Radar performance multi-precision combined test design method based on Bayesian framework

Abstract

The invention discloses a radar performance multi-precision joint test design method based on a Bayesian framework. The problem that a traditional test design method cannot cope with joint design of multiple precision test modes can be effectively solved. The method comprises the following steps: firstly, generalizing a low-precision model based on the low-precision model and the credibility thereof, and calibrating hyper-parameters in a high-precision model through the credibility to obtain a high-precision Bayesian prior model; secondly, based on the high-precision Bayesian prior model, a prediction precision function and a cost function are given through a multilayer DETMAX algorithm and an analytic hierarchy process; then, based on a prediction precision function and a cost function, according to a sample size distribution criterion, giving an objective function and a constraint condition; and finally, solving by optimizing an iterative algorithm to obtain a multi-precision combined test sample size distribution scheme. The method is different from a traditional test design method for solely resolving test design under a certain test precision, and the problem of simultaneous test design of multiple precision radar test modes can be effectively solved.

Description

Technical Field

[0001] The invention belongs to the field of experimental design, and in particular relates to a radar performance multi-precision joint experimental design method based on a Bayesian framework. Background Art

[0002] The multi-precision joint test design of radar performance refers to the combination of various means such as indoor full-digital test, indoor semi-physical test, outdoor test, etc. According to the cost constraints and accuracy information of different test sample conditions under different test means, based on certain allocation criteria, the number of test samples and test sample condition settings under various types of tests are comprehensively designed to cover all test sample condition sets that can complete the inspection or test of a certain performance of the radar.

[0003] The high-value radar test equipment makes the test cost grow exponentially. In order to reduce the consumption of the test, the commonly used method is to reduce the sample size of the test. However, the traditional test and identification mode based on classical statistics mostly adopts the field test method, which still requires a large number of test samples and is very consuming. Therefore, how to use Bayesian theory and successful technologies in other fields to create a scientific, reasonable, advanced and practical indoor and outdoor joint test design method, determine reasonable test points, achieve the optimal design of simulation + field test, and improve the test efficiency is the primary key technical problem we need to solve. Summary of the invention

[0004] The present invention proposes a multi-precision joint test design method for radar performance based on a Bayesian framework, which can effectively solve the problem that traditional test design methods are unable to cope with the joint design of multiple precision test modes.

[0005] The technical solution to realize the present invention is: a radar performance multi-precision joint test design method based on a Bayesian framework, the steps are as follows:

[0006] Step 1: According to the composition structure of different types of radar simulation test systems and the simulation test output parameters of each subsystem, data consistency check is performed, and the test results are mapped to the radar performance test credibility under different simulation test modes through conversion, and then go to step 2.

[0007] Step 2: Based on the prior information of radar performance mechanism, in different situations such as the presence or absence of clear radar performance mechanism analysis equations, the test data obtained by low-precision test methods (full digital simulation test, semi-physical simulation test) are used to construct a low-precision radar performance prediction model f L (X), go to step 3.

[0008] Step 3: Based on the low-precision radar performance prediction model and its credibility, a mapping between hyperparameters and credibility is established through uniform sampling to calibrate the high-precision radar performance prediction model fH The hyperparameters in (X) are used to generalize the low-precision radar performance prediction model to obtain the Bayesian prior model of the high-precision radar performance prediction model. As the basis for solving the optimal joint experimental design, go to step 4.

[0009] Step 4: Bayesian prior model based on high-precision radar performance prediction model and low-precision radar performance prediction model f L (X), a multi-layer DETMAX algorithm is given to construct a multi-precision maximum entropy design D max The prediction accuracy corresponding to the experimental design is characterized by information entropy. By calculating various costs under various experimental methods, multiple indicators are converted and normalized into comprehensive cost indicators to characterize the experimental cost corresponding to the experimental design. This serves as the basis for solving the optimal joint experimental design and then proceeds to step 5.

[0010] Step 5: Based on the prediction accuracy and test cost corresponding to the multi-precision joint test design, the optimization criteria of the joint test design and the corresponding optimization objective function and constraint space are constructed. Generally, they are divided into three categories: the first category is to maximize the information entropy as the objective function and the test cost as the constraint; the second category is to minimize the test cost as the goal and reach a certain minimum threshold of prediction accuracy as the constraint; the third category is to use the prediction accuracy and test cost together as the objective function and maximize the prediction accuracy under the unit test cost as the goal of the unconstrained optimization problem. As the basis for solving the optimization problem of the joint test design, go to step 6.

[0011] Step 6. According to the difference between the optimization objective function and constraint space of the joint test design, the corresponding optimization iterative algorithm for solving the optimization problem is given. First, the initial point of the iteration is taken in the constraint space, and the proxy objective function is constructed according to different algorithms. The proxy objective function is optimized to obtain the iterative value of the sample size. After several steps of iteration, its convergence is judged. Under the condition of its convergence, the obtained solution is used as the output under the initial value, and finally the sample size distribution scheme is obtained, and the radar performance multi-precision joint test design scheme is obtained according to the maximum entropy design.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] (1) The present invention is used for radar performance testing and evaluation, and for the first time proposes a set of scientific methods and complete processes for radar performance multi-precision joint test design under multiple test modes based on test credibility. The above technical solution can solve the problem that the existing test design method is limited to test sample reduction under a single test mode, and can realize the application of test design to multi-precision joint tests, solving the problems of lack of quantitative differences in multi-precision test modes, lack of optimization objectives and constraint space in test design, and lack of quantitative basis in multi-precision joint test design of radar performance.

[0014] (2) Based on the credibility results of different test methods, the present invention takes into account the joint relationship between various equipment systems and the randomness of their effectiveness, and can adapt to the test design of different types of radar performance in different scenarios.

[0015] (3) The present invention realizes for the first time the use of radar performance mechanism prior information of different forms and degrees of completeness for multi-precision test design, and for the first time realizes the generalization of low-precision prediction models to high-precision prediction models through the difference in credibility of different tests, which can provide support for the optimization of multi-precision joint test design.

[0016] (4) This invention firstly describes the prediction accuracy and test results of multi-precision joint design by experimental design and prediction models with multiple precisions before the experiment.

[0017] Test cost.

[0018] (5) This invention presents for the first time the optimization objective function and constraint space of multi-precision joint test design for radar performance.

[0019] (6) This invention provides for the first time an optimization solution method for multi-precision joint test design of radar performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 The present invention is a flow chart of the multi-precision joint test design method for radar performance based on the Bayesian framework. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0023] The technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0024] The following will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention in combination with this design example.

[0025] Combination Figure 1 The radar performance multi-precision joint test design method based on the Bayesian framework described in the present invention comprises the following specific steps:

[0026] Step 1: According to the composition structure of different types of radar simulation test systems and the simulation test output parameters of each subsystem, data consistency test is performed, and the test results are mapped to the radar performance test credibility under different simulation test modes through conversion. The specific method is as follows:

[0027] Step 1-1: According to the composition structure of different types of radar simulation test systems, a radar simulation test system credibility evaluation index system consisting of each subsystem and its related testable simulation test output parameters is established. Based on the verification theory, the evaluation level of each subsystem is decomposed and divided, and the credibility evaluation level and related index items of each model module are established and standardized to form a complete and clear credibility evaluation index system.

[0028] Step 1-2: According to the properties of the subsystem simulation test output parameters, they are divided into static randomness, static determinism, dynamic periodicity, and dynamic non-periodic data. The data consistency test is performed through precision calculation, hypothesis testing method, time domain analysis method, and frequency domain analysis method to form the test results. Through mapping normalization, the credibility value of the i1th subsystem is obtained.

[0029] Step 1-3: Based on the expert scoring method or the hierarchical analysis method, the weight of the credibility index of the i1th subsystem aggregated to the entire radar simulation test system is obtained as i1=1,2,...,m1, m1 is the total number of subsystems in the radar simulation test system, calculate the total credibility p of the radar simulation test system T (i.e. the reliability of this test method) is:

[0030]

[0031] Go to step 2.

[0032] Step 2: Based on the prior information of radar performance mechanism, in different situations such as the presence or absence of clear radar performance mechanism analysis equations, the test data obtained by low-precision test methods (full digital simulation test, semi-physical simulation test) are used to construct a low-precision radar performance prediction model f L (X), the specific construction method is as follows:

[0033] Step 2-1: For radar performance with clear mechanism equations, the relationship between radar performance and test conditions is called a mechanism model, which can usually be expressed as a variety of function types:

[0034]

[0035] Among them, y0 is the radar performance index, f0(X) is the radar performance mechanism model, and X is the test condition value set. Set the value for the k2th test condition, is the basis spline function, is the coefficient of the basis function, and m2 is the number of different basis splines. Through the radar performance mechanism model f0(X), a low-precision radar performance prediction model f is constructed. L (X)

[0036]

[0037] in, is the coefficient of the basis function in the low-precision radar performance prediction model, N is the symbol of the normal distribution, σ is the undetermined hyperparameter, and σ is calibrated by the test data obtained through low-precision test methods (full digital simulation test, semi-physical simulation test) to achieve f L (X) Model construction.

[0038] Step 2-2: In the absence of a clear radar performance mechanism equation, the test data obtained by low-precision test methods such as full digital simulation test and semi-physical simulation test are used to predict the low-precision radar performance model f through Gaussian process based on the test data. L (X) Perform statistical modeling and proceed to step 3.

[0039] Step 3: Based on the low-precision radar performance prediction model and its credibility, a mapping between hyperparameters and credibility is established through uniform sampling to calibrate the high-precision radar performance prediction model f H The hyperparameters in (X) are used to generalize the low-precision radar performance prediction model to obtain the Bayesian prior model of the high-precision radar performance prediction model. As the basis for solving the optimal joint experimental design, the specific method is as follows:

[0040] Step 3-1: Use the Gaussian process model to predict the high-precision radar performance model f H (X) and the low-precision radar performance prediction model f L Modeling the deviation δ(X) between

[0041] δ(X)=f H (X)-f L (X)

[0042] Its prior distribution is

[0043]

[0044] Where GP is the Gaussian process symbol, σ 2 is the variance, R is the given covariance function, θ is the unknown hyperparameter in the covariance function of the Gaussian process, where θ>0 controls the decay speed of the correlation, X∈[0,1] d Represents normalizing the test condition value set X to the multidimensional test sample space [0,1] d , d is the dimension of the test sample space, then

[0045] f H (X) = f L (X)+δ(X)

[0046] f H (X)~GP(f L (X),σ 2 ,R(θ))

[0047]

[0048] Among them, X i , X j are two vectors representing the test samples in the test sample space,

[0049] ||X i -X j || is the modulus length after subtracting the two vectors.

[0050] Step 3-2: Use uniform sampling method to predict the high-precision radar performance model f H (X) and low-precision radar performance prediction model f L (X) The corresponding experimental sample space is discretized to obtain uniform sampling points D3 = {x1, x2, ..., x a}, evenly select points within the range of θ For each sampling point θj , j = 1, 2, ..., k3, from the high-precision radar performance prediction model f H (X) generates the corresponding virtual sample, that is, high-precision prediction data And the samples calculated by the existing low-precision model, that is, the low-precision prediction data

[0051]

[0052] Step 3-3: Take θ as the hyperparameter j When, based on the sampling point D3 = {x1, x2, ..., x a}Corresponding high-precision prediction data and low-precision prediction data Calculate the prediction accuracy A of the low-precision radar performance prediction model j :

[0053]

[0054] The obtained accuracy A j Can be used as a credibility indicator. j The closer it is to 1, the higher the credibility; A j The closer it is to 0, the lower the credibility. j is the hyperparameter θ j When calculated, for multiple θ j , j=1,2,...,k3, the corresponding According to the data Polynomial interpolation is applied to obtain the mapping relationship between prediction accuracy and hyperparameter θ. The prediction accuracy is characterized as a representation of credibility, so the mapping relationship between hyperparameter θ and credibility p is obtained as θ = θ (p), and the estimated (calibrated) value θ of hyperparameter θ is obtained from the credibility value p B , substitute this value back into f H (X), and obtain the radar performance prediction model f H (X) Prior model under the Bayesian framework, that is, a high-precision Bayesian prior model Go to step 4.

[0055] Step 4: Bayesian prior model based on high-precision radar performance prediction model and low-precision radar performance prediction model f L (X), a multi-layer DETMAX algorithm is given to construct a multi-precision maximum entropy design D maxThe prediction accuracy corresponding to the experimental design is characterized by information entropy. By calculating various costs under various experimental methods, multiple indicators are converted and normalized into comprehensive cost indicators to characterize the experimental cost corresponding to the experimental design, which serves as the basis for solving the optimal joint experimental design. The specific characterization method is as follows:

[0056] Step 4-1: π ξ (·) is the prior distribution of ξ, which is the parameter to be estimated in the radar performance prediction model. Observe the a4 input points in the experimental design D4 Response. ξ|D (·) represents the posterior distribution of ξ given the observations collected using design D4. The amount of information I about ξ contained in the prior before the experiment is

[0057] I=∫π ξ (ξ * )ln(π ξ (ξ * ))dξ *

[0058] Among them, ξ * represents the independent variable to be integrated.

[0059] After the experiment is conducted using experimental design D4, the amount of information about ξ I D for

[0060] I D =∫π ξ|D (ξ * )ln(π ξ|D (ξ * ))dξ *

[0061] Therefore I D -I is the amount of information change, and the amount of information is the negative value of the entropy measure. The design that maximizes the entropy of the observed response of each design point has the largest expected change in the amount of information. This design is called the maximum entropy design. For the joint test of multi-precision radar performance, the multi-layer DETMAX algorithm is used to construct the maximum entropy design of the joint test.

[0062] In the Gaussian process model, the part of the observation related to the design at each input point is ln(det(σ 2 R)) / 2, where det(σ 2 R) represents the variance σ of the corresponding observation vector y 2 The determinant of R, σ 2 The variance is the observed value y j ,j=1,2,...,a4, and R is an n×n correlation matrix. Therefore, the maximum entropy design D max Maximize the determinant of the covariance matrix of the corresponding vector y corresponding to each point in the design. The maximum entropy criterion is expressed as

[0063]

[0064] Due to σ 2 Regardless of design D4, the above formula can be equivalent to

[0065]

[0066] In this case, it is assumed that the relevant parameters ξ in R are known.

[0067] The maximum entropy design can be generated by the DETMAX algorithm. The algorithm is optimized through a series of "offsets". The basic process is: first randomly generate an initial design of n4 points, then take appropriate points to add to the current design, or delete appropriate points from the current design, so that the det(R) corresponding to the new design is improved, and so on, until the det(R) corresponding to the design composed of n4 points cannot be increased. Among them, for the existing design D4, the best additional point x j To make the variance function σ 2 (x j ) is the largest point, and the random search algorithm can be used for optimization. The deleted point is the inverse matrix R of R -1 The point associated with the maximum diagonal element. If the det(R) of a "shift" is not improved, all designs generated in this "shift" process are included in the "failed design set" F; if det(R) is improved, F is cleared and the current optimal design D is selected. best Start optimizing.

[0068] If D4 is any current design in this "shift" process, the rule for continuing this "shift" is:

[0069] ①When the number of points in D4 is greater than n4, if D4 is not in F, delete one point, otherwise add one point.

[0070] ②When the number of points in D4 is less than n4, if D4 is not in F, add one point, otherwise delete one point.

[0071] By extending the DETMAX algorithm to multi-precision experiments, we can obtain a multi-layer DETMAX algorithm. Assume that there are k types of precision experiments in the experiment. If the optimization of the i-1th, i=1, 2, ..., kth layers has been completed, then the i-1th layer is fixed, points are added randomly, and the i-th layer is optimized using the DETMAX algorithm. The information entropy of the k-precision maximum entropy design is expressed as

[0072]

[0073] Among them, E n represents the maximum information entropy, d is the dimension of the test space, n iis the number of design points in the i-th layer.

[0074] For the multi-precision joint test design D=(D1,D2,...,D k ), the experimental design of the ith experimental method is expressed as D i , i = 1, 2, ..., k, according to the multiple test methods required to participate in the multi-precision radar performance joint test, the maximum information entropy of the i-th test method is calculated respectively (Characterization of prediction accuracy) and the i-th test method test design D in the multi-precision joint test design D i The mapping relationship between them is

[0075]

[0076] Since the experimental sample size n under the i-th experimental method i After being determined, its maximum entropy design is also clear, and the corresponding maximum information entropy is also clear, so the mapping relationship can be expressed as

[0077]

[0078] For the joint test of multi-precision radar performance, the prediction accuracy E n The experimental sample size allocation scheme (n1,...n i ,...,n k ) is the mapping relationship between

[0079]

[0080] Step 4-2: For the test cost, consider the monetary cost, time cost and labor cost comprehensively, and use the hierarchical analysis method to integrate multiple types of costs:

[0081] ① Use the hierarchical analysis method to stratify the evaluation index system. For the i-th test method, i = 1, 2, ..., k, the top-level index is the comprehensive cost, and the second-level index is the time cost. and monetary cost The importance of the second-level indicators is compared using the 1-9 scale method (the relative importance scale between indicators can be specified by experts), and the judgment matrix J is obtained. i :

[0082]

[0083] in It is the relative importance value of the bth indicator to the cth indicator under the i-th test method.

[0084] Calculate the weight vector J W for:

[0085] J W =λ max W

[0086] where λ max is the matrix J i The largest characteristic root of max The corresponding feature vector.

[0087] ② After calculating the weight value vector, perform a consistency check on it to verify the rationality of the weight value, so as to obtain the weight vector under the indicator.

[0088]

[0089] Among them, CR is the consistency ratio, CI is the consistency index, q is the number of indicators, RI is the random consistency index, and the value of RI is related to the order of the judgment matrix. The corresponding relationship is shown in Table 1

[0090] Table 1 Correspondence table of evaluation random consistency indicators

[0091] Matrix order RI 1 0 2 0 3 0.58 4 0.9 5 1.12 6 1.24 7 1.32 8 1.41 9 1.45 10 1.49

[0092] When the CR value is smaller, the consistency is better. When the CR value is less than the established value (specified by the expert), the result is valid. When the CR value is greater than the established value, it is necessary to ask the experts again about the relative importance of the indicators, make corresponding corrections to the judgment matrix, and recalculate.

[0093] ③ After passing the consistency test, due to the different dimensions of various cost indicators, we normalized each indicator. The normalized time cost for:

[0094]

[0095] in and Time cost index Theoretically, the maximum and minimum values ​​are determined by experts before calculation.

[0096] Normalized monetary cost for:

[0097]

[0098] in and Cost of Money Index Theoretically, the maximum and minimum values ​​are determined by experts before calculation.

[0099] The time cost value after normalization of each indicator Normalized monetary cost value Multiply and add the weights of each indicator to get the comprehensive cost value C of the i-th test method i :

[0100]

[0101] in, is the time cost weight under the i-th test mode, is the monetary cost weight under the ith trial mode. Go to step 5.

[0102] Step 5. Based on the prediction accuracy and test cost corresponding to the multi-precision joint test design, construct the optimization criteria of the joint test design and the corresponding optimization objective function and constraint space. Generally, they are divided into three categories: the first category is to maximize the information entropy as the objective function and the test cost as the constraint; the second category is to minimize the test cost as the goal and to achieve a certain minimum threshold of prediction accuracy as the constraint; the third category is to use the prediction accuracy and test cost together as the objective function and to maximize the prediction accuracy under the unit test cost as the goal of the unconstrained optimization problem. It serves as the basis for solving the joint test design optimization problem. The specific construction method is as follows:

[0103] 5-1): For the first type, the information entropy maximization is used as the objective function, and the trial cost is used as the constraint. The optimization problem is expressed as

[0104] max E n (n1,...n i ,...,n k )

[0105] The set of non-negative integers

[0106] Where B is the total cost budget.

[0107] 5-2): For the second type, the goal is to minimize the test cost, and the prediction accuracy reaches a certain minimum threshold ε as a constraint. The optimization problem is expressed as

[0108]

[0109] E n (n1,...,n i ,...,n k )≥ε,n i ∈The set of non-negative integers

[0110] 5-3): For the third type, prediction accuracy and test cost are combined as the objective function, and the maximization of prediction accuracy under unit test cost is taken as the goal of the unconstrained optimization problem. The optimization problem is expressed as

[0111] n i ∈The set of non-negative integers

[0112] Go to step 6.

[0113] Step 6. According to the difference between the optimization objective function and constraint space of the joint test design, the corresponding optimization iterative algorithm for solving the optimization problem is given. First, take the initial point of the iteration in the constraint space, construct the proxy objective function according to different algorithms, and optimize the proxy objective function to obtain the iterative value of the sample size. After several steps of iteration, its convergence is judged. Under the condition of its convergence, the obtained solution is used as the output under the initial value, and finally the sample size distribution plan is obtained, and the radar performance multi-precision joint test design plan is obtained according to the maximum entropy design. The specific algorithm for solving the optimization is as follows:

[0114] 6-1): For the joint test design of 2 or less precisions, the grid search method is used to obtain the multi-precision joint test design scheme of radar performance.

[0115] 6-2): For the joint test design of three or more precisions, the simulated annealing method is used to obtain the multi-precision joint test design scheme of radar performance.

Claims

1. A multi-precision joint test design method for radar performance based on a Bayesian framework, characterized in that: Here are the steps: Step 1: According to the composition structure of different types of radar simulation test systems and the simulation test output parameters of each subsystem, data consistency test is performed, and the test results are mapped to the radar performance test credibility under different simulation test modes through conversion, and then the process goes to step 2; Step 2: Based on the prior information of radar performance mechanism, in the absence of clear radar performance mechanism analysis equations, use full digital simulation tests or semi-physical simulation tests to obtain test data and build a low-precision radar performance prediction model f L (X), go to step 3; Step 3: Based on the low-precision radar performance prediction model f L (X) and its credibility, a mapping between hyperparameters and credibility is established through uniform sampling, and a high-precision radar performance prediction model f is calibrated. H The hyperparameters in (X) are used to generalize the low-precision radar performance prediction model to obtain the Bayesian prior model of the high-precision radar performance prediction model. As the basis for solving the optimal joint experimental design, go to step 4; Step 4: Bayesian prior model based on high-precision radar performance prediction model and low-precision radar performance prediction model f L (X), a multi-layer DETMAX algorithm is given to construct a multi-precision maximum entropy design D max , the prediction accuracy corresponding to the experimental design is characterized by information entropy, and the various costs under various experimental methods are calculated. Multiple indicators are converted and normalized into comprehensive cost indicators to characterize the experimental cost corresponding to the experimental design, which serves as the basis for solving the optimal joint experimental design, and then proceed to step 5; Step 5. Based on the prediction accuracy and test cost corresponding to the multi-precision joint test design, the optimization criteria of the joint test design and the corresponding optimization objective function and constraint space are constructed. Generally, they are divided into three categories: the first category is to maximize the information entropy as the objective function and the test cost as the constraint; the second category is to minimize the test cost as the goal and to achieve a certain minimum threshold of prediction accuracy as the constraint; the third category is to use the prediction accuracy and test cost together as the objective function and to maximize the prediction accuracy under the unit test cost as the goal of the unconstrained optimization problem; as the basis for solving the joint test design optimization problem, proceed to step 6; Step 6: According to the difference between the optimization objective function and the constraint space of the joint test design, the corresponding optimization iterative algorithm for solving the optimization problem is given; first, the initial point of the iteration is taken in the constraint space, and the proxy objective function is constructed according to different algorithms, and the iterative value of the sample size is obtained by optimizing the proxy objective function; after several steps of iteration, its convergence is judged; Under the condition of convergence, the obtained solution is used as the output under the initial value, and finally the sample size distribution scheme is obtained, and the multi-precision joint test design scheme of radar performance is obtained according to the maximum entropy design.

2. The radar performance multi-precision joint test design method based on the Bayesian framework according to claim 1 is characterized in that: Step 1 is as follows: Step 1-1: According to the composition structure of different types of radar simulation test systems, a radar simulation test system credibility evaluation index system consisting of each subsystem and its related testable simulation test output parameters is established. Based on the verification theory, the evaluation level of each subsystem is decomposed and divided, and the credibility evaluation level and related index items of each model module are established and standardized to form a complete and clear credibility evaluation index system. Step 1-2: According to the properties of the subsystem simulation test output parameters, they are divided into static randomness, static determinism, dynamic periodicity, and dynamic non-periodic data. The data consistency test is performed through precision calculation, hypothesis testing method, time domain analysis method, and frequency domain analysis method to form the test results. Through mapping normalization, the credibility value of the i1th subsystem is obtained. Step 1-3: Based on the expert scoring method or the hierarchical analysis method, the weight of the credibility index of the i1th subsystem aggregated to the entire radar simulation test system is obtained as m1 is the total number of subsystems in the radar simulation test system. The total credibility p of the radar simulation test system is calculated. T for:

3. The radar performance multi-precision joint test design method based on the Bayesian framework according to claim 2 is characterized in that: The specific construction method of step 2 is as follows: Step 2-1: For radar performance with clear mechanism equations, the relationship between radar performance and test conditions is called a mechanism model, which is expressed as a variety of function types: Among them, y0 is the radar performance index, f0(X) is the radar performance mechanism model, and X is the test condition value set. Set the value for the k2th test condition, is the basis spline function, is the coefficient of the basis function, and m2 is the number of different basis splines. Through the radar performance mechanism model f0(X), a low-precision radar performance prediction model f is constructed. L (X) in, is the coefficient of the basis function in the low-precision radar performance prediction model, N is the symbol of the normal distribution, σ is the undetermined hyperparameter, and σ is calibrated by the test data obtained through low-precision test methods (full digital simulation test, semi-physical simulation test) to achieve f L (X) Model construction. Step 2-2: In the case of no clear radar performance mechanism equation, use full digital simulation test and semi-physical simulation test to obtain test data, and use Gaussian process to predict the low-precision radar performance model f according to the test data. L (X) Perform statistical modeling.

4. The radar performance multi-precision joint test design method based on the Bayesian framework according to claim 3 is characterized in that: The specific method of step 3 is as follows: Step 3-1: Use the Gaussian process model to predict the high-precision radar performance model f H (X) and the low-precision radar performance prediction model f L The deviation δ(X) between (X) is modeled as: δ(X)=f H (X)-f L (X) Its prior distribution is Where GP is the Gaussian process symbol, σ 2 is the variance, R is the given covariance function, θ is the unknown hyperparameter in the covariance function of the Gaussian process, where θ>0 controls the decay speed of the correlation, X∈[0,1] d Represents normalizing the test condition value set X to the multidimensional test sample space [0,1] d , d is the dimension of the test sample space, then f H (X)=f L (X)+δ(X) f H (X)~GP(f L (X),σ 2 ,R(θ)) Among them, X i , X j are two vectors representing the test samples in the test sample space, ||X i -X j || is the modulus length after subtracting the two vectors; Step 3-2: Use uniform sampling method to predict the high-precision radar performance model f H (X) and low-precision radar performance prediction model f L (X) The corresponding experimental sample space is discretized to obtain uniform sampling points D3 = {x1, x2, ..., x a }, evenly select points within the range of θ For each sampling point θ j , j = 1, 2, ..., k3, from the high-precision radar performance prediction model f H (X) generates the corresponding virtual sample, that is, high-precision prediction data And the samples calculated by the existing low-precision model, that is, the low-precision prediction data Step 3-3: Take θ as the hyperparameter j When, based on the sampling point D3 = {x1, x2, ..., x a }Corresponding high-precision prediction data and low-precision prediction data Calculate the prediction accuracy A of the low-precision radar performance prediction model j : The obtained accuracy A j Can be used as a credibility indicator; A j The closer it is to 1, the higher the credibility; A j The closer it is to 0, the lower the credibility. j is the hyperparameter θ j When calculated, for multiple θ j , j=1,2,...,k3, the corresponding According to the data Polynomial interpolation is applied to obtain the mapping relationship between prediction accuracy and hyperparameter θ; the prediction accuracy is characterized as a representation of credibility, so the mapping relationship between hyperparameter θ and credibility p is obtained as θ = θ(p), and the estimated (calibrated) value θ of hyperparameter θ is obtained from the credibility value p B , substitute this value back into f H (X), and obtain the radar performance prediction model f H (X) Prior model under the Bayesian framework, that is, a high-precision Bayesian prior model Go to step 4.

5. The radar performance multi-precision joint test design method based on the Bayesian framework according to claim 4 is characterized in that: The specific characterization method of step 4 is as follows: Step 4-1: Set π ξ (·) is the prior distribution of ξ, ξ is the parameter to be estimated in the radar performance prediction model; observe the a4 input points D4 in the experimental design D4 = {x1, x2, ..., x a4 } response; use π ξ|D (·) represents the posterior distribution of ξ given the observations collected using design D4; the amount of information I about ξ contained in the prior before the experiment is I=∫π ξ (x) * )ln(π ξ (x) * ))dξ * Among them, ξ * represents the independent variable to be integrated; After the experiment is conducted using experimental design D4, the amount of information about ξ I D for I D =∫π ξ|D (x) * )ln(π ξ|D (x) * ))dξ * In the Gaussian process model, the part of the observation related to the design at each input point is ln(det(σ 2 R)) / 2, where det(σ 2 R) represents the variance σ of the corresponding observation vector y 2 The determinant of R, σ 2 The variance is the observed value y j , j = 1, 2, ..., a4, R is an n × n correlation matrix; therefore, the maximum entropy design D max Maximize the determinant of the covariance matrix of the corresponding vector y corresponding to each point in the design; the maximum entropy criterion is expressed as Due to σ 2 Regardless of design D4, the above formula can be equivalent to In which, it is assumed that the relevant parameters ξ in R are known; By extending the DETMAX algorithm to multi-precision experiments, we can obtain a multi-layer DETMAX algorithm. Assume that there are k types of precision experiments in the experiment. If the optimization of the i-1th, i=1, 2, ..., kth layers has been completed, then the i-1th layer is fixed, points are added randomly, and the i-th layer is optimized using the DETMAX algorithm. The information entropy of the k-precision maximum entropy design is expressed as Among them, E n represents the maximum information entropy, d is the dimension of the test space, n i is the number of design points in the i-th layer; For the multi-precision joint test design D=(D1,D2,...,D k ), the experimental design of the ith experimental method is expressed as D i , i = 1, 2, ..., k, according to the multiple test methods required to participate in the multi-precision radar performance joint test, the maximum information entropy of the i-th test method is calculated respectively The experimental design D of the i-th experimental mode in the multi-precision joint experimental design D i The mapping relationship between them is Since the experimental sample size n under the i-th experimental method i After being determined, its maximum entropy design is also clear, and the corresponding maximum information entropy is also clear, so the mapping relationship is expressed as For the joint test of multi-precision radar performance, the prediction accuracy E n The experimental sample size allocation scheme (n1,...n i ,...,n k ) is the mapping relationship between Step 4-2: For the test cost, consider the monetary cost, time cost and labor cost comprehensively, and use the hierarchical analysis method to integrate multiple types of costs: ① The evaluation index system is layered using the hierarchical analysis method; for the i-th test method, i = 1, 2, ..., k, the top-level index is the comprehensive cost, and the second-level index is the time cost and monetary cost The importance of the second-level indicators is compared using the 1-9 scale method, and the judgment matrix J is obtained. i : in is the relative importance value of the bth indicator to the cth indicator under the i-th test method; Calculate the weight vector J W for: J W =λ max W where λ max is the matrix J i The largest characteristic root of max The corresponding eigenvector; ② After calculating the weight value vector, perform a consistency check on it to verify the rationality of the weight value, thereby obtaining the weight vector under the indicator; Among them, CR is the consistency ratio, CI is the consistency index, q is the number of indicators, and RI is the random consistency index; ③ After passing the consistency test, due to the different dimensions of various cost indicators, each indicator is normalized. The normalized time cost for: in and Time cost index Theoretical maximum and minimum values; Normalized monetary cost for: in and Cost of Money Index Theoretical maximum and minimum values; The time cost value after normalization of each indicator Normalized monetary cost value Multiply and add the weights of each indicator to get the comprehensive cost value C of the i-th test method i : in, is the time cost weight under the i-th test mode, is the monetary cost weight under the i-th experimental method.

6. The radar performance multi-precision joint test design method based on the Bayesian framework according to claim 5 is characterized in that: Step 5: The specific construction method is as follows: 5-1): For the first type, the information entropy maximization is used as the objective function, the trial cost is used as the constraint, and the optimization problem is expressed as max E n (n1,...n i ,...,n k ) Where B is the total cost budget; 5-2): For the second type, the goal is to minimize the test cost, and the prediction accuracy reaches a certain minimum threshold ε as a constraint. The optimization problem is expressed as: oeLh n (n1,...,n i ,...,n k )≥ε,n i ∈The set of non-negative integers 5-3): For the third type, prediction accuracy and test cost are combined as the objective function, and the maximization of prediction accuracy under unit test cost is taken as the goal of the unconstrained optimization problem. The optimization problem is expressed as:

7. The radar performance multi-precision joint test design method based on the Bayesian framework according to claim 6 is characterized in that: Step 6: The specific optimization algorithm is as follows: 6-1): For joint test designs with 2 or less precisions, a grid search method is used to obtain a multi-precision joint test design scheme for radar performance; 6-2): For the joint test design of three or more precisions, the simulated annealing method is used to obtain the multi-precision joint test design scheme of radar performance.

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