Warhead performance prediction method based on small samples

Abstract

The invention discloses a warhead performance prediction method based on a small sample, and the method comprises the steps: determining the to-be-predicted performance of a warhead and the influence parameters of the to-be-predicted performance, and constructing an implicit function relation; testing influence parameters and corresponding warhead performance; constructing an embedded proxy model according to a test result; and predicting the warhead performance corresponding to the new influence parameter by using the embedded agent model. According to the method, the performance of the warhead can be predicted with high precision, few test samples are needed, and the calculation efficiency is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of warhead design and relates to a method for predicting warhead performance based on small samples. Background Art

[0002] The design of a warhead includes parameter selection, optimization, and decision-making for aspects such as materials, structures, processes, and manufacturing. Among them, warhead performance prediction is an essential link. Researchers have established numerous theoretical models or empirical models to predict some performance parameters of the warhead and provide a basis for subsequent optimization. However, due to the diversity of warhead designs, these theoretical models or empirical models cannot cover all situations. Due to the limitations of the models, there is still a risk that the performance of warheads designed for established requirements cannot be predicted. Summary of the Invention

[0003] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a method for predicting warhead performance based on small samples, which can accurately and efficiently analyze the performance of warheads using a small number of samples.

[0004] To solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0005] A method for predicting warhead performance based on small samples includes the following steps:

[0006] Step S10: Determine the performance to be predicted of the warhead and its influencing parameters, and construct an implicit function relationship;

[0007] Step S20: Test the influencing parameters and the corresponding warhead performance;

[0008] Step S30: Construct an embedded surrogate model according to the test results;

[0009] Step S40: Use the embedded surrogate model to predict the warhead performance corresponding to new influencing parameters.

[0010] The present invention also includes the following technical features:

[0011] Specifically, step S10 includes: Let the performance to be predicted be Y, and its influencing parameters be X. Construct its implicit function relationship Y = g(X), where X = {X1,..., X n} is a multi-dimensional influencing parameter;

[0012] The influencing parameters include charge type, liner material, charge structure parameters, and shell structure parameters;

[0013] The performance to be predicted includes the scattering angle, jet head velocity, jet diameter, and jet kinetic energy in the warhead.

[0014] Specifically, step S20 includes: testing the specific values of the N0 groups of the influencing parameters, obtaining the measured values of the corresponding warhead performance according to the tests, and constructing a data set

[0015]

[0016] where x (m) is the m-th specific value of the N0 groups of influencing parameters X, and g(x (m) ) is the measured value of the warhead performance of the m-th sample.

[0017] Specifically, step S30 includes:

[0018] Generating N groups of samples x s = [x (1) ,..., x (j) ,..., x (N) T , and setting the dimensionality reduction dimension d;

[0019] Constructing an embedded surrogate model g K (X);

[0020] Judging the convergence of the model. If the model converges, the model is the final surrogate model. If it does not converge, determine the next set of design parameter values to be measured through self-learning; add the new test results to the data set T, and construct an embedded surrogate model according to the new data set T until the model converges.

[0021] Specifically, constructing an embedded surrogate model according to the data set T includes:

[0022] Slicing the data set T, and obtaining the direction matrix β = {β1,..., β l ,..., β d} by using the sliced inverse regression method, where β l = (β l,1 ,..., β l,i ,..., β l,n ) T is the l-th column vector of the direction matrix;

[0023] Constructing an embedded Kriging surrogate model g K (X), where the kernel function of the Kriging surrogate model is defined as:

[0024]

[0025] In the above formula, and are respectively the j1-th sample and the j2-th sample in the N groups of samples generated, and θ lis the l-th hyperparameter in the kernel function;

[0026] Use g K (X) to calculate the predicted mean and predicted variance of the samples in x s ; and

[0027] Specifically, to judge the convergence of the judgment model, if the model converges, then the model is the final surrogate model; if it does not converge, then judge the next set of design parameter values to be measured through self-learning, including:

[0028] Define the learning function as the predicted variance of the sample x (j) ;

[0029] If then the current model converges, and the model is the final surrogate model; if then select s from x the N h with the largest values, and obtain the performance of the warhead according to the test.

[0030] Specifically, the method of using sliced inverse regression to obtain the direction matrix β = {β1,..., β l ,..., β d} includes:

[0031] Sort ;

[0032] According to the sorting, divide the N0 samples into h slices, then the number of samples in each slice is N h = N0 / h;

[0033] In each slice, calculate the sample mean, where is the k-th slice among the h slices, is the sample mean of the k-th slice:

[0034]

[0035] Calculate the covariance matrix of the slice means:

[0036]

[0037] where, is the mean of the N0 samples,

[0038] Calculate the covariance matrix:

[0039]

[0040] The direction matrix β is calculated through eigenvalue decomposition:

[0041]

[0042] Where is the l-th eigenvalue, and β l is the l-th eigenvector.

[0043] Specifically, step S40 includes: substituting the new influence parameter into the converged embedded surrogate model g K (X) to obtain the corresponding predicted value of the warhead performance.

[0044] Compared with the prior art, the present invention has the following technical effects:

[0045] The warhead performance prediction method based on small samples provided by the present invention determines the key performance of the warhead and its influence parameters, and establishes a forward transfer model for predicting performance through a surrogate model; in the process of establishing the surrogate model, a dimensionality reduction algorithm is embedded in its kernel function to reduce the calculation of invalid dimensions, thereby improving the convergence speed of the surrogate model, so that a high-precision performance prediction model can be obtained with a small number of test samples. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a schematic flow chart of the warhead performance prediction method based on small samples of the present invention.

[0047] Figure 2 is a schematic diagram of the typical structure of Embodiment 1.

[0048] The meanings of the labels in the figure are as follows:

[0049] 1. partition, 2. charge, 3. shell, 4. liner. DETAILED DESCRIPTION OF THE INVENTION

[0050] The following are specific embodiments of the present invention. It should be noted that the present invention is not limited to the following specific embodiments, and any equivalent transformation made on the basis of the technical solution of the present application falls within the protection scope of the present invention.

[0051] Embodiment:

[0052] The present invention provides a method for predicting the performance of a warhead based on small samples, which establishes a surrogate model through a small number of test samples to predict the performance of new samples of the warhead. After determining the performance to be predicted of the warhead and its influencing parameters, a functional relationship is constructed; a data set for constructing the surrogate model is obtained through a small number of experiments. During the process of constructing the surrogate model, a dimensionality reduction algorithm is embedded in its kernel function to accelerate the convergence speed of the Kriging model and significantly reduce the number of test samples. The present disclosure can apply the embedded surrogate model to solve the problem of warhead performance prediction, thereby providing guidance for warhead design.

[0053] As Figure 1 shown, a method for predicting the performance of a warhead based on small samples provided by the present disclosure includes the following steps:

[0054] Step S10, determining the performance to be predicted of the warhead and its influencing parameters, and constructing an implicit functional relationship Y = g(X);

[0055] Step S20, testing the influencing parameters and the corresponding warhead performance;

[0056] Step S30, constructing an embedded surrogate model according to the test results;

[0057] Step S40, using the embedded surrogate model to predict the warhead performance corresponding to new influencing parameters.

[0058] The above steps will be described in detail below with reference to examples.

[0059] Considering the performance prediction of a shaped charge warhead, its basic structure includes converting the technical index requirements of the shaped charge warhead into design performances such as the head velocity and jet diameter during shaped charge jet formation.

[0060] Figure 2 In, the typical structure includes a partition 1, a charge 2, a casing 3, and a liner 4.

[0061] Determine the head velocity during jet formation as the performance to be predicted, and its influencing factors are considered to include parameters such as partition thickness, explosive detonation velocity, explosive detonation pressure, explosive density, explosive length-diameter ratio, acoustic impedance of the casing material, casing thickness, density of the liner material, sound velocity of the liner material, liner cone angle, liner wall thickness, and liner wall thickness change rate.

[0062] Let the head velocity during jet formation of the shaped charge warhead be Y, and its influencing factors be X, and construct its implicit functional relationship Y = g(X), where X = {X1,..., X n} is a multi-dimensional influencing parameter.

[0063] In step S10, determine the performance to be predicted of the warhead and its influencing parameters, and construct an implicit functional relationship Y = g(X).

[0064] According to the technical indicators of the shaped-charge armor-piercing warhead, its design performance includes the head speed, jet diameter, jet kinetic energy, etc. when the shaped-charge jet is formed;

[0065] As an example, this embodiment takes the head speed during jet forming as the performance to be predicted, and its influencing parameters include the density of the liner material, the sound velocity of the liner material, the detonation velocity of the explosive, the detonation pressure of the explosive, the density of the explosive, the aspect ratio of the explosive, the cone angle of the liner, the wall thickness of the liner, the change rate of the wall thickness of the liner, the acoustic impedance of the shell material, the shell thickness, the explosion height and other parameters.

[0066] Assume that the head velocity of the shaped charge warhead during jet formation is Y, and its influencing parameter is X, and construct its implicit function relationship Y=g(X), where X={X1,...,X n} is a multidimensional influencing parameter.

[0067] However, the present invention is not limited thereto, and design properties such as jet diameter and jet kinetic energy may also be determined as properties to be predicted.

[0068] In step S20, the influencing parameters and the corresponding warhead performance are tested. Specifically, the values ​​of N0 groups (specifically 10 groups) of influencing parameters and the head speed of the corresponding shaped charge warhead during jet formation are obtained through data measurement, partition test, static explosion test, speed test, etc., and a data set is constructed. in, is the mth group of specific values ​​of the N0 group of influencing parameters X, g(x (m) ) is the measured value of the warhead performance of the mth group of samples.

[0069] In step S30, an embedded agent model is constructed according to the test results.

[0070] Generate N groups of samples x according to the value of X s =[x (1) ,...,x (j) ,...,x (N) ] T , set the dimension reduction dimension d;

[0071] Construct an embedded proxy model g based on the dataset T K (X);

[0072] Determine the convergence of the model. If the model converges, then the model is the final proxy model. If it does not converge, then the next set of design parameter values ​​to be tested is determined through autonomous learning.

[0073] Add the new test results to the dataset T and build an embedded proxy model based on the new dataset T until the model converges.

[0074] Specifically, an embedded proxy model is constructed based on the dataset T, including:

[0075] Slice the dataset T, and use the slice inverse regression method to obtain the direction matrix β = {β1,..., β l ,..., β d}; where β l = (β l,1 ,..., β l,i ,..., β l,n ) T is the l-th column vector of the direction matrix;

[0076] Construct the embedded Kriging proxy model g K (X), where the kernel function of the Kriging proxy model is defined as:

[0077]

[0078] In the above formula, and are respectively the j1-th sample and the j2-th sample in the N groups of samples generated, and θ l is the l-th hyperparameter in the kernel function and can be obtained through an optimization algorithm;

[0079] Use g K (X) to calculate the sample prediction mean and prediction variance in x s and

[0080] In an exemplary embodiment of the present disclosure, the direction matrix β = {β1,..., β l ,..., β d} is obtained by using the slice inverse regression method, including:

[0081] Sort ;

[0082] According to the sorting, divide the N0 samples into h slices, and the number of samples in each slice is N h = N0 / h;

[0083] In each slice, calculate the sample mean, where is the k-th slice among the h slices, is the sample mean of the k-th slice:

[0084]

[0085] Calculate the covariance matrix of the slice means:

[0086] ​

[0087] Among them, is the mean of N0 samples,

[0088] Calculate the covariance matrix

[0089]

[0090] The direction matrix β can be calculated by eigenvalue decomposition:

[0091]

[0092] where β l is the l-th eigenvector.

[0093] Specifically, judge the convergence of the model. If the model converges, the model is the final surrogate model. If it does not converge, the next set of design parameter values to be measured is judged through self-learning, including:

[0094] Define the learning function is the predicted variance of the sample x (j) ;

[0095] If then the current model converges, and the model is the final surrogate model; if then select s from x the largest N h samples, and obtain the head velocity during the jet formation of the shaped charge warhead according to the experiment.

[0096] In step S40, use the embedded surrogate model to predict the warhead performance corresponding to the new influencing parameters.

[0097] Specifically, substitute the new influencing parameters into the converged embedded surrogate model g K (X) to obtain the predicted value of the head velocity during the jet formation of the shaped charge warhead.

[0098] In this embodiment, 10,000 groups of influencing parameters are calculated to obtain the true value of the jet head velocity, and the prediction results of 10 test samples are shown to illustrate the effectiveness of the method of the present invention as shown in Table 1.

[0099] Table 1 Prediction Results

[0100] Jet head velocity (m / s) True result Predicted result Relative error Test sample 1 6948 6952 0.06％ Test sample 2 7012 7025 0.19％ Test sample 3 7108 7153 0.63％ Test sample 4 7234 7198 -0.50％ Test sample 5 7367 7336 -0.42％ Test sample 6 7419 7483 0.86％ Test sample 7 7001 6982 -0.27％ Test sample 8 7156 7038 -1.65％ Test sample 9 7289 7302 0.18％ Test sample 10 7342 7336 -0.08％

[0101] Among them, the relative error = (embedded surrogate model - true result) / true result × 100%.

[0102] As can be seen from the table, the embedded proxy model shown in the present invention does not exceed 2% compared with the real results and can accurately predict the real values. In this embodiment, the proxy model only needs 65 calculations to obtain the prediction results of 10,000 real values, demonstrating the effectiveness of the present invention.

[0103] The preferred embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solutions of the present invention, and these simple modifications all fall within the protection scope of the present invention.

[0104] In addition, it should be noted that, in the case of no contradiction, the various specific technical features described in the above specific embodiments can be combined in any suitable way. To avoid unnecessary repetition, the present invention will not describe various possible combination methods separately.

[0105] Furthermore, any combination can be made between various different embodiments of the present invention, as long as it does not violate the idea of the present invention, and it should also be regarded as the content disclosed by the present invention.

Claims

1. A warhead performance prediction method based on small samples, characterized in that, It includes the following steps: Step S10: Determine the performance to be predicted of the warhead and its influencing parameters, and construct an implicit function relationship; Step S20: Test the influencing parameters and the corresponding warhead performance; Step S30: Construct an embedded surrogate model based on the test results; Step S40: Use the embedded surrogate model to predict the warhead performance corresponding to new influencing parameters.

2. The method for predicting the performance of a warhead based on small samples according to claim 1, wherein Step S10 includes: setting the performance to be predicted as Y, its influencing parameters as X, and constructing its implicit functional relationship Y = g(X), where X = {X1,..., X n} is a multi-dimensional influencing parameter; The influencing parameters include the charge type, liner material, charge structure parameters, and shell structure parameters; The performance to be predicted includes the scattering angle, jet head velocity, jet diameter, and jet kinetic energy in the warhead.

3. The small-sample-based warhead performance prediction method according to claim 1, characterized in that Step S20 includes: testing the specific values of the N0 groups of the influencing parameters, obtaining the measured values of the corresponding warhead performance according to the tests, and constructing a data set where x (m) is the m-th specific value of the N0 groups of influencing parameters X, and g(x (m) ) is the measured value of the warhead performance of the m-th group of samples.

4. The method for predicting the performance of a warhead based on small samples according to claim 1, wherein Step S30 includes: Generate N sets of samples x according to the value of X s = [x (1) ,..., x (j) ,..., x (N) T , set the dimensionality reduction dimension d;​ Construct an embedded proxy model g based on the dataset T K (X); Judge the convergence of the model. If the model converges, the model is the final surrogate model. If it does not converge, determine the next set of design parameter values to be measured through self-learning; add the new test results to the data set T, and construct an embedded surrogate model based on the new data set T until the model converges.

5. The method for predicting the performance of a warhead based on small samples according to claim 4, characterized in that Constructing an embedded surrogate model based on the data set T includes: Slice the dataset T, and use the sliced inverse regression method to obtain the direction matrix β = {β1,..., β l ,..., β d}, where β l = (β l,1 ,..., β l,i ,..., β l,n ) T is the l-th column vector of the direction matrix; Construct the embedded Kriging surrogate model \(g\) K (X), where the kernel function of the Kriging surrogate model is defined as: In the above formula, and are the j1-th sample and the j2-th sample in the N groups of samples respectively, and θ l is the l-th hyperparameter in the kernel function; Using g K (X) Calculate the predicted mean and predicted variance of the samples in xs and 6. The small-sample-based warhead performance prediction method according to claim 4, wherein The judgment of the convergence of the model. If the model converges, the model is the final surrogate model. If it does not converge, determine the next set of design parameter values to be measured through self-learning, including: Define the learning function For sample x (j) The predicted variance; If the current model converges, then this model is the final surrogate model; if then select from x s the N largest h samples, and obtain the performance of the warhead according to the test.

7. The small-sample-based warhead performance prediction method according to claim 5, characterized in that The direction matrix β = {β1,..., β l ,..., β d} is obtained by using the sliced inverse regression method, It includes: Sort ; Sort N0 samples into h slices, and the number of samples in each slice is N h = N0 / h; Within each slice, calculate the sample mean, where is the k-th slice out of h slices, is the sample mean of the k-th slice: Calculate the covariance matrix of the slice means: Among them, is the mean of N0 samples, Calculate the covariance matrix: The direction matrix β is calculated through eigenvalue decomposition: wherein is the l-th eigenvalue, and β l is the l-th eigenvector.

8. The small-sample-based warhead performance prediction method according to claim 1, wherein Step S40 includes: substituting the new influence parameter into the converged embedded surrogate model g K (X) to obtain the corresponding predicted value of the warhead performance.

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