A high-precision high-speed prediction method for the burning rate of hydroxyl-terminated propellant based on machine learning

Abstract

The application discloses a high-precision high-speed prediction method for the burning rate of hydroxyl-terminated propellant, which comprises the following steps: establishing a database containing a plurality of groups of data, wherein each group of data comprises the burning rate of the propellant and its influencing factors; standardizing the database to obtain a sample library, wherein each sample in the sample library comprises the standardized burning rate of the hydroxyl-terminated propellant and its standardized influencing factors; dividing the sample library into a training set and a test set; training a plurality of algorithm models by using the training set to obtain a plurality of propellant burning rate models; preliminarily screening the plurality of propellant burning rate models by using prior knowledge; finely screening the plurality of propellant burning rate models obtained through the preliminary screening; fusing the plurality of propellant burning rate models obtained through the fine screening to obtain a propellant burning rate fusion prediction model; and predicting the burning rate of the propellant by using the propellant burning rate fusion prediction model. The application is convenient to use, simple to operate, fast in calculation, high in calculation precision and high in engineering application value.

Description

TECHNICAL FIELD

[0001] The application relates to a propellant burning rate high-precision high-speed prediction method based on machine learning, and belongs to the technical field of solid rocket propellants. BACKGROUND

[0002] Solid propellant is an energetic composite material with high molecular as base and specific performance, and is a power source of a solid rocket engine. In the design of the solid rocket engine, the combustion performance of the propellant directly affects the safety and reliability of the engine work. The solid propellant is generally divided into two categories of double-base propellant and composite propellant, and the hydroxyl propellant has the advantages of simple manufacturing process, good mechanical property and high specific impulse, and is one of the most widely used categories of composite propellants.

[0003] In the design process of the propellant, the burning rate calculation is an important method for selecting a high-energy characteristic propellant formula. Since the design process of the hydroxyl propellant involves a large number of complex physical and chemical problems, the principles of some physical and chemical processes have not been accurately described so far. At present, the performance prediction of the hydroxyl propellant formula is still mainly based on the test debugging method, and there is a lack of effective prediction means, which leads to the problems of long development cycle, high test cost and high safety risk in the design of the propellant formula for a long time. SUMMARY

[0004] The application aims to overcome the above-mentioned defects, and provides a high-precision high-speed prediction method for the burning rate of the hydroxyl propellant, which solves the technical problem of the lack of effective prediction means for the burning rate of the hydroxyl propellant. The application has the advantages of convenient use, simple operation, fast calculation speed, high calculation precision and high engineering application value.

[0005] To achieve the above-mentioned application purposes, the application provides the following technical scheme:

[0006] A high-precision high-speed prediction method for the burning rate of a hydroxyl propellant based on machine learning comprises the following steps:

[0007] A database containing a plurality of groups of data is established, wherein each group of data comprises the burning rate of the hydroxyl propellant and its influencing factors;

[0008] The database is standardized to obtain a sample library, each sample in the sample library comprises the standardized burning rate of the hydroxyl propellant and its standardized influencing factors; and the sample library is divided into a training set and a test set;

[0009] A plurality of propellant burning rate models are obtained by training a plurality of algorithm models by using the training set;

[0010] The plurality of propellant burning rate models are preliminarily screened by using prior knowledge;

[0011] The plurality of propellant burning rate models obtained by the preliminary screening are finely screened.

[0012] The multiple propellant burning rate models obtained through refined screening are fused to obtain a propellant burning rate fusion prediction model;

[0013] The burning rate of hydroxyl propellant was predicted using a propellant burning rate fusion prediction model.

[0014] Furthermore, the standardized burning rate of hydroxyl propellant included in each sample was used as the output variable, and the standardized influencing factors were used as the input variables.

[0015] Influencing factors include the raw material properties and control parameters of hydroxyl-butyl propellant;

[0016] The raw material properties of hydroxyl-butyl propellant include the content of ultrafine oxidant, the average particle size of ultrafine oxidant, the proportion of ultrafine oxidant with a particle size of 0-5 μm, the proportion of ultrafine oxidant with a particle size of 5-10 μm, the proportion of ultrafine oxidant with a particle size of 10-15 μm, and the proportion of ultrafine oxidant with a particle size of >15 μm.

[0017] The control parameters for hydroxyl-butyl propellant include the average discharge rate of ultrafine oxidant.

[0018] Furthermore, the standardized burning rate or influencing factors of hydroxyl-butyl propellant are denoted as x′:

[0019] x′=(x-μ) / σ

[0020] Where x represents the original propellant burning rate or influencing factor, and μ and σ represent the mean and standard deviation of the original propellant burning rate or influencing factor, respectively.

[0021] Furthermore, the various algorithm models include Random Forest Regression (RFR), Gaussian Process Regression (GPR), Support Vector Regression (SVR), Kernel Ridge Regression (KRR), or Radial Basis Function (RBF).

[0022] The mean squared error is used as the modeling criterion to construct the RFR; the linear superposition of the Gaussian function, the Matern function, and the rational quadratic function is used as the Gaussian kernel to construct the GPR; the Gaussian function is used as the regression function kernel to construct the SVR; the Gaussian function is used as the kernel function to construct the KRR; and multiple quadratic functions are used as basis functions to construct the RBF.

[0023] Furthermore, prior knowledge includes that increasing the content of ultrafine oxidizer increases the burning rate of hydroxyl-butyl propellant; and that increasing the average particle size of ultrafine oxidizer decreases the burning rate of hydroxyl-butyl propellant.

[0024] Furthermore, methods for preliminary screening of multiple hydroxyl-butyl propellant burning rate models using prior knowledge include:

[0025] Input variables from each sample in the test set into a certain propellant burning rate model to obtain the predicted burning rate of hydroxyl propellant corresponding to the model;

[0026] Determine whether the predicted burning rate of hydroxyl-butyl propellant varies with the content and average particle size of the ultrafine oxidant according to prior knowledge. If it does not, exclude the burning rate model.

[0027] Furthermore, methods for preliminary screening of multiple propellant burning rate models using prior knowledge include:

[0028] Let the input variables be m-dimensional variables x1, x2, ... x m m≥7;

[0029] Make variable x j As a single-factor variable, with other m-1 dimension variables being fixed values, plot the propellant burning rate as a function of the variable x. j The single-factor variation curve, j = 1, 2…m; when the other m-1 dimensional variables are fixed values, the fixed values ​​are the average of the upper and lower limits of the range of the variable in the training set;

[0030] Determine the burning rate of hydroxyl-butyl propellant with respect to variable x j The single-factor variation curve is compared to the corresponding prior knowledge. If it does not conform, the combustion rate model is excluded.

[0031] Furthermore, the method for refining the screening of multiple propellant burning rate models obtained from the initial screening is as follows:

[0032] The corresponding propellant burning rate prediction values ​​were obtained by using multiple propellant burning rate models obtained from the initial screening.

[0033] The predicted propellant burning rate is compared with the output variables in the training set to obtain the maximum absolute error, maximum relative error, mean absolute error, and root mean square error between the two.

[0034] Propellant burning rate models with the largest absolute error, largest relative error, average absolute error, or root mean square error exceeding a preset threshold are discarded, or the propellant burning rate model with the largest maximum absolute error is discarded.

[0035] Furthermore, by averaging the outputs of the propellant burning rate models obtained from each refined screening, a propellant burning rate fusion prediction model is obtained.

[0036] Furthermore, when establishing the database, the propellant burning rate used is the propellant burning rate under standard conditions.

[0037] Compared with the prior art, the present invention has at least one of the following advantages:

[0038] (1) This invention creatively proposes a high-precision and high-speed prediction method for propellant burning rate based on machine learning. Based on machine learning, a prediction model is established according to existing experimental data, which is a high-precision and high-speed prediction method for the burning rate of hydroxyl propellant in solid rocket engines.

[0039] (2) The present invention has higher prediction speed and accuracy. Compared with traditional combustion performance theory and simulation calculation, it eliminates the influence of a large number of idealized assumptions and numerical errors on the prediction results. The mathematical prediction model constructed based on the sample set formed by actual test data has achieved a leapfrog improvement in both prediction speed and accuracy.

[0040] (3) The present invention has higher development efficiency and economic benefits. Compared with traditional prediction methods such as testing and debugging, the present invention significantly improves the efficiency of scheme optimization and iteration, while greatly saving the cost of engine ground ignition test and manpower design, etc., to find better performance at a lower cost, thereby generating higher economic benefits.

[0041] (4) This invention has higher safety and success rate. Compared with traditional prediction methods such as theoretical simulation calculation and experimental debugging, it significantly reduces the risk of test failure or even explosion caused by improper propellant design and excessive performance prediction errors, and greatly improves the success rate of propellant formulation meeting performance requirements. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the prediction model construction method of the present invention;

[0043] Figure 2 This is a comparison chart of the absolute errors of multiple propellant burning rate models obtained by fine screening in this invention;

[0044] Figure 3 This is a comparison chart of the relative errors of multiple propellant burning rate models obtained by fine screening in this invention;

[0045] Figure 4 This is a schematic diagram illustrating the process of determining the benchmark point for the single-factor variation curve in this invention.

[0046] Figure 5 This diagram illustrates the prediction of data outside the sample set using the method of this invention. Detailed Implementation

[0047] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0048] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0049] This invention mines and analyzes experimental data and related professional knowledge of hydroxyl-butyl propellant (Hbutyl) propellant formulation design. Using a data-driven approach and advanced mathematical methods, it constructs a surrogate model to conduct more efficient and intelligent Hbutyl propellant performance prediction at a lower cost, representing an effective approach to Hbutyl propellant design optimization. This invention proposes a machine learning-based high-precision, high-speed prediction method for Hbutyl propellant burning rate. This method can accurately and efficiently predict the burning rate of Hbutyl propellant under small sample and multi-feature conditions. The application of this method is expected to fundamentally change the development model of Hbutyl propellants and find a breakthrough in solving the urgent problem of "small sample, multi-feature, high-precision, high-speed design" in my country's weaponry development.

[0050] This invention discloses a high-precision, high-speed prediction method for the burning rate of hydroxyl-butyl propellant based on machine learning, comprising the following steps:

[0051] 1) Establish a database of burning rate of hydroxyl-butyl propellant and its influencing factors, and construct the database into a sample library that can be used for machine learning through standardization, and divide it into training set and test set;

[0052] 2) Using the training set, multiple algorithms were employed to train and construct multiple hydroxyl propellant burn rate prediction models;

[0053] 3) Use prior knowledge to initially screen multiple prediction models, and use a test set to test the prediction models after initial screening. Use indicators such as burning rate prediction error to refine the initial screening models and form the final fusion prediction model.

[0054] 4) Use a fusion prediction model to predict the burning rate of hydroxyl propellant outside the sample set.

[0055] In one specific implementation, a database of the burning rate of hydroxyl-butyl propellant and its influencing factors is compiled and established. This database is then standardized to create a sample library suitable for machine learning, and the method for dividing it into training and test sets is as follows:

[0056] (a) Record input parameter data: Raw material property parameters of hydroxyl-butyl propellant, including the content of ultrafine oxidizer, average particle size of ultrafine oxidizer, proportion of ultrafine oxidizer particles with a diameter of 0-5μm, proportion of ultrafine oxidizer particles with a diameter of 5-10μm, proportion of ultrafine oxidizer particles with a diameter of 10-15μm, and proportion of ultrafine oxidizer particles with a diameter >15μm; the control parameter for hydroxyl-butyl propellant is the average discharge rate of ultrafine oxidizer. Record output burning rate data: Propellant burning rate under standard conditions. Organize the input parameter data and output burning rate data into a table.

[0057] (b) Read in the data stored in tabular form and standardize the input parameters and output combustion rate: Calculate the mean and standard deviation for each input parameter and output combustion rate, and standardize them through algebraic calculations to form dimensionless input and output data with a mean of 0 and a standard deviation of 1. A set of input parameter data and its corresponding output data is called a sample.

[0058] (c) The standardized samples are randomly divided, with 90% used as the training set and the remaining 10% used as the test set.

[0059] In one specific implementation, the steps of training a neural network and building multiple models to predict the burning rate of hydroxyl-butyl propellant are as follows:

[0060] (d) Using the same training set, multiple prediction models were constructed, including the Random Forest Regression (RFR), Gaussian Process Regression (GPR), Support Vector Regression (SVR), Kernel Ridge Regression (KRR), and Radial Basis Function (RBF) models: the mean squared error was used as the modeling criterion to construct RFR; the linear superposition of the Gaussian function, Matern function, and rational quadratic function was used as the Gaussian kernel to construct GPR; the Gaussian function was used as the regression function kernel to construct SVR; the Gaussian function was used as the kernel function to construct KRR; and multiple quadratic functions were used as basis functions to construct RBF.

[0061] In one specific implementation, the method of initially screening multiple prediction models using prior knowledge, testing the initially screened prediction models using a test set, and then refining the initial screening models using indicators such as combustion rate prediction error to form the final fusion prediction model is as follows:

[0062] (e) Perform preliminary screening of the prediction models trained in step (d) based on existing prior knowledge: plot the single-factor variation curves of the corresponding model at the center point of the sample space enclosed by the sample points regarding the content and particle size of ultrafine oxidant, and compare the single-factor variation curves shown by the prediction models with the existing laws on the influence of changes in raw material property parameters on the combustion rate (i.e., prior knowledge), and discard the corresponding models whose variation curves and influence laws are significantly different.

[0063] (f) For the models that passed the initial screening in step (e), fine-tuning and fusion of models using indicators such as error are performed on the same test set to obtain the final combustion rate prediction model: The models that passed the initial screening are applied to the test set for prediction and compared with the actual results. The maximum absolute error, maximum relative error, mean absolute error and root mean square error of the prediction results are calculated. Models with a maximum relative error greater than 5% or a maximum absolute error significantly higher than other models are discarded. Finally, the models that have passed the fine screening are fused to obtain the final combustion rate prediction model with better performance, i.e., the fused prediction model.

[0064] In one specific implementation, the method for predicting the burning rate of hydroxyl-butyl propellant outside the sample set using a fusion prediction model is as follows:

[0065] (g) For the final burning rate prediction model obtained in step (f), the combination of input parameters that need to be predicted outside the sample set is standardized according to the input quantity standardization parameters used in the modeling, and then input into the prediction model. The standardized output is then inversely standardized according to the output quantity standardization parameters used in the modeling to obtain the final burning rate prediction result of the burning rate prediction model for the corresponding combination of input parameters.

[0066] like Figure 1 This invention discloses a high-precision, high-speed prediction method for propellant burning rate based on machine learning, which mainly includes the following steps:

[0067] 1) Using the raw material properties and burning rate of hydroxyl-butyl propellant, the raw data were standardized to serve as the training and testing sets;

[0068] 2) Using the training set, multiple algorithms were employed to train and construct multiple hydroxyl propellant burn rate prediction models;

[0069] 3) Use prior knowledge to initially screen multiple prediction models, and use a test set to test the prediction models after initial screening. Use indicators such as burning rate prediction error to refine the initial screening models and form the final fusion prediction model.

[0070] 4) Use a fusion prediction model to predict the burning rate of hydroxyl propellant outside the sample set.

[0071] As can be seen from the above-described workflow of this invention, this invention, as a machine learning-based method for predicting the burning rate of hydroxyl-butyl propellant, mainly includes four steps: parameter standardization and input, learning or training, model selection and optimization, and model validation. These four parts will be described in detail below.

[0072] (I) Parameter Standardization and Parameter Input:

[0073] Record the input parameter data (raw material properties and control parameters of hydroxyl-butyl propellant), including the content of ultrafine oxidizer in the propellant, the average particle size of the ultrafine oxidizer, the proportion of ultrafine oxidizer particles with a diameter of 0-5μm, the proportion of ultrafine oxidizer particles with a diameter of 5-10μm, the proportion of ultrafine oxidizer particles with a diameter of 10-15μm, the proportion of ultrafine oxidizer particles with a diameter >15μm, and the average discharge rate of ultrafine oxidizer. Record the output burning rate data (propellant burning rate under standard conditions). Organize the input parameter data and output burning rate data into a corresponding table.

[0074] Calculate the sample mean and standard deviation of all parameters in the database:

[0075]

[0076]

[0077] Where: x is the input or output parameter, n is the number of parameters, μ is the sample mean, and σ is the standard deviation.

[0078] Then, it is standardized into dimensionless input / output data with a mean of 0 and a standard deviation of 1 by the following formula:

[0079] x′=(x-μ) / σ

[0080] Where: x′ is the standardized input or output parameter.

[0081] The standardized samples were randomly divided, with 90% used as the training set and 10% as the test set.

[0082] (II) Conduct learning and training:

[0083] The same training set was used to build multiple prediction models, including random forest regression, Gaussian process regression, support vector regression, kernel ridge regression, and radial basis function model.

[0084] Random Forest Regression Model (RFR)

[0085] Random forest regression model is an ensemble learning approach that obtains data through random sampling, inputs it into numerous base estimators, and then determines the final output by averaging multiple estimators.

[0086] A random forest regression model consists of multiple decision regression trees, and each tree in the forest is independent of the others. The final output of the model is determined by the combined decisions of each tree in the forest. To ensure the model's generalization ability (or versatility), random forest models often follow two basic principles when building each tree: "data randomness" and "feature randomness".

[0087] The principle of constructing a combustion performance prediction model for hydroxyl-butyl propellant using this model is as follows: Select n sample points from the training set S to obtain a new S1…S n Sub-training sets; a decision regression tree is constructed on each sub-training set using the CART algorithm. The final prediction result of each decision regression tree is the mean of the leaf nodes reached by the sample point. For each node of each decision regression tree, the splitting rule is to first randomly select k (k<7) features from 7 features (6 raw material attribute parameters and 1 control parameter of hydroxyl propellant), and then select the optimal splitting point from these k features to divide the left and right subtrees. The final regression result is obtained by averaging the prediction results of multiple decision regression trees.

[0088] The CART decision regression tree uses the principle of minimum mean squared error (MSE). Other hyperparameters of the random forest regression model include: the number of evaluators in the random forest is set to 1000.

[0089] Gaussian process regression model (GPR)

[0090] Gaussian process regression is essentially a stochastic process, corresponding to infinite-dimensional random variables following a Gaussian distribution. The distribution of a Gaussian process is the joint probability distribution of all these (infinite-dimensional) random variables, which follows a multivariate Gaussian distribution:

[0091] f~GP(μ,k)

[0092] Where μ(x) is the mean function of the random variable x; k(x,x′) is the mean function and covariance function of the random variable x, which is the kernel function of the Gaussian process, and determines the properties of the Gaussian process.

[0093] There are several different types of kernel functions, including constant, linear, white noise, Gaussian, Matern, periodic, and rational quadratic functions, which can be superimposed. Here, a linear superposition of a Gaussian, Matern, and rational quadratic function is used as the kernel function to construct a Gaussian process regression model for predicting the combustion performance of hydroxyl-terminated polybutadiene (HTPB) propellant. This newly constructed kernel function can balance the advantages and disadvantages of each kernel function, exhibiting better performance. Subsequently, based on the kernel function and the prior hypothesis GP(0,σ... 2 The posterior distribution can be calculated:

[0094]

[0095]

[0096] Where: μ * Σ is the average value of the predicted output. * Let K be the variance of the predicted output, K be the covariance matrix, and X be the training samples. * The input matrix is ​​formed by the input transformation of the test sample set, σ 2 Let I be the variance of the output noise, and let I be the identity matrix. This is the output vector in the training sample set.

[0097] In addition, to improve the performance of the Gaussian process regression model, an optimizer is used to optimize the hyperparameters in the kernel function. The optimization algorithm used is the L-BFGS-B algorithm, which is a quasi-Newton optimization algorithm. It saves storage space and improves computational efficiency by using finite storage space to approximate the estimation of the inverse Hessian matrix of the multivariate function.

[0098] Support Vector Regression (SVR) model

[0099] In machine learning, Support Vector Machines (SVMs) are supervised learning models with relevant learning algorithms used for classification and regression analysis of data. Support Vector Regression (SVR) is an important application branch of Support Vector Machines (SVMs). Both SVMs and SVRs require the construction of a hyperplane. The goal of SVM is to maximize the distance between the hyperplane and the nearest data point, thus achieving classification of the data points through the hyperplane; while the goal of SVR is to minimize the distance between the hyperplane and the farthest data point, thus achieving data fitting through the hyperplane. SVR is characterized by using kernels, sparse solutions, and Vapnik-Chervonenkis theory to control the margins and the number of support vectors.

[0100] SVR is characterized by using kernels, sparse solutions, and Vapnik-Chervonenkis theory to control the margins and the number of support vectors. As a supervised learning method, SVR is trained using a symmetric loss function, which also penalizes both high and low error estimates. Using Vapnik's method, a flexible tube with a minimum radius is symmetrically formed around the estimation function. Points outside the tube are penalized, but points inside the tube, whether above or below the actual value, are not penalized.

[0101] One of the main advantages of SVR is that its computational complexity is independent of the dimensionality of the input space. Furthermore, it exhibits excellent generalization ability and high prediction accuracy. To transform the nonlinear regression problem into a linear regression problem, a nonlinear transformation is used to map the training data to a high-dimensional feature space, and feature fitting is performed in the high-dimensional feature space to obtain:

[0102]

[0103] Where x and f(x) are the input and output vectors in the training sample set, respectively. Let ω be the mapping of the input vector x in the high-dimensional feature space, ω be the slope matrix of the linear function, and b be the intercept of the linear function. After introducing the kernel function in SVR, the above equation becomes:

[0104]

[0105] in: and a i For Lagrange multipliers, k(x,x) i ) is the kernel function. The parameters are optimized by minimizing the penalty function.

[0106] In predicting the combustion performance of hydroxyl-butadiene propellant (HPT) propellant, a Gaussian function is used as the kernel function to construct the SVR (Special Dynamic Range), which maps a sample to a higher-dimensional space. Other hyperparameter settings include: regularization coefficient of 1, L2 penalty function, tube width of 0.1, and Gaussian kernel coefficient of 1 / 7.

[0107] Nuclear Ridge Regression (KRR) model

[0108] Kernel ridge regression is an improved form of ridge regression, which uses a kernel function to handle nonlinear problems. Ridge regression addresses linear regression problems, and when faced with issues such as too many variables, too few samples, or poor model generalization, it solves the overfitting problem by adding a penalty term (a penalty coefficient multiplied by other model parameters excluding the intercept), thereby increasing the model's predictive performance.

[0109] Since it has the same final model form as SVR, its ability to handle nonlinear problems can also be improved by introducing a kernel function. In the problem of predicting the combustion performance of hydroxyl propellant, the Gaussian function is also used as the kernel function to construct the kernel ridge regression model. Other hyperparameter settings include: regularization coefficient of 1, L2 penalty function, and Gaussian kernel function coefficient of 1.

[0110] Radial Basis Function Model (RBF)

[0111] The radial basis function model is a model that obtains its final functional form by linearly superimposing a class of basis functions with the Euclidean distance between unknown points and known data points as independent variables. Its basic form is:

[0112]

[0113] in: For radial functions, ||xx i ‖ represents the radial distance from the unknown point to point i, and λ represents the radial distance from the unknown point to point i. i These are the weighting coefficients.

[0114] Radial functions significantly affect model characteristics, and commonly used radial functions include linear functions, cubic functions, Gaussian functions, multiple quadratic functions, and inverse multiple quadratic functions. In predicting the combustion performance of hydroxyl-butadiene propellant, multiple quadratic functions are used as basis functions to construct a radial basis function model. Multiple quadratic functions are nonlocal functions, and their corresponding interpolation matrix has only one positive eigenvalue, thus more closely approximating a smooth input-output mapping.

[0115] (III) Model Selection and Optimization:

[0116] The trained prediction model is initially screened based on prior knowledge. For propellant combustion data sample points (in this embodiment, the sample points are 7-dimensional inputs, abbreviated as x1, x2, x3, x4, x5, x6, x7), the maximum and minimum value ranges of each input variable dimension are [x i,min ,x i,max The intersections of these elements result in a hypercube-shaped sample space that encloses all sample points: [x] 1,min ,x 1,max ]×[x 2,min ,x 2,max ]×…×[x 7,min ,x 7,max For this sample space, the center point (x) of the sample space, which serves as the single-factor benchmark, can be determined based on the maximum and minimum values ​​of each dimension. 1,c ,x 2,c ,x 3,c ,x 4,c ,x 5,c ,x 6,c ,x 7,c ),in:

[0117]

[0118] The process for determining the baseline point of the single-factor change curve above can be referred to Figure 4 Then, the model is plotted at the center point of the sample space enclosed by the sample points, i.e., x1 = x 1,c x2=x 2,c x3=x3,c x4=x 4,c x5=x 5,c x6=x 6,c x7=x 7,c At that time, the single-factor variation curves of ultrafine oxidant content and ultrafine oxidant particle size on propellant burning rate were obtained, and the law of single-factor variation curves shown by the prediction model was compared with the known law of the influence of ultrafine oxidant content and ultrafine oxidant particle size on burning rate. The corresponding models with obvious differences between the variation curves and the law of influence were discarded.

[0119] Based on long-term research and development experience, the changes in single parameters have the following macroscopic trend influencing the burning rate: an increase in oxidant content increases the burning rate, while an increase in oxidant particle size decreases the burning rate. If the single-factor change pattern shown by the prediction model is opposite to the above pattern, it is discarded.

[0120] For the models that have undergone initial screening, a refined model selection and fusion process is performed on the same test set using indicators such as error, resulting in the final combustion rate prediction model. The models that underwent initial screening are then used to predict the test set, and the results are compared with actual results. The maximum absolute error, maximum relative error, mean absolute error, and root mean square error of the prediction results are calculated. Models with a maximum relative error greater than 5% or a maximum absolute error significantly higher than other models are discarded. Finally, the refined models are fused to obtain a better-performing fused prediction model.

[0121] The fusion prediction model uses the method of averaging the outputs of each refined screening model to improve the various error indicators of the fused model and achieve better performance.

[0122] (iv) Verification of the optimized model:

[0123] The obtained fusion prediction model is then standardized by combining the input parameters to be predicted outside the sample set, and then input into the prediction model. The standardized output is then inversely standardized according to the output standardization parameters used in the modeling process.

[0124] y=σy′+μ

[0125] Where: y is the parameter after inverse standardization, y′ is the parameter directly output by the model, σ is the average value of the output, and μ is the standard deviation of the output.

[0126] This yields the combustion rate prediction results from the fusion prediction model.

[0127] The method of this invention can successfully predict the burning rate of a certain type of hydroxyl-butyl propellant:

[0128] In this embodiment, a total of 83 samples were used. After random partitioning, the test set had 9 samples and the training set had 74 samples. Among the various models, the KRR and RFR models were discarded because they did not conform to existing prior knowledge. The test set error results for each model are summarized in the table below. After multi-model fusion, the test set performance of the final burning rate prediction model is also listed in Table 1. The absolute error comparison chart and relative error comparison chart of the multiple propellant burning rate models obtained by the present invention are shown below. Figure 2 and Figure 3 As shown, Figure 2 In the diagram, the horizontal axis represents the absolute error interval, and the vertical axis represents the number of test set errors that fall within the absolute error interval. Figure 3 In the graph, the horizontal axis represents the relative error interval, and the vertical axis represents the number of test set errors that fall within the relative error interval. RFR refers to the results of the Random Forest model, GPR refers to the results of the Gaussian Process Regression model, SVR refers to the results of the Support Vector Regression model, KRR refers to the results of the Kernel Ridge Regression model, and RBF refers to the results of the Radial Basis Function model.

[0129] Table 1 Prediction errors of different models

[0130] Model Maximum absolute error Maximum relative error Mean absolute error Root mean square error RFR 0.3279 1.85％ 0.1355 0.1891 GPR 0.416 2.37％ 0.1448 0.2031 SVR 0.4265 2.43％ 0.1518 0.2066 KRR 0.3738 2.13％ 0.1726 0.2071 RBF 0.5161 2.84％ 0.157 0.2217 Prediction model 0.3382 1.91％ 0.1512 0.1953

[0131] In this embodiment, data from outside the sample set is used to validate the burn rate prediction model. The prediction results and comparisons are shown below. Figure 5 , Figure 5 In the graph, the horizontal axis represents the data sequence number, the dotted curve represents the actual value, the square curve represents the predicted value, the left vertical axis corresponding to the dotted and square curves represents the combustion rate value, the bar chart represents the prediction error, and the corresponding right vertical axis represents the error value.

[0132] Its maximum absolute error is 0.7499, maximum relative error is 4.38%, mean absolute error is 0.2631, and root mean square error is 0.3645, which meets the requirement that the maximum relative error is less than 5%.

[0133] The above prediction model was used to predict the burning rate of four groups of hydroxyl-butyl propellants, and experimental tests were conducted. The predicted and measured results are shown in Table 2. The predicted values ​​and measured values ​​showed good agreement, with a maximum relative error of only 3.35%, which meets the actual engineering requirements.

[0134] Table 2. Experimental and Predictive Results

[0135]

[0136]

[0137] This invention utilizes machine learning methods to predict the burning rate of hydroxyl-butyl propellant. The constructed burning rate prediction model has significant advantages such as simple and convenient operation, fast calculation speed, and high prediction accuracy, thereby promoting the development of hydroxyl-butyl propellant development mode from experimental debugging to intelligent prediction.

[0138] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0139] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A high-precision, high-speed prediction method for the burning rate of hydroxyl-butyl propellant based on machine learning, characterized in that, include: Establish a database containing several sets of data, where each set of data includes the burning rate of hydroxyl-butyl propellant and its influencing factors; The database is standardized to obtain a sample library, in which each sample contains a standardized burning rate of hydroxyl-butyl propellant and its standardized influencing factors; the sample library is then divided into a training set and a test set. Multiple algorithm models were trained using the training set to obtain multiple propellant burning rate models; Multiple propellant burning rate models were initially screened using prior knowledge. The multiple propellant burning rate models obtained from the initial screening were further refined. The multiple propellant burning rate models obtained through refined screening are fused to obtain a propellant burning rate fusion prediction model; Predict the burning rate of hydroxyl propellant using a propellant burning rate fusion prediction model; Each sample includes standardized hydroxyl propellant burn-up rate as the output variable and standardized influencing factors as the input variables; Influencing factors include the raw material properties and control parameters of hydroxyl-butyl propellant; The raw material properties of hydroxyl-butyl propellant include the content of ultrafine oxidant, the average particle size of ultrafine oxidant, the proportion of ultrafine oxidant with a particle size of 0-5 μm, the proportion of ultrafine oxidant with a particle size of 5-10 μm, the proportion of ultrafine oxidant with a particle size of 10-15 μm, and the proportion of ultrafine oxidant with a particle size of >15 μm. The control parameters for hydroxyl-butyl propellant include the average discharge rate of ultrafine oxidant; Prior knowledge includes that increasing the content of ultrafine oxidizer increases the burning rate of hydroxyl butyrate propellant; and that increasing the average particle size of ultrafine oxidizer decreases the burning rate of hydroxyl butyrate propellant. Methods for initial screening of multiple hydroxyl-butyl propellant burning rate models using prior knowledge include: Input variables from each sample in the test set into a certain propellant burning rate model to obtain the predicted burning rate of hydroxyl propellant corresponding to the model; Determine whether the predicted burning rate of hydroxyl-butyl propellant varies with the content and average particle size of the ultrafine oxidant according to prior knowledge. If it does not, exclude the burning rate model. Methods for initial screening of multiple propellant burning rate models using prior knowledge include: Let the input variable be m Dimensional variables ; m ≥7; Make variables For single-factor variables, others m The -1 dimension variable is a fixed value; plot the propellant burning rate with respect to the variable. The single-factor change curve, j =1, 2… m ;other m When the -1 dimension variable is a fixed value, the fixed value is the average of the upper and lower limits of the range of the variable in the training set; Determining the burning rate of hydroxyl-butyl propellant with respect to variables Compare whether the single-factor change curve conforms to the corresponding prior knowledge; if it does not conform, exclude the combustion rate model. The method for refining the multiple propellant burning rate models obtained from the initial screening is as follows: The corresponding propellant burning rate prediction values ​​were obtained by using multiple propellant burning rate models obtained from the initial screening. The predicted propellant burning rate is compared with the output variables in the training set to obtain the maximum absolute error, maximum relative error, mean absolute error, and root mean square error between the two. Propellant burning rate models with the largest absolute error, largest relative error, average absolute error, or root mean square error exceeding a preset threshold are discarded, or the propellant burning rate model with the largest maximum absolute error is discarded.

2. The high-precision, high-speed prediction method for the burning rate of hydroxyl-butyl propellant based on machine learning according to claim 1, characterized in that, Standardized burning rate or influencing factors of hydroxyl-butyl propellant are denoted as : in, Original propellant burning rate or influencing factors The mean and standard deviation of the original propellant burning rate or influencing factors.

3. The high-precision, high-speed prediction method for the burning rate of hydroxyl-butyl propellant based on machine learning according to claim 1, characterized in that, The various algorithm models include Random Forest Regression (RFR), Gaussian Process Regression (GPR), Support Vector Regression (SVR), Kernel Ridge Regression (KRR), or Radial Basis Function (RBF). The mean squared error is used as the modeling criterion to construct the RFR; the linear superposition of the Gaussian function, the Matern function, and the rational quadratic function is used as the Gaussian kernel to construct the GPR; the Gaussian function is used as the regression function kernel to construct the SVR; the Gaussian function is used as the kernel function to construct the KRR; and multiple quadratic functions are used as basis functions to construct the RBF.

4. The high-precision, high-speed prediction method for the burning rate of hydroxyl-butyl propellant based on machine learning according to claim 1, characterized in that, By averaging the output of each refined propellant burning rate model, a propellant burning rate fusion prediction model is obtained.

5. The high-precision, high-speed prediction method for the burning rate of hydroxyl-butyl propellant based on machine learning according to claim 1, characterized in that, When establishing the database, the propellant burning rate used is the propellant burning rate under standard conditions.

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