Bayesian framework based radar performance multi-precision joint test design method

Abstract

The application discloses a radar performance multi-precision joint test design method based on a Bayesian framework, which can effectively solve the problem that a traditional test design method cannot cope with joint design of multiple precision test methods. Firstly, based on a low-precision model and its reliability, the low-precision model is generalized, hyperparameters in a high-precision model are calibrated through the reliability, and a high-precision Bayesian prior model is obtained; secondly, based on the high-precision Bayesian prior model, a prediction accuracy function and a cost function are given through a multi-layer DETMAX algorithm and an analytic hierarchy process; then, based on the prediction accuracy function and the cost function, a target function and constraint conditions are given according to a sample size allocation criterion; finally, a multi-precision joint test sample size allocation scheme is obtained through an optimization iterative algorithm. The application is different from a traditional test design method which solves test design under a certain test precision in isolation, and can effectively solve the problem of joint test design of multiple precision radar test methods.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of test design, and particularly relates to a radar performance multi-precision joint test design method based on a Bayesian framework. BACKGROUND

[0002] The radar performance multi-precision joint test design refers to jointly using an in-field full-digital test, an in-field semi-physical test, an out-field test and the like, according to cost limitations and precision information under different test methods of different test samples, based on a certain distribution criterion, comprehensively designing test sample quantities and test sample condition settings under various types of tests to cover all test sample condition sets capable of completing the inspection or test of a certain performance of the radar.

[0003] High-value radar test equipment makes the test cost increase exponentially, and in order to reduce the consumption of the test, a commonly used method is to reduce the sample quantity of the test. However, the traditional test and identification mode based on classical statistics mostly uses the out-field test method, still needs a large number of test samples, and the consumption is very high. Therefore, how to use the Bayesian theory, successful technologies in other fields, create a scientific and reasonable, advanced and practical in-out field joint test design method, determine reasonable test points, realize optimal design of simulation + field test, and improve test efficiency is a primary key technical problem to be solved. SUMMARY

[0004] The application provides a radar performance multi-precision joint test design method based on a Bayesian framework, which can effectively solve the problem that the traditional test design method cannot cope with the joint design of multiple precision test methods.

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

[0006] Step 1: According to the structure of different types of radar simulation test systems, data consistency is tested according to the simulation test output parameters of each subsystem, and the test results are mapped into the radar performance test reliability under different simulation test methods through conversion, and step 2 is entered.

[0007] Step 2: Based on the mechanism prior information of the radar performance, under different conditions with or without explicit radar performance mechanism analysis equation, the test data obtained by using the low-precision test method (full-digital simulation test, semi-physical simulation test) are used to construct a low-precision radar performance prediction model f L (X), and step 3 is entered.

[0008] Step 3: Based on the low-precision radar performance prediction model and its reliability, a mapping between the hyperparameters and the reliability is established through uniform sampling, and a 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 a basis for solving the optimal joint experimental design, proceed 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) presents a multi-level DETMAX algorithm for constructing multi-precision maximum entropy design D. max The prediction accuracy corresponding to the experimental design is characterized by information entropy. Various costs under multiple experimental methods are calculated and multi-indicator conversion and normalization are transformed into a comprehensive cost index to characterize the experimental cost corresponding to the experimental design. This serves as the basis for solving the optimal joint experimental design. Proceed to step 5.

[0010] Step 5: Based on the prediction accuracy and experimental cost corresponding to the multi-precision joint experimental design, construct the optimization criteria, corresponding objective function, and constraint space for the joint experimental design. These are generally divided into three categories: The first category uses maximizing information entropy as the objective function and experimental cost as the constraint; the second category uses minimizing experimental cost as the objective and achieving a certain minimum threshold for prediction accuracy as the constraint; the third category combines prediction accuracy and experimental cost as the objective function, aiming to maximize prediction accuracy per unit experimental cost as the objective of the unconstrained optimization problem. This forms the basis for solving the joint experimental design optimization problem, leading to Step 6.

[0011] Step 6: Based on the differences in the objective function and constraint space of the joint experimental design, a corresponding optimization iterative algorithm for solving the optimization problem is given. First, an initial point for iteration is chosen in the constraint space. A surrogate objective function is constructed according to different algorithms, and the iterative value of the sample size is obtained by optimizing this surrogate objective function. Through several iterations, its convergence is determined. Under the condition of convergence, the obtained solution is used as the output under the initial value, and finally, the sample size allocation scheme is obtained. Based on the maximum entropy design, a multi-precision joint experimental design scheme for radar performance is obtained.

[0012] Compared with the prior art, the significant advantages of this invention are:

[0013] (1) This invention is used for radar performance testing and evaluation. It is the first to propose a scientific method and complete process for multi-precision joint test design of radar performance under multiple test modes based on test credibility. The above technical solution can solve the problem that the existing test design methods are limited to the reduction of test samples under a single test mode. It can realize the application of test design to multi-precision joint tests and solve the problems of lack of quantitative differences in multi-precision test modes, lack of optimization targets 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 reliability results of different test methods, this invention takes into account the joint relationship between various equipment systems and the randomness of performance, and can adapt to the test design of different types of radar performance in different scenarios.

[0015] (3) This invention is the first to realize the use of prior information on radar performance mechanisms of different forms and different degrees of completeness for multi-precision test design. It is also the first to realize the generalization of low-precision prediction model to high-precision prediction model 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, for the first time, characterizes the prediction accuracy and experimental accuracy corresponding to multi-precision joint design through experimental design and prediction models of various accuracies before the experiment.

[0017] Verification costs.

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

[0019] (6) This invention provides for the first time an optimized solution method for multi-precision joint test design of radar performance. Attached Figure Description

[0020] Figure 1 This is a flowchart of the multi-precision joint test design method for radar performance based on a Bayesian framework, as described in this invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

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

[0023] The technical solutions of the various embodiments of the present invention can be combined with each other, but only if they can be implemented by those skilled in the art. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

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

[0025] Combination Figure 1 The present invention discloses a multi-precision joint experimental design method for radar performance based on a Bayesian framework, the specific steps of which are as follows:

[0026] Step 1: Based on the composition structure of different types of radar simulation test systems, and according to the simulation test output parameters of each subsystem, perform data consistency verification. Then, map the verification results to the radar performance test credibility under different simulation test methods through conversion. The specific method is as follows:

[0027] Step 1-1: For different types of radar simulation test system composition structures, establish a radar simulation test system credibility evaluation index system consisting of each subsystem and its related testable simulation test output parameters. Based on the verification theory, decompose and divide the evaluation level of each subsystem, establish and standardize the credibility evaluation level and related index items of each model module, and form a complete and clear credibility evaluation index system.

[0028] Steps 1-2: Based on the properties of the simulation test output parameters of the subsystems, the data are categorized into static randomness, static determinism, dynamic periodicity, and dynamic aperiodicity. Data consistency is verified using precision calculation, hypothesis testing, time-domain analysis, and frequency-domain analysis to generate verification results. Through mapping normalization, the reliability value of the i1th subsystem is obtained.

[0029] Steps 1-3: Based on expert scoring or analytic hierarchy process (AHP), obtain the credibility index weight of the i1th subsystem aggregated into the entire radar simulation test system. i1 = 1, 2, ..., m1, where m1 is the total number of subsystems in the radar simulation test system. Calculate the overall reliability p of the radar simulation test system. T (That is, the reliability of this testing method) is:

[0030]

[0031] Proceed to step 2.

[0032] Step 2: Based on prior information about the radar performance mechanism, and under different conditions such as the presence or absence of explicit analytical equations for radar performance mechanisms, a low-precision radar performance prediction model f is constructed using experimental data obtained through low-precision experimental methods (fully digital simulation experiments and hardware-in-the-loop simulation experiments). L (X), the specific construction method is as follows:

[0033] Step 2-1: For radar performance with a clearly defined mechanism equation, the relationship between radar performance and experimental conditions is called a mechanism model, which can usually be expressed as a multi-strand function type:

[0034]

[0035] Where y0 is the radar performance index, f0(X) is the radar performance mechanism model, and X is the set of experimental condition values. Set a value for the k2th test condition. For basis spline functions, Let f be the coefficient of the basis function, and m2 be the number of different basis splines. A low-precision radar performance prediction model f is constructed using the radar performance mechanism model f0(X). L (X)

[0036]

[0037] in, In the low-precision radar performance prediction model, σ represents the coefficients of the basis function, N is the sign of the normal distribution, and σ is the undetermined hyperparameter. σ is calibrated using experimental data obtained through low-precision experimental methods (fully digital simulation experiments and hardware-in-the-loop simulation experiments) to achieve f L Model construction of (X).

[0038] Step 2-2: For cases where there is no clear radar performance mechanism equation, test data obtained using low-precision testing methods such as fully digital simulation experiments and semi-physical simulation experiments are used to predict the low-precision radar performance model f using a 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 reliability, establish the mapping between hyperparameters and reliability through uniform sampling, and 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 a basis for solving the optimal joint experimental design, the specific method is as follows:

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

[0041] δ(X)=f H (X)-f L (X)

[0042] Its prior distribution is taken as

[0043]

[0044] Where GP is the symbol for a Gaussian process, σ 2 Let X be the variance, R be a given covariance function, and θ be an undetermined hyperparameter in the covariance function of the Gaussian process, where θ > 0 controls the decay rate of the correlation, and X ∈ [0,1]. d This represents normalizing the set of experimental condition values ​​X to a multidimensional experimental sample space [0,1]. d Let d be the dimension of the experimental 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 Let each be a vector representing a test sample within the test sample space.

[0049] ||X i -X j || represents the magnitude of the vector difference between the two vectors.

[0050] Step 3-2: Using a uniform sampling method, the high-precision radar performance prediction model f H (X) and low-precision radar performance prediction model f L (X) The experimental sample space corresponding to the sample is discretized to obtain uniform sampling points D3={x1,x2,...,x a Points are selected uniformly within the range of values ​​for θ. For each sampling point θj , j = 1, 2, ..., k3, from the high-precision radar performance prediction model f H (X) generates corresponding virtual samples, i.e., high-precision prediction data. And the samples calculated using existing low-precision models, i.e., low-precision prediction data.

[0051]

[0052] Step 3-3: When taking the hyperparameter θ j At that time, based on sampling points 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 precision A j It can be used as a credibility indicator. A j The closer to 1, the higher the credibility; A j The closer to 0, the lower the credibility. This credibility level A j When taking the hyperparameter θ j Calculated over time for multiple θ j For j = 1, 2, ..., k3, the corresponding values ​​can be calculated. According to the data Polynomial interpolation is used to obtain the mapping relationship between prediction accuracy and hyperparameter θ. Prediction accuracy is characterized as a representation of confidence level, thus obtaining the mapping relationship between hyperparameter θ and confidence level p: θ = θ(p). Therefore, the estimated (calibrated) value θ of hyperparameter θ is obtained from the confidence level value p. B Substitute this value back into f H (X), thus obtaining the radar performance prediction model f H (X) The prior model within the Bayesian framework, i.e., a high-precision Bayesian prior model. Proceed 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) presents a multi-level DETMAX algorithm for constructing multi-precision maximum entropy design D. maxInformation entropy is used to characterize the prediction accuracy corresponding to the experimental design. By calculating various costs under multiple experimental methods and converting and normalizing multiple indicators into a comprehensive cost index, the experimental cost corresponding to the experimental design is characterized. This serves as the basis for solving the optimal joint experimental design. The specific characterization method is as follows:

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

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

[0058] Where, ξ * Let represent the independent variable to be integrated.

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

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

[0061] Therefore I D -I represents the change in information, and information content is the negative value of entropy. The design that maximizes the entropy of the observed response at each design point maximizes the expected change in information content; this design is called the maximum entropy design. For joint tests of multi-precision radar performance, a multi-layer DETMAX algorithm is used to construct the maximum entropy design for the joint test.

[0062] In the Gaussian process model, the observation- and design-related parts at each input point are 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 Let the variance of a₁, j = 1, 2, ..., a₄ be given, and R be an n × n correlation matrix. Therefore, the maximum entropy design D... max The goal is to maximize the determinant of the covariance matrix of the corresponding vector y at each point in the design. The maximum entropy criterion is expressed as...

[0063]

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

[0065]

[0066] Here, it is assumed that the relevant parameter ξ in R is known.

[0067] Maximum entropy design can be generated using the DETMAX algorithm. This algorithm optimizes the design through a series of "offsets." The basic process is as follows: First, an initial design with n4 points is randomly generated. Then, appropriate points are added to or removed from the current design to improve the det(R) of the new design. This process continues until the det(R) of the design formed by the resulting n4 points can no longer increase. For the existing design D4, the optimal addition point x... j To make the variance function σ 2 (x j The point with the largest value can be optimized using a random search algorithm. The point to be deleted is the inverse matrix R of R. -1 The points associated with the largest diagonal element. If det(R) of a single "offset" does not improve the design, all designs generated during this "offset" are added to the "failed design set" F; if det(R) improves the design, F is cleared, and the design starts from the current optimal design D. best Start optimizing.

[0068] If D4 is any current design during this "offset" process, the rule for continuing this "offset" is as follows:

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

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

[0071] Extending the DETMAX algorithm to multi-precision experiments yields a multi-layer DETMAX algorithm. Assume there are k types of experiments with varying precision. If optimization of the (i-1)th, i = 1, 2, ..., kth layers has been completed, then the (i-1)th layer is fixed, points are randomly added, and the DETMAX algorithm is used to optimize the i-th layer. The information entropy of this k-precision maximum entropy design is expressed as...

[0072]

[0073] Among them, E n Let d represent the maximum information entropy, d be the dimension of the test space, and n be the number of elements. iLet be the number of design points in the i-th layer.

[0074] For a multi-precision joint experimental design, D = (D1, D2, ..., D... k In the diagram, the experimental design for the i-th experimental method is represented as D. i Let i = 1, 2, ..., k. Based on the various test methods required for participating in the multi-precision radar performance joint test, the maximum information entropy of the i-th test method is calculated for each method. (Characterizing prediction accuracy) and the i-th experimental design in multi-precision joint experimental design D i The mapping relationship between them is

[0075]

[0076] Because the sample size n under the i-th test method i Once determined, its maximum entropy design is also clear, and the corresponding maximum information entropy is also clear. Therefore, this mapping relationship can be expressed as follows:

[0077]

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

[0079]

[0080] Step 4-2: Regarding the cost of the experiment, considering monetary cost, time cost, and labor cost, the analytic hierarchy process (AHP) is used to synthesize the various cost categories:

[0081] ① The evaluation index system is divided into layers using the analytic hierarchy process (AHP). For the i-th experimental method (i = 1, 2, ..., k), the top-level index is the comprehensive cost, and the second-level index is the time cost. and monetary costs 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), resulting in the judgment matrix J. i :

[0082]

[0083] in Let be the relative importance value of the b-th indicator to the c-th 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 For matrix J i The largest eigenvalue, W, is λ. max The corresponding eigenvector.

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

[0088]

[0089] Where CR is the consistency ratio, CI is the consistency index, q is the number of indices, and RI is the random consistency index. The value of RI is related to the order of the judgment matrix, and the correspondence is shown in Table 1.

[0090] Table 1. Correspondence Table for Evaluation Indicators of Random Consistency

[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] The smaller the CR (Consistency Ratio), the better the consistency. When the CR value is less than a predetermined value (specified by experts), it indicates that the results are valid. When the CR value is greater than the predetermined value, it is necessary to consult experts again about the relative importance of the indicators, adjust the judgment matrix accordingly, and recalculate.

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

[0094]

[0095] in and These are time cost metrics The theoretical maximum and minimum values ​​are determined by experts before calculation.

[0096] Normalized monetary cost for:

[0097]

[0098] in and These are monetary cost indicators The theoretical maximum and minimum values ​​are determined by experts before calculation.

[0099] Time cost value after normalization of each indicator Normalized monetary cost The overall cost C of the i-th test method is obtained by multiplying and summing the weights of each indicator. i :

[0100]

[0101] in, Let the time cost weight be the i-th test method. Let be the monetary cost weight for the i-th trial method. Proceed to step 5.

[0102] Step 5: Based on the prediction accuracy and experimental cost corresponding to the multi-precision joint experimental design, construct the optimization criteria, corresponding objective function, and constraint space for the joint experimental design. These are generally divided into three categories: The first category uses maximizing information entropy as the objective function and experimental cost as the constraint; the second category uses minimizing experimental cost as the objective and achieving a certain minimum threshold for prediction accuracy as the constraint; the third category combines prediction accuracy and experimental cost as the objective function, maximizing prediction accuracy per unit experimental cost as the objective of the unconstrained optimization problem. This forms the basis for solving the joint experimental design optimization problem. The specific construction method is as follows:

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

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

[0105] set of nonnegative integers

[0106] Where B represents the total cost budget.

[0107] 5-2): For the second approach, minimizing the experimental cost is the objective, while achieving a certain minimum threshold ε for prediction accuracy is the constraint. The optimization problem is expressed as follows:

[0108]

[0109] stE n (n1,...,n i ,...,n k )≥ε,n i ∈ set of nonnegative integers

[0110] 5-3): For the third approach, the prediction accuracy and experimental cost are combined as the objective function, with maximizing the prediction accuracy per unit experimental cost as the objective of the unconstrained optimization problem. The optimization problem is expressed as:

[0111] n i ∈ set of nonnegative integers

[0112] Proceed to step 6.

[0113] Step 6: Based on the differences in the objective function and constraint space of the joint experimental design, corresponding optimization iterative algorithms for solving the optimization problem are given. First, an initial point for iteration is chosen in the constraint space. A surrogate objective function is constructed according to different algorithms, and the iterative value of the sample size is obtained by optimizing this surrogate objective function. After several iterations, its convergence is determined. Under the condition of convergence, the obtained solution is used as the output under the initial value, finally obtaining the sample size allocation scheme. Based on the maximum entropy design, a multi-precision joint experimental design scheme for radar performance is obtained. The specific optimization algorithm is as follows:

[0114] 6-1): For joint test designs with two or fewer levels of precision, a grid search method is used to obtain a multi-precision joint test design scheme for radar performance.

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

Claims

1. A multi-precision joint experimental design method for radar performance based on a Bayesian framework, characterized in that, The steps are as follows: Step 1: Based on the composition structure of different types of radar simulation test systems, and according to the simulation test output parameters of each subsystem, perform data consistency verification. Through conversion, map the verification results to the radar performance test credibility under different simulation test methods, and proceed to Step 2. Step 2: Based on prior information about the radar performance mechanism, and in cases where there are or are not explicit analytical equations for the radar performance mechanism, use fully digital simulation experiments or hardware-in-the-loop simulation experiments to obtain experimental data and construct a low-precision radar performance prediction model f. L (X), proceed to step 3; Step 3: Based on the low-precision radar performance prediction model f L (X) and its credibility, establishing a mapping between hyperparameters and credibility through uniform sampling, and calibrating 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 this serves as the basis for solving the optimal joint experimental design, proceed 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) presents a multi-level DETMAX algorithm for constructing multi-precision maximum entropy design D. max Information entropy is used to characterize the prediction accuracy corresponding to the experimental design. Various costs under multiple experimental methods are calculated and multiple indicators are converted and normalized into a comprehensive cost index to characterize the experimental cost corresponding to the experimental design. This serves as the basis for solving the optimal joint experimental design. Proceed to step 5. Step 5: Based on the prediction accuracy and experimental cost corresponding to the multi-precision joint experimental design, construct the optimization criteria and corresponding objective function and constraint space for the joint experimental design. These are generally divided into three categories: The first category uses maximizing information entropy as the objective function and experimental cost as the constraint; the second category uses minimizing experimental cost as the objective and achieving a certain minimum threshold for prediction accuracy as the constraint; the third category combines prediction accuracy and experimental cost as the objective function, maximizing prediction accuracy per unit experimental cost as the objective of the unconstrained optimization problem. This forms the basis for solving the joint experimental design optimization problem, and proceeds to Step 6. Step 6: Based on the differences in the objective function and constraint space of the joint experimental design, provide the corresponding optimization iterative algorithm for solving the optimization problem; first, take the initial point of iteration in the constraint space, construct a surrogate objective function according to different algorithms, optimize the surrogate objective function to obtain the iterative value of the sample size; through several iterations, determine its convergence; Under the condition of convergence, the obtained solution is used as the output at the initial point, and finally the sample allocation scheme is obtained. Based on the maximum entropy design, the multi-precision joint test design scheme of radar performance is obtained.

2. The method for multi-precision joint experimental design of radar performance based on a Bayesian framework as described in claim 1, characterized in that, Step 1 is as follows: Step 1-1: For different types of radar simulation test system composition structures, establish a radar simulation test system credibility evaluation index system consisting of each subsystem and its related testable simulation test output parameters. Based on the verification theory, decompose and divide the evaluation level of each subsystem, establish and standardize the credibility evaluation level and related index items of each model module, and form a complete and clear credibility evaluation index system. Steps 1-2: Based on the properties of the simulation test output parameters of the subsystems, the data are categorized into static randomness, static determinism, dynamic periodicity, and dynamic aperiodicity. Data consistency is verified using precision calculation, hypothesis testing, time-domain analysis, and frequency-domain analysis to generate verification results. Through mapping normalization, the reliability value of the i1th subsystem is obtained. Steps 1-3: Based on expert scoring or analytic hierarchy process (AHP), obtain the credibility index weight of the i1th subsystem aggregated into the entire radar simulation test system. m1 represents the total number of subsystems in the radar simulation test system. The overall reliability p of the radar simulation test system is calculated. T for:

3. The method for multi-precision joint experimental design of radar performance based on a Bayesian framework according to claim 2, characterized in that, The specific construction method for step 2 is as follows: Step 2-1: For radar performance with a clearly defined mechanism equation, the relationship between radar performance and experimental conditions is called a mechanism model, which is represented by a variety of bar function types: Where y0 is the radar performance index, f0(X) is the radar performance mechanism model, and X is the set of experimental condition values. Set a value for the k2th test condition. For basis spline functions, Let f be the coefficient of the basis function, and m2 be the number of different basis splines; a low-precision radar performance prediction model f is constructed using the radar performance mechanism model f0(X). L (X) in, In the low-precision radar performance prediction model, σ represents the coefficients of the basis functions, N is the sign of the normal distribution, and σ is an undetermined hyperparameter. σ is calibrated using experimental data obtained through low-precision experiments to achieve f. L Model construction of (X); Step 2-2: In the absence of a clear radar performance mechanism equation, experimental data is obtained through fully digital simulation experiments and semi-physical simulation experiments. Based on the experimental data, the low-precision radar performance prediction model f is then performed using a Gaussian process. L (X) Perform statistical modeling.

4. The method for multi-precision joint experimental design of radar performance based on a Bayesian framework according to claim 3, characterized in that, The specific method for step 3 is as follows: Step 3-1: Develop a high-precision radar performance prediction model f using a Gaussian process model. H (X) and low-precision radar performance prediction model f L Modeling the deviation δ(X) between (X): δ(X)=f H (X)-f L (X) Its prior distribution is taken as Where GP is the symbol for a Gaussian process, σ 2 Let X be the variance, R be a given covariance function, and θ be an undetermined hyperparameter in the covariance function of the Gaussian process, where θ > 0 controls the decay rate of the correlation, and X ∈ [0,1]. d This represents normalizing the set of experimental condition values ​​X to a multidimensional experimental sample space [0,1]. d Let d be the dimension of the experimental 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 Let |X| be two vectors representing the test samples that belong to the test sample space. i -X j || represents the magnitude of the vector difference between the two vectors; Step 3-2: Using a uniform sampling method, the high-precision radar performance prediction model f H (X) and low-precision radar performance prediction model f L (X) The experimental sample space corresponding to the sample is discretized to obtain uniform sampling points D3={x1,x2,...,x a Points are selected uniformly within the range of values ​​for θ. For each sampling point θ j , j = 1, 2, ..., k3, from the high-precision radar performance prediction model f H (X) generates corresponding virtual samples, i.e., high-precision prediction data. And the samples calculated using existing low-precision models, i.e., low-precision prediction data. Step 3-3: When taking the hyperparameter θ j At that time, based on sampling points 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 precision A j It can be used as a credibility indicator; A j The closer to 1, the higher the credibility; A j The closer the value is to 0, the lower the credibility; this credibility A j When taking the hyperparameter θ j Calculated over time for multiple θ j For j = 1, 2, ..., k3, the corresponding values ​​can be calculated. According to the data Polynomial interpolation is used to obtain the mapping relationship between prediction accuracy and hyperparameter θ; prediction accuracy is characterized as a representation of confidence, thus obtaining the mapping relationship between hyperparameter θ and confidence p: θ = θ(p). Therefore, the estimated value θ of hyperparameter θ is obtained from the confidence value p. B Substitute this value back into f H (X), thus obtaining the radar performance prediction model f H (X) The prior model within the Bayesian framework, i.e., a high-precision Bayesian prior model. Proceed to step 4.

5. The method for multi-precision joint experimental design of radar performance based on a Bayesian framework according to claim 4, characterized in that, The specific depiction method for step 4 is as follows: Step 4-1: Let π ξ (·) represents the prior distribution of ξ, where ξ is the parameter to be estimated in the radar performance prediction model; observe the a4 input points in experimental design D4. The response; using 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 a priori is... I=∫π ξ (x) * )ln(π ξ (x) * ))dξ * Where, ξ * Represents the independent variable to be integrated; After conducting the experiment using experimental design D4, the amount of information I about ξ is... D for I D =∫π ξ|D (x) * )ln(π ξ|D (x) * ))dξ * In the Gaussian process model, the observation- and design-related parts at each input point are 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 The variance of a₁, j = 1, 2, ..., a₄ is given, 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 at each point in the design; the maximum entropy criterion is expressed as... Due to σ 2 Regardless of design D4, the above equation can be equivalent to: Here, it is assumed that the relevant parameter ξ in R is known; Extending the DETMAX algorithm to multi-precision experiments yields a multi-layer DETMAX algorithm. Assuming there are k types of experiments with varying precision, if optimization of the (i-1)th, i = 1, 2, ..., kth layers has been completed, then the (i-1)th layer is fixed, points are randomly added, and the DETMAX algorithm is used to optimize the i-th layer. The information entropy of this k-precision maximum entropy design is expressed as... Among them, E n Let d represent the maximum information entropy, d be the dimension of the test space, and n be the number of elements. i Let i be the number of design points in the i-th layer; For a multi-precision joint experimental design, D = (D1, D2, ..., D... k In the diagram, the experimental design for the i-th experimental method is represented as D. i Let i = 1, 2, ..., k. Based on the various test methods required for participating in the multi-precision radar performance joint test, the maximum information entropy of the i-th test method is calculated for each method. Experimental design D of the i-th experimental method in multi-precision joint experimental design D i The mapping relationship between them is Because the sample size n under the i-th test method i Once determined, its maximum entropy design is also clear, and the corresponding maximum information entropy is also clear. Therefore, this mapping relationship is expressed as follows: For the joint performance test of multi-precision radar, its prediction accuracy E n With the experimental sample size allocation scheme (n1,...n) i ,...,n k The mapping relationship between ) is Step 4-2: Regarding the cost of the experiment, considering monetary cost, time cost, and labor cost, the analytic hierarchy process (AHP) is used to synthesize the various cost categories: ① The evaluation index system is divided into layers using the analytic hierarchy process (AHP); for the i-th experimental method, i = 1, 2, ..., k, the top-level index is the comprehensive cost, and the second-level index is the time cost. and monetary costs The importance of the second-level indicators was compared using the 1-9 scaling method, resulting in the judgment matrix J. i : in Let be the relative importance value of the b-th indicator to the c-th indicator under the i-th test method; Calculate the weight vector J W for: J W =λ max W Where λ max For matrix J i The largest eigenvalue, W, is λ. max The corresponding feature vector; ② After calculating the weight value vector, perform a consistency check on it to verify the rationality of the weight values, thereby obtaining the weight vector under the indicator; Where CR is the consistency ratio, CI is the consistency index, q is the number of indices, and RI is the random consistency index; ③ After passing the consistency check, due to the different dimensions among various cost indicators, each indicator is normalized. The normalized time cost is... for: in and These are time cost metrics Theoretically, the maximum and minimum values; Normalized monetary cost for: in and These are monetary cost indicators Theoretically, the maximum and minimum values; Time cost value after normalization of each indicator Normalized monetary cost The overall cost C of the i-th test method is obtained by multiplying and summing the weights of each indicator. i : in, Let the time cost weight be the i-th test method. Let be the monetary cost weight for the i-th test method.

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

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

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