Particle size distribution measurement method and system based on machine learning and light scattering

Abstract

The present invention relates to the field of particle size distribution measurement, and in particular to providing a particle size distribution measurement method and system based on machine learning and light scattering method, comprising: irradiating a particle sample to be measured with a light source, and collecting light scattering intensity data of different scattering angles and different wavelengths with a multi-angle scattered light detector; constructing a multimodal deep learning model, and forming an integrated learning architecture in combination with a support vector machine model and a random forest model; inputting the preprocessed multi-wavelength light scattering intensity data into the trained integrated learning architecture to obtain a preliminary particle size distribution result of the particle sample to be measured; constructing a high-precision theoretical model considering particle shape, refractive index, surface roughness and internal structure based on an improved Mie scattering theory; and optimizing and adjusting the preliminary particle size distribution result by minimizing the error between the theoretical light scattering intensity and the actually collected light scattering intensity using an improved Bayesian optimization algorithm to obtain a corrected particle size distribution result.

Description

Technical Field

[0001] The present invention belongs to the technical field of particle size distribution measurement, and in particular relates to a particle size distribution measurement method and system based on machine learning and light scattering. Background Art

[0002] Traditional particle size distribution measurement methods mainly include screening method, sedimentation method, microscopy method, etc. Traditional particle size distribution measurement methods have the following problems:

[0003] First, factors such as noise and instrument errors in actual measurements will affect the quality of scattering data, and thus the accuracy of the inversion results. Traditional particle size distribution measurement methods have limited resistance to these interference factors, which can easily lead to unstable inversion results.

[0004] Secondly, for multimodal or complex shaped particle size distributions, traditional particle size distribution measurement methods often perform poorly. Traditional particle size distribution measurement methods usually assume that the particle size distribution has a certain mathematical form (such as log-normal distribution), which may not be flexible enough when dealing with complex distributions.

[0005] In addition, traditional particle size distribution measurement methods usually require a lot of prior knowledge and empirical parameter settings, which not only increases the complexity of the operation but also limits the versatility and automation of the method.

[0006] As a non-contact and rapid particle size distribution measurement technology, light scattering has been widely used in recent years. However, the relationship between light scattering intensity and particle size distribution is highly nonlinear, which makes accurate inversion of particle size distribution from scattering data a complex inverse problem. Traditional mathematical inversion algorithms, such as the Fredholm integral equation method or regularization method, often require complex iterative calculations and are prone to fall into local optimal solutions.

[0007] Machine learning methods can automatically learn complex nonlinear relationships from large amounts of data. However, how to effectively combine machine learning technology with light scattering methods to design a particle size distribution measurement method that can fully utilize light scattering data information and have good generalization capabilities is still a topic worthy of in-depth study, especially in processing multi-wavelength light scattering data, improving measurement accuracy and robustness, and achieving accurate inversion of complex particle size distributions. There is still much room for improvement. Summary of the invention

[0008] In view of this, the present invention aims to provide a particle size distribution measurement method and system based on machine learning and light scattering method, which effectively combines the machine learning method with the light scattering method, can fully utilize the light scattering data information, and has good generalization ability, especially in processing multi-wavelength light scattering data, improving the accuracy and robustness of measurement, and realizing the accurate inversion of complex particle size distribution, etc., to achieve great improvement.

[0009] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0010] A method for measuring particle size distribution based on machine learning and light scattering method, comprising the following steps:

[0011] S1: Use the light source module to illuminate the particle sample to be tested to generate scattered light of different wavelengths and different scattering angles. At the same time, use the multi-angle scattered light detector to synchronously collect the scattered light intensity data of all scattered light, and pre-process the scattered light intensity data. The pre-processing includes denoising, normalization and feature extraction.

[0012] S2: Build a multimodal deep learning model, a support vector machine model, and a random forest model respectively, and integrate the multimodal deep learning model, the support vector machine model, and the random forest model based on the stacking strategy to build an integrated learning architecture;

[0013] S3: Using sample data of known particle size distribution to train the integrated learning framework, establish a mapping relationship between scattered light intensity data and particle size distribution, input the preprocessed scattered light intensity data into the trained integrated learning framework, and obtain the preliminary particle size distribution results of the particle sample to be tested;

[0014] S4: Based on the improved Mie light scattering theory, a light scattering theoretical model is constructed which takes into account the particle shape, refractive index, surface roughness and internal structure. The preliminary particle size distribution results of the particle sample to be tested are substituted into the light scattering theoretical model to calculate the theoretical scattered light intensity. The error between the theoretical scattered light intensity and the scattered light intensity data collected by the multi-angle scattered light detector is also calculated. The error is minimized using an improved Bayesian optimization algorithm to optimize the preliminary particle size distribution results of the particle sample to be tested and obtain the corrected particle size distribution results.

[0015] Furthermore, the light source module includes a light source and a collimating optical system, the light source adopts a tunable quantum cascade laser, and the collimating optical system includes a beam expander and a collimating lens.

[0016] Furthermore, the discrete wavelet transform method is used to denoise the scattered light intensity data. The specific process is as follows:

[0017] Select wavelet basis functions to perform multi-scale decomposition on scattered light intensity data to obtain wavelet coefficients of different frequency components;

[0018] The threshold of each wavelet coefficient subband is calculated using an adaptive threshold method;

[0019] Use soft threshold function to perform threshold shrinkage processing on wavelet coefficients;

[0020] The wavelet coefficients after threshold shrinkage are recombined through inverse wavelet transform to obtain the denoised scattered light intensity data;

[0021] The denoised scattered light intensity data is normalized by Z-score. The specific process is as follows:

[0022] Calculate the mean and standard deviation of the scattered light intensity data, then subtract the mean from the scattered light intensity data and divide it by the standard deviation to complete the normalization of the scattered light intensity data;

[0023] The local binary pattern feature extraction method is used to extract features from the normalized scattered light intensity data. The specific process is as follows:

[0024] The normalized scattered light intensity data is divided into a plurality of small regions, and the local binary pattern features are calculated in each small region;

[0025] Count the local binary pattern feature histogram of each small area, and connect the local binary pattern feature histograms of all small areas to form a high-dimensional feature vector;

[0026] The principal component analysis method is used to reduce the dimensionality of high-dimensional feature vectors, and the principal components whose cumulative explained variance reaches a preset threshold are selected as feature vectors.

[0027] Furthermore, the multimodal deep learning model includes a convolutional neural network module, a long short-term memory network module and a multi-head attention mechanism module; wherein the convolutional neural network module performs wavelet transform on the input scattered light intensity data, decomposes the data into different frequency sub-bands, designs convolution kernels of corresponding scales for different frequency sub-bands, performs weighted fusion of features of different scales through the attention mechanism module, and adds a residual connection after the convolution block; the long short-term memory network module reconstructs the scattered light intensity data into a time series format, uses a bidirectional long short-term memory network to capture bidirectional temporal dependencies, and adds an attention layer on top of the long short-term memory network layer; the multi-head attention mechanism module performs position encoding on the input data, calculates the attention score by setting multiple attention heads, splices the outputs of multiple attention heads and fuses them through linear transformation;

[0028] The feature dimensions are reduced by principal component analysis and then input into the support vector machine model. The support vector machine model uses a radial basis function kernel, and the parameters of the support vector machine are optimized through grid search and cross validation.

[0029] The random forest model was used to extract statistical features, set the number of trees and use the Gini index as the splitting criterion, and calculate the feature importance score.

[0030] Furthermore, based on the Stacking strategy, the multimodal deep learning model, support vector machine model and random forest model are integrated to build an integrated learning architecture. The specific process is as follows:

[0031] Train multimodal deep learning models, support vector machine models, and random forest models as base learners;

[0032] The meta-features are generated by using the cross-validation method. The training data is divided into multiple parts. Some of the data are used cyclically to train the base learner and prediction is performed on the remaining data. The prediction results of each base learner are collected as meta-features.

[0033] Design XGBoost as a meta-learner and set model parameters including maximum tree depth, learning rate, subsampling ratio, feature sampling ratio, minimum child node weight, and regularization parameter;

[0034] The importance scores of the original features of the scattered light intensity data were calculated using the random forest model, and the importance scores were normalized;

[0035] The meta-features are weighted according to the normalized importance scores, where the weights of the meta-features generated by the multimodal deep learning model are fixed, and the weights of the meta-features generated by the support vector machine model and the random forest model are calculated according to the importance scores of the original features;

[0036] The weighted meta-features are concatenated with the original features to form the final training feature set;

[0037] Use the training feature set to train the XGBoost meta-learner, use the mean square error as the optimization objective, and set the early stopping strategy.

[0038] Furthermore, the specific process of inputting the preprocessed scattered light intensity data into the trained integrated learning framework to obtain the preliminary particle size distribution results of the particle sample to be tested is as follows:

[0039] The preprocessed scattered light intensity data is input into the multimodal deep learning model, and the local features in the scattered light intensity data are extracted using the convolutional neural network module. The temporal dependencies in the scattered light intensity data are captured using the long short-term memory network module. The long-range dependencies between local features are established using the multi-head attention mechanism module to obtain the first preliminary particle size distribution prediction result.

[0040] The pre-processed scattered light intensity data is reduced in dimension using principal component analysis, and the reduced scattered light intensity data is input into the support vector machine model to obtain the second preliminary particle size distribution prediction result;

[0041] The preprocessed scattered light intensity data is fed into the random forest model, and the third preliminary particle size distribution prediction result is obtained through decision tree integration;

[0042] The three preliminary particle size distribution prediction results are standardized to obtain a standardized preliminary particle size distribution prediction result;

[0043] The standardized preliminary particle size distribution prediction results were weighted according to the feature importance scores calculated by the random forest model to generate meta-features;

[0044] The weighted meta-features were concatenated with the original features of the scattered light intensity data and input into the trained XGBoost meta-learner to obtain the final preliminary particle size distribution results.

[0045] Furthermore, based on the improved Mie light scattering theory, the specific process of constructing a light scattering theoretical model that takes into account particle shape, refractive index, surface roughness and internal structure is as follows:

[0046] The improved Mie light scattering theory includes the introduction of T-matrix method, wavelength-dependent complex refractive index model, perturbation method and discrete dipole approximation method;

[0047] For non-spherical particles, the T-matrix method is introduced to expand the incident field and the scattered field into spherical vector wave functions, and the relationship between the two is established through the T-matrix; for axisymmetric particles, the extended boundary condition method is used to calculate the T-matrix method;

[0048] A wavelength-dependent complex refractive index model is introduced. The real part of the refractive index is described by the Sellmeier equation, and the imaginary part is described by the exponential decay model.

[0049] The perturbation method is used to represent the rough surface as an average surface plus random fluctuations, and the corrected scattering amplitude is obtained by expanding the surface current to the first-order perturbation.

[0050] The discrete dipole approximation method is introduced to discretize particles with complex internal structures into multiple dipoles, and the polarization intensity of each dipole is obtained by solving a set of linear equations.

[0051] A light scattering theoretical model is constructed based on the calculation results of the T-matrix method, complex refractive index model, perturbation method and discrete dipole approximation method.

[0052] Furthermore, the preliminary particle size distribution result of the particle sample to be tested is substituted into the light scattering theoretical model to calculate the theoretical scattered light intensity, and the error between the theoretical scattered light intensity and the scattered light intensity data collected by the multi-angle scattered light detector is calculated. The improved Bayesian optimization algorithm is used to minimize the error to optimize the preliminary particle size distribution result of the particle sample to be tested. The specific process of obtaining the corrected particle size distribution result is as follows:

[0053] The improved Bayesian optimization algorithm includes the introduction of multi-scale radial basis function kernel, adaptive acquisition function and local penalty strategy;

[0054] Construct a Gaussian process regression model. The Gaussian process regression model uses a multi-scale radial basis function kernel as the covariance function and captures feature changes in different dimensions by introducing different length scales.

[0055] The kernel function parameters are automatically determined by using the maximum marginal likelihood estimation method based on gradient descent, and the kernel function parameters that best explain the observed data are obtained by maximizing the logarithmic marginal likelihood function.

[0056] Design an adaptive acquisition function, which combines the expected improvement function and the probability improvement function, and introduces a weight function that is dynamically adjusted during the optimization process;

[0057] A local penalty strategy is introduced to improve the global search capability by defining a penalty function to inhibit the algorithm from continuing to sample in the fully explored area.

[0058] The particle size distribution was represented by a mixture model of lognormal distribution, including the weight, log mean and log standard deviation parameters of each component;

[0059] A comprehensive objective function is constructed, including the root mean square error between the theoretical scattering intensity and the measured scattering intensity, a smooth regularization term and a physical constraint term, wherein the smooth regularization term adopts total variation regularization, and the physical constraint term includes a non-negative constraint and a normalization constraint;

[0060] Latin hypercube sampling was used to generate an initial set of particle size distribution parameters, and the Gaussian process regression model was updated by iteratively applying a modified Bayesian optimization algorithm;

[0061] A batch parallel evaluation strategy is adopted to select multiple candidate points for evaluation at the same time in each iteration, ensuring diversity by maximizing the minimum distance between candidate points;

[0062] Set a multi-criteria convergence judgment method; perform an iterative optimization process, update the particle size distribution parameters, including the weight, logarithmic mean and logarithmic standard deviation of each component, and obtain the optimal particle size distribution parameters when the convergence condition is met or the maximum number of iterations is reached;

[0063] The preliminary particle size distribution result is corrected based on the optimal particle size distribution parameter to obtain a corrected particle size distribution result.

[0064] A particle size distribution measurement system based on machine learning and light scattering method, used to execute the above-mentioned particle size distribution measurement method based on machine learning and light scattering method, including a light source module, a multi-angle scattered light detector, a preprocessing unit, a modal deep learning model construction unit, a support vector machine model construction unit, a random forest model construction unit, an integrated learning architecture construction unit, an integrated learning architecture training unit, a light scattering theory model construction unit, a theoretical scattered light intensity calculation unit, an error calculation unit and a step particle size distribution result optimization unit; wherein,

[0065] The light source module is used to illuminate the particle sample to be tested and generate scattered light of different wavelengths and different scattering angles;

[0066] The multi-angle scattered light detector is used to synchronously collect scattered light intensity data of all scattered light and preprocess the scattered light intensity data, and the preprocessing includes denoising, normalization and feature extraction;

[0067] The modal deep learning model building unit is used to build a multimodal deep learning model;

[0068] The support vector machine model building unit is used to build a support vector machine model;

[0069] The random forest model building unit is used to build a random forest model;

[0070] The integrated learning architecture building unit is used to integrate the multimodal deep learning model, support vector machine model and random forest model based on the stacking strategy to build an integrated learning architecture;

[0071] The integrated learning framework training unit is used to train the integrated learning framework using sample data of known particle size distribution, establish a mapping relationship between scattered light intensity data and particle size distribution; input the preprocessed scattered light intensity data into the trained integrated learning framework to obtain a preliminary particle size distribution result of the particle sample to be tested;

[0072] The light scattering theoretical model building unit is used to build a light scattering theoretical model that takes into account particle shape, refractive index, surface roughness and internal structure based on the improved Mie light scattering theory;

[0073] The theoretical scattered light intensity calculation unit is used to substitute the preliminary particle size distribution result of the particle sample to be tested into the light scattering theoretical model to calculate the theoretical scattered light intensity;

[0074] The error calculation unit is used to calculate the error between the theoretical scattered light intensity and the scattered light intensity data collected by the multi-angle scattered light detector;

[0075] The step particle size distribution result optimization unit is used to minimize the error by adopting an improved Bayesian optimization algorithm, so as to optimize the preliminary particle size distribution result of the particle sample to be tested and obtain a corrected particle size distribution result.

[0076] A computer device comprising:

[0077] at least one processor; and

[0078] a memory communicatively connected to at least one processor; wherein,

[0079] The memory stores instructions that can be executed by at least one processor, and the instructions are executed by at least one processor so that the at least one processor can execute the above-mentioned particle size distribution measurement method based on machine learning and light scattering method.

[0080] A non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable a computer to execute the above-mentioned particle size distribution measurement method based on machine learning and light scattering method.

[0081] Compared with the prior art, the invention can achieve the following beneficial effects:

[0082] (1) First, the multimodal deep learning model adopted by the present invention can capture the features of multi-wavelength scattered light intensity data from different angles, thereby improving the comprehensiveness and effectiveness of feature extraction; second, the support vector machine model and the random forest model, as traditional machine learning methods, have good generalization ability and interpretability, which supplement the deficiencies of the multimodal deep learning model; third, the integrated learning architecture based on the stacking strategy fully utilizes the advantages of each model and significantly improves the accuracy and robustness of particle size distribution analysis; finally, the entire technical solution has strong versatility and scalability, and can be flexibly adjusted and optimized according to specific application scenarios, providing an efficient and reliable solution for particle size distribution analysis;

[0083] (2) First, by introducing the T-matrix method, the present invention significantly improves the applicability of the light scattering theoretical model to non-spherical particles, so that the light scattering theoretical model can accurately describe the scattering characteristics of particles of various shapes; secondly, the wavelength-dependent complex refractive index model provides a more accurate description of the optical properties of the material, which helps to improve the accuracy of the model over a wide wavelength range; thirdly, the application of the perturbation method enables the model to effectively deal with the influence of surface roughness, especially in high-angle scattering, and the performance is more accurate; finally, the introduction of the discrete dipole approximation method enables the model to deal with particles with complex internal structures, greatly expanding the scope of application of the light scattering theoretical model. Combining these improvements, the constructed light scattering theoretical model can more accurately describe the scattering characteristics of actual particles, providing a solid theoretical basis for particle size distribution analysis, and is expected to significantly improve the accuracy and reliability of particle size measurement;

[0084] (3) First, by introducing a multi-scale radial basis function kernel and an adaptive acquisition function, the present invention significantly improves the search efficiency and accuracy of the Bayesian optimization algorithm in complex parameter spaces. Second, the introduction of a local penalty strategy effectively enhances the global search capability of the algorithm and reduces the risk of falling into local optimality. Third, the design of a comprehensive objective function ensures a balance between fitting accuracy, smoothness, and physical rationality in the optimization results. Finally, a batch parallel evaluation strategy greatly improves computational efficiency, enabling this method to be applied to large-scale particle size distribution analysis problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings:

[0086] Figure 1 A schematic diagram of a process for measuring particle size distribution based on machine learning and light scattering method according to an embodiment of the present invention;

[0087] Figure 2 A schematic diagram of the structure of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0088] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0089] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0090] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0091] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0092] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0093] like Figure 1 As shown, the present invention provides a particle size distribution measurement method based on machine learning and light scattering method, comprising the following steps:

[0094] S1: Use the light source module to illuminate the particle sample to be tested to generate scattered light of different wavelengths and different scattering angles. At the same time, use the multi-angle scattered light detector to synchronously collect the scattered light intensity data of all scattered light, and pre-process the scattered light intensity data. The pre-processing includes denoising, normalization and feature extraction.

[0095] The light source module includes a light source and a collimating optical system. The light source adopts a tunable quantum cascade laser, which has the characteristics of adjustable wavelength and high spectral purity, and can provide monochromatic light of multiple wavelengths. By adjusting the working parameters of the tunable quantum cascade laser, scattering measurements at different wavelengths can be achieved, thereby obtaining richer particle characteristic information; the collimating optical system includes a beam expander and a collimator. The beam expander is used to expand the laser output by the tunable quantum cascade laser, and the collimator is used to collimate the laser after expansion. The collimating optical system can effectively control the divergence angle of the light beam to ensure that the light beam incident on the particle sample has good parallelism and uniformity.

[0096] The multi-angle scattered light detector uses an annular photodiode array, which consists of multiple photodiodes arranged in a ring. Each photodiode is responsible for detecting the light intensity within a specific scattering angle range. In order to improve the angular resolution and reduce the interference between adjacent angles, a micro-shielding partition is set between adjacent photodiodes to effectively reduce the crosstalk of scattered light and improve the accuracy of angle measurement.

[0097] In order to ensure the time consistency of the data, a high-speed data acquisition card is used to synchronously collect the signals of all photodiodes. During the data acquisition process, the influence of ambient light also needs to be considered. The background signal is collected without samples and subtracted in subsequent processing to improve the signal-to-noise ratio.

[0098] The collected scattered light intensity data is preprocessed to improve the data quality and the effectiveness of feature extraction. The preprocessing is divided into three steps: denoising, normalization and feature extraction.

[0099] Data denoising: The discrete wavelet transform method is used for denoising. The specific steps include: selecting appropriate wavelet basis functions, performing multi-scale decomposition on the scattered light intensity data, and obtaining wavelet coefficients of different frequency components; then, using the adaptive threshold method to calculate the threshold of each wavelet coefficient subband, here we use the threshold selection method based on the statistical characteristics of the wavelet coefficient, such as the universal threshold or the SURE threshold; next, using the soft threshold function to perform threshold shrinkage processing on the wavelet coefficients to suppress the noise component; finally, through the inverse wavelet transform, the wavelet coefficients after threshold shrinkage processing are recombined to obtain the denoised scattered light intensity data.

[0100] Normalization: In order to eliminate the scale differences between different wavelengths and angles, the denoised scattered light intensity data is subjected to Z-score normalization. The Z-score normalization process includes calculating the mean and standard deviation of the scattered light intensity data, then subtracting the mean from the scattered light intensity data and dividing it by the standard deviation to complete the normalization of the scattered light intensity data. The normalized data has zero mean and unit variance, which is beneficial for subsequent feature extraction and pattern recognition.

[0101] Feature extraction: Aims to extract the most representative features from high-dimensional scattered light intensity data. This technology uses the local binary pattern (LBP) feature extraction method, which can effectively capture the local texture information of scattered light intensity data. First, the normalized two-dimensional scattered light intensity data (angle-wavelength) is divided into multiple small areas, and the LBP features are calculated in each area; then, the LBP feature histogram of each area is counted, and the histograms of all areas are connected to form a high-dimensional feature vector.

[0102] Considering the "dimensionality disaster" problem that may be caused by the high dimensionality of LBP feature vectors, the principal component analysis (PCA) method is introduced for dimensionality reduction. The PCA method projects the original high-dimensional features into a new feature space through linear transformation, so that the projected features have the maximum variance. In actual operation, the covariance matrix of the feature vector is first calculated, and then its eigenvalues ​​and eigenvectors are solved. The eigenvectors are sorted according to the corresponding eigenvalues, and the first few principal components whose cumulative explained variance reaches the preset threshold (such as 95%) are selected as the final eigenvectors.

[0103] S2: Build a multimodal deep learning model, a support vector machine model, and a random forest model respectively, and integrate the multimodal deep learning model, the support vector machine model, and the random forest model based on the Stacking strategy to build an integrated learning architecture.

[0104] Multimodal deep learning model: including a convolutional neural network module, a long short-term memory network module and a multi-head attention mechanism module; wherein the convolutional neural network module performs wavelet transform on the input scattered light intensity data, decomposes the data into multiple frequency sub-bands, and designs convolution kernels of corresponding scales for different frequency sub-bands, performs weighted fusion of features of different scales through the attention mechanism, and adds residual connections after the convolution block; the long short-term memory network module reconstructs the scattered light intensity data into a time series format, uses a bidirectional long short-term memory network to capture bidirectional temporal dependencies, and adds an attention layer on top of the long short-term memory network layer; the multi-head attention mechanism module performs position encoding on the input data, sets multiple attention heads to calculate attention scores, splices the outputs of multiple attention heads and fuses them through linear transformation.

[0105] Support vector machine model: The input feature dimension is reduced by principal component analysis, radial basis function kernel is adopted, and the parameters of the support vector machine are optimized by grid search and cross validation.

[0106] Build a random forest model: extract statistical features, set the number of trees and use the Gini index as the splitting criterion, and calculate feature importance scores.

[0107] For example, particle size measurement analysis is a complex pattern recognition problem that requires extracting effective features from multi-angle scattered light intensity data and accurately classifying them. In order to improve the accuracy and robustness of the analysis, the present invention integrates a multimodal deep learning model, a support vector machine model, and a random forest model based on a stacking strategy to construct an integrated learning architecture.

[0108] Firstly, a multimodal deep learning model is constructed, which integrates convolutional neural network module, long short-term memory network module and multi-head attention mechanism module to make full use of the different characteristics of scattered light intensity data.

[0109] According to the characteristics of scattered light intensity data, the convolutional neural network module performs wavelet transform on the input scattered light intensity data and decomposes it into multiple frequency subbands. For example, 5 layers of decomposition are performed using Daubechies wavelet to obtain 5 subbands of different frequencies. Convolution kernels of different scales are designed for these subbands. Low-frequency subbands use larger convolution kernels (such as 7x7), medium-frequency subbands use medium-sized convolution kernels (such as 5x5), and high-frequency subbands use smaller convolution kernels (such as 3x3). This design can capture features of different scales. After the convolution operation, an attention mechanism is introduced to perform weighted fusion of features of different scales. Specifically, a dual attention mechanism combining channel attention and spatial attention is used to calculate the importance weight of each feature map. In order to alleviate the problem of network degradation, a residual connection is added after each convolution block. The typical convolution block structure includes: convolution layer, batch normalization layer, ReLU activation function, attention layer, and residual connection.

[0110] The long short-term memory (LSTM) network module is designed to capture the temporal dependencies in the scattered light intensity data. First, the two-dimensional scattered intensity data is reconstructed into a time series format, where the scattered intensity data of each wavelength is regarded as a time step. A bidirectional long short-term memory network structure is adopted, including two LSTM layers, forward and backward, each containing 128 hidden units. The bidirectional structure can consider both past and future contextual information. On top of the LSTM layer, an attention layer is added to adaptively give different weights to the outputs of different time steps. This design can highlight important time steps and improve the model's sensitivity to key features.

[0111] The multi-head attention mechanism module is designed to handle long-range dependencies in scattered light intensity data. First, the input data is positionally encoded, and a combination of sine and cosine functions is used to represent the position information. Eight attention heads are set, and each head calculates the attention score independently. The attention calculation process includes three linear transformations of query, key, and value, and then the attention weight is obtained through dot product and softmax function. The outputs of multiple heads are fused through splicing and linear transformation to finally obtain the fused feature representation.

[0112] When constructing the support vector machine model, considering the computational complexity that may be caused by high-dimensional features, we first perform dimensionality reduction through principal component analysis. Retaining the principal components with a cumulative explained variance of 95% can usually reduce the feature dimension from the original thousands of dimensions to dozens of dimensions. The radial basis function is selected as the kernel function, and its parameters C (regularization parameter) and gamma (kernel function parameter) are optimized through grid search and 5-fold cross validation. The search range is set to C: [0.1, 1, 10, 100], gamma: [0.01, 0.1, 1, 10].

[0113] The construction of the random forest model focuses on feature engineering and model parameter optimization. First, statistical features are extracted, including mean, variance, skewness, kurtosis, etc. The number of trees is set to 500, and the Gini index is used as the criterion for node splitting. In order to improve the interpretability of the model, feature importance scores are calculated to identify the most critical features for particle size distribution analysis.

[0114] Finally, the stacking strategy is used to integrate the multimodal deep learning model, the support vector machine model, and the random forest model to build an integrated learning architecture. Specifically, these three models are used as base learners, and their outputs are input into a meta-learner (such as logistic regression) as new features. The prediction results of the base learners are generated using k-fold cross validation (k=5) to avoid overfitting. The meta-learner is trained on these prediction results to learn how to optimally combine the predictions of the base learners.

[0115] The multimodal deep learning model adopted in the present invention can capture the characteristics of scattered light intensity data from different angles, thereby improving the comprehensiveness and effectiveness of feature extraction. Secondly, as traditional machine learning methods, support vector machines and random forest models have good generalization ability and interpretability, which supplement the deficiencies of deep learning models. Thirdly, the integrated learning architecture based on Stacking makes full use of the advantages of each model and significantly improves the accuracy and robustness of particle size distribution analysis. Finally, the entire technical solution has strong versatility and scalability, and can be flexibly adjusted and optimized according to specific application scenarios, providing an efficient and reliable solution for particle size distribution analysis.

[0116] In an optional embodiment, the steps of integrating the multimodal deep learning model, the support vector machine model and the random forest model based on the stacking strategy to construct an integrated learning architecture include:

[0117] Multimodal deep learning models, support vector machine models, and random forest models are trained as base learners.

[0118] The cross-validation method is used to generate meta-features. The training data is divided into multiple parts. Some of the data are used cyclically to train the base learner and predictions are made on the remaining data. The prediction results of each base learner are collected as meta-features.

[0119] Design XGBoost as a meta-learner and set model parameters including maximum tree depth, learning rate, subsampling ratio, feature sampling ratio, minimum child node weight, and regularization parameter.

[0120] The importance scores of the original features of the scattered light intensity data were calculated using the random forest model, and the scores were normalized.

[0121] The meta-features are weighted according to the normalized importance scores, where the weights of the meta-features generated by the multimodal deep learning model are fixed, and the weights of the meta-features generated by the support vector machine and random forest models are calculated according to the importance scores of the original features.

[0122] The weighted meta-features are concatenated with the original features to form the final training feature set.

[0123] Use the training feature set to train the XGBoost meta-learner, use the mean square error as the optimization objective, and set the early stopping strategy.

[0124] Exemplarily, ensemble learning is an effective method to improve model performance in machine learning. The present invention revolves around an ensemble learning architecture based on a stacking strategy, aiming to integrate the advantages of multimodal deep learning models, support vector machine models, and random forest models to improve the accuracy and robustness of particle size distribution analysis.

[0125] First, a multimodal deep learning model, a support vector machine model, and a random forest model were trained as base learners. The multimodal deep learning model used the Adam optimizer, with a learning rate of 0.001, a batch size of 64, and 100 training rounds. The support vector machine model used a radial basis function kernel with a C parameter of 10 and a gamma parameter of 0.1. The random forest model set the number of trees to 500, the maximum depth to 10, and the minimum number of leaf node samples to 5. These parameters were selected based on previous grid search and cross-validation results.

[0126] Next, the meta-features are generated using the cross-validation method. Specifically, the training data is divided into 5 parts, and 5-fold cross-validation is used. In each round, 4 parts of the data are used to train the base learner, and then predictions are made on the remaining 1 part of the data. This process is repeated 5 times to ensure that each part of the data is used as a validation set once. The prediction results of each base learner on the validation set are collected, and these prediction results will be used as meta-features. For example, for a data set containing 1000 samples, each base learner will generate 1000 prediction values, forming a 1000x3 meta-feature matrix.

[0127] In order to further improve the performance of ensemble learning, XGBoost (extreme gradient boosting) is selected as the meta-learner. XGBoost is an efficient gradient boosting decision tree algorithm with good generalization and anti-overfitting capabilities. The key parameters for setting XGBoost include: maximum tree depth of 6, learning rate of 0.1, subsampling ratio of 0.8, feature sampling ratio of 0.8, minimum child node weight of 1, L1 regularization parameter of 0.1, and L2 regularization parameter of 1. The selection of these parameters is based on experience and preliminary experimental results, and can be fine-tuned according to the characteristics of the specific data set.

[0128] Considering the different contributions of different features to the particle size distribution analysis, a feature importance weighting mechanism is introduced. The importance scores of the original features of the scattered light intensity data are calculated using the random forest model. For example, for a dataset containing 100 features, the random forest model may output 100 importance scores ranging from 0 to 1. These scores are normalized so that their sum is 1.

[0129] The meta-features are weighted based on the normalized importance scores. The weights of the meta-features generated by the multimodal deep learning model are fixed to 1 because the multimodal deep learning model already has strong feature extraction capabilities. The weights of the meta-features generated by the support vector machine and random forest models are calculated based on the importance scores of the original features. Specifically, for each prediction value of the support vector machine and random forest model, its weight is equal to the sum of the importance scores of the original features used to generate the prediction. This weighting method can highlight the contribution of important features and suppress the influence of unimportant features.

[0130] The weighted meta-features are concatenated with the original features to form the final training feature set. For example, for a case with 100 original features and 3 base learners, the dimension of the final training feature set is 103. This feature combination method not only retains the information of the original data, but also introduces the prediction results of the base learners, which is conducive to improving the performance of the model.

[0131] The XGBoost meta-learner is trained using the constructed training feature set. The mean square error is used as the optimization objective, which is a common loss function for regression problems. To prevent overfitting, an early stopping strategy is set: when the performance on the validation set does not improve for 10 consecutive rounds, the training is stopped. During the training process, 5-fold cross validation is used to evaluate the model performance, and the model with the best performance on the validation set is selected as the final model.

[0132] The stacking-based integrated learning architecture adopted by the present invention makes full use of the advantages of multiple models and significantly improves the accuracy of particle size distribution analysis. Secondly, the method of cross-validation to generate meta-features effectively reduces the risk of overfitting and improves the generalization ability of the model. Thirdly, the feature importance weighting mechanism is introduced to make the model pay more attention to key features and improve the reliability of prediction. Finally, the strategy of combining the original features with the meta-features not only retains the information of the original data, but also introduces the prediction results of the model, providing more abundant information for the XGBoost meta-learner, thereby further improving the performance of the overall model. This integrated learning method is not only suitable for particle size distribution analysis, but can also be extended to other complex regression and classification problems, and has broad application prospects.

[0133] S3: Use sample data of known particle size distribution to train the integrated learning framework, establish a mapping relationship between scattered light intensity data and particle size distribution, input the preprocessed scattered light intensity data into the trained integrated learning framework, and obtain the preliminary particle size distribution results of the particle sample to be tested.

[0134] The preprocessed scattered light intensity data is input into the trained integrated learning architecture, local features are extracted using a convolutional neural network, temporal information is processed using a long short-term memory network, and the long-range dependencies between features are captured using a multi-head attention mechanism to obtain the first preliminary particle size distribution prediction result.

[0135] The input scattered light intensity data was reduced in dimension using principal component analysis, and the reduced data was input into the support vector machine model to obtain the second preliminary particle size distribution prediction result.

[0136] The input scattered light intensity data was fed into the random forest model, and the third preliminary particle size distribution prediction result was obtained through decision tree integration.

[0137] The three preliminary particle size distribution prediction results were standardized.

[0138] The standardized preliminary particle size distribution prediction results were weighted according to the feature importance calculated by the random forest model to generate meta-features.

[0139] The weighted meta-features were concatenated with the original features of the scattered light intensity data and input into the trained XGBoost model to obtain the final preliminary particle size distribution results.

[0140] For example, particle size distribution analysis is an important research topic in the fields of materials science, environmental monitoring, and biomedicine. In order to improve the accuracy and robustness of particle size distribution measurement, the present invention comprehensively utilizes multiple machine learning algorithms to fully mine the information in the scattered light intensity data, thereby obtaining a more accurate preliminary particle size distribution result.

[0141] First, the preprocessed scattered light intensity data is input into the trained ensemble learning architecture. The first part of the ensemble learning architecture is a multimodal deep learning model, which includes a convolutional neural network module, a long short-term memory network module, and a multi-head attention mechanism module. The convolutional neural network module is used to extract local features. Three convolutional layers can be set, each layer uses 32, 64, and 128 3x3 convolution kernels, and each layer is followed by a maximum pooling layer and a batch normalization layer. The long short-term memory network module is used to process temporal information. Two layers of LSTM can be set, each layer contains 128 hidden units. The multi-head attention mechanism module is used to capture the long-range dependencies between features. Eight attention heads can be set, and the dimension of each head is 64. The combination of multimodal deep learning models can comprehensively analyze the various features of the scattered light intensity data and obtain the first preliminary particle size distribution prediction results.

[0142] Next, principal component analysis is used to reduce the dimensionality of the input scattered light intensity data. Assuming that the original data has 100 features, it can be reduced to 20 principal components, retaining 95% of the variance information. The reduced-dimensional data is input into the support vector machine model, and a radial basis function kernel can be used, with the kernel parameter gamma set to 0.1 and the regularization parameter C set to 10. The support vector machine can effectively handle nonlinear problems and obtain the second preliminary particle size distribution prediction result.

[0143] Then, the input scattered light intensity data is fed into the random forest model. 500 decision trees can be set, with a maximum depth of 10 and a minimum number of leaf node samples of 5 for each tree. The random forest can process high-dimensional data and has strong robustness to noise through decision tree integration, thereby obtaining the third preliminary particle size distribution prediction result.

[0144] The three preliminary particle size distribution prediction results are standardized, converting each prediction result to a distribution with a mean of 0 and a standard deviation of 1. This can eliminate the differences in the output scales of different models and make the subsequent integration more fair and effective.

[0145] The standardized preliminary particle size distribution predictions are weighted according to the feature importance calculated by the random forest model. For example, if the random forest model calculates the importance of three predictions as 0.4, 0.3, and 0.3, then these weights can be used to weight the standardized predictions and generate meta-features. This weighting based on feature importance can fully utilize the random forest model's understanding of the data features.

[0146] Finally, the weighted meta-features are concatenated with the original features of the scattered light intensity data. Assuming that the meta-features have 50 dimensions and the original features have 100 dimensions, a 150-dimensional feature vector is obtained after concatenation. This feature vector is input into the trained XGBoost model. The XGBoost model can set the maximum tree depth to 6, the learning rate to 0.1, the regularization parameter alpha to 1, the gamma to 0.1, and the minimum sum of child node weights to 1. As an efficient integrated learning algorithm, XGBoost can comprehensively utilize meta-features and original features to obtain the final preliminary particle size distribution results.

[0147] The present invention fully exploits various features in scattered light intensity data by comprehensively utilizing deep learning and traditional machine learning methods, and improves the accuracy and robustness of particle size distribution prediction. Among them, convolutional neural network effectively extracts local features, long short-term memory network effectively captures temporal information, and multi-head attention mechanism effectively establishes long-range dependencies between features. The combination of these deep learning technologies greatly enhances the expression ability of the model. Secondly, the combination of principal component analysis and support vector machine effectively handles the dimensionality reduction and nonlinear mapping problems of high-dimensional data, while the random forest model provides another angle of prediction results and feature importance evaluation. Thirdly, through feature importance weighting and meta-feature generation, the effective fusion of prediction results of different models is achieved. Finally, the XGBoost model, as the final integrated learner, further improves the accuracy and generalization ability of the prediction. This multi-level, multi-angle integrated learning architecture can not only process complex multi-wavelength light scattering data, but also has strong noise resistance and generalization ability, and provides a new method for particle size distribution analysis that is efficient and accurate, which is expected to have an important impact in multiple scientific research and industrial fields.

[0148] S4: Based on the improved Mie light scattering theory, a light scattering theoretical model is constructed which takes into account the particle shape, refractive index, surface roughness and internal structure. The preliminary particle size distribution results of the particle sample to be tested are substituted into the light scattering theoretical model to calculate the theoretical scattered light intensity. The error between the theoretical scattered light intensity and the scattered light intensity data collected by the multi-angle scattered light detector is also calculated. The error is minimized using an improved Bayesian optimization algorithm to optimize the preliminary particle size distribution results of the particle sample to be tested and obtain the corrected particle size distribution results.

[0149] The improved Mie light scattering theory includes the introduction of the T-matrix method, the wavelength-dependent complex refractive index model, the perturbation method and the discrete dipole approximation method; for non-spherical particles, the T-matrix method is introduced to expand the incident field and the scattered field into spherical vector wave functions, and the relationship between the two is established through the T-matrix; for axisymmetric particles, the extended boundary condition method is used to calculate the T-matrix method; the wavelength-dependent complex refractive index model is introduced, the real part of the refractive index is described by the Sellmeier equation, and the imaginary part is described by the exponential decay model; the perturbation method is used to represent the rough surface as an average surface plus random fluctuations, and the corrected scattering amplitude is obtained by expanding the surface current to a first-order perturbation; the discrete dipole approximation method is introduced to discretize particles with complex internal structures into multiple dipoles, and the polarization intensity of each dipole is obtained by solving a set of linear equations; based on the calculation results of the T-matrix method, the complex refractive index model, the perturbation method and the discrete dipole approximation method, a light scattering theoretical model is constructed.

[0150] For example, in particle size distribution analysis, an accurate theoretical model is the key to achieving high-precision measurement. Although the traditional Mie light scattering theory provides a basis for light scattering of spherical particles, it has limitations when dealing with particles with complex shapes, non-uniform materials and rough surfaces. To this end, the present invention proposes a light scattering theoretical model based on an improved Mie light scattering theory, which comprehensively considers factors such as particle shape, refractive index, surface roughness and internal structure.

[0151] The improved Mie light scattering theory first introduced the T-matrix method to deal with the scattering problem of non-spherical particles. The core idea of ​​the T-matrix method is to expand the incident field and the scattered field into linear combinations of spherical vector wave functions, respectively, and then establish the relationship between the two through the T-matrix. For axisymmetric particles, such as ellipsoids or cylinders, the extended boundary condition method is used to calculate the T-matrix. In the specific implementation, the particle surface is first discretized into a series of points, and then the boundary conditions are applied to these points to construct a linear equation system to solve the T-matrix elements. For example, for an ellipsoidal particle with a major-minor axis ratio of 2:1, its surface can be discretized into 500 points, and the T-matrix can be obtained by solving a 500x500 linear equation system. This method can accurately describe the scattering characteristics of non-spherical particles and significantly improve the scope of application of the theoretical model.

[0152] In order to more accurately describe the optical properties of particle materials, a wavelength-dependent complex refractive index model is introduced. The real part of the refractive index is described using the Sellmeier equation, which takes into account the dispersion characteristics of the material. Taking silica as an example, its Sellmeier equation parameters can be set to A1=0.6961663, A2=0.4079426, A3=0.8974794, B1=0.0684043, B2=0.1162414, B3=9.896161. The imaginary part of the refractive index is described using an exponential decay model, which can reflect the absorption characteristics of the material at different wavelengths.

[0153] Surface roughness has a significant effect on the scattering properties of particles, so the perturbation method is used to deal with this problem. The basic idea of ​​the perturbation method is to represent the rough surface as an average surface plus random fluctuations. By expanding the surface current to a first-order perturbation, the corrected scattering amplitude can be obtained. In the specific implementation, it is first necessary to define the statistical properties of the surface roughness, such as the root mean square height and the correlation length. For example, it can be assumed that the roughness of the particle surface follows a Gaussian distribution with a root mean square height of 50nm and a correlation length of 200nm. Then, a random realization of the surface roughness is generated based on these parameters, the first-order perturbation term is calculated, and it is superimposed on the scattering amplitude of the smooth surface. This method can effectively capture the effect of surface roughness on the scattering characteristics, especially in high-angle scattering and backscattering.

[0154] For particles with complex internal structures, such as porous materials or particles containing internal defects, the discrete dipole approximation method is introduced for processing. The core idea of ​​this method is to discretize particles with complex internal structures into multiple dipoles, and then obtain the polarization strength of each dipole by solving a set of linear equations. When implementing it, the particle volume first needs to be discretized into a series of small cubes, each cube represents a dipole. For example, for a spherical particle with a diameter of 1μm, it can be discretized into 10 4 Then, considering the interaction between each dipole, a large-scale linear system of equations is constructed and solved. This method can accurately describe the scattering characteristics of particles with inhomogeneous internal structures and is particularly effective for studying composite particles or biological particles.

[0155] Finally, a theoretical model of light scattering is constructed based on the calculation results of the T-matrix method, the complex refractive index model, the perturbation method, and the discrete dipole approximation method. This process involves integrating and weighing the results of each method. For example, the basic scattering properties of the particles can be calculated using the T-matrix method, and then the perturbation method can be applied to correct the surface roughness, and then the influence of the internal structure can be considered through the discrete dipole approximation method. Throughout the process, the wavelength-dependent complex refractive index model is used to describe the optical properties of the material. Through this comprehensive method, a theoretical model of light scattering that fully considers the particle shape, material properties, surface roughness, and internal structure can be obtained.

[0156] The present invention significantly improves the applicability of the model to non-spherical particles by introducing the T-matrix method, so that the theoretical model can accurately describe the scattering characteristics of particles of various shapes. Secondly, the wavelength-dependent complex refractive index model provides a more accurate description of the optical properties of the material, which helps to improve the accuracy of the model over a wide wavelength range. Thirdly, the application of the perturbation method enables the model to effectively deal with the influence of surface roughness, especially in high-angle scattering. More accurate performance. Finally, the introduction of the discrete dipole approximation method enables the model to handle particles with complex internal structures, greatly expanding the scope of application of the theoretical model. Combining these improvements, the constructed light scattering theoretical model can more accurately describe the scattering characteristics of actual particles, provides a solid theoretical basis for particle size distribution analysis, and is expected to significantly improve the accuracy and reliability of particle size measurement.

[0157] In an optional embodiment, the improved Bayesian optimization algorithm is used to optimize and adjust the preliminary particle size distribution result by minimizing the error between the theoretical light scattering intensity and the actually collected light scattering intensity, and the step of obtaining the corrected particle size distribution result includes:

[0158] The improved Bayesian optimization algorithm includes the introduction of multi-scale radial basis function kernel, adaptive acquisition function and local penalty strategy;

[0159] A Gaussian process regression model is constructed, wherein the Gaussian process regression model uses a multi-scale radial basis function kernel as a covariance function and captures feature changes in different dimensions by introducing different length scales;

[0160] The kernel function parameters are automatically determined by using the maximum marginal likelihood estimation method based on gradient descent, and the kernel function parameters that best explain the observed data are obtained by maximizing the logarithmic marginal likelihood function.

[0161] Designing an adaptive acquisition function, the adaptive acquisition function combines the expected improvement function and the probability improvement function, and introduces a weight function that is dynamically adjusted along with the optimization process;

[0162] A local penalty strategy is introduced to improve the global search capability by defining a penalty function to inhibit the algorithm from continuing to sample in the fully explored area.

[0163] The particle size distribution was represented by a mixture model of lognormal distribution, including the weight, log mean and log standard deviation parameters of each component;

[0164] A comprehensive objective function is constructed, including the root mean square error between the theoretical scattering intensity and the measured scattering intensity, a smooth regularization term and a physical constraint term, wherein the smooth regularization term adopts total variation regularization, and the physical constraint term includes a non-negative constraint and a normalization constraint;

[0165] Latin hypercube sampling was used to generate an initial set of particle size distribution parameters, and the Gaussian process regression model was updated by iteratively applying a modified Bayesian optimization algorithm;

[0166] A batch parallel evaluation strategy is adopted to select multiple candidate points for evaluation at the same time in each iteration, ensuring diversity by maximizing the minimum distance between candidate points;

[0167] Set a multi-criteria convergence judgment method; perform an iterative optimization process, update the particle size distribution parameters, including the weight, logarithmic mean and logarithmic standard deviation of each component, and obtain the optimal particle size distribution parameters when the convergence condition is met or the maximum number of iterations is reached;

[0168] The preliminary particle size distribution result is corrected based on the optimal particle size distribution parameter to obtain a corrected particle size distribution result.

[0169] For example, the accuracy of particle size distribution analysis directly affects scientific research and industrial applications in multiple fields. In order to further improve the accuracy of particle size distribution measurement, the present invention proposes a particle size distribution optimization method based on an improved Bayesian optimization algorithm. The method optimizes and adjusts the initially obtained particle size distribution results by minimizing the error between the theoretical light scattering intensity and the actual collected light scattering intensity, thereby obtaining a more accurate corrected particle size distribution result.

[0170] The improved Bayesian optimization algorithm first introduced a multi-scale radial basis function kernel. This kernel function can capture feature changes in different dimensions and improve the model's adaptability to complex particle size distributions. In specific implementation, the weighted sum of radial basis functions of multiple different length scales can be used as the kernel function. For example, for a three-dimensional optimization problem, three different length scale parameters can be set, namely 0.1, 1, and 10, to capture changes at different scales. This multi-scale kernel function can better describe the complex structure of the particle size distribution parameter space.

[0171] In order to automatically determine the optimal parameters of the kernel function, the maximum marginal likelihood estimation method based on gradient descent is used. This method finds the kernel function parameters that best explain the observed data by maximizing the logarithmic marginal likelihood function. When implemented, the L-BFGS-B algorithm (limited memory BFGS algorithm) can be used for optimization, with a learning rate of 0.01 and a maximum number of iterations of 100. This automatic parameter adjustment mechanism enables the model to better adapt to different data characteristics and improve optimization efficiency.

[0172] The design of the adaptive acquisition function is another key point to improve the Bayesian optimization algorithm. This function combines the expected improvement function and the probability improvement function, and introduces a weight function that is dynamically adjusted during the optimization process. For example, the initial weight ratio can be set to 0.5:0.5, and then dynamically adjusted according to the performance during the optimization process. When the algorithm falls into a local optimum, the weight of the probability improvement function is increased to promote global search; when a potential high-quality area is found, the weight of the expected improvement function is increased to strengthen local search. This adaptive mechanism can achieve a better balance between exploration and exploitation.

[0173] In order to further improve the global search capability, a local penalty strategy is introduced. By defining a penalty function, the algorithm is inhibited from continuing to sample in areas that have been fully explored. In specific implementation, a Gaussian kernel function can be used to define the local area, and the penalty intensity increases as the distance from the sampled points decreases. For example, the length scale of the penalty function is set to 0.1 and the amplitude parameter is set to 1.0. This strategy can encourage the algorithm to explore more unknown areas and increase the probability of finding the global optimal solution.

[0174] The representation of particle size distribution adopts the mixture model of lognormal distribution, including the weight, logarithmic mean and logarithmic standard deviation parameters of each component. For example, for a three-component mixture model, 9 parameters need to be optimized: 3 weights, 3 logarithmic means and 3 logarithmic standard deviations. This representation method can describe complex multi-peak distribution while ensuring physical rationality.

[0175] The construction of a comprehensive objective function is the core of the optimization process. This function includes the root mean square error between the theoretical scattering intensity and the measured scattering intensity, a smooth regularization term, and a physical constraint term. The smooth regularization term uses total variation regularization, and the regularization parameter can be set to 0.01. The physical constraint term includes non-negative constraints and normalization constraints to ensure that the optimization results are in line with physical meaning. This comprehensive objective function design can achieve a good balance between fitting accuracy, solution smoothness, and physical rationality.

[0176] The generation of the initial particle size distribution parameter set uses the Latin hypercube sampling method. For the above three-component mixture model, 50 initial sample points can be generated. This sampling method can evenly distribute the sampling points in the parameter space and improve the efficiency of the initial exploration. Then, the Gaussian process regression model is updated by iteratively applying the improved Bayesian optimization algorithm.

[0177] In order to improve computational efficiency, a batch parallel evaluation strategy is adopted. In each iteration, multiple candidate points are selected for evaluation at the same time, for example, 5 candidate points are selected each time. Diversity is ensured by maximizing the minimum distance between candidate points, and the minimum distance threshold can be set to 0.1. This strategy can make full use of parallel computing resources and accelerate the optimization process.

[0178] Set the multi-criteria convergence judgment method, including the continuous iteration improvement, objective function value and parameter change range. For example, if the improvement of the best objective function value for 10 consecutive iterations is less than 0.1%, or the L2 norm of the parameter change is less than 0.01, the algorithm is considered to have converged. At the same time, set the maximum number of iterations to 500 as a guarantee mechanism.

[0179] An iterative optimization process is performed to continuously update the particle size distribution parameters, including the weight, logarithmic mean, and logarithmic standard deviation of each component. When the convergence condition is met or the maximum number of iterations is reached, the optimal particle size distribution parameters are obtained. Finally, the preliminary particle size distribution results are corrected based on these optimal parameters to obtain the corrected particle size distribution results.

[0180] The present invention significantly improves the search efficiency and accuracy of the Bayesian optimization algorithm in complex parameter spaces by introducing a multi-scale radial basis function kernel and an adaptive acquisition function. Secondly, the introduction of a local penalty strategy effectively enhances the global search capability of the algorithm and reduces the risk of falling into a local optimum. Thirdly, the design of a comprehensive objective function ensures a balance between the fitting accuracy, smoothness, and physical rationality of the optimization results. Finally, the batch parallel evaluation strategy greatly improves the computational efficiency, enabling the method to be applied to large-scale particle size distribution analysis problems.

[0181] The invention provides a particle size distribution measurement system based on machine learning and light scattering method, including a light source module, a multi-angle scattered light detector, a preprocessing unit, a modal deep learning model construction unit, a support vector machine model construction unit, a random forest model construction unit, an integrated learning architecture construction unit, an integrated learning architecture training unit, a light scattering theory model construction unit, a theoretical scattered light intensity calculation unit, an error calculation unit and a step particle size distribution result optimization unit; wherein,

[0182] The light source module is used to illuminate the particle sample to be tested and generate scattered light of different wavelengths and different scattering angles;

[0183] The multi-angle scattered light detector is used to synchronously collect scattered light intensity data of all scattered light and preprocess the scattered light intensity data, and the preprocessing includes denoising, normalization and feature extraction;

[0184] The modal deep learning model building unit is used to build a multimodal deep learning model;

[0185] The support vector machine model building unit is used to build a support vector machine model;

[0186] The random forest model building unit is used to build a random forest model;

[0187] The integrated learning architecture building unit is used to integrate the multimodal deep learning model, support vector machine model and random forest model based on the stacking strategy to build an integrated learning architecture;

[0188] The integrated learning framework training unit is used to train the integrated learning framework using sample data of known particle size distribution, establish a mapping relationship between scattered light intensity data and particle size distribution; input the preprocessed scattered light intensity data into the trained integrated learning framework to obtain a preliminary particle size distribution result of the particle sample to be tested;

[0189] The light scattering theoretical model building unit is used to build a light scattering theoretical model that takes into account particle shape, refractive index, surface roughness and internal structure based on the improved Mie light scattering theory;

[0190] The theoretical scattered light intensity calculation unit is used to substitute the preliminary particle size distribution result of the particle sample to be tested into the light scattering theoretical model to calculate the theoretical scattered light intensity;

[0191] The error calculation unit is used to calculate the error between the theoretical scattered light intensity and the scattered light intensity data collected by the multi-angle scattered light detector;

[0192] The step particle size distribution result optimization unit is used to minimize the error by adopting an improved Bayesian optimization algorithm, so as to optimize the preliminary particle size distribution result of the particle sample to be tested and obtain a corrected particle size distribution result.

[0193] Accordingly, according to an embodiment of the present invention, the present invention also provides a computer device, a readable storage medium and a computer program product.

[0194] Figure 2 FIG. 1 is a schematic diagram of the structure of a computer device 12 provided in an embodiment of the present invention. Figure 2 A block diagram of an exemplary computer device 12 suitable for use in implementing embodiments of the present invention is shown. Figure 2The computer device 12 shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present invention.

[0195] like Figure 2 As shown, computer device 12 is in the form of a general-purpose computing device. Computer device 12 is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or required herein.

[0196] Components of computer device 12 may include, but are not limited to, one or more processors or processing units 16 , a system memory 28 , and a bus 18 that connects various system components including system memory 28 and processing unit 16 .

[0197] Bus 18 represents one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor or a local bus using any of a variety of bus architectures. By way of example, these architectures include, but are not limited to, an Industry Standard Architecture (ISA) bus, a Micro Channel Architecture (MAC) bus, an Enhanced ISA bus, a Video Electronics Standards Association (VESA) local bus, and a Peripheral Component Interconnect (PCI) bus.

[0198] The computer device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by the computer device 12, including volatile and non-volatile media, removable and non-removable media.

[0199] The system memory 28 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. The computer device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the storage system 34 may be used to read and write non-removable, non-volatile magnetic media ( Figure 2 not shown, usually called a "hard drive"). Although Figure 2Not shown in the figure, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk"), and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, a DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to the bus 18 via one or more data medium interfaces. The memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to perform the functions of the various embodiments of the present invention.

[0200] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in the memory 28, such program modules 42 including but not limited to an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment. The program modules 42 generally perform the functions and / or methods of the embodiments described herein.

[0201] The computer device 12 may also communicate with one or more external devices 14 (e.g., keyboards, pointing devices, displays 24, etc.), may communicate with one or more devices that enable a user to interact with the computer device 12, and / or may communicate with any device that enables the computer device 12 to communicate with one or more other computing devices (e.g., network cards, modems, etc.). This communication may be performed via an input / output (I / O) interface 22. In addition, the computer device 12 may also communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via a network adapter 20. As shown, the network adapter 20 communicates with other modules of the computer device 12 via a bus 18. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the computer device 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0202] The processing unit 16 executes various functional applications and data processing by running programs stored in the system memory 28, such as implementing the particle size distribution measurement method based on machine learning and light scattering provided in an embodiment of the present invention.

[0203] An embodiment of the present invention also provides a non-transitory computer-readable storage medium storing computer instructions, on which a computer program is stored, wherein when the program is executed by a processor, the particle size distribution measurement method based on machine learning and light scattering method provided in all the inventive embodiments of the present application is implemented.

[0204] The computer storage medium of the embodiment of the present invention may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. More specific examples (non-exhaustive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this document, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in combination with an instruction execution system, an apparatus, or a device.

[0205] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, which carry computer-readable program code. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Computer-readable signal media may also be any computer-readable medium other than a computer-readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0206] The program code contained on the computer-readable medium can be transmitted with any appropriate medium, including but not limited to wireless, wire, optical cable, RF, etc., or any suitable combination of the above. The computer program code for performing the operation of the present invention can be written in one or more programming languages ​​or a combination thereof, and the programming language includes object-oriented programming languages ​​such as Java, Smalltalk, C++, and also includes conventional procedural programming languages-such as "C" language or similar programming languages. The program code can be executed completely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer, partially on the remote computer, or completely on the remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (for example, using an Internet service provider to connect through the Internet).

[0207] An embodiment of the present invention further provides a computer program product, including a computer program, which implements the above-mentioned image super-resolution reconstruction method when executed by a processor.

[0208] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0209] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A particle size distribution measurement method based on machine learning and light scattering, characterized in that: The steps include: S1: Use the light source module to illuminate the particle sample to be tested to generate scattered light of different wavelengths and different scattering angles. At the same time, use the multi-angle scattered light detector to synchronously collect the scattered light intensity data of all scattered light, and pre-process the scattered light intensity data. The pre-processing includes denoising, normalization and feature extraction. S2: Build a multimodal deep learning model, a support vector machine model, and a random forest model respectively, and integrate the multimodal deep learning model, the support vector machine model, and the random forest model based on the stacking strategy to build an integrated learning architecture; S3: Using sample data of known particle size distribution to train the integrated learning framework, establish a mapping relationship between scattered light intensity data and particle size distribution, input the preprocessed scattered light intensity data into the trained integrated learning framework, and obtain the preliminary particle size distribution results of the particle sample to be tested; S4: Based on the improved Mie light scattering theory, a light scattering theoretical model is constructed which takes into account the particle shape, refractive index, surface roughness and internal structure. The preliminary particle size distribution results of the particle sample to be tested are substituted into the light scattering theoretical model to calculate the theoretical scattered light intensity. The error between the theoretical scattered light intensity and the scattered light intensity data collected by the multi-angle scattered light detector is also calculated. The error is minimized using an improved Bayesian optimization algorithm to optimize the preliminary particle size distribution results of the particle sample to be tested and obtain the corrected particle size distribution results.

2. The particle size distribution measurement method based on machine learning and light scattering method according to claim 1, characterized in that: The discrete wavelet transform method is used to denoise the scattered light intensity data. The specific process is as follows: Select wavelet basis functions to perform multi-scale decomposition on scattered light intensity data to obtain wavelet coefficients of different frequency components; The threshold of each wavelet coefficient subband is calculated using an adaptive threshold method; Use soft threshold function to perform threshold shrinkage processing on wavelet coefficients; The wavelet coefficients after threshold shrinkage are recombined through inverse wavelet transform to obtain the denoised scattered light intensity data; The denoised scattered light intensity data is normalized by Z-score. The specific process is as follows: Calculate the mean and standard deviation of the scattered light intensity data, then subtract the mean from the scattered light intensity data and divide it by the standard deviation to complete the normalization of the scattered light intensity data; The local binary pattern feature extraction method is used to extract features from the normalized scattered light intensity data. The specific process is as follows: The normalized scattered light intensity data is divided into a plurality of small regions, and the local binary pattern features are calculated in each small region; Count the local binary pattern feature histogram of each small area, and connect the local binary pattern feature histograms of all small areas to form a high-dimensional feature vector; The principal component analysis method is used to reduce the dimensionality of high-dimensional feature vectors, and the principal components whose cumulative explained variance reaches a preset threshold are selected as feature vectors.

3. The particle size distribution measurement method based on machine learning and light scattering method according to claim 1, characterized in that: The multimodal deep learning model includes a convolutional neural network module, a long short-term memory network module and a multi-head attention mechanism module; the convolutional neural network module performs wavelet transform on the input scattered light intensity data, decomposes the data into different frequency sub-bands, and designs convolution kernels of corresponding scales for different frequency sub-bands. The attention mechanism module performs weighted fusion of features of different scales, and adds residual connections after the convolution block; the long short-term memory network module reconstructs the scattered light intensity data into a time series format, uses a bidirectional long short-term memory network to capture bidirectional temporal dependencies, and adds an attention layer on top of the long short-term memory network layer; the multi-head attention mechanism module performs position encoding on the input data, calculates the attention score by setting multiple attention heads, and splices the outputs of multiple attention heads and fuses them through linear transformation; The feature dimensions are reduced by principal component analysis and then input into the support vector machine model. The support vector machine model uses a radial basis function kernel, and the parameters of the support vector machine are optimized through grid search and cross validation. The random forest model was used to extract statistical features, set the number of trees and use the Gini index as the splitting criterion, and calculate the feature importance score.

4. The particle size distribution measurement method based on machine learning and light scattering method according to claim 1, characterized in that: Based on the Stacking strategy, the multimodal deep learning model, support vector machine model and random forest model are integrated to build an integrated learning architecture. The specific process is as follows: Train multimodal deep learning models, support vector machine models, and random forest models as base learners; The meta-features are generated by using the cross-validation method. The training data is divided into multiple parts. Some of the data are used cyclically to train the base learner and prediction is performed on the remaining data. The prediction results of each base learner are collected as meta-features. Design XGBoost as a meta-learner and set model parameters including maximum tree depth, learning rate, subsampling ratio, feature sampling ratio, minimum child node weight, and regularization parameter; The importance scores of the original features of the scattered light intensity data were calculated using the random forest model, and the importance scores were normalized; The meta-features are weighted according to the normalized importance scores, where the weights of the meta-features generated by the multimodal deep learning model are fixed, and the weights of the meta-features generated by the support vector machine model and the random forest model are calculated according to the importance scores of the original features; The weighted meta-features are concatenated with the original features to form the final training feature set; Use the training feature set to train the XGBoost meta-learner, use the mean square error as the optimization objective, and set the early stopping strategy.

5. The particle size distribution measurement method based on machine learning and light scattering method according to claim 1, characterized in that: The specific process of inputting the preprocessed scattered light intensity data into the trained integrated learning framework to obtain the preliminary particle size distribution results of the particle sample to be tested is as follows: The preprocessed scattered light intensity data is input into the multimodal deep learning model, and the local features in the scattered light intensity data are extracted using the convolutional neural network module. The temporal dependencies in the scattered light intensity data are captured using the long short-term memory network module. The long-range dependencies between local features are established using the multi-head attention mechanism module to obtain the first preliminary particle size distribution prediction result. The pre-processed scattered light intensity data is reduced in dimension using principal component analysis, and the reduced scattered light intensity data is input into the support vector machine model to obtain the second preliminary particle size distribution prediction result; The preprocessed scattered light intensity data is fed into the random forest model, and the third preliminary particle size distribution prediction result is obtained through decision tree integration; The three preliminary particle size distribution prediction results are standardized to obtain a standardized preliminary particle size distribution prediction result; The standardized preliminary particle size distribution prediction results were weighted according to the feature importance scores calculated by the random forest model to generate meta-features; The weighted meta-features were concatenated with the original features of the scattered light intensity data and input into the trained XGBoost meta-learner to obtain the final preliminary particle size distribution results.

6. The particle size distribution measurement method based on machine learning and light scattering method according to claim 1, characterized in that: Based on the improved Mie light scattering theory, the specific process of constructing a light scattering theoretical model that takes into account particle shape, refractive index, surface roughness and internal structure is as follows: The improved Mie light scattering theory includes the introduction of T-matrix method, wavelength-dependent complex refractive index model, perturbation method and discrete dipole approximation method; For non-spherical particles, the T-matrix method is introduced to expand the incident field and the scattered field into spherical vector wave functions, and the relationship between the two is established through the T-matrix; for axisymmetric particles, the extended boundary condition method is used to calculate the T-matrix method; A wavelength-dependent complex refractive index model is introduced. The real part of the refractive index is described by the Sellmeier equation, and the imaginary part is described by the exponential decay model. The perturbation method is used to represent the rough surface as an average surface plus random fluctuations, and the corrected scattering amplitude is obtained by expanding the surface current to the first-order perturbation. The discrete dipole approximation method is introduced to discretize particles with complex internal structures into multiple dipoles, and the polarization intensity of each dipole is obtained by solving a set of linear equations. A light scattering theoretical model is constructed based on the calculation results of the T-matrix method, complex refractive index model, perturbation method and discrete dipole approximation method.

7. The particle size distribution measurement method based on machine learning and light scattering method according to claim 1, characterized in that: Substitute the preliminary particle size distribution results of the particle sample to be tested into the light scattering theoretical model, calculate the theoretical scattered light intensity, and calculate the error between the theoretical scattered light intensity and the scattered light intensity data collected by the multi-angle scattered light detector. Use the improved Bayesian optimization algorithm to minimize the error to optimize the preliminary particle size distribution results of the particle sample to be tested. The specific process of obtaining the corrected particle size distribution results is as follows: The improved Bayesian optimization algorithm includes the introduction of multi-scale radial basis function kernel, adaptive acquisition function and local penalty strategy; Construct a Gaussian process regression model. The Gaussian process regression model uses a multi-scale radial basis function kernel as the covariance function and captures feature changes in different dimensions by introducing different length scales. The kernel function parameters are automatically determined by using the maximum marginal likelihood estimation method based on gradient descent, and the kernel function parameters that best explain the observed data are obtained by maximizing the logarithmic marginal likelihood function. Design an adaptive acquisition function, which combines the expected improvement function and the probability improvement function, and introduces a weight function that is dynamically adjusted during the optimization process; A local penalty strategy is introduced to improve the global search capability by defining a penalty function to inhibit the algorithm from continuing to sample in the fully explored area. The particle size distribution was represented by a mixture model of lognormal distribution, including the weight, log mean and log standard deviation parameters of each component; A comprehensive objective function is constructed, including the root mean square error between the theoretical scattering intensity and the measured scattering intensity, a smooth regularization term and a physical constraint term, wherein the smooth regularization term adopts total variation regularization, and the physical constraint term includes a non-negative constraint and a normalization constraint; Latin hypercube sampling was used to generate an initial set of particle size distribution parameters, and the Gaussian process regression model was updated by iteratively applying a modified Bayesian optimization algorithm; A batch parallel evaluation strategy is adopted to select multiple candidate points for evaluation at the same time in each iteration, ensuring diversity by maximizing the minimum distance between candidate points; Set up multi-criteria convergence judgment method; An iterative optimization process is performed to update the particle size distribution parameters, including the weight, logarithmic mean and logarithmic standard deviation of each component. When the convergence condition is met or the maximum number of iterations is reached, the optimal particle size distribution parameters are obtained; The preliminary particle size distribution result is corrected based on the optimal particle size distribution parameter to obtain a corrected particle size distribution result.

8. A particle size distribution measurement system based on machine learning and light scattering method, used to perform the particle size distribution measurement method based on machine learning and light scattering method according to any one of claims 1 to 7, characterized in that: It includes a light source module, a multi-angle scattered light detector, a preprocessing unit, a modal deep learning model building unit, a support vector machine model building unit, a random forest model building unit, an integrated learning architecture building unit, an integrated learning architecture training unit, a light scattering theory model building unit, a theoretical scattered light intensity calculation unit, an error calculation unit and a step particle size distribution result optimization unit; wherein, The light source module is used to illuminate the particle sample to be tested and generate scattered light of different wavelengths and different scattering angles; The multi-angle scattered light detector is used to synchronously collect scattered light intensity data of all scattered light and preprocess the scattered light intensity data, and the preprocessing includes denoising, normalization and feature extraction; The modal deep learning model building unit is used to build a multimodal deep learning model; The support vector machine model building unit is used to build a support vector machine model; The random forest model building unit is used to build a random forest model; The integrated learning architecture building unit is used to integrate the multimodal deep learning model, support vector machine model and random forest model based on the stacking strategy to build an integrated learning architecture; The integrated learning framework training unit is used to train the integrated learning framework using sample data of known particle size distribution, establish a mapping relationship between scattered light intensity data and particle size distribution; input the preprocessed scattered light intensity data into the trained integrated learning framework to obtain a preliminary particle size distribution result of the particle sample to be tested; The light scattering theoretical model building unit is used to build a light scattering theoretical model that takes into account particle shape, refractive index, surface roughness and internal structure based on the improved Mie light scattering theory; The theoretical scattered light intensity calculation unit is used to substitute the preliminary particle size distribution result of the particle sample to be tested into the light scattering theoretical model to calculate the theoretical scattered light intensity; The error calculation unit is used to calculate the error between the theoretical scattered light intensity and the scattered light intensity data collected by the multi-angle scattered light detector; The step particle size distribution result optimization unit is used to minimize the error by using an improved Bayesian optimization algorithm to optimize the preliminary particle size distribution result of the particle sample to be tested and obtain a corrected particle size distribution result.

9. A computer device, characterized in that: include: at least one processor; as well as a memory communicatively connected to at least one processor; wherein, The memory stores instructions that can be executed by at least one processor, and the instructions are executed by at least one processor so that the at least one processor can execute the particle size distribution measurement method based on machine learning and light scattering method described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium storing computer instructions, characterized in that: The computer instructions are used to cause a computer to execute the particle size distribution measurement method based on machine learning and light scattering method according to any one of claims 1 to 7.

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