Forward inner ballistic prediction and reverse grain design method based on machine learning

Abstract

The invention belongs to the technical field of solid rocket engine design, and discloses a forward inner trajectory prediction and reverse grain design method based on machine learning. Obtaining an inner ballistic parameter data set based on parameterized calculation software; establishing an inner ballistic parameter forward prediction model; after the inner trajectory parameter forward prediction model is trained, parameter prediction is carried out according to design data; establishing an inner ballistic parameter reverse prediction model; and training an inner ballistic parameter reverse prediction model and performing parameter prediction by using the new inner ballistic parameters. The inner ballistic parameter forward prediction model avoids the problem of low efficiency in the inner ballistic calculation process by using parameterized calculation software, and the inner ballistic parameter reverse prediction model can realize the reverse design of the metal wire embedded grain according to the task requirement of the inner ballistic design.

Description

Technical Field

[0001] The present invention relates to the technical field of solid rocket engine design, and particularly relates to a forward interior ballistics prediction and reverse grain design method based on machine learning. Background Art

[0002] As the core power device of missiles and launch vehicles, the accurate prediction of the interior ballistics performance of solid rocket engines is directly related to the attitude control, orbital accuracy, and guidance system design of aircraft. The end-burning engine with embedded metal wires enhances the thermal feedback of the combustion surface by embedding metal wires (such as silver, copper, etc.) in the solid propellant, significantly increasing the local burning rate and improving the overall thrust of the engine. Due to its high loading ratio, long working time and other characteristics, such engines are widely used in tactical missiles, cruise missile weapon systems and other fields. However, once such an engine contains a complex metal skeleton structure, the law of combustion surface change caused by it will be very complex, the interior ballistics prediction is difficult, and the calculation process takes a long time. At the same time, for a given interior ballistics, it is also very difficult to quickly design the corresponding embedded metal wire grain structure by the current design methods. The patent application document with the application number CN202310818681.1 discloses a high-precision and high-speed prediction method for the burning rate of hydroxyl-terminated polybutadiene propellant, which can realize the burning rate prediction based on machine learning methods, but does not consider the physically accelerated propellant, and at the same time, it has not been extended to the interior ballistics prediction of solid rocket engines. The patent application document with the application number CN202411226718.2 discloses a two-dimensional charge reverse design method for solid engines. The method used in this patent for reverse design is based on solving equations by the iterative method, but it does not involve the embedded metal wire physically accelerated propellant. To sum up, for the end-burning engine with embedded metal wires, whether it is forward interior ballistics prediction or reverse grain structure design, the current research is still relatively limited.

[0003] At present, the interior ballistics design of embedded metal wire grains mainly relies on parametric calculations using 3D design software such as Creo. The steps of modeling and computational analysis are cumbersome, and it is impossible to complete the design of embedded metal wire grains based on the desired interior ballistics parameters. Therefore, how to solve the problems existing in the interior ballistics design of embedded metal wire grains, such as the complex forward calculation process and the inability to perform reverse auxiliary design, is the top priority for engineering applications. Summary of the Invention

[0004] To solve the above problems, the present invention provides a forward interior ballistics prediction and reverse grain design method based on machine learning. This method is based on machine learning, can quickly predict the interior ballistics of the end-burning engine with embedded metal wires, solve the problem of cumbersome calculation process for the interior ballistics prediction of such engines, improve the iteration rate of the structure of such engines, and greatly save time costs and labor costs. At the same time, this method can also provide guiding opinions for the design of the engine structure corresponding to the specified interior ballistics.

[0005] The technical solution of the present invention is as follows: A forward interior ballistics prediction and reverse grain design method based on machine learning, including the following steps:

[0006] Step 1: Obtain an interior ballistics parameter dataset based on parametric calculation software;

[0007] Step 2: Establish a forward prediction model for interior ballistics parameters;

[0008] Step 3: After training the forward prediction model for interior ballistics parameters, perform parameter prediction according to the design data;

[0009] Step 4: Establish a reverse prediction model for interior ballistics parameters;

[0010] Step 5: Train the reverse prediction model for interior ballistics parameters and perform design parameter prediction with new interior ballistics parameters.

[0011] The construction process of the interior ballistics parameter dataset is as follows:

[0012] Grain model establishment: Given the grain length and grain radius, determine them as invariant quantities, and establish a grain model based on parametric calculation software;

[0013] Parametric design: Drive each dimension of the grain model, specify the combustion web thickness range for calculation, and output the grain burning surface area at different combustion web thicknesses to achieve parametric design of the grain model;

[0014] Interior ballistics calculation: Based on the grain burning surface area at different combustion web thicknesses obtained above, perform interior ballistics calculation based on the zero-dimensional interior ballistics calculation equation to obtain interior ballistics data with time as the independent variable and pressure as the dependent variable;

[0015] Establish an interior ballistics dataset: Establish different grain models, and respectively set the gradient to change the growth rate ratio k of the metal wires embedded in the grain and the proportion b1 and b3 of the total grain length occupied by the two sections of metal wires; when performing interior ballistics calculation, respectively set the gradient to change the engine nozzle throat radius r, pressure exponent n, burning rate a, and characteristic velocity v to obtain interior ballistics data under different input variables;

[0016] Extract output variables: According to the curve characteristics of the interior ballistics data, extract the first maximum value of the pressure as the first peak pressure P1, the second maximum value as the second peak pressure P2, the time taken for the pressure to rise from the initial value to the first maximum value as the rise time T r , the time taken for the pressure value to maintain the first maximum value as the first peak duration T1, the time taken for the pressure value to maintain the second maximum value as the second peak duration T2, the pressure remains basically unchanged between the first maximum value and the second maximum value, and the time it occupies is the cruise time T c ;

[0017] Process the interior ballistic data under m groups of different input conditions, extract the input variables and output variables of each group, and store them in matrix InputMatrix and matrix OutputMatrix respectively. The storage method is as follows:

[0018]

[0019] The process of establishing the forward prediction model of interior ballistic parameters is as follows;

[0020] Import the interior ballistic data set constructed in step 1 to train the forward prediction model of interior ballistic parameters. Use the data stored in InputMatrix as the input of the forward prediction model of interior ballistic parameters, and use the data stored in OutputMatrix as the output of the forward prediction model of interior ballistic parameters. Establish a non-linear mapping relationship between input x and output y through a data-driven method:

[0021] f:x→y (2)

[0022] Analyze the data: There are 7 features in the input and 6 features in the output, i∈{1,2,3,…,m - 1,m}

[0023] Input of the forward prediction model of interior ballistic parameters:

[0024]

[0025] Where k is the speed increase ratio, b1 is the first segment ratio, b3 is the third segment ratio, a is the burning rate, n is the pressure exponent, r is the throat radius, and v is the characteristic velocity;

[0026] Output of the forward prediction model of interior ballistic parameters:

[0027]

[0028] Where, T r is the rise time, P1 is the first peak pressure, T1 is the first peak duration, T c is the cruise time, P2 is the second peak pressure, and T2 is the second peak duration.

[0029] Use the Bayesian regularization method to train the forward prediction model of interior ballistic parameters;

[0030] Given the design data:

[0031] x'=[k',b1',b3',a',n',r',v'] (5)

[0032] After training the forward prediction model of interior ballistic parameters is completed, import the design data x’, and obtain the prediction result:

[0033] y' = [T r ', P1', T1', T c ', P2', T2'] (6)

[0034] y’ is the prediction of interior ballistic parameters based on design data.

[0035] The process of establishing the reverse prediction model of interior ballistic parameters is as follows:

[0036] Import the interior ballistic data set constructed in step 1 to train the reverse prediction model of interior ballistic parameters. Use the data stored in OutputMatrix as the input of the reverse prediction model of interior ballistic parameters, and the data stored in InputMatrix as the output of the reverse prediction model of interior ballistic parameters. Establish a non-linear mapping relationship between input X and output Y through a data-driven method:

[0037] f: X → Y (7)

[0038] Analyze the data: There are 6 features in the input and 7 features in the output, i = {1, 2, 3, …, m - 1, m};

[0039] Input of the reverse prediction model of interior ballistic parameters:

[0040]

[0041] Among them, T r is the rise time, P1 is the first peak pressure, T1 is the first peak duration, T c is the cruise time, P2 is the second peak pressure, T2 is the second peak duration;

[0042] Output of the reverse prediction model of interior ballistic parameters:

[0043]

[0044] Among them, k is the speed increase ratio, b1 is the first segment ratio, b3 is the third segment ratio, a is the burning rate, r is the throat radius, and v is the characteristic velocity.

[0045] Use the Bayesian regularization method to train the reverse prediction model of interior ballistic parameters,

[0046] Given new interior ballistic parameters:

[0047] X' = [k', b1', b3', a', n', r', v'] (10)

[0048] After training the reverse prediction model of interior ballistic parameters is completed, import the new interior ballistic parameters X’, and obtain the prediction result:

[0049] Y' = [Tr ',P1',T1',T c ',P2',T2'] (11)

[0050] Y’ is the inverse prediction of the design parameters based on the interior ballistic parameters.

[0051] Both the forward prediction model and the inverse prediction model of the interior ballistic parameters are feedforward neural network models, and other machine learning models suitable for fitting the multi-input multi-output nonlinear relationship can also achieve similar effects.

[0052] Advantages of the present invention:

[0053] (1) The forward prediction model of the interior ballistic parameters can replace the traditional method of using Creo software for parametric calculation of the end-burning motor with embedded metal wire, which is simple, efficient and the accuracy meets the engineering standards.

[0054] (2) The inverse prediction model of the interior ballistic parameters can assist in solving the actual engineering problem of designing the embedded metal wire grain according to the interior ballistic requirements. Description of the drawings

[0055] Figure 1 Shown is the flow block diagram of the forward interior ballistic prediction and inverse grain design method based on machine learning. Detailed implementation manners

[0056] The following further describes the detailed implementation manners of the present invention in combination with the drawings and technical solutions.

[0057] Step 1: Obtain the interior ballistic parameter dataset based on the parametric calculation software;

[0058] Grain model establishment: Given the grain length and grain radius, determine them as invariant quantities, and based on parametric calculation software such as Creo software, establish the grain model through feature operations such as stretching, rotating, and cutting.

[0059] Parametric design: By driving the various dimensions of the grain model, using the sensitivity analysis function of Creo software, specify the combustion web thickness range for calculation, and output the grain burning surface area under different combustion web thicknesses to achieve the parametric design of the grain model;

[0060] Interior ballistic calculation: Based on the grain burning surface areas under different combustion web thicknesses obtained above, establish a processing table for interior ballistic calculation based on the zero-dimensional interior ballistic calculation equation, and obtain the interior ballistic data with time as the independent variable and pressure as the dependent variable.

[0061] Establish the interior ballistic dataset: Establish different grain models, and respectively set the gradient to change the growth rate ratio k of the metal wires embedded in the grain, as well as the proportions b1 and b3 of the total grain length occupied by the two sections of metal wires; when performing interior ballistic calculations, respectively set the gradient to change the engine throat radius r, pressure exponent n, burning rate a, and characteristic velocity v to obtain the interior ballistic data under different input variables;

[0062] Extract the output variables: According to the curve characteristics of the interior ballistic data, extract the first maximum value of the pressure as the first peak pressure P1, the second maximum value as the second peak pressure P2, the time taken for the pressure to rise from the initial value to the first maximum value as the rise time T r , the time for which the pressure value remains at the first maximum value as the first peak duration T1, the time for which the pressure value remains at the second maximum value as the second peak duration T2, and the pressure remains basically unchanged between the first maximum value and the second maximum value, and the time it occupies is the cruise time T c ;

[0063] Process the interior ballistic data under m different input conditions, extract the input variables and output variables for each group, and store them in matrix InputMatrix and matrix OutputMatrix respectively. The storage method is as follows:

[0064]

[0065] Step 2: Establish the forward prediction model for interior ballistic parameters

[0066] Import the interior ballistic dataset constructed in Step 1 to train the forward prediction model for interior ballistic parameters. Use the data stored in InputMatrix as the input of the forward prediction model for interior ballistic parameters, and the data stored in OutputMatrix as the output of the forward prediction model for interior ballistic parameters. Finally, establish a non - linear mapping relationship between the input x and the output y through a data - driven method:

[0067] f:x→y (2)

[0068] Analyze the data: The input has 7 features, and the output has 6 features, i ∈ {1, 2, 3, …, m - 1, m} (m groups of data are obtained through simulation);

[0069] Input of the forward prediction model for interior ballistic parameters:

[0070]

[0071] Among them, k is the growth rate ratio, b1 is the proportion of the first section, b3 is the proportion of the third section, a is the burning rate, n is the pressure exponent, r is the throat radius, and v is the characteristic velocity.

[0072] Output of the forward prediction model for interior ballistic parameters:

[0073]

[0074] where T r is the rise time, P1 is the first peak pressure, T1 is the first peak duration, T c is the cruise time, P2 is the second peak pressure, and T2 is the second peak duration.

[0075] A feedforward neural network (FNN) is a type of artificial neural network structure with forward propagation. It propagates information in the order from the input layer to the output layer and has no feedback connections. FNN is mainly used for regression and classification problems, learning the mapping relationship between inputs and outputs by adjusting weights and biases. Through optimization algorithms and regularization methods, the generalization ability of the model can be improved, enabling it to better handle complex nonlinear problems.

[0076] In this method, a feedforward neural network is used, and the Bayesian regularization training method is adopted to fit the mapping model.

[0077] A two-layer feedforward neural network (FNN) is adopted, and the structure is as follows:

[0078] Input layer: 7 neurons (corresponding to 7-dimensional input features)

[0079] Hidden layer (K neurons): The tanh activation function is adopted:

[0080] h = tanh(w1x + b1) (15)

[0081] Output layer: Linear transformation:

[0082] y = w2h + b2 (16)

[0083] where w1 is the weight matrix from the input layer to the hidden layer, b1 is the bias matrix of the hidden layer, w2 is the weight matrix from the hidden layer to the output layer, and b2 is the bias matrix of the output layer.

[0084] Step 3: After training the forward prediction model of interior ballistic parameters, parameter prediction is carried out according to the design data;

[0085] The Bayesian regularization training is used for the forward prediction model of interior ballistic parameters, and its loss function is:

[0086] E(w) = E D (w) + λE w (w) (17)

[0087] w represents all the weight parameters in the forward prediction model of interior ballistic parameters, that is, the set of trainable parameters of the model. In the feedforward neural network (FFNN), the weight w mainly includes: w1, b1, w2, b2.

[0088] Among them: Data error term (MSE):

[0089]

[0090] Regularization term (weight norm):

[0091] E w (w) = ∑w 2 (19)

[0092] Bayesian weight coefficient:

[0093]

[0094] The overall training process is as follows:

[0095] 01. Initialize weights and biases w1, b1, w2, b2;

[0096] 02. Forward propagation, calculate the predicted value using equations (5) and (6);

[0097] 03. Calculate the loss function E(w);

[0098] 04. Calculate the gradient using the backpropagation algorithm

[0099] 05. Update the weights using the Gradient Descent algorithm, and the update rule is as follows:

[0100]

[0101] α is the learning rate.

[0102] 06. Dynamically adjust the regularization factor λ. If the data error is large (the model is underfitting): increase λ and reduce the weight decay; if the data error is small (the model may be overfitting): decrease λ and increase the weight decay, and repeat the above process until convergence.

[0103] After training is completed, import the new data x', and obtain the prediction result Use MSE to evaluate the forward prediction model of ballistic parameters, and the calculation formula is as follows:

[0104]

[0105] Among them: N is the total number of samples; y j is the actual value (true value) of the jth sample; is the predicted value of the jth sample; is the error of the j-th sample (i.e., the difference between the predicted value and the true value); is the square of the error, aiming to eliminate the directional difference of positive and negative errors and emphasize the impact of larger errors. In this prediction model, the MSE needs to be calculated for 6 output quantities respectively.

[0106] Step 4: Establish an internal ballistic parameter inverse prediction model;

[0107] Import the internal ballistic data set constructed in Step 1 to train the internal ballistic parameter inverse prediction model. Contrary to before, the data stored in OutputMatrix is used as the input of the internal ballistic parameter inverse prediction model, and the data stored in InputMatrix is used as the output of the internal ballistic parameter inverse prediction model. Finally, a non-linear mapping relationship between the input X and the output Y is established through a data-driven method:

[0108] f: X → Y (23)

[0109] Analyze the data: There are 6 features in the input and 7 features in the output, i = {1, 2, 3, …, m - 1, m} (m groups of data are obtained through simulation)

[0110] Input of the internal ballistic parameter inverse prediction model:

[0111]

[0112] where T r is the rise time, P1 is the first peak pressure, T1 is the first peak duration, T c is the cruise time, P2 is the second peak pressure, T2 is the second peak duration.

[0113] Output of the internal ballistic parameter inverse prediction model:

[0114]

[0115] where k is the speed increase ratio, b1 is the first segment ratio, b3 is the third segment ratio, a is the burning rate, r is the throat radius, and v is the characteristic velocity.

[0116] The feedforward neural network (FNN) is a forward-propagating artificial neural network structure. It propagates information in the order from the input layer to the output layer and has no feedback connections. FNN is mainly used for regression and classification problems and learns the mapping relationship between the input and the output by adjusting the weights and biases. Through optimization algorithms and regularization methods, the generalization ability of the model can be improved, enabling it to better handle complex non-linear problems.

[0117] In this method, the feedforward neural network is used, and the Bayesian regularization training method is adopted to fit the mapping model

[0118] A two - layer feed - forward neural network (FNN) is adopted, and its structure is as follows:

[0119] Input layer: 6 neurons (corresponding to 6 - dimensional input features)

[0120] Hidden layer (J neurons): The tanh activation function is adopted:

[0121] H = tanh(W1X + B1) (26)

[0122] Output layer: Linear transformation:

[0123] Y = W2H + B2 (27)

[0124] Among them, W1 is the weight matrix from the input layer to the hidden layer, B1 is the bias matrix of the hidden layer, W2 is the weight matrix from the hidden layer to the output layer, and B2 is the bias matrix of the output layer.

[0125] Step 5: The interior ballistic parameter inverse prediction model is used to predict the design parameters with the new interior ballistic parameters;

[0126] The Bayesian regularization is used to train the interior ballistic parameter inverse prediction model, and its loss function is:

[0127] E(W)=E D (W)+λE w (W) (28)

[0128] W represents all the weight parameters in the interior ballistic parameter inverse prediction model, that is, the set of trainable parameters of the model. In the feed - forward neural network (FNN), the weight W mainly includes: W1, B1, W2, B2.

[0129] Among them: Data error term (MSE):

[0130]

[0131] Regularization term (weight norm):

[0132] Ew(W)=∑W 2 (30)

[0133] Bayesian weight coefficient:

[0134]

[0135] The overall training process is as follows:

[0136] 01. Initialize the weights and biases W1, B1, W2, B2;

[0137] 02. Forward propagation, calculate the predicted values using formulas (26) and (27);

[0138] 03. Calculate the loss function E(W);

[0139] 04. Use the backpropagation algorithm to calculate the gradient

[0140] 05. Update the weights using the gradient descent algorithm, and the update rule is as follows:

[0141]

[0142] 06. Dynamically adjust the regularization factor λ. If the data error is large (the model is underfitting): increase λ and reduce the weight decay; if the data error is small (the model may be overfitting): decrease λ and increase the weight decay. Repeat the above process until convergence.

[0143] After the training is completed, import the new interior ballistic parameters X' to obtain the prediction results Evaluate the model accuracy based on the prediction results. Use MSE to evaluate the reverse prediction model of ballistic parameters, and the calculation formula is as follows:

[0144]

[0145] where: N is the total number of samples; Y j is the actual value (true value) of the jth sample; is the predicted value of the jth sample; is the error of the jth sample (i.e., the difference between the predicted value and the true value); is the square of the error, aiming to eliminate the direction difference of positive and negative errors and emphasize the impact of larger errors. In this prediction model, MSE needs to be calculated for 7 output quantities respectively.

[0146] Figure 1 Figure 34 is the flow chart of the forward interior ballistic prediction and reverse grain design method based on machine learning. The whole prediction method is divided into the following six parts: obtaining the interior ballistic parameter dataset based on the parametric calculation software, establishing the forward prediction model of interior ballistic parameters, training the forward prediction model of interior ballistic parameters and making parameter predictions according to the design data; establishing the reverse prediction model of interior ballistic parameters, training the reverse prediction model of interior ballistic parameters and making parameter predictions with new interior ballistic parameters.

[0147] Furthermore, import the prediction results of the reverse prediction model of interior ballistic parameters into the forward model of interior ballistic parameters for cross-validation and prediction.

[0148] Specifically, establish an interior ballistic parameter dataset: establish different grain models, specify the total grain length as 300, the engine throat radius r = 0.005, the pressure exponent n = 0.32, and the burning rate a = 0.0135. Change the wire speed ratio k at a gradient of 0.2 within the range of 2 - 3, and change the lengths of the two segments of wire at a gradient of 20 within the range of 20 - 80. Thus, 10 sets of interior ballistic data are obtained. When using an Excel processing table for interior ballistic calculations, the gradients of the proportions b1 and b3 of the two segments of wire are fixed with the speed ratio k = 2, the proportions b1 and b3 are 0.1, and the engine throat radius r is changed at a gradient of 5e -04 as a gradient within the range of 0.003 - 0.007, the pressure exponent n is changed at a gradient of 0.005 within the range of 0.02 - 0.05, the burning rate a is changed at a gradient of 0.001 within the range of 0.01 - 0.015, and the characteristic velocity v is changed at a gradient of 100 within the range of 1500 - 2200. A total of 300 sets of simulated interior ballistic data are obtained.

[0149] Process the interior ballistic data under 300 different input conditions, extract the input variables and output variables for each group, and store them in matrix InputMatrix and matrix OutputMatrix respectively according to formula (12);

[0150] Import the constructed interior ballistic dataset to build a forward prediction model for interior ballistic parameters. Use the data stored in InputMatrix as the input of the model and the data stored in OutputMatrix as the output of the model. Finally, establish a non - linear mapping relationship between the input x and the output y through a data - driven method:

[0151] f:x→y (34)

[0152] After training the forward prediction model for interior ballistic parameters, perform parameter prediction according to the design data;

[0153] Verify the trained forward prediction model for interior ballistic parameters as follows: Import the design data x’, and obtain the prediction result Evaluate the accuracy of the model based on the prediction result, and calculate the MSE of the model: T r : 0.9351, P1: 1.3178, T1: 0.0404, T c : 30.7466, P2: 0.0184, T2: 0.0145; all within the allowable error range, with a relatively accurate prediction effect.

[0154] Train the inverse prediction model of interior ballistic parameters using the interior ballistic dataset constructed in Step 1. Contrary to before, use the data stored in OutputMatrix as the input of the model and the data stored in InputMatrix as the output of the model. Finally, establish a non-linear mapping relationship between input X and output Y through a data-driven method:

[0155] f:X→Y (35)

[0156] Train the inverse prediction model of interior ballistic parameters and predict the design parameters using the new interior ballistic parameters.

[0157] Verify the trained inverse prediction model of interior ballistic parameters as follows: Import the new interior ballistic parameters X’, and obtain the prediction results Evaluate the model accuracy based on the prediction results, and calculate the MSE of the inverse prediction model of interior ballistic parameters: where k: 0.1943, b1: 0.0020, b3: 5.2191e-08, a: 0.0047, n: 0.0047, r: 0, v: 1.1730e+03.

[0158] Based on the above description, the present invention proposes a forward interior ballistic prediction and inverse grain design method based on machine learning. The forward prediction model of interior ballistic parameters avoids the problem of low efficiency in the interior ballistic calculation process using parametric calculation software, while the inverse prediction model of interior ballistic parameters can achieve the inverse design of the wire-embedded grain according to the task requirements of interior ballistic design.

Claims

1. A forward interior ballistics prediction and reverse grain design method based on machine learning, characterized in that The steps are as follows: Step 1: Obtain the internal ballistic parameter dataset based on parametric calculation software; Step 2: Establish a forward prediction model for internal ballistic parameters; Step 3: After training the forward prediction model for internal ballistic parameters, perform parameter prediction according to the design data; Step 4: Establish a reverse prediction model for internal ballistic parameters; Step 5: Train the reverse prediction model for internal ballistic parameters and use the new internal ballistic parameters to predict the design parameters.

2. The method for forward interior ballistics prediction and reverse grain design based on machine learning according to claim 1, characterized in that The construction process of the internal ballistic parameter dataset is as follows: Establishment of the grain model: Given the grain length and grain radius, determine them as invariant quantities, and based on parametric calculation software, establish the grain model; Parametric design: By driving the various dimensions of the grain model, specify the combustion web thickness range for calculation, and output the grain burning surface under different combustion web thicknesses to achieve the parametric design of the grain model; Internal ballistic calculation: Based on the grain burning surfaces obtained above under different combustion web thicknesses, perform internal ballistic calculation according to the zero-dimensional internal ballistic calculation equation to obtain the internal ballistic data with time as the independent variable and pressure as the dependent variable; Establish an internal ballistic dataset: Establish different grain models, and respectively set the gradient to change the growth rate ratio k of the metal wires embedded in the grain, as well as the proportions b1 and b3 of the two sections of metal wires in the total grain length; when performing internal ballistic calculation, respectively set the gradient to change the engine throat radius r, pressure exponent n, burning rate a, and characteristic velocity v to obtain the internal ballistic data under different input variables; Extract output variables: According to the curve characteristics of the internal ballistic data, the first maximum value of the extracted pressure is the first peak pressure P1, the second maximum value is the second peak pressure P2, and the time taken for the pressure to rise from the initial value to the first maximum value is the rise time T r The time that the pressure value maintains the first maximum value is the first peak duration T1, and the time that the pressure value maintains the second maximum value is the second peak duration T2. ​​The pressure remains basically unchanged between the first maximum value and the second maximum value, and the time it occupies is the cruising time T c ; Process the internal ballistic data under m groups of different input conditions, extract each group of input variables and output variables, and store them in matrix InputMatrix and matrix OutputMatrix respectively. The storage method is as follows:

3. The method for predicting the forward interior ballistics and designing the reverse grain based on machine learning according to claim 2, wherein The establishment process of the forward prediction model for internal ballistic parameters is as follows; Import the internal ballistic dataset constructed in Step 1 to train the forward prediction model for internal ballistic parameters. Use the data stored in InputMatrix as the input of the forward prediction model for internal ballistic parameters, and use the data stored in OutputMatrix as the output of the forward prediction model for internal ballistic parameters. Establish a non-linear mapping relationship between the input x and the output y through a data-driven method: f:x→y Analyze the data: The input has 7 features, the output has 6 features, i∈{1,2,3,…,m - 1,m} Input of the forward prediction model for internal ballistic parameters: x = {x1, x2,..., x m} T Where k is the growth rate ratio, b1 is the first section ratio, b3 is the third section ratio, a is the burning rate, n is the pressure exponent, r is the throat radius, and v is the characteristic velocity; Output of the forward prediction model for internal ballistic parameters: y = {y1, y2,..., y m} T Among them, T r is the rise time, P1 is the first peak pressure, T1 is the first peak duration, T c is the cruise time, P2 is the second peak pressure, T2 is the second peak duration.

4. The method for predicting the forward interior ballistics and designing the reverse grain based on machine learning according to claim 3, wherein Use the Bayesian regularization method to train the forward prediction model for internal ballistic parameters; Given the design data: x'=[k',b1',b3',a',n',r',v'] After the training of the forward prediction model for internal ballistic parameters is completed, import the design data x’, and obtain the prediction result: y' = [T r ', P1', T1', T c ', P2', T2'] y’ is the prediction of the internal ballistic parameters based on the design data.

5. The method for predicting forward interior ballistics and designing reverse grain based on machine learning according to claim 2, characterized in that, The establishment process of the reverse prediction model for internal ballistic parameters is as follows: Train the internal ballistics parameter inverse prediction model using the internal ballistics dataset constructed in Step 1. Use the data stored in OutputMatrix as the input of the internal ballistics parameter inverse prediction model, and the data stored in InputMatrix as the output of the internal ballistics parameter inverse prediction model. Establish a non-linear mapping relationship between the input X and the output Y through a data-driven method: f:X→Y Analyze the data: There are 6 features in the input and 7 features in the output, i = {1, 2, 3, …, m - 1, m}; Input of the internal ballistics parameter inverse prediction model: X = {X1, X2,..., X m} T where T r is the rise time, P1 is the first peak pressure, T1 is the first peak duration, T c is the cruise time, P2 is the second peak pressure, T2 is the second peak duration; Output of the internal ballistics parameter inverse prediction model: Y = {Y1, Y2,..., Y m} T where k is the speed increase ratio, b1 is the first-stage ratio, b3 is the third-stage ratio, a is the burning rate, r is the throat radius, and v is the characteristic velocity.

6. The method for predicting the forward interior ballistics and designing the reverse grain based on machine learning according to claim 5, wherein Train the internal ballistics parameter inverse prediction model using the Bayesian regularization method, Given new internal ballistics parameters: X' = [k', b1', b3', a', n', r', v'] After training the internal ballistics parameter inverse prediction model is completed, import the new internal ballistics parameter X’, and obtain the prediction result: Y' = [T r ', P1', T1', T c ', P2', T2'] Y’ is the inverse prediction of the design parameters based on the internal ballistics parameters.

7. The method for predicting the forward interior ballistics and designing the reverse grain based on machine learning according to claim 3 or 5, characterized in that, Both the internal ballistics parameter forward prediction model and the internal ballistics parameter inverse prediction model are feedforward neural network models.

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