset according to the seasonal category of the input feature dataset and outputs a non-ideal mixed deviation term; The contribution analysis module is used to: calculate the main effect value of the input feature dataset, and analyze the direct contribution of each input feature data in the input feature dataset to the non-ideal mixture bias term, as well as the interaction contribution of each input feature data and other input feature data to the non-ideal mixture bias term based on the main effect value; The correction analysis module is used to: extract key features from the input feature dataset based on direct and interactive contributions, and generate empirical correction terms based on the key features; The calibration generation module is used to obtain the calibration results of the hygroscopic parameters based on the ZSR hygroscopicity observation parameters, the pre-constructed seasonal calibration coefficients, and the empirical calibration terms based on key features.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the method for correcting the hygroscopic parameters of non-ideal mixed aerosols as described in any one of claims 1 to 8.

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