Intelligent prediction method for rheological property of cast explosive

Abstract

The invention discloses a casting explosive rheological property intelligent prediction method comprising the following steps: 1, calculating morphology parameters of solid-phase particles based on a CT image, and carrying out weighted calculation according to accumulated volume distribution of the morphology parameters to obtain the special-shape degree of the solid-phase particles; 2, selecting characteristic variables, and preparing casting explosive suspensions with different process characteristics; testing the casting explosive suspension by using a rotational rheometer to obtain rheological property data; constructing an initial data set in combination with the characteristic variables and the rheological characteristic data, and preprocessing the initial data set; 3, training an XGBoost fused cast explosive rheological parameter prediction model by using the preprocessed data set, and optimizing hyper-parameters of the XGBoost fused cast explosive rheological parameter prediction model by using a Bayesian optimization method; and 4, inputting the characteristic variables into the XGBoost fused cast explosive rheological parameter prediction model, and outputting predicted values of yield stress and plastic viscosity values as prediction results of the fused cast explosive rheological characteristic parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of melt-cast explosives, and specifically relates to an intelligent prediction method for the rheological properties of melt-cast explosives. Background Art

[0002] In the preparation process of melt-cast explosives, the rheological properties of melt-cast explosives are the key factors that determine the formula components, process parameters and product quality, and are also the basis for the process design of melt-cast explosives. Plastic viscosity, as an important rheological parameter, is an important indicator in the charging of melt-cast explosives. Melt-cast explosives are usually a mixture of solid and liquid phases. Too low viscosity of melt-cast explosives will cause the solid phase particles to settle, affecting the homogeneity of the melt-cast explosives. Excessive viscosity will affect its melt mixing efficiency and subsequent casting quality, resulting in defects such as cracks, cavities, and shrinkage cavities in the charge column. These defects significantly reduce the quality and actual application performance of the melt-cast explosives. Therefore, it is of great significance to study the rheological properties and laws of melt-cast explosives.

[0003] Currently, the rheological properties of melt-cast explosives are typically measured using instruments such as viscometers and rotational rheometers. However, the accuracy of test results is easily affected by multiple factors, including the performance of the test equipment, environmental conditions, and the experimental staff's operating procedures, and the testing cycle is relatively long. Furthermore, existing research on the rheological properties of melt-cast explosives has focused solely on factors such as temperature, solids content, and additives, ignoring the influence of solid-phase particle morphology on the rheological properties of melt-cast explosives. Furthermore, there is a lack of methods to characterize the morphological characteristics of solid-phase particles in melt-cast explosives. In recent years, the rise of technologies such as machine learning has provided a new approach to solving this problem. Machine learning (ML), as a modern data processing method, can automatically infer logic or rules from provided data and use these induction results to predict or classify new data. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide an intelligent prediction method for the rheological properties of molten-cast explosives, which can realize the intelligent prediction of the rheological properties of molten-cast explosives through the distribution ratios of each component of the molten-cast explosives, physical properties parameters and process parameters without experimental equipment and related experimental environment.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] An intelligent prediction method for rheological properties of cast explosives, comprising the following steps:

[0007] Step 1: Solid phase particle morphology characterization

[0008] A microfocus industrial CT system was used to obtain two-dimensional and three-dimensional CT images of the solid phase particles of the molten-cast explosive. The morphological parameters of the solid phase particles were calculated based on the CT images, and the degree of irregularity of the solid phase particles was obtained by weighted calculation based on the cumulative volume distribution of the morphological parameters.

[0009] Step 2: Build the initial dataset

[0010] The characteristic variables affecting the rheological properties of fused-cast explosives are selected as follows: particle size of solid particles, solid particle shape, solid particle gradation, solid particle content of explosive suspension, additive content, aluminum powder content, explosive suspension temperature, shear rate and suspension stirring time;

[0011] preparing molten-cast explosive suspensions with different process characteristics; testing the molten-cast explosive suspensions using a rotational rheometer to obtain rheological property data;

[0012] An initial data set is constructed by combining characteristic variables and rheological property data, and the initial data set is preprocessed including outlier removal, missing value interpolation, and standardization and normalization;

[0013] Step 3: Build an XGBoost model for predicting rheological parameters of cast explosives

[0014] The preprocessed dataset was used to train the XGBoost model for predicting rheological parameters of cast explosives, and the Bayesian optimization method was used to optimize the hyperparameters of the XGBoost model for predicting rheological parameters of cast explosives.

[0015] Step 4: Prediction of rheological properties of cast explosives

[0016] The characteristic variables are input into the XGBoost rheological parameter prediction model of molten-cast explosives, and the predicted values ​​of yield stress and plastic viscosity are output as the prediction results of the rheological characteristic parameters of molten-cast explosives.

[0017] Furthermore, in step 1, the method steps for characterizing the morphology of solid phase particles are:

[0018] 11) Fixing the solid particles in a centrifuge tube and performing CT scanning to obtain two-dimensional and three-dimensional CT images;

[0019] 12) Convert the two-dimensional bitmap into a vector image and perform cropping, sharpening and binarization processing;

[0020] 13) Calculate the morphological parameters of solid particles based on the binary image, including roundness, angularity, roughness, sphericity and aspect ratio;

[0021] 14) After normalizing the morphological parameters, the cumulative volume distribution is calculated, and the degree of heteromorphism of the solid phase particles is obtained by weighted calculation according to the size of the cumulative volume distribution.

[0022] Furthermore, in step 2, the rheological property data obtained using the rotational rheometer include shear stress and plastic viscosity, and the yield stress is obtained by fitting the experimental data using the Herschel-Bulkley model. The expression of the Herschel-Bulkley model is:

[0023]

[0024] Where: τ is the shear stress; τ0 is the yield stress; is the shear rate; K is the consistency coefficient; n is the power exponent.

[0025] Furthermore, in step 2, the method for preprocessing the initial data set is:

[0026] Eliminate abnormal data caused by insufficient measurement accuracy at low shear rates;

[0027] Newton interpolation method was used to fill missing values;

[0028] Normalization was performed using the Z-score method;

[0029] Min-max normalization is used to map the data to the interval [0,1].

[0030] Furthermore, in step 3, before training the XGBoost cast explosive rheological parameter prediction model, PCA principal component analysis dimensionality reduction is performed on the preprocessed data set, including:

[0031] Construct the rheological data matrix X with the preprocessed data set and obtain the transposed matrix X of the rheological data matrix T ; With rheological data matrix X and transposed matrix X T Construct the covariance matrix of the standardized data:

[0032]

[0033] Where: Cov(X) is the covariance matrix; n is the number of samples;

[0034] Perform eigendecomposition on the covariance matrix and sort the eigenvalues ​​and corresponding eigenvectors;

[0035] The first six principal components with cumulative variance contribution greater than or equal to 80% are selected to form the projection matrix W;

[0036] Multiply the rheological data matrix X by the projection matrix W to reduce the dimensionality to a 6-dimensional data set.

[0037] Furthermore, in step 3, the method for constructing the XGBoost cast explosive rheological parameter prediction model includes:

[0038] Build an XGBoost model to predict rheological parameters of cast explosives and define the hyperparameter search space;

[0039] The Bayesian optimization method is used to optimize hyperparameters, with Gaussian process as the surrogate model and expected lift function as the acquisition function.

[0040] An early stopping strategy is set during training, and training is terminated when the validation loss does not improve for a set number of consecutive rounds.

[0041] The beneficial effects of the present invention are:

[0042] The present invention provides an intelligent prediction method for the rheological properties of melt-cast explosives. Even without experimental equipment and experimental conditions, the rheological properties of the melt-cast explosives can be quickly predicted by using the melt-cast explosives' proportions, physical properties, and process parameters. First, a microfocus industrial CT system is used to obtain two-dimensional and three-dimensional CT images of the melt-cast explosives' solid phase particles. Based on these images, the morphological parameters of the solid phase particles are calculated to obtain the degree of irregularity of the solid phase particles, and the morphology of the solid phase particles is characterized by the degree of irregularity. Second, multiple groups of test samples with different process characteristics are prepared. These characteristics include the degree of irregularity, particle size, and gradation of the melt-cast explosives' solid phase particles, the solid phase particle content, additive content, and aluminum powder content in the explosive suspension, as well as the temperature, shear rate, and stirring time of the explosive suspension. Subsequently, a rotational rheometer is used to perform rheological tests on these melt-cast explosive samples to obtain rheological property data for each group of melt-cast explosive systems and construct a rheological property data set. Finally, an XGBoost model for predicting the rheological parameters of melt-cast explosives was constructed using eXtreme Gradient Boosting (XGBoost), and the model was optimized using Bayesian Optimization (BO). The model inputs included characteristic variables such as the particle size, particle shape, and gradation of the melt-cast explosive solid phase particles, the solid phase particle content of the explosive suspension, the additive content, the aluminum powder content, the explosive suspension temperature, the shear rate, and the stirring time of the explosive suspension. The plastic viscosity and yield stress of the melt-cast explosive were used as the model outputs. After the model was trained, the rheological properties of the melt-cast system could be quickly obtained by inputting the characteristic variables of different melt-cast explosive systems. Compared with the traditional use of rheometers to obtain the rheological property parameters of molten-cast explosives, the present invention can greatly shorten the cycle of obtaining the rheological properties of molten-cast explosives, and the predicted results have high accuracy. It solves the problems existing in traditional experiments, such as the accuracy of results being greatly affected by test equipment, environmental factors and experimenter operation, long test cycles, high test costs and lack of safety guarantee under high shear rates. It is of great significance for the early formulation research of molten-cast explosives.

[0043] Specifically, the present invention also has the following advantages.

[0044] (1) The present invention proposes a method for characterizing the morphology of solid-phase particles in melt-cast explosives, which can quantitatively, accurately, and intuitively characterize the morphology of the solid-phase particles in melt-cast explosives. Based on this, the present invention focuses on the influence of the morphology of the solid-phase particles in melt-cast explosives on the rheological properties of the melt-cast explosive system, providing an important basis for controlling the rheological properties of melt-cast explosives.

[0045] (2) For the design of melt-cast explosive formula, a large number of mix ratio experiments are required to obtain melt-cast explosives that meet the rheological performance requirements, which will consume a lot of time and material costs. In addition, rheological experiments have problems such as the experimental results are greatly affected by environmental factors and poor repeatability. At the same time, the traditional statistical method is to establish a nonlinear equation model through nonlinear fitting of experimental data to describe the rheological properties of melt-cast explosives. However, due to the large number of influencing factors, the existing nonlinear equation model can only explain the influence of shear rate, temperature, etc. on the rheological properties of melt-cast explosives, but cannot explain the influence of complex factors such as solid phase particle anomaly, particle size, particle grading, additive content and sample composition on the rheological properties of melt-cast explosives. It is difficult to quickly obtain the rheological properties of melt-cast explosives. The present invention can quickly and intelligently obtain the rheological data of melt-cast explosives through the XGBoost rheological parameter prediction model, which greatly saves experimental time and experimental costs while ensuring the accuracy of the prediction results.

[0046] (3) The present invention models the rheological properties of molten-cast explosives from multiple dimensions and analyzes the rheological laws of molten-cast explosives under different process conditions based on data mining technology. The XGBoost rheological parameter prediction model can efficiently and accurately predict the rheological properties of molten-cast explosives with high accuracy, providing a new method for accurately predicting the working performance of molten-cast explosives and other types of explosives, with high economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0048] Figure 1 Flowchart of an embodiment of the intelligent prediction method for rheological properties of molten-cast explosives according to the present invention;

[0049] Figure 2 The process of characterizing the irregularity and the calculation results of the irregularity of a group of particles are shown;

[0050] Figure 3 The corresponding relationship diagram between different process conditions and rheological characteristic curves;

[0051] Figure 4 Fitting rheological data and viscosity-shear rate curves for a set of melt-cast explosives;

[0052] Figure 5 Flowchart for Bayesian optimization of XGBoost prediction model for rheological parameters of cast explosives;

[0053] Figure 6 This is a comparison chart of the yield stress predicted value and the actual value of the XGBoost rheological parameter prediction model in the test set;

[0054] Figure 7 This is a comparison chart of the viscosity prediction value and the actual value of the XGBoost rheological parameter prediction model in the test set. DETAILED DESCRIPTION

[0055] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0056] like Figure 1 As shown, the intelligent prediction method of rheological properties of molten-cast explosives in this embodiment includes the following steps:

[0057] Step 1: Solid phase particle morphology characterization

[0058] A microfocus industrial CT system was used to acquire two-dimensional and three-dimensional CT images of the solid phase particles of the molten-cast explosive. Image processing software was used to obtain the geometric parameters of the solid phase particles based on the CT images and calculate the morphological parameters of the solid phase particles. The two-dimensional and three-dimensional morphological parameters were combined according to the cumulative volume distribution of the solid phase particle morphological parameters. The morphological degree of the solid phase particles was obtained by weighted calculation based on the cumulative volume distribution of the morphological parameters, and the morphology of the solid phase particles was quantitatively characterized.

[0059] Specifically, in this embodiment, a microfocus industrial CT system is first used to obtain two-dimensional and three-dimensional CT images of various solid particles. Then, Image-Pro Plus 6.0 image processing software is used to obtain the geometric parameters of the solid particles and calculate the two-dimensional and three-dimensional morphological parameters of the solid particles, wherein the two-dimensional morphological parameters include roundness, angularity and roughness, and the three-dimensional morphological parameters include sphericity and aspect ratio. Finally, based on the obtained solid particle morphological parameters, a weighted calculation is performed according to the cumulative volume distribution size of the morphological parameters to obtain the heteromorphism of the solid particles, and the heteromorphism is used to quantitatively characterize the morphology of the particles. Specifically, as Figure 2 As shown, the method steps for characterizing the solid phase particle morphology are as follows.

[0060] 11) The solid particles are fixed in a centrifuge tube and subjected to CT scanning to obtain two-dimensional and three-dimensional CT images. Specifically, two-dimensional and three-dimensional CT images of the solid particles of the fused-cast explosive are obtained using a microfocus industrial CT system. The solid particles are fixed in a 10 mm diameter plastic centrifuge tube using silicone sealant to prepare a test sample. The test sample is then subjected to cone-beam scanning using a microfocus CT system to obtain CT images of the solid particles.

[0061] 12) Convert the 2D bitmap to a vector map and perform cropping, sharpening, and binarization. Specifically, convert the 2D bitmap obtained by microfocus CT into a vector map to smooth out jagged edges of solid particles. Subsequently, the 2D CT image of the solid particles is cropped and sharpened to enhance image contrast. To facilitate accurate calculation of solid particle morphology parameters using image processing software, the vector map is further converted into a binary image.

[0062] 13) The morphological parameters of the solid-phase particles are calculated based on the binary image, including roundness, angularity, roughness, sphericity and aspect ratio. In the present embodiment, the binary image is imported into Image-Pro Plus 6.0 image processing software, and the geometric parameters such as the maximum main axis length and the maximum main axis width, the perimeter of a certain plane projection, the equivalent ellipse perimeter, and the projected plane area are calculated. The geometric parameters are substituted into the following formula to calculate the morphological parameters such as roundness, angularity, roughness, sphericity, aspect ratio. Specifically, the calculation formula of the morphological parameters is as follows, and Table 1 is the morphological parameters of three groups of solid-phase particles calculated.

[0063] (1) Roundness:

[0064]

[0065] Where: p is the perimeter of the particle projected onto a plane; A is the area of ​​the projection plane.

[0066] (2) Angle:

[0067]

[0068] Where: P c is the minimum circumscribed polygon perimeter of the particle boundary; P e is the equivalent ellipse circumference of the particle.

[0069] (3) Roughness:

[0070]

[0071] Where: P is the perimeter of the particle projected on a certain plane; P e is the equivalent ellipse circumference of the particle.

[0072] (4) Sphericity:

[0073]

[0074] Among them: A L is the actual three-dimensional surface area of ​​the particle; V is the actual three-dimensional volume of the particle.

[0075] (5) Aspect ratio:

[0076]

[0077] Where: L and W are the maximum length and maximum width of the solid particles respectively.

[0078] Table 1 Morphological parameters of a group of solid particles

[0079]

[0080] 14) After normalizing the morphology parameters, the cumulative volume distribution is calculated, and the degree of irregularity of the solid phase particles is calculated by weighting the cumulative volume distribution. Specifically, in this embodiment, the morphology parameters are first normalized, and then a MATLAB script is written to calculate the cumulative volume distribution of roundness, angularity, roughness, sphericity, and aspect ratio. The morphology parameters are weighted according to the size of the cumulative volume distribution, and the degree of irregularity of the solid phase particles is calculated according to the following formula. Table 2 shows the calculated degrees of irregularity of three groups of solid phase particles.

[0081] Heterogeneous particle shape = ∑(particle morphology characterization parameter × weight)

[0082] Table 2 Characterization results of the morphology of a group of solid particles

[0083] Solid particles <![CDATA[S1]]> <![CDATA[S2]]> <![CDATA[S3]]> Degree of heteromorphism 0.2172 0.2747 0.3573

[0084] Step 2: Build the initial dataset

[0085] Based on the factors influencing the rheological properties of melt-cast explosives, this example selects the particle size, particle shape, and gradation of the solid particles of the explosive suspension, the solid particle content of the explosive suspension, the additive content, the aluminum powder content, the explosive suspension temperature, the shear rate, and the suspension stirring time as characteristic variables affecting the rheological properties of melt-cast explosives. Based on these characteristics, melt-cast explosive suspensions with different process characteristics were designed and prepared. These suspensions were then tested using a rotational rheometer to obtain rheological property data.

[0086] In this embodiment, the rheological property data obtained using a rotational rheometer include shear stress and plastic viscosity, and the yield stress is obtained by fitting the experimental data using the Herschel-Bulkley model. Specifically, the Herschel-Bulkley model is based on the Bingham model and further introduces an exponential structure. This exponential correction term can more accurately describe fluids that thin and thicken under shear force. The power exponent n has no clear physical meaning. When n is greater than 1, it indicates the presence of thixotropy. This model is more accurate in calculating the yield stress of the fluid. Specifically, the expression of the Herschel-Bulkley model is:

[0087]

[0088] Where: τ is shear stress, unit: Pa; τ0 is yield stress, unit: Pa; is the shear rate, unit: s -1 ; K is the consistency coefficient; n is the power exponent.

[0089] like Figure 3 As shown, since the rheological properties of melt-cast explosives may be affected by many factors such as stirring equipment and process, and in order to ensure the repeatability of the experimental results, each group of melt-cast explosives is processed using the same stirring equipment and preparation process. After the stirring is completed, the same group of melt-cast explosives is divided into three samples, and each sample corresponds to a specific time period. These melt-cast explosive samples are then subjected to rheological testing using a rheometer, and the rotor of the rheometer is used to apply shearing action to the melt-cast explosives to extract relevant data on their rheological properties. After the rheological test is completed, the sheared samples will be discarded. This practice is intended to ensure that each sample in the repeated test has the same shear history, thereby ensuring the comparability of the data. In this embodiment, a total of 120 groups of rheological data of melt-cast explosives were collected as original data sets, and on this basis, the Herschel-Bulkley model was used to fit the experimental data to obtain the yield stress of the melt-cast explosives. The rheological data fitting curve and viscosity-shear rate curve of a group of melt-cast explosives are shown in Figure 2. Figure 4 shown.

[0090] This embodiment constructs an initial dataset by combining characteristic variables and rheological property data. This initial dataset is then preprocessed, including removing outliers, filling missing values ​​in the rheological data using interpolation, and standardizing and normalizing the rheological data. Specifically, the method for preprocessing the initial dataset is as follows.

[0091] (1) Outlier elimination: eliminate outlier data caused by insufficient measurement accuracy at low shear rates. Specifically, eliminate outlier data with large fluctuations due to reasons such as small stress signals measured by the rheometer at low shear rates, insufficient detection accuracy, signal fluctuations or deviations.

[0092] (2) Missing value interpolation: Newton interpolation is used to fill missing values. Specifically, a polynomial function is constructed using Newton interpolation to fill missing values ​​in the data.

[0093] (3) Standardization: Use the Z-score method for standardization. Specifically, the rheological data is subjected to Z-score standardization to eliminate the influence of dimension and highlight the differences between variables. The standardization formula is as follows:

[0094]

[0095] Where: μ is the mean of the data column; σ is the standard deviation of the data column.

[0096] (4) Normalization: Use minimum-maximum normalization to map the data to the [0,1] interval. The formula is as follows:

[0097]

[0098] Where: x min is the minimum value of the data column; x max The maximum value of the data column.

[0099] Step 3: Build an XGBoost model for predicting rheological parameters of cast explosives

[0100] The preprocessed dataset is used to train the XGBoost model for predicting rheological parameters of cast explosives, and the Bayesian optimization method is used to optimize the hyperparameters of the XGBoost model for predicting rheological parameters of cast explosives.

[0101] 31) PCA principal component analysis dimensionality reduction

[0102] Before training the XGBoost cast explosive rheological parameter prediction model, the pre-processed data set is subjected to PCA principal component analysis dimensionality reduction. In this embodiment, based on the standardized and normalized rheological data and the corresponding 9 characteristic variables affecting the rheological characteristic parameters of cast explosives, PCA principal component analysis is used to perform feature selection on the data. Through PCA principal component analysis, the original data is subjected to data dimensionality reduction to obtain a 6-dimensional data set. Specifically, Figure 5 As shown in Figure 2, the method for performing PCA principal component analysis dimensionality reduction on the preprocessed data set is as follows.

[0103] (1) Constructing the covariance matrix: Construct a 120×9 rheological data matrix X with the preprocessed data set, and obtain the 9×120 transposed matrix X of the rheological data matrix T ; With rheological data matrix X and transposed matrix X T Construct a 9×9 covariance matrix for the standardized data:

[0104]

[0105] Where: Cov(X) is the covariance matrix (each column has a mean of 0 and a standard deviation of 1); n is the number of samples.

[0106] (2) Eigendecomposition: Perform eigendecomposition on the covariance matrix and sort the eigenvalues ​​and corresponding eigenvectors. Specifically, perform eigendecomposition on the covariance matrix, sort the eigenvalues ​​from large to small, and simultaneously sort the corresponding eigenvectors. The method is:

[0107] Cov(X)·v i =λ i v i

[0108] Where: i is the i-th eigenvalue (reflecting the variance contribution of the corresponding principal component); v i is the corresponding eigenvector (direction of principal component).

[0109] (3) Select principal components: Select the first 6 principal components whose cumulative variance contribution rate is greater than or equal to 80% to form the projection matrix W. Specifically, select the first 6 principal components based on the variance contribution rate and the cumulative variance contribution rate, and check whether the cumulative variance contribution rate of the first 6 principal components reaches 80%.

[0110]

[0111] Contribution i Cumulative Contribution is the contribution of the i-th principal component; k is the cumulative contribution of the first k principal components.

[0112] (4) Dimensionality reduction: Multiply the rheological data matrix X by the projection matrix W to reduce the dimensionality to a 6-dimensional dataset. Select the first 6 eigenvectors to form a 9×6 projection matrix W, which is multiplied with the original data matrix X to obtain the reduced 6-dimensional matrix. 80% of the preprocessed dataset is randomly used as the training set for the model, and 20% is used as the test set.

[0113] 32) Model Training

[0114] An XGBoost model for predicting the rheological parameters of cast explosives was established. Bayesian optimization of the XGBoost model's hyperparameters was used, combined with an early stopping strategy to prevent overfitting, improve model generalization, and enhance model training efficiency and prediction accuracy. Specifically, the construction of the XGBoost model for predicting the rheological parameters of cast explosives included the following steps.

[0115] (1) Based on the construction of the XGBoost cast explosive rheological parameter prediction model, the hyperparameter search space of the XGBoost cast explosive rheological parameter prediction model is defined.

[0116] (2) The Bayesian optimization method is used to optimize hyperparameters using the Gaussian process as the proxy model and the expected lift function as the acquisition function. Specifically, a Bayesian optimization framework is designed based on the 6-dimensional rheological parameter data set obtained by principal component analysis. The Bayesian optimization formula (Gaussian process prior) is:

[0117] P(L\θ)~GP(μ(θ),K(θ,θ′))

[0118] Where P(L\θ) is the probability distribution of the loss function L under the given hyperparameter θ; GP(μ(θ),K(θ,θ′)) is a Gaussian process, which means that P(L\θ) is modeled using a Gaussian process; K(θ,θ′) is the covariance function (kernel function) used to quantify the similarity of different hyperparameter combinations. (Matern kernel); μ(θ) is the mean function, which represents the prior mean at the hyperparameter point θ; θ is a hyperparameter vector, which represents the hyperparameter combination to be optimized; θ′ is another hyperparameter vector, which represents other hyperparameter combinations compared with θ; L is the loss function value, which represents the performance indicator of the model on the validation set; σ 2 is the variance; l is the length scale; ||θ―θ′|| 2 is the square of the Euclidean distance in the hyperparameter space.

[0119] Define the XGBoost hyperparameter space, including the objective function, surrogate model, acquisition function, tree depth, learning rate, regularization coefficient, etc., use the validation set loss as the optimization target, and iteratively search for the optimal parameter combination through the Gaussian process surrogate model and the expected improvement function.

[0120] XGBoost split gain formula:

[0121]

[0122] Where: G is the first-order gradient; H is the second-order gradient; G L is the sum of the first-order gradients of all samples of the left child node; G R is the sum of the first-order gradients of all samples of the right child node; H L is the sum of the second-order gradients of all samples of the left child node; H R is the sum of the second-order gradients of all samples of the right child node; λ is the L2 regularization coefficient; γ is the minimum loss reduction threshold for node splitting.

[0123] The objective function of XGBoost can be expressed as:

[0124]

[0125] in: is the loss function, usually the square root error is used: Ω(f k ) is a regularization term used to control model complexity and is defined as: So the final objective function of XGBoost can be written as:

[0126]

[0127] Where: T is the number of leaf nodes in the decision tree; w is the weight of the leaf node; γ is the minimum loss reduction threshold for node splitting that controls the number of leaf nodes; λ is the L2 regularization coefficient that controls the weight of the leaf node.

[0128] (3) Early stopping strategy: An early stopping strategy is set during training, and training is terminated when the validation loss has not improved for the set number of consecutive rounds. Specifically, an early stopping strategy is set during model training. The number of rounds set in this embodiment is 50, that is, training is terminated if the validation loss has not improved for 50 consecutive rounds, to prevent overfitting and achieve automatic tuning. The core principle is: when the loss or accuracy of the model on the validation set no longer improves after several consecutive rounds of iterations, training is terminated in advance to avoid overfitting and save computing resources. Ultimately, the generalization ability of the XGBoost prediction model is improved through the coordination of parameter tuning and training strategy.

[0129] (4) Model Verification

[0130] The optimized hyperparameters were brought into the model for training, and the K-fold cross validation method was used to verify the prediction results of the rheological properties of the cast explosive system. The root mean square error (RMSE) and the coefficient of determination (R 2 ) and mean absolute percentage error (MAPE) are used to test the performance of the XGBoost prediction model. The specific calculation formula is as follows:

[0131] Root mean square error RMSE:

[0132]

[0133] Where: y i is the actual value; is the predicted value.

[0134] Coefficient of determination R 2 :

[0135]

[0136] Where: y i is the actual value; is the predicted value; is the mean of the actual values.

[0137] Mean Absolute Percentage Error (MAPE):

[0138]

[0139] Where: y i is the actual value; is the predicted value; n is the number of data samples.

[0140] (5) XGBoost Principle

[0141] In this example, XGBoost is based on Gradient Boosting Trees (GBT). The core idea is to construct multiple weak learners (decision trees) through ensemble learning, where each tree reduces the prediction error based on the previous tree. XGBoost's optimization objective consists of two parts: a loss function that measures the error between the predicted value and the true value, and a regularization term that controls model complexity and prevents overfitting.

[0142] Let the dataset Among them, x i is the input feature, y i is the target variable. Assume that the prediction function of the model is:

[0143]

[0144] Among them, f k (x) represents the kth decision tree, and the objective function of XGBoost can be expressed as:

[0145]

[0146] in: is the loss function, usually the squared error is used:

[0147]

[0148] Ω(f k ) is a regularization term used to control model complexity and is defined as:

[0149]

[0150] Where: T is the number of leaf nodes in the decision tree; ω is the weight of the leaf node; γ is the penalty for controlling the number of leaf nodes; λ is the L2 regularization for controlling the weight of the leaf node.

[0151] XGBoost’s additive training process: XGBoost uses the gradient boosting method to gradually optimize the predicted value. Assume that the predicted value of the current model is The goal of the next tree is to fit the residuals:

[0152]

[0153] That is, the learning goal of each tree is to minimize the following second-order approximate objective function:

[0154]

[0155] Among them, g i is the first-order gradient: h i is the second-order gradient:

[0156] Thus, each new tree f t (x) is trained to minimize this objective function.

[0157] Leaf node weight calculation: Assume that the leaf node of a tree is represented by I j , where I j Contains all samples that fall into leaf node j, then the optimal weight calculation formula for the leaf node is:

[0158]

[0159] The optimal score for the entire tree is:

[0160]

[0161] (5) Principles of Bayesian Optimization

[0162] Bayesian Optimization (BO) is a method for optimizing black-box functions. The core idea of ​​BO is to use a probabilistic model (usually a Gaussian process, GP) to represent the objective function and use an acquisition function to determine the next evaluation point, thereby finding the optimal solution with a smaller number of queries.

[0163] Assume the objective function is:

[0164]

[0165] in: is the input space, usually a high-dimensional space; f(x) is the function we want to optimize, and the global optimal solution is:

[0166]

[0167] The core of Bayesian optimization is to use Gaussian Process (GP) to estimate the target function f(x). Gaussian process is a probability distribution that assumes that the function f(x) obeys a Gaussian distribution at each point:

[0168] f(x)~GP(m(x),k(x,x′))

[0169] Where: m(x) is the mean function. In order to simplify the calculation, m(x) = 0 is usually taken; k(x, x ′ ) is the covariance function (kernel function), and a common choice is RBF (radial basis function):

[0170]

[0171] Among them, σ 2 Controls the size of the variance; l controls the smoothness of the function.

[0172] Prediction formula of Gaussian process: Assuming that there are n sampling points, that is:

[0173]

[0174] The goal is to find the new point x * Predict f(x * ), the output of known data:

[0175] y=[y1,y2,…y n ] T

[0176] Covariance matrix:

[0177]

[0178] Covariance of new points with existing points:

[0179] K * =[k(x * ,x1),k(x * ,x2),…,k(x * ,x n )]

[0180] The covariance of the new point itself:

[0181] K ** =k(x * ,x * )

[0182] Then the mean (expected) and variance of the Gaussian process prediction are:

[0183] μ(x * )=K* K ―1 y

[0184]

[0185] Where: μ(x * ) represents the value of f(x * )’s predicted value (surrogate objective function); σ 2 (x * ) represents the uncertainty of the prediction (the confidence of the model).

[0186] The acquisition function is used to determine the next sampling point, that is, how to balance exploration and exploitation. Common acquisition functions include expected improvement (EI), upper confidence bound (UCB), and probability improvement (PI).

[0187] Expected to improve EI:

[0188] α EI (x) = E[max(f(x)-f(x) + ),0)]

[0189] Where: x + is the current optimal point. The specific calculation formula is:

[0190] α EI (x)=(μ(x)-f(x+)-ξ)Φ(Z)+σ(x)φ(Z)

[0191]

[0192] where Φ(Z) and φ(Z) are the CDF and PDF of the standard normal distribution; ξ is the exploration parameter, and a larger value increases the exploration.

[0193] Confidence upper bound UCB:

[0194] α UCB (x)=μ(x)+kσ(x)

[0195] Where: k controls the trade-off between exploration and exploitation.

[0196] Probability improvement PI:

[0197]

[0198] Step 4: Prediction of rheological properties of cast explosives

[0199] In this embodiment, the nine characteristic variables of the cast explosive sample of the test formula are used as model inputs, and the characteristic variables are input into the XGBoost cast explosive rheological parameter prediction model for prediction, and the plastic viscosity and yield stress values ​​are output. The yield stress and plastic viscosity values ​​output by the XGBoost cast explosive rheological parameter prediction model are used as the prediction results of the cast explosive rheological characteristic parameters, as shown in FIG. Figure 6-7 Shown are the yield stress and plastic viscosity prediction results of the test set, respectively.

[0200] The above embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention. The scope of protection of the present invention shall be subject to the claims.

Claims

1. An intelligent prediction method for rheological properties of cast explosives, characterized by: The steps include: Step 1: Solid phase particle morphology characterization A microfocus industrial CT system was used to obtain two-dimensional and three-dimensional CT images of the solid phase particles of the molten-cast explosive. The morphological parameters of the solid phase particles were calculated based on the CT images, and the degree of irregularity of the solid phase particles was obtained by weighted calculation based on the cumulative volume distribution of the morphological parameters. Step 2: Build the initial dataset The characteristic variables affecting the rheological properties of fused-cast explosives are selected as follows: particle size of solid particles, solid particle shape, solid particle gradation, solid particle content of explosive suspension, additive content, aluminum powder content, explosive suspension temperature, shear rate and suspension stirring time; preparing molten-cast explosive suspensions with different process characteristics; testing the molten-cast explosive suspensions using a rotational rheometer to obtain rheological property data; An initial data set is constructed by combining characteristic variables and rheological property data, and the initial data set is preprocessed including outlier removal, missing value interpolation, and standardization and normalization; Step 3: Build an XGBoost model for predicting rheological parameters of cast explosives The preprocessed dataset was used to train the XGBoost model for predicting rheological parameters of cast explosives, and the Bayesian optimization method was used to optimize the hyperparameters of the XGBoost model for predicting rheological parameters of cast explosives. Step 4: Prediction of rheological properties of cast explosives The characteristic variables are input into the XGBoost rheological parameter prediction model of molten-cast explosives, and the predicted values ​​of yield stress and plastic viscosity are output as the prediction results of the rheological characteristic parameters of molten-cast explosives.

2. The intelligent prediction method for rheological properties of molten-cast explosive according to claim 1, characterized in that: In step 1, the method steps for characterizing the morphology of solid phase particles are: 11) Fixing the solid particles in a centrifuge tube and performing CT scanning to obtain two-dimensional and three-dimensional CT images; 12) Convert the two-dimensional bitmap into a vector image and perform cropping, sharpening and binarization processing; 13) Calculate the morphological parameters of solid particles based on the binary image, including roundness, angularity, roughness, sphericity and aspect ratio; 14) After normalizing the morphological parameters, the cumulative volume distribution is calculated, and the degree of heteromorphism of the solid phase particles is obtained by weighted calculation according to the size of the cumulative volume distribution.

3. The intelligent prediction method for rheological properties of molten-cast explosive according to claim 1, characterized in that: In the second step, the rheological property data obtained using the rotational rheometer include shear stress and plastic viscosity, and the yield stress is obtained by fitting the experimental data using the Herschel-Bulkley model. The expression of the Herschel-Bulkley model is: Where: τ is the shear stress; τ0 is the yield stress; is the shear rate; K is the consistency coefficient; n is the power exponent.

4. The intelligent prediction method for rheological properties of molten-cast explosive according to claim 1, characterized in that: In step 2, the method for preprocessing the initial data set is: Eliminate abnormal data caused by insufficient measurement accuracy at low shear rates; Newton interpolation method was used to fill missing values; Normalization was performed using the Z-score method; Min-max normalization is used to map the data to the interval [0,1].

5. The intelligent prediction method for rheological properties of molten-cast explosive according to claim 1, characterized in that: In the step 3, before training the XGBoost cast explosive rheological parameter prediction model, PCA principal component analysis dimensionality reduction is performed on the preprocessed data set, including: Construct the rheological data matrix X with the preprocessed data set and obtain the transposed matrix X of the rheological data matrix T ; With rheological data matrix X and transposed matrix X T Construct the covariance matrix of the standardized data: Where: Cov(X) is the covariance matrix; n is the number of samples; Perform eigendecomposition on the covariance matrix and sort the eigenvalues ​​and corresponding eigenvectors; The first six principal components with cumulative variance contribution greater than or equal to 80% are selected to form the projection matrix W; Multiply the rheological data matrix X by the projection matrix W to reduce the dimensionality to a 6-dimensional data set.

6. The intelligent prediction method for rheological properties of molten-cast explosive according to claim 1, characterized in that: In step 3, the method for constructing the XGBoost cast explosive rheological parameter prediction model includes: Build an XGBoost model to predict rheological parameters of cast explosives and define the hyperparameter search space; The Bayesian optimization method is used to optimize hyperparameters, with Gaussian process as the surrogate model and expected lift function as the acquisition function. An early stopping strategy is set during training, and training is terminated when the validation loss does not improve for a set number of consecutive rounds.

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