A method for predicting dispersion based on robust statistical features of milk powder particle morphology

Abstract

The application discloses a kind of based on robust statistical characteristics of milk powder particle morphology dispersion prediction method, belong to milk powder quality detection and analysis technical field.The method is by using quartile distance and 5% tail cut mean to represent particle morphology, effectively reduce abnormal value interference, compared with traditional mean-standard deviation method can reflect the real characteristics of particle group, specifically, the present application is directed to the quartile distance and tail cut mean of 9 kinds of shape factor parameters of milk powder particle are calculated, and further based on dispersion correlation 14 key features are screened out, the reliability of feature is improved, and then the accuracy of milk powder dispersion prediction is improved possibly;Further, the present application scheme is directed to small sample application scene, using Bootstrap resampling, vertically splicing original data and 3 groups of resampling data, generate enhanced data set, and using CatBoost regression model further improves the prediction accuracy.

Description

Technical Field

[0001] This invention relates to a dispersion prediction method based on robust statistical characteristics of milk powder particle morphology, belonging to the field of milk powder quality testing and analysis technology. Background Technology

[0002] As an important raw material for dairy products, the rehydration performance of milk powder directly affects the product's solubility, taste stability, and consumer experience. Among these, dispersibility is an important physicochemical indicator characterizing the rehydration performance of milk powder particles and is widely used to evaluate the processing quality and process stability of instant milk powder.

[0003] Traditional methods for detecting the dispersibility of milk powder mainly rely on standardized wet processing procedures, typically requiring precise weighing, timed stirring, filtration, and drying. These methods are time-consuming and highly dependent on manual labor, making them unsuitable for the rapid feedback and online quality control demands of industrial production. Some studies have attempted to introduce image analysis or machine learning methods to assess milk powder quality. For example, Chinese invention patent CN119804217A discloses a method, system, and medium for detecting the bulk density of milk powder dispersibility based on the Swing Transformer model. This method constructs multiple sets of milk powder particle samples according to different proportions of large, medium, and small particles, and then uses the images of these samples as input to a deep neural network model, achieving rapid detection of milk powder dispersibility. However, this method directly uses images of milk powder samples as input. In milk powder production, common image noise and abnormal agglomeration or fine particles can amplify model errors and reduce accuracy. Therefore, its predictive accuracy needs further improvement.

[0004] Furthermore, existing methods often employ simple mean or single-scale statistics to represent particle morphology characteristics, making them susceptible to interference from anomalous particles and resulting in insufficient model stability and generalization ability. Therefore, there is an urgent need for a prediction method that can fully characterize the overall morphological characteristics of particle groups and establish a robust quantitative mapping relationship with physicochemical properties, in order to achieve rapid, objective, and high-precision assessment of milk powder dispersibility. Summary of the Invention

[0005] To address the existing problems, this invention provides a dispersion prediction method based on robust statistical characteristics of milk powder particle morphology, comprising: Step S101: Obtain an optical microscope image of the milk powder particles; Step S102: Extract particle morphology parameters based on optical microscope images and calculate robust statistical indices, and use the calculated robust statistical indices as initial features. Step S103: Analyze the correlation between initial features and dispersion, and select key features based on the correlation results with dispersion; Step S104: Construct a CatBoost regression prediction model and use the key features as input to obtain dispersion prediction results.

[0006] Optionally, step S102 includes: Nine shape factor parameters of milk powder particles were extracted based on optical microscope images: maximum Feret diameter, minimum Feret diameter, roundness, solidity, convexity, elongation, area, equivalent diameter, and perimeter. The interquartile range and truncated mean were calculated for the nine extracted shape factor parameters to generate 18 robust feature vectors.

[0007] Optionally, the key features obtained by screening in step S103 are the interquartile range of the maximum Ferrette diameter, the interquartile range of the minimum Ferrette diameter, the interquartile range of solidity, the interquartile range of elongation, the interquartile range of area, the interquartile range of equivalent diameter, and the interquartile range of circumference, as well as the truncated mean of the maximum Ferrette diameter, the truncated mean of the minimum Ferrette diameter, the truncated mean of solidity, the truncated mean of elongation, the truncated mean of area, the truncated mean of equivalent diameter, and the truncated mean of circumference.

[0008] Optionally, the truncation rate of the truncation mean is 5%.

[0009] Optionally, in step S103, Spearman correlation analysis is used for screening, with a significance level of P < 0.05, to screen out features that are significantly related to dispersion.

[0010] Optionally, step S101 includes mixing the milk powder sample with soybean oil under the action of a magnetic stirrer to make the milk powder particles evenly dispersed in the liquid oil; using a pipette to evenly drop and spread the mixture of milk powder particles and soybean oil onto a clean glass slide to avoid particle agglomeration. Place the slide on the stage of the optical microscope and adjust the magnification to 10x eyepiece and 10x objective lens until the particle morphology can be clearly observed. Scan and capture images of the particle morphology using a digital microscope camera and digitize the images as high-resolution files. Preprocess the captured images by binarizing them with a fixed threshold, inverting the values, and filling the holes. Extract the particle boundary contours using the bwboundaries function.

[0011] Optionally, step S104, constructing the CatBoost regression prediction model, includes: Data augmentation was performed using Bootstrap resampling to obtain the augmented dataset; The augmented dataset was divided into training and testing sets in a 7:3 ratio to construct a CatBoost regression model. Hyperparameters were optimized using grid search: the learning rate was searched in the range of 0.01 to 0.1, the tree depth was searched in the range of 4 to 8, the number of iterations was set to 100 to 1000, and L2 regularization parameters were introduced to control the model complexity. During model training, the goal is to minimize the mean squared error loss, and an ordered boosting mechanism is used to correct gradient bias.

[0012] The second objective of this invention is to provide a dispersion prediction system based on robust statistical features of milk powder particle morphology. The system includes an image acquisition module, a statistical calculation module, and a modeling and prediction module. The image acquisition module is used to acquire optical microscope images of milk powder particles and perform preliminary processing. The statistical calculation module is used to extract particle morphology parameters and calculate robust statistical indices. The modeling and prediction module is used to screen initial robust features and perform data augmentation.

[0013] Optionally, the image acquisition module includes an optical microscope, an image acquisition unit, and a preprocessing unit. The optical microscope is equipped with a 10x objective lens and a high-definition camera, supporting autofocus and batch shooting. The image acquisition unit controls the shooting parameters and transmits the raw images to the preprocessing unit. The preprocessing unit integrates denoising, particle segmentation, and boundary extraction algorithms, and transmits the processed images to the morphological feature extraction module. The statistical calculation module includes a parameter calculation unit and a statistical processing unit. The parameter calculation unit is used to calculate boundary complexity and shape regularity, while the statistical processing unit is used for anomaly removal, interquartile range, and truncated mean statistics, and includes an outlier removal unit for filtering abnormal data based on a threshold. The modeling and prediction module includes a correlation analysis unit and a data augmentation unit. The correlation analysis unit uses the Spearman rank correlation algorithm to screen key features that are significantly correlated with dispersion and generates a feature screening report. The data augmentation unit generates an augmented dataset through Bootstrap resampling.

[0014] The beneficial effects of this invention are: This invention employs robust statistical feature analysis of milk powder particles, screening out features significantly correlated with milk powder dispersibility, reducing redundant features, avoiding noise generated by direct image analysis, and model errors caused by abnormal particles in milk powder images. Furthermore, by using interquartile range and 5% truncated mean to characterize particle morphology, outlier interference is effectively reduced, reflecting the true characteristics of the particle group better than the traditional mean-standard deviation method. Specifically, this application calculates interquartile range and truncated mean for nine shape factor parameters of milk powder particles, and further selects 14 key features based on dispersibility correlation, improving feature reliability and thus providing the possibility of improving the accuracy of milk powder dispersibility prediction. Furthermore, for small sample application scenarios, this application uses Bootstrap resampling, vertically concatenating the original data with three sets of resampled data to generate an enhanced dataset, and further improves prediction accuracy using a CatBoost regression model. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 The diagram illustrates a process for modeling the correlation between milk powder particle morphology and dispersion using robust statistical features, according to an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram illustrating the correlation between the quartiles, truncated means, and dispersion of each shape factor.

[0018] Figure 3 Scanning electron microscope images of coarse, medium, and fine particles of whole and skim milk powder at 100x magnification.

[0019] Figure 4 This is a scatter plot of the dispersion predictions and actual values ​​obtained using the method described in this application.

[0020] Figure 5 The diagram shows the architecture of a rapid prediction system for milk powder dispersibility provided in one embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0022] Example 1 This embodiment provides a dispersion prediction method based on robust statistical characteristics of milk powder particle morphology. (See [link to relevant documentation]). Figure 1 The method includes: Step S101: Obtain an optical microscope image of the milk powder particles; This includes sample dispersion and preparation, slide loading, multi-magnification optical observation, and digital image storage.

[0023] Specifically, 0.20g of milk powder sample was mixed with 36mL of soybean oil using a magnetic stirrer to ensure that the milk powder particles were evenly dispersed in the liquid oil. The mixture of milk powder particles and soybean oil was then evenly added and spread onto a clean glass slide using a pipette to prevent particle agglomeration.

[0024] Place the slide on the stage of the optical microscope and adjust the magnification to 10x eyepiece and 10x objective lens until the particle morphology can be clearly observed. Scan and capture images of the particle morphology using a digital microscope camera and digitize the images as high-resolution files. Preprocess the captured images by binarizing them with a fixed threshold, inverting the values, and filling the holes. Extract the particle boundary contours using the bwboundaries function.

[0025] Step S102: Extract particle morphology parameters and calculate robust statistical indices; This includes particle morphology parameter calculation, outlier removal, interquartile range statistics, and truncated mean statistics.

[0026] The particle morphology parameters of milk powder include boundary complexity and shape regularity parameters; further, the boundary complexity and shape regularity parameters specifically refer to nine shape factor parameters: maximum Feret diameter (MaxFeret), minimum Feret diameter (MinFeret), roundness (Circularity), solidity (Solidity), convexity (Convexity), elongation (Elongation), area (Area), equivalent diameter (EquivDiameter), and perimeter (Perimeter).

[0027] Specifically, MATLAB image processing software was used to segment particle contours from the acquired images. Nine shape factor parameters were calculated for each segmented particle. Then, box plots were used to remove outlier particle data. For the remaining particle data, interquartile range (ICM) and truncated mean were applied to remove outliers and retain valid data samples. For the valid parameter set after outlier removal, two robust statistical indices, ICM and truncated mean, were calculated. For each sample, ICM and truncated mean were calculated for each of the nine shape factor parameters, generating 18 robust feature vectors as initial features for subsequent modeling.

[0028] In this application, the truncation rate of the truncation mean is 5%.

[0029] Step S103: Analyze the correlation between initial characteristics and dispersion; Specifically, Spearman's rank correlation coefficient is used to analyze the correlation between initial characteristics and dispersion. This method does not rely on the assumption of normality of data and is suitable for skewed particle morphology data.

[0030] Set a significance level of P < 0.05 to screen out features that are significantly associated with dispersion; Figure 2 The diagram illustrates the correlation between quartiles, truncated means, and dispersion for each shape factor. It shows that the four initial features—circularity IQR, circularity trimmed mean, convexity IQR, and convexity trimmed mean—are not significantly correlated with dispersion (p > 0.05), while the other 14 initial features are significantly correlated with dispersion (p < 0.05). Therefore, by removing the four features that are not significantly correlated with circularity IQR and truncated mean, and convexity IQR and truncated mean, 14 key features are obtained.

[0031] The 14 key features are: Max Feret IQR, Min Feret IQR, Solidity IQR, Elongation IQR, Area IQR, EquivDiameter IQR, and Perimeter IQR; Max Feret trimmed mean, Min Feret trimmed mean, Solidity trimmed mean, Elongation trimmed mean, Area trimmed mean, EquivDiameter trimmed mean, and Perimeter trimmed mean.

[0032] Considering the limited number of samples in actual production, Bootstrap resampling is used for data augmentation: the original dataset of 40 samples is sampled three times with replacement, with the sample size of each sample being the same as that of the original dataset. The original data and the three resampled data are then concatenated vertically to generate an augmented dataset, which effectively alleviates the risk of overfitting with small samples.

[0033] Step S104: Construct a CatBoost regression prediction model; A regression prediction model was constructed by correlating 14 key features with experimentally measured dispersion values. The 14 key features were then standardized using Z-score, with the following formula:

[0034] in These are the original values ​​of the key features. The corresponding feature mean, The corresponding feature standard deviation is used to ensure that each feature participates in modeling on the same scale.

[0035] Natural logarithmic transformation of the dispersed objective variable ( This satisfies the normal residual assumption of the regression model and compresses the magnitude difference.

[0036] The augmented dataset was divided into training and testing sets in a 7:3 ratio to construct a CatBoost regression model. Hyperparameters were optimized using grid search: the learning rate was searched from 0.01 to 0.1, the tree depth from 4 to 8, and the number of iterations was set from 100 to 1000. L2 regularization was introduced to control model complexity.

[0037] During model training, with the goal of minimizing mean squared error loss, an ordered boosting mechanism is used to correct gradient bias, thereby improving the stability of the training process and its robustness to noise.

[0038] Step S105: Input the key features of the milk powder to be tested into the trained CatBoost model to obtain the predicted value after logarithmic transformation, and then perform anti-logarithmic transformation on it to obtain the final dispersion prediction value.

[0039] Example 2 This embodiment provides a dispersion prediction method based on robust statistical characteristics of milk powder particle morphology. Taking the actual dispersion prediction of four types of milk powder as examples, the method includes: Step 1, prepare milk powder samples; Purchase whole milk powder and skim milk powder from two New Zealand brands, Brand 1 and Brand 2, for a total of four types.

[0040] To reduce the impact of different particle size distributions in the sampled milk powder on dispersibility, this embodiment also used a sieving instrument to sieve the whole milk powder and skim milk powder of two brands separately. Specifically, the milk powder was sieved into three particle size groups using vibrating screens with different pore sizes: coarse particles (>355 μm), medium particles (180-355 μm), and fine particles (<180 μm). For each sieve, 100 g of milk powder sample was shaken for 30 min. The milk powder from the three particle size groups was then remixed according to a simple lattice design, resulting in a total of 10 different combinations including coarse, medium, and fine particles. The proportions of coarse, medium, and fine particles in the 10 milk powder samples are shown in Table 1 below. Table 1: Explanation of the proportions of coarse, medium, and fine particles in 10 samples

[0041] Table 1 lists 10 types of samples, with 4 groups of each type, for a total of 40 groups of milk powder samples.

[0042] This embodiment uses the standardized experimental method—ISO 17758 | IDF 087 (International Organization for Standardization 2014 edition)—to determine the dispersibility of milk powder samples. The specific measurement method is as follows: A 300 μm stainless steel sieve was placed in the filtration section of the vacuum funnel to filter undissolved milk powder. 13 g of milk powder was poured into 100 ml of distilled water at room temperature (20°C), and stirred rapidly with a stirring rod for 5 seconds before being poured into the vacuum funnel for filtration. The sieve and the remaining undissolved milk powder were transferred to an evaporating dish and placed in an oven to dry. The mass increment was then measured. The undissolved milk powder rate was calculated according to formula (1): (1) In the formula M ud For undissolved milk powder quality, M total The total mass of the milk powder. The dispersibility is calculated using formula (2): (2) Step 2: Obtain the particle morphology parameters of milk powder through optical microscope images of milk powder samples, and construct the original dataset; Specifically, images of milk powder particles were acquired using a Novel NSS-4 optical microscope with a camera. Forty groups of milk powder samples were collected, with 50 optical microscope images taken from each group, totaling 2000 images. Some of the optical microscope images are shown below. Figure 3 As shown.

[0043] The specific procedure is as follows: Weigh 0.2 g of milk powder and mix it with 32 ml of soybean oil. Stir the mixture at 600 rpm for 10 seconds using a magnetic stirrer. Then, use a disposable dropper to add the milk powder and soybean oil mixture evenly onto a glass slide. Observe the sample under 10x objective lens and photograph the sample on the slide using a microscope camera. Take 50 photos of each milk powder sample ratio.

[0044] MATLAB functions were used to calculate and extract the boundaries of the particle images to obtain the particle morphology parameters of the milk powder, including boundary complexity and shape regularity parameters. Specifically, the boundary complexity and shape regularity parameters refer to nine shape factor parameters: maximum Feret diameter (MaxFeret), minimum Feret diameter (MinFeret), roundness (Circularity), solidity (Solidity), convexity (Convexity), elongation (Elongation), area (Area), equivalent diameter (EquivDiameter), and perimeter (Perimeter).

[0045] Step 3: Calculate the interquartile range and 5% truncated mean for each of the nine shape factor parameters; The interquartile range (IQR) is defined as the difference between the third quartile and the first quartile. It measures the dispersion of a data distribution and is naturally robust to outliers. The truncated mean is the arithmetic mean of the remaining data after removing the top 5% extreme values.

[0046] Based on observations of milk powder samples, it was found that the particle size distribution of milk powder often exhibits skewed or heavy-tailed characteristics. The standard deviation is easily amplified by a few excessively large or small particles, thus masking the true dispersion of the particle group. The combined use of IQR and truncated mean not only preserves the typical characteristics of the particle group but also faithfully reflects its natural heterogeneity, providing a more robust and materially meaningful independent variable for subsequent machine learning modeling.

[0047] Step 4: Analyze the correlation between initial characteristics and dispersion; Spearman's rank correlation coefficient was used to analyze the correlation between initial characteristics and dispersion. Figure 2The diagram illustrates the correlation between quartiles, truncated means, and dispersion for each shape factor. It shows that the four initial features—circularity IQR, circularity trimmed mean, convexity IQR, and convexity trimmed mean—are not significantly correlated with dispersion (p > 0.05), while the other 14 initial features are significantly correlated with dispersion (p < 0.05). Therefore, by removing the four features that are not significantly correlated with circularity IQR and truncated mean, and convexity IQR and truncated mean, 14 key features are obtained.

[0048] The 14 key features are: Max Feret IQR, Min Feret IQR, Solidity IQR, Elongation IQR, Area IQR, EquivDiameter IQR, and Perimeter IQR; Max Feret trimmed mean, Min Feret trimmed mean, Solidity trimmed mean, Elongation trimmed mean, Area trimmed mean, EquivDiameter trimmed mean, and Perimeter trimmed mean.

[0049] Step 5, standardization and logarithmic transformation; To eliminate the influence of different dimensions among variables, this embodiment employs a standardization method to process all independent variables (particle shape factors). The standardization process uses the Z-score standardization formula:

[0050] in, These are the original values ​​of the key features. The mean of this feature. This represents the standard deviation of the feature. The standardized data has a mean of 0 and a standard deviation of 1, thus allowing all features to be compared on the same scale and avoiding model bias towards certain features due to differences in units.

[0051] To satisfy the normal residual assumption of the regression model and compress the magnitude difference, this embodiment performs a logarithmic transformation on the target variable. The transformation formula is as follows:

[0052] Where y is the original dispersion value. All model training is performed based on the logarithmically transformed target variable, while model performance evaluation is calculated after inverse transformation back to the original scale to ensure that the results have practical application significance.

[0053] Step 6, Bootstrap data augmentation; The original sample size is only 40 groups, which is a typical scenario for small-sample food quality modeling. To mitigate the risk of overfitting caused by the small sample size and improve the model's generalization ability, this embodiment uses Bootstrap resampling for data augmentation. Specifically, the original dataset is sampled three times with replacement, and the original data is concatenated vertically with the three resampled data to generate the augmented dataset. The augmentation process maintains the logarithmic transformation form of the target variable. This strategy effectively expands the diversity of training samples while avoiding the introduction of external noise, making it particularly suitable for scenarios in the food industry where it is difficult to obtain large-scale labeled data.

[0054] Step 7, Category feature encoding processing; To explore the additional contribution of whole milk powder and skim milk powder to dispersion prediction, this embodiment introduces milk powder type as a candidate feature and uses one-hot encoding for numerical transformation. Specifically, the two categorical variables, "whole milk powder" and "skim milk powder," are encoded into binary vectors (whole milk powder: 1, 0; skim milk powder: 0, 1), so that the categorical information can adapt to the input requirements of the machine learning model. The encoded milk powder type feature is combined with the particle morphology feature filtered by Spearman correlation to form an extended feature set, which is used to compare the prediction performance with the basic feature set containing only particle morphology features to verify the effectiveness of the categorical features.

[0055] Step 8: Construct a CatBoost regression prediction model; CatBoost regression model is a gradient boosting framework based on symmetric decision trees. Its structure consists of multiple trees sequentially integrated, with each tree trained on the residuals of the previous trees.

[0056] The augmented dataset was divided into training and testing sets in a 7:3 ratio to construct a CatBoost regression model. Hyperparameters were optimized using grid search: the learning rate was searched from 0.01 to 0.1, the tree depth from 4 to 8, and the number of iterations was set from 100 to 1000. L2 regularization was introduced to control model complexity.

[0057] During model training, with the goal of minimizing mean squared error loss, an ordered boosting mechanism is used to correct gradient bias, thereby improving the stability of the training process and its robustness to noise.

[0058] The trained CatBoost regression model was used to predict the dispersion of the milk powder samples to be predicted. The prediction results are as follows: Figure 4 As shown, the data points in both the training set (purple) and the test set (yellow) are closely clustered near the ideal prediction line, indicating high prediction accuracy.

[0059] Table 2 lists the dispersibility results of two types of milk powder, whole milk and skim milk, at different particle size distributions. The results show that for both whole and skim milk powder, the undissolved rate is highest at 100% coarse particle size.

[0060] Table 2 Undissolved content of whole milk powder and skim milk powder with different particle ratios

[0061] Example 3 This embodiment provides a dispersion prediction system based on robust statistical characteristics of milk powder particle morphology, such as... Figure 5 As shown, the system includes an image acquisition module, a statistical calculation module, and a modeling and prediction module. The image acquisition module is used to acquire optical microscope images of milk powder particles and perform preliminary processing. It includes an optical microscope, an image acquisition unit, and a preprocessing unit. The optical microscope is equipped with a 10x objective lens and a high-definition camera, supporting autofocus and batch shooting. The image acquisition unit controls the shooting parameters and transmits the raw images to the preprocessing unit. The preprocessing unit integrates denoising, particle segmentation, and boundary extraction algorithms, which can automatically remove abnormal particles, output clear particle outline images, and transmit the processed images to the morphological feature extraction module.

[0062] The statistical calculation module is used to extract particle morphology parameters and calculate robust statistical indicators, including a parameter calculation unit and a statistical processing unit. The parameter calculation unit is used for boundary complexity and shape regularity calculation, etc., and the statistical processing unit is used for anomaly removal, interquartile range and truncated mean statistics, and includes an outlier removal unit for filtering outlier data based on threshold.

[0063] The modeling and prediction module is used to screen initial robust features and perform data augmentation, including a correlation analysis unit and a data augmentation unit. The correlation analysis unit uses the Spearman rank correlation algorithm to screen key features significantly related to dispersion and generates a feature screening report. The data augmentation unit generates an augmented dataset through Bootstrap resampling, providing diverse data support for subsequent model training. A gradient boosting regression model is constructed, trained using the augmented dataset, and inputs robust features to output dispersion prediction values. The modeling and prediction module includes a model building unit, a training unit, and a prediction unit. The model building unit is used for weak learner ensemble and residual fitting, the training unit is used for Bootstrap augmentation and cross-validation, and the prediction unit is used for feature input and dispersion value output.

[0064] In summary, the method and system provided by this invention, through optical microscope images, robust statistical features, scientific feature selection and data augmentation, combined with a gradient boosting model, achieves correlation modeling between milk powder particle morphology and dispersibility. This effectively reduces data interference and provides rapid, non-destructive, and accurate predictions. Compared to traditional detection methods, this application is simple to operate, fast in detection, and reliable in results. It can be widely applied to online quality control, batch inspection, and process optimization in milk powder manufacturing enterprises, and has significant practical application value.

[0065] Some steps in the embodiments of the present invention can be implemented using software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk.

[0066] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A dispersion prediction method based on robust statistical characteristics of milk powder particle morphology, characterized in that, The method includes: Step S101: Obtain an optical microscope image of the milk powder particles; Step S102: Extract particle morphology parameters based on optical microscope images and calculate robust statistical indices, and use the calculated robust statistical indices as initial features. Step S103: Analyze the correlation between initial features and dispersion, and select key features based on the correlation results with dispersion; Step S104: Construct a CatBoost regression prediction model and use the key features as input to obtain dispersion prediction results.

2. The method according to claim 1, characterized in that, Step S102 includes: Nine shape factor parameters of milk powder particles were extracted based on optical microscope images: maximum Feret diameter, minimum Feret diameter, roundness, solidity, convexity, elongation, area, equivalent diameter, and perimeter. The interquartile range and truncated mean were calculated for the nine extracted shape factor parameters to generate 18 robust feature vectors.

3. The method according to claim 2, characterized in that, The key features obtained by screening in step S103 are the interquartile range of the maximum Freret diameter, the interquartile range of the minimum Freret diameter, the interquartile range of solidity, the interquartile range of elongation, the interquartile range of area, the interquartile range of equivalent diameter, and the interquartile range of perimeter, as well as the truncated mean of the maximum Freret diameter, the truncated mean of the minimum Freret diameter, the truncated mean of solidity, the truncated mean of elongation, the truncated mean of area, the truncated mean of equivalent diameter, and the truncated mean of perimeter.

4. The method according to claim 3, characterized in that, The truncation rate of the truncation mean is 5%.

5. The method according to claim 4, characterized in that, In step S103, Spearman correlation analysis is used for screening, with a significance level of P < 0.05, to screen out features that are significantly related to dispersion.

6. The method according to claim 5, characterized in that, Step S101 includes mixing the milk powder sample with soybean oil under the action of a magnetic stirrer to make the milk powder particles evenly dispersed in the liquid oil; using a pipette to evenly drop the mixture of milk powder particles and soybean oil onto a clean glass slide to avoid particle agglomeration. Place the slide on the stage of the optical microscope and adjust the magnification to 10x eyepiece and 10x objective lens until the particle morphology can be clearly observed. Scan and capture images of the particle morphology using a digital microscope camera and digitize the images as high-resolution files. Preprocess the captured images by binarizing them with a fixed threshold, inverting the values, and filling the holes. Extract the particle boundary contours using the bwboundaries function.

7. The method according to claim 6, characterized in that, Step S104, which constructs the CatBoost regression prediction model, includes: Data augmentation was performed using Bootstrap resampling to obtain the augmented dataset; The augmented dataset was divided into training and testing sets in a 7:3 ratio to construct a CatBoost regression model. Hyperparameters were optimized using grid search: the learning rate was searched in the range of 0.01 to 0.1, the tree depth was searched in the range of 4 to 8, the number of iterations was set to 100 to 1000, and L2 regularization parameters were introduced to control the model complexity. During model training, the goal is to minimize the mean squared error loss, and an ordered boosting mechanism is used to correct gradient bias.

8. A dispersion prediction system based on robust statistical characteristics of milk powder particle morphology, characterized in that, The system includes an image acquisition module, a statistical calculation module, and a modeling and prediction module; wherein the image acquisition module is used to acquire optical microscope images of milk powder particles and perform preliminary processing; the statistical calculation module is used to extract particle morphology parameters and calculate robust statistical indices; and the modeling and prediction module is used to screen initial robust features and perform data augmentation.

9. The system according to claim 8, characterized in that, The image acquisition module includes an optical microscope, an image acquisition unit, and a preprocessing unit. The optical microscope is equipped with a 10x objective lens and a high-definition camera, supporting autofocus and batch shooting. The image acquisition unit is used to control the shooting parameters and transmit the raw images to the preprocessing unit. The preprocessing unit integrates denoising, particle segmentation, and boundary extraction algorithms, and transmits the processed image to the morphological feature extraction module; The statistical calculation module includes a parameter calculation unit and a statistical processing unit. The parameter calculation unit is used to calculate boundary complexity and shape regularity, while the statistical processing unit is used for outlier removal, interquartile range and truncated mean statistics, and includes an outlier removal unit for filtering outlier data based on a threshold. The modeling and prediction module includes a correlation analysis unit and a data augmentation unit. The correlation analysis unit uses the Spearman rank correlation algorithm to screen key features that are significantly correlated with dispersion and generates a feature screening report. The data augmentation unit generates augmented datasets using Bootstrap resampling.

10. The application of the dispersion prediction method based on robust statistical characteristics of milk powder particle morphology as described in any one of claims 1-7 in milk powder quality testing.

Images