Independent fusion modeling and response prediction method for missile low- and high-precision performance data

Abstract

The present invention proposes an independent fusion modeling and response prediction method for low- and high-precision missile performance data. The method utilizes collected missile reliability test data of different accuracies to respectively construct a low-precision response model and a high-precision response model. Based on Bayesian theory, the posterior probability density distribution of each model parameter, and the high-precision response model, the posterior probability density function of the high-precision missile performance response data at the influencing factor data of any application scenario is obtained, and then a high-precision missile performance response data prediction model at the influencing factor data of any application scenario is obtained. The method can predict the high-precision missile performance response data at the influencing factor data of any application scenario, and ensure the accuracy of the response prediction result and the efficiency of the solution operation.

Description

Technical Field

[0001] The invention mainly relates to the technical field of missile reliability test and identification, in particular to an independent fusion modeling and response prediction method for low- and high-precision performance data of a missile. Background Art

[0002] Missile reliability testing and evaluation is a critical assessment tool throughout the missile's lifecycle, from development and production to finalization and deployment. Due to its high reliability, long lifespan, and small sample size, missile testing and evaluation, compared to conventional products, is costly, time-consuming, and subject to numerous constraints. Consequently, the acquisition of high-precision response data is limited. With technological advancements, simulated virtual testing is playing an increasingly important role in equipment reliability evaluation. Due to its low cost, short cycle time, and ease of operation, it can supplement data for missile reliability assessments. However, compared to physical testing, data obtained through simulation does not necessarily better reflect equipment performance indicators, and is therefore considered to have limited accuracy.

[0003] The main idea of ​​the current missile reliability test and identification method is to simulate a series of combat processes such as missile transportation, launch, cruising and hitting the target in a certain test environment through computer programs, generate simulation data of missile tests as input of the simulation test and identification system; at the same time, record the missile performance output indicators as the response variables of the test, and use them as the basis to evaluate the missile combat effectiveness and carry out reliability assessment.

[0004] However, for computer simulation tests, higher-precision test results are often limited by complex algorithms and expensive computational costs. Different scenario modeling methods also produce varying data accuracy. The question is how to comprehensively analyze the response data from tests of varying precision to achieve high-precision response predictions for untested points under arbitrary conditions and conduct subsequent reliability assessments. The current approach involves introducing a fusion model between low- and high-precision data, correlating and fusing low-precision test responses into the response model of high-precision data, and deriving the posterior distribution of parameters based on Bayesian theory. With the help of correction effects between multiple sources of information, a more accurate response prediction result is obtained, achieving the equivalent of a high-precision reliability test at a low test cost and with a small number of tests. The key to achieving this goal lies in establishing a fusion calibration model for low- and high-precision data and solving for related parameters.

[0005] However, current research on low- and high-precision data fusion technology mainly focuses on proxy models, including Kriging models, Co-Kriging models, multi-task Gaussian process models (MTGP), and Bayesian Kriging proxy models. At this stage, different precision data fusion technology is expanding in two aspects: how to establish a better calibration model and introduce a difference function. However, due to the complexity of the correlation model, the model parameters are high in dimension, and the model parameters can only be estimated step by step, resulting in low accuracy of the parameter estimation results, low running solution efficiency, and poor robustness, which in turn affects the results of the response prediction. This is a technical problem that those skilled in the art urgently need to solve. Summary of the Invention

[0006] When missile reliability test data of varying precision is collected simultaneously, how can a calibration model be constructed and solved to fuse these data? This allows for the prediction of high-precision missile performance response data for any application scenario's impact factor data, while ensuring both accuracy and operational efficiency. This paper addresses this technical issue by proposing a method for independent fusion modeling and response prediction of missile low- and high-precision performance data.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] Independent fusion modeling and response prediction methods for missile low- and high-precision performance data, including:

[0009] Obtain reliability test data obtained when the missile is tested under reliability test conditions with different precision, including high-precision reliability test data and low-precision reliability test data;

[0010] Based on the low-precision reliability test data and the high-precision reliability test data, a low-precision response model and a high-precision response model are constructed respectively;

[0011] Determine the model parameters and their pre-test distribution and post-test probability density distribution based on the low-precision response model and the high-precision response model;

[0012] Based on Bayesian theory, the posterior probability density distribution of each model parameter and the high-precision response model, the posterior probability density function of the high-precision missile performance response data at the influencing factor data of any application scenario is obtained, and then the high-precision missile performance response data prediction model at the influencing factor data of any application scenario is obtained;

[0013] A large number of model parameter samples are randomly generated, and the high-precision missile performance response data prediction model is iteratively solved to obtain the high-precision missile performance response data prediction results at the influencing factor data of any application scenario.

[0014] Furthermore, the low-precision reliability test data of the present invention is the application scenario impact factor data set when the missile is tested under the low-precision reliability test conditions. And the corresponding low-precision missile performance response data obtained Composition: High-precision reliability test data consists of application scenario impact factor data set when the missile is tested under high-precision reliability test conditions. And the corresponding high-precision missile performance response data obtained where T represents matrix transpose, n and m represent the number of samples in low-precision reliability test data and high-precision reliability test data, respectively. represents the value of the i-th group of application scenario impact factors in the low-precision reliability test data. Each group of application scenario impact factors contains k application scenario impact factors x1,...,x k , The corresponding missile performance response data is represents the value of the impact factor of the jth group of application scenarios in the high-precision reliability test data, The corresponding missile performance response data is i=1,...,n,j=1,...,m, m≤n.

[0015] Furthermore, the low-precision response model constructed in the present invention is:

[0016]

[0017] in The basis function representing the value of the influencing factor of the i-th group of application scenarios in the low-precision reliability test data, β=[β1,...,β k ] T represents the regression coefficient, It follows a Gaussian process The error term of the Gaussian process is 0, and the variance parameter is The correlation parameter is φ.

[0018] At the same time, based on the fact that the trends between the application scenario impact factors and missile performance responses corresponding to low-precision reliability test data and high-precision reliability test data are the same, that is, the mechanisms between the application scenario impact factor data and missile performance response data are consistent between different precision tests in missile evaluation tests, the regression coefficients β corresponding to the low-precision reliability test data and the high-precision reliability test data in the independent model are set to be equal, and the Gaussian correlation parameters φ corresponding to the two error terms are set to be equal. The high-precision response model constructed by the present invention is:

[0019]

[0020] in The basis function representing the value of the j-th group of application scenario influencing factors in the high-precision reliability test data, β=[β1,...,β k ] T represents the regression coefficient, It follows a Gaussian process The error term of the Gaussian process is 0, and the variance parameter is The correlation parameter is φ.

[0021] In the present invention, the regression coefficient β and the variance parameter and the correlation parameter φ are all model parameters to be determined. Those skilled in the art can determine the prior distribution of each model parameter based on their own experience and existing technology, and then obtain the posterior probability density distribution of each model parameter.

[0022] Furthermore, the present invention generates a large number of model parameter samples based on the Monte Carlo Markov chain (MCMC) sampling method, iteratively solves the high-precision missile performance response data prediction model, and then obtains the high-precision missile performance response data prediction results at the influencing factor data of any application scenario.

[0023] In another aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are performed:

[0024] Obtain reliability test data obtained when the missile is tested under reliability test conditions with different precision, including high-precision reliability test data and low-precision reliability test data;

[0025] Based on the low-precision reliability test data and the high-precision reliability test data, a low-precision response model and a high-precision response model are constructed respectively;

[0026] Determine the model parameters and their pre-test distribution and post-test probability density distribution based on the low-precision response model and the high-precision response model;

[0027] Based on Bayesian theory, the posterior probability density distribution of each model parameter and the high-precision response model, the posterior probability density function of the high-precision missile performance response data at the influencing factor data of any application scenario is obtained, and then the high-precision missile performance response data prediction model at the influencing factor data of any application scenario is obtained;

[0028] A large number of model parameter samples are randomly generated, and the high-precision missile performance response data prediction model is iteratively solved to obtain the high-precision missile performance response data prediction results at the influencing factor data of any application scenario.

[0029] In another aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the following steps:

[0030] Obtain reliability test data obtained when the missile is tested under reliability test conditions with different precision, including high-precision reliability test data and low-precision reliability test data;

[0031] Based on the low-precision reliability test data and the high-precision reliability test data, a low-precision response model and a high-precision response model are constructed respectively;

[0032] Determine the model parameters and their pre-test distribution and post-test probability density distribution based on the low-precision response model and the high-precision response model;

[0033] Based on Bayesian theory, the posterior probability density distribution of each model parameter and the high-precision response model, the posterior probability density function of the high-precision missile performance response data at the influencing factor data of any application scenario is obtained, and then the high-precision missile performance response data prediction model at the influencing factor data of any application scenario is obtained;

[0034] A large number of model parameter samples are randomly generated, and the high-precision missile performance response data prediction model is iteratively solved to obtain the high-precision missile performance response data prediction results at the influencing factor data of any application scenario.

[0035] Through the above technical solution, the present invention can produce the following technical effects:

[0036] The present invention utilizes the collected missile reliability test data of different accuracies to construct and solve a high-precision missile performance response data prediction model that integrates the reliability test data of different accuracies, thereby realizing the prediction of high-precision missile performance response data at the influencing factor data of any application scenario, and ensuring the accuracy of the response prediction results and the efficiency of the solution operation.

[0037] Furthermore, the present invention is simple and has high precision, and can realize the model parameters The joint sampling of φ and φ takes into account the relationship between different parameters, making the model parameters to be determined more accurate and improving the accuracy of the prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0039] Figure 1 is a flow chart of an embodiment of the present invention;

[0040] Figure 2 This is a flow chart of solving high-precision response model parameters based on the MCMC sampling method in one embodiment of the present invention;

[0041] Figure 3 is a schematic diagram of prediction results in one embodiment of the present invention;

[0042] Figure 4 It is a structural diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clearly understood, the following drawings and detailed descriptions clearly illustrate the spirit of the present invention. After understanding the embodiments of the present invention, any person skilled in the art will be able to make changes and modifications based on the techniques taught by the present invention without departing from the spirit and scope of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to illustrate the present invention and are not intended to limit the present invention.

[0044] Reference Figure 1 In one embodiment of the present invention, a method for independent fusion modeling and response prediction of missile low- and high-precision performance data is provided, comprising:

[0045] Obtain reliability test data obtained when the missile is tested under reliability test conditions with different precision, including high-precision reliability test data and low-precision reliability test data;

[0046] Based on the low-precision reliability test data and the high-precision reliability test data, a low-precision response model and a high-precision response model are constructed respectively;

[0047] Determine the model parameters and their pre-test distribution and post-test probability density distribution based on the low-precision response model and the high-precision response model;

[0048] Based on Bayesian theory, the posterior probability density distribution of each model parameter and the high-precision response model, the posterior probability density function of the high-precision missile performance response data at the influencing factor data of any application scenario is obtained, and then the high-precision missile performance response data prediction model at the influencing factor data of any application scenario is obtained;

[0049] A large number of model parameter samples are randomly generated, and the high-precision missile performance response data prediction model is iteratively solved to obtain the high-precision missile performance response data prediction results at the influencing factor data of any application scenario.

[0050] Those skilled in the art will appreciate that by setting application scenario influencing factor data and conducting missile reliability tests under reliability test conditions of varying precision, missile performance response data of varying precision will be obtained. The missile reliability test conducted in the present invention can be a computer simulation test or a hardware-in-the-loop simulation test involving a computer. Regardless of the reliability test method employed, the accuracy of the reliability test conditions, such as sensor detection accuracy and computer algorithm accuracy, will result in missile performance response data of varying precision under reliability test conditions of varying precision. Accordingly, the reliability test data is divided into low-precision reliability test data and high-precision reliability test data.

[0051] In the present invention, each group of application scenario impact factor data includes k application scenario impact factors x1,...,x k The application scenario influencing factors described herein include various factors, including but not limited to environmental factors, radar observation angle, target reflected radiation interference intensity and transmitted radiation interference intensity, missile's own reflected anti-interference intensity and missile's own transmitted anti-interference intensity, etc. The missile performance response data represents missile performance parameters corresponding to each set of application scenario influencing factor data, such as missile launch and interception time. It will be appreciated that those skilled in the art may select other parameters as application scenario influencing factor data and missile performance response data based on experimental requirements.

[0052] In one embodiment, the low-precision reliability test data is the application scenario impact factor data set when the missile is tested under low-precision reliability test conditions. And the corresponding low-precision missile performance response data obtained The high-precision reliability test data consists of the application scenario impact factor data set when the missile is tested under high-precision reliability test conditions. And the corresponding high-precision missile performance response data obtained where T represents matrix transpose, n and m represent the number of samples in low-precision reliability test data and high-precision reliability test data, respectively. represents the value of the i-th group of application scenario impact factors in the low-precision reliability test data. Each group of application scenario impact factors contains k application scenario impact factors x1,...,x k , The corresponding missile performance response data is represents the value of the impact factor of the jth group of application scenarios in the high-precision reliability test data, The corresponding missile performance response data is i=1,...,n,j=1,...,m, m≤n.

[0053] In one embodiment, the low-precision response model constructed based on the low-precision reliability test data is:

[0054]

[0055] in The basis function representing the value of the influencing factor of the i-th group of application scenarios in the low-precision reliability test data, β=[β1,...,β k ] T represents the regression coefficient, It follows a Gaussian process The error term of the Gaussian process is 0, and the variance parameter is The correlation parameter is φ, and the correlation parameter φ includes k parameters φ1, φ2...φ k .

[0056] Further according to the above content, the corresponding low-precision missile performance response data y obtained when the missile is tested under low-precision reliability test conditions l The probability density function of is:

[0057]

[0058] in is the basis function set of the impact factor values ​​of each group of application scenarios in the low-precision reliability test data, R l is the low-precision missile performance response data y l The n×n dimensional correlation matrix, the element at the i-th row and the f-th column for:

[0059]

[0060] in They represent the corresponding low-precision missile performance response data y obtained when the missile is tested under low-precision reliability test conditions. l The performance response data of the i-th and f-th low-precision missiles, is the value combination of the application scenario impact factor data of group i and group f in the corresponding low-precision reliability test data, The value combinations The corresponding rth specific factor value, φ r are the Gaussian process correlation parameters in the low-precision response model, i = 1, ..., n, f = 1, ..., n, r = 1, ..., k.

[0061] The high-precision response model constructed based on high-precision reliability test data is:

[0062]

[0063] in represents the value of the impact factor of the jth group of application scenarios in the high-precision reliability test data, express Corresponding low-precision missile performance response data in high-precision reliability tests. The basis function representing the influence factor value of the i-th group of application scenarios in the high-precision reliability test data, β=[β1,...,β k ] T As with the low-precision response model, this represents the regression coefficient in the high-precision response model. It follows a Gaussian process The error term of the Gaussian process is 0, and the variance parameter is The correlation parameter φ is consistent with the low-precision response model, and the correlation parameter φ includes k parameters φ1, φ2...φ k .

[0064] The response model parameters include the regression coefficient β, the variance parameter and correlation parameter φ, are all model parameters to be determined, and the correlation parameter φ includes k parameters φ1, φ2...φ k .

[0065] Further based on the above content, the corresponding high-precision missile performance response data y obtained when the missile is tested under high-precision reliability test conditions can be obtained. h The probability density function of is:

[0066]

[0067] in is the basis function set for the values ​​of the impact factors of each group of application scenarios in the high-precision reliability test data, R h High-precision missile performance response data y h The m×m dimensional correlation matrix, the element at the jth row and gth column for:

[0068]

[0069] in They represent the high-precision missile performance response data y in the high-precision reliability test. h The j-th and g-th high-precision missile performance response data, are the value combinations of the jth and gth group application scenario influencing factors in the corresponding high-precision reliability test data, The value combinations The corresponding rth specific factor value, φr are the Gaussian process correlation parameters in the high-precision response model, j = 1, ..., m, g = 1, ..., m, r = 1, ..., k.

[0070] Furthermore, in one embodiment, the response model parameters include the regression coefficient β, the variance parameter and the correlation parameter φ are all model parameters to be determined. Those skilled in the art can determine the posterior distribution form of each parameter based on their own experience and existing technology.

[0071] In one embodiment, the two cases of low-precision and high-precision reliability tests are considered as a whole, and the response set Regression coefficient vector Overall trend matrix Covariance matrix in is the basis function set of the impact factor values ​​of each group of application scenarios in the low-precision reliability test data, R l is the low-precision missile performance response data y l The n×n dimensional correlation matrix, is the basis function set for the values ​​of the impact factors of each group of application scenarios in the high-precision reliability test data, R h High-precision missile performance response data y h The m×m dimensional correlation matrix.

[0072] Based on the above assumptions, it can be obtained that the overall response set y of the reliability test obeys the multivariate normal distribution, that is,

[0073]

[0074] In one embodiment, the model parameters are determined The prior distributions of and φ obey the multivariate normal distribution, inverse Gamma distribution, inverse Gamma distribution, and Gamma distribution respectively, which are:

[0075]

[0076]

[0077]

[0078] φ r ~G(a φ ,b φ )

[0079] The correlation parameter φ includes k parameters φ1, φ2...φ k , r=1,...,k, any one of the correlation parameters φ rAll obey the same gamma distribution; H=(I m×m ,I m×m ), I m×m is the m-order unit matrix, N(0,(H T H) -1 ) has a mean of 0, and the covariance matrix is ​​a multivariate normal distribution similar to the identity matrix. G(a,b) represents the Gamma distribution, IG(α,γ) represents the inverse Gamma distribution, and the corresponding parameter α in these prior distributions is h , γ h , α l , γ l , a φ ,b φ These are all pre-given hyperparameters, and their values ​​need to be determined based on specific case data in practical applications.

[0080] For the mean parameter to be determined Variance parameter And the correlation parameter φ, according to Bayes' theorem, its posterior distribution is:

[0081]

[0082] in represents the prior distribution, f(y l ),f(y h ) represent the probability density functions of low-precision missile performance response data and high-precision missile performance response data, respectively.

[0083] Model parameters and φ, their posterior probability density distribution functions are:

[0084]

[0085]

[0086]

[0087]

[0088] in Indicates the model parameters and φ, except All other parameters except are known; similarly, Indicates the model parameters and φ, except All other parameters except are known; Indicates the model parameters and φ, except All other parameters except φ are known; π(φ) is the prior distribution of φ, specifically

[0089]

[0090] In one embodiment, according to Bayesian theory, the high-precision missile performance response data y at the impact factor data x0 of any application scenario is h The posterior probability density function of (x0) is:

[0091]

[0092] in represents the conditional distribution of the untested point response based on known response information. Represents model parameters The joint posterior probability density distribution function of can be expressed as follows because the parameters are independent of each other:

[0093]

[0094] Therefore, the high-precision missile performance response data prediction model at the influencing factor data x0 of any application scenario is constructed as follows:

[0095]

[0096] In one embodiment, a large number of model parameter samples are generated based on the MCMC sampling method, so as to discretize the posterior probability density function of the high-precision surface-to-air missile performance response data, and then calculate the prediction results of the high-precision missile performance response data at the influencing factor data x0 of any application scenario.

[0097] The performance response data of high-precision surface-to-air missiles is predicted using the concept of statistical sampling. Based on the iterative calculation of a large number of high-precision response model parameter samples, the continuous integral in the high-precision surface-to-air missile performance response data prediction model is discretized, and the posterior probability density function of the high-precision surface-to-air missile performance response data is approximated.

[0098] Specifically, in one embodiment, the prediction result of the high-precision missile performance response data at the application scenario impact factor data x0 is obtained by the following steps:

[0099] (i) Randomly generate M groups of model parameter samples

[0100]

[0101] (ii) Based on the iterative calculation of M sets of model parameter samples, continuous integral discretization sampling is performed on the high-precision missile performance response data prediction model to obtain the high-precision missile performance response data prediction result at the application scenario influencing factor data x0 as follows:

[0102]

[0103] in is the expected value of the high-precision missile performance response data at the application scenario influencing factor data x0.

[0104] It can be understood that the specific process of generating M groups of model parameter samples in the above step (i) is not limited, and those skilled in the art can implement it by using any existing method in the art.

[0105] In one embodiment, referring to Figure 2 The method for randomly generating M groups of model parameter samples in step (i) includes:

[0106] Based on the prior distribution of each model parameter, the initial value of each model parameter is generated, which is recorded as

[0107] Generate random model parameter samples from the derived posterior probability density function using the Gibbs algorithm q=1,...,M, where M is the number of iterations of the sampling algorithm set manually;

[0108] The posterior probability density distribution function p(φ|y l ,y h ) sampling, and obtain a random sample. When it meets the transition probability condition, it is recorded as a successful sampling, that is, the model parameter sample φ is obtained (q) , q=1,...,M, M is the number of iterations of the sampling algorithm set manually;

[0109] So far, a large number of posterior probability density distribution functions have been obtained Sample model parameters

[0110] The Gibbs algorithm is used to generate random samples from the derived posterior probability density function of the model parameters. When , it can be obtained directly according to the distribution. Using the MH method, the sampling objective function p(φ|y l ,y h ) Sampling φ (q) When , it is generated by comparing the probability of candidate samples and making selections.

[0111] In one embodiment, in step (ii), in order to fully consider the uncertainty and error term in predicting the high-precision surface-to-air missile performance response data value, the present invention predicts the high-precision surface-to-air missile performance response data value from the perspective of statistical distribution based on Bayesian thinking, specifically as follows:

[0112] From the above, we know that the overall response set y of the experiment obeys the multivariate normal distribution, that is,

[0113]

[0114] Then there is the high-precision surface-to-air missile performance response data y at the application scenario impact factor data x0 h (x0) obeys the multivariate normal distribution, that is,

[0115]

[0116] The mean variance

[0117] Then combining the two we get p[y h (x0)|y l ,y h ] obeys the conditional normal distribution,

[0118]

[0119] The trend matrix

[0120] Correlation Matrix

[0121] Using the mean of the conditional normal distribution

[0122]

[0123] The high-precision response value y corresponding to the application scenario simulation input data x0 can be obtained h Expectation of (x0)

[0124] Then M groups of model parameter samples Substitute the expectations in turn The predicted value of the high-precision surface-to-air missile performance response data at the application scenario influencing factor data x0 is:

[0125]

[0126] So far, by establishing a high-precision response model with calibration effect for correlating low- and high-precision test data, the predicted value of high-precision surface-to-air missile performance response data at the influence factor data x0 of arbitrary precision reliability test application scenario is calculated.

[0127] In one embodiment of the present invention, taking the anti-interference and electronic countermeasure performance test of a certain type of missile as an example, an index function of a six-dimensional input vector is used as a generator of low-precision and high-precision response data sets in this example. This example considers six application scenario influencing factors q, l, A C ,E C ,A S ,E S, respectively represent the simulated environmental factors, radar observation angle, target reflection radiation interference intensity and emission radiation interference intensity, missile's own reflection anti-interference intensity and missile's own emission anti-interference intensity. Through standardization, (q, l, A C ,E C ,A S ,E S )∈[0,1] 6 .y h (q,l,A C ,E C ,A S ,E S ) and y l (q,l,A C ,E C ,A S ,E S ) represent the missile launch and interception times in high-precision and low-precision simulation tests, respectively. To demonstrate the missile interception effect, only data with a time of 3 to 20 minutes is selected as usable data. That is, in this example, the time of missile launch and target interception is used as missile performance response data. 40 sets of low-precision missile performance response data and high-precision missile performance response data are randomly generated. The first 30 sets of data are used as training sets to calculate model parameters, and the 31st to 40th sets of data are used as test sets for predictive analysis to verify the effectiveness of the invention. See Table 1 for the training set data used in this embodiment.

[0128] run q l AC EC AS ES L H 1 0.265476 0.967729 0.696816 0.100001 0.5777 0.465205 11.57435 10.31952 2 0.302766 0.407477 0.360567 0.829768 0.868086 0.443931 3.443065 3.393788 3 0.717921 0.550037 0.888327 0.452572 0.774852 0.106762 5.421788 5.512639 4 0.165944 0.712892 0.272959 0.188272 0.65063 0.269576 6.968826 6.397912 5 0.625094 0.127545 0.495533 0.364345 0.990043 0.133968 3.163408 3.150613 6 0.845555 0.813792 0.46489 0.647987 0.1275 0.730659 9.966363 9.937366 7 0.276248 0.826063 0.854807 0.341622 0.382748 0.761923 4.767839 4.594938 8 0.24228 0.46628 0.495039 0.431553 0.836596 0.968217 3.593049 3.506455 9 0.571184 0.936495 0.76717 0.343924 0.280065 0.921127 8.217902 7.713961 10 0.392019 0.941798 0.972955 0.190752 0.21555 0.535675 8.644062 8.270539 11 0.492136 0.678765 0.853115 0.27184 0.837529 0.5666 5.450972 5.132462 12 0.84899 0.235161 0.841792 0.786564 0.126728 0.775361 3.378068 3.405046 13 0.648922 0.26004 0.588385 0.353271 0.633617 0.422217 3.556729 3.494832 14 0.768005 0.103418 0.055577 0.320581 0.608774 0.706326 4.062537 3.889045 15 0.18223 0.909779 0.614015 0.400362 0.663205 0.704893 4.548442 4.351132 16 0.450814 0.048399 0.865513 0.690571 0.780722 0.477858 3.005318 3.004965 17 0.225007 0.016401 0.035231 0.535896 0.388204 0.209088 3.007666 3.006529 18 0.843722 0.75345 0.565182 0.855266 0.740584 0.692704 5.687146 5.415126 19 0.319526 0.564759 0.955745 0.668716 0.869177 0.336755 3.521902 3.500493 20 0.256722 0.071956 0.541431 0.513305 0.002804 0.173124 4.248713 4.556336 21 0.579156 0.124348 0.49052 0.91318 0.677684 0.639801 3.055038 3.049755 22 0.868992 0.323044 0.036985 0.911429 0.678229 0.910428 9.216328 8.207933 23 0.851451 0.995849 0.868092 0.773766 0.521774 0.078729 15.16485 17.00868 24 0.455693 0.06758 0.564807 0.655572 0.418576 0.9989 3.015099 3.01352 25 0.165002 0.216084 0.651283 0.234859 0.229476 0.26201 3.173061 3.16835 26 0.255861 0.388684 0.291597 0.961441 0.936873 0.738846 3.340427 3.294206 27 0.334601 0.485704 0.20676 0.556672 0.437652 0.571535 4.7104 4.484766 28 0.457957 0.757725 0.366337 0.947349 0.825456 0.979805 4.878885 4.626965 29 0.144973 0.066552 0.495199 0.463374 0.119508 0.985757 3.008861 3.00841 30 0.996953 0.267073 0.599215 0.267278 0.370831 0.983885 4.10309 3.955948 31 0.7745 0.100985 0.214706 0.524238 0.703942 0.160756 3.191959 3.173111 32 0.601981 0.598166 0.196957 0.386557 0.68497 0.762879 9.653547 8.622252 33 0.853533 0.769766 0.317449 0.780842 0.530571 0.058012 15.09122 16.17061 34 0.137069 0.152943 0.100872 0.614897 0.683839 0.859141 3.120634 3.101556 35 0.031203 0.652757 0.558331 0.280664 0.27582 0.287478 3.269744 3.256366 36 0.481932 0.508593 0.465096 0.418448 0.43616 0.242584 4.996808 4.885902 37 0.649602 0.865612 0.581446 0.124163 0.633537 0.731487 18.88702 16.43699 38 0.974318 0.085389 0.672284 0.439589 0.242875 0.7419 3.072772 3.068069 39 0.730071 0.142423 0.783099 0.923532 0.481903 0.702026 3.066595 3.06374 40 0.541811 0.092749 0.050533 0.339418 0.656398 0.835931 3.625046 3.522471

[0129] Table 1

[0130]

[0131]

[0132] The prior distribution hyperparameter values ​​are set to give the prior distribution shown in Table 2.

[0133] Table 2 Prior distribution of model parameters

[0134]

[0135] Where H=(I m×m , I m×m ), L m×m is an m-order unit matrix, and the low-precision and high-precision test data in the training set are combined to determine the posterior distribution form of each high-precision response model parameter.

[0136] Set up a Markov chain and sample 5000 times to generate a large number of high-precision response model parameter samples. The mean values ​​of the parameters to be determined for the high-precision response model are:

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] Calculate and record the high-precision response estimate for the test set.

[0143] Repeat the above process 1000 times and obtain the high-precision response value:

[0144] (3.1731,8.6223,16.1706,3.1016,3.2564,4.8859,16.4370,3.0681,3.0637,3.5225) T , combined with the test set high-precision response true value:

[0145] (5.4090,7.9231,12.9484,1.2707,5.3732,7.0078,9.6799,4.3920,3.8527,3.0725) T ,For comparison, the mean absolute error (MAE) is 2.1547 and the root mean square error (RMSE) is 2.7648, see Figure 3 This is the prediction result diagram of this example.

[0146] From the above examples, it can be seen that the independent fusion modeling and response prediction of missile low- and high-precision performance data proposed in the present invention simplifies the prediction model by reducing the introduction of parameters, and realizes the joint sampling of model parameters with different statistical characteristics, thereby reducing unnecessary parameter optimization solutions. Ultimately, it is possible to achieve high-precision response prediction at the input variable, while the prediction result error is relatively small, which can ensure a certain prediction effect.

[0147] In this embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as shown in FIG. Figure 4As shown. The computer device includes a processor, memory, a network interface, and a database connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device is used to store sample data. The network interface of the computer device is used to communicate with an external terminal via a network connection. When executed by the processor, the computer program implements the steps of the independent fusion modeling and response prediction method for missile low- and high-precision performance data in the above-mentioned embodiment.

[0148] Those skilled in the art will understand that Figure 4 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0149] In one embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the independent fusion modeling and response prediction method of missile low- and high-precision performance data in any of the above embodiments.

[0150] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the independent fusion modeling and response prediction method of low- and high-precision missile performance data in any of the above embodiments are implemented.

[0151] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0152] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0153] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

[0154] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. An independent fusion modeling and response prediction method for missile low- and high-precision performance data, characterized by: include: Obtain the reliability test data obtained when the missile is tested under different precision reliability test conditions, including high-precision reliability test data and low-precision reliability test data, where the low-precision reliability test data is the application scenario influencing factor data set when the missile is tested under low-precision reliability test conditions. And the corresponding low-precision missile performance response data obtained Composition: High-precision reliability test data consists of application scenario impact factor data set when the missile is tested under high-precision reliability test conditions. And the corresponding high-precision missile performance response data obtained Composition, of which T represents the matrix transpose, n and m Respectively represent the number of samples in the low-precision reliability test data and the high-precision reliability test data, Indicates the first The impact factor value of each group application scenario includes Application scenario impact factors , The corresponding missile performance response data is , Indicates the first The impact factor value of the group application scenario, The corresponding missile performance response data is , i= 1, ... , n , j= 1, ... , m , , ; Based on the low-precision reliability test data and the high-precision reliability test data, a low-precision response model and a high-precision response model are constructed respectively. The constructed low-precision response model is: in Indicates the first The basis function of the impact factor of the group application scenario, represents the regression coefficient, It follows a Gaussian process The error term of the Gaussian process is 0, and the variance parameter is , the correlation parameter is ; The constructed high-precision response model is: in Indicates the first The basis function of the impact factor of the group application scenario, represents the regression coefficient, It follows a Gaussian process The error term of the Gaussian process is 0, and the variance parameter is , the correlation parameter is ; According to the low-precision response model and the high-precision response model, the model parameters and their pre-test distribution and post-test probability density distribution are determined, including: introducing the response set , regression coefficient vector , overall trend matrix , the covariance matrix ,in is the basis function set for the values ​​of the impact factors of each group of application scenarios in the low-precision reliability test data, Provides performance response data for low-precision missiles of dimensional correlation matrix, is the basis function set for the values ​​of the impact factors of each group of application scenarios in the high-precision reliability test data, High-precision missile performance response data of dimensional correlation matrix; Determine model parameters 、 、 and The prior distribution of obeys the multivariate normal distribution, inverse Gamma distribution, inverse Gamma distribution and Gamma distribution respectively, which are: in , for m The identity matrix of order, The mean is , , , These are all pre-given hyperparameters; According to Bayes' theorem, the model parameters 、 、 and The posterior probability density distribution functions are: in Indicates the model parameters 、 and In addition All other parameters except are known; similarly, Indicates the model parameters 、 and In addition All other parameters except are known; Indicates the model parameters 、 and In addition All other parameters except are known; For the setting The prior distribution of Based on Bayesian theory, the posterior probability density distribution of each model parameter and the high-precision response model, the posterior probability density function of the high-precision missile performance response data at the influencing factor data of any application scenario is obtained, and then the high-precision missile performance response data prediction model at the influencing factor data of any application scenario is obtained; A large number of model parameter samples are randomly generated, and the high-precision missile performance response data prediction model is iteratively solved to obtain the high-precision missile performance response data prediction results at the influencing factor data of any application scenario.

2. The independent fusion modeling and response prediction method for missile low- and high-precision performance data according to claim 1 is characterized in that: Impact factor data for any application scenario High-precision missile performance response data at The posterior probability density function of is: in represents the conditional distribution of the untested point response based on known response information. Represents model parameters The joint posterior probability density distribution function of is independent of each other, which is expressed as ; Application scenario impact factor data The high-precision missile performance response data prediction model at is: 。 3. The independent fusion modeling and response prediction method for missile low- and high-precision performance data according to claim 1 or 2 is characterized in that: Application scenario impact factor data The high-precision missile performance response data prediction results at are obtained through the following steps: Random Generation M Group model parameter samples ; based on M Iterative calculation of model parameter samples is performed to perform continuous integral discretization sampling on the high-precision missile performance response data prediction model to obtain application scenario impact factor data. The prediction results of the high-precision missile performance response data at are as follows: in Application scenario impact factor data The expected value of high-precision missile performance response data at .

4. The independent fusion modeling and response prediction method for missile low- and high-precision performance data according to claim 3 is characterized in that: Random Generation M Methods for grouping model parameter samples include: Based on the prior distribution of each model parameter, the initial value of each model parameter is generated, which is recorded as ; Generate random model parameter samples from the derived posterior probability density function using the Gibbs algorithm , , The number of sampling algorithm iterations is set manually; The MH method was used to The posterior probability density distribution function of Sampling, get a random sample, when it meets the transition probability condition, it is recorded as a successful sampling, that is, the model parameter sample is obtained , , The number of sampling algorithm iterations is set manually; So far, a large number of posterior probability density distribution functions have been obtained Sample model parameters .

5. A computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the independent fusion modeling and response prediction method of missile low- and high-precision performance data as claimed in claim 1.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the independent fusion modeling and response prediction method of missile low- and high-precision performance data as claimed in claim 1 is implemented.

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