Global sensitivity index optimization method, device and equipment for radar anti-interference

Abstract

The present invention relates to a global sensitivity index optimization method, device, and equipment for radar anti-interference. The method comprises: obtaining simulation sample data under a radar anti-interference test, constructing a proxy model between factors and response results based on the simulation sample data; constructing a high-order Shapley model of the relationship between the response results and each factor based on the proxy model; setting linear attribution conditions for the high-order Shapley model to obtain a high-order linear model; calculating the Shapley value of each factor based on the high-order linear model using the least squares method; determining the degree of influence of each factor on the response result based on the Shapley value, and optimizing the radar anti-interference system using the degree of influence of each factor on the response result as a global sensitivity index. The present invention can quickly calculate the Shapley value without relying on the internal structure of the model, thereby analyzing the interaction relationship between factors in the radar anti-interference system and optimizing the global sensitivity index.

Description

Technical Field

[0001] The present invention relates to the field of radar anti-interference technology, and in particular to a global sensitivity index optimization method, device and equipment for radar anti-interference. Background Art

[0002] With the rapid development of radio communication technology, radar systems are being used in more and more applications, including air traffic management, maritime navigation, traffic monitoring, weather forecasting, and autonomous driving. They can continuously monitor, track, and communicate with objects in the environment.

[0003] However, in complex electromagnetic environments, radar systems often face threats from various interference sources, such as interference from communication base stations, wireless local area networks (Wi-Fi), false targets, noise suppression, and natural clutter. These interferences not only reduce radar detection accuracy but can also lead to misjudgments, compromising system safety and reliability.

[0004] Considering limitations in testing costs, capabilities, and resources, to study radar anti-interference performance, radar, target, and environmental parameters are controlled, and only the sample space of interference patterns and their associated parameters is explored. For example, in traffic monitoring or aviation navigation systems, if multiple false targets with characteristics similar to those of real targets appear within the radar's monitoring range, this can lead to false alarms or tracking failures, increasing the risk of traffic accidents or causing loss of control of air traffic trajectories. Therefore, analyzing uncertain interference factors and improving the radar's anti-interference performance are particularly important in ensuring its reliability and safety in complex environments. Summary of the Invention

[0005] Based on this, it is necessary to provide a global sensitivity index optimization method, device and equipment for radar anti-interference, which can analyze the interaction relationship of factors in the radar anti-interference system to address the above technical problems.

[0006] A global sensitivity index optimization method for radar anti-interference, the method comprising:

[0007] Acquire simulation sample data under a radar anti-interference test, and construct a proxy model between factors and response results based on the simulation sample data;

[0008] Based on the surrogate model, a high-order Shapley model of the relationship between the response result and each factor is constructed; a linear attribution condition is set for the high-order Shapley model to obtain a high-order linear model;

[0009] Based on the high-order linear model, the Shapley value of each factor is calculated using the least squares method;

[0010] The influence degree of each factor on the response result is determined based on the Shapley value, and the influence degree of each factor on the response result is used as a global sensitivity index to optimize the radar anti-interference system.

[0011] A global sensitivity index optimization device for radar anti-interference, the device comprising:

[0012] An agent model construction module is used to obtain simulation sample data under the radar anti-interference test and construct an agent model between factors and response results according to the simulation sample data;

[0013] A high-order linear model construction module is used to construct a high-order Shapley model of the relationship between the response result and each factor based on the surrogate model; a linear attribution condition is set on the high-order Shapley model to obtain a high-order linear model;

[0014] A Shapley value calculation module, configured to calculate the Shapley value of each factor using the least squares method based on the high-order linear model;

[0015] The optimization module is used to determine the influence of each factor on the response result based on the Shapley value, and optimize the radar anti-interference system by taking the influence of each factor on the response result as a global sensitivity index.

[0016] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the global sensitivity index optimization method for radar anti-interference when executing the computer program.

[0017] The above-mentioned global sensitivity index optimization method, device and equipment for radar anti-interference obtains simulation sample data under the radar anti-interference test, constructs a proxy model between factors and response results based on the simulation sample data; based on the proxy model, constructs a high-order Shapley model of the relationship between the response results and each factor; sets linear attribution conditions for the high-order Shapley model to obtain a high-order linear model; based on the high-order linear model, uses the least squares method to calculate the Shapley value of each factor; determines the degree of influence of each factor on the response result based on the Shapley value, and uses the degree of influence of each factor on the response result as a global sensitivity index to optimize the radar anti-interference system.

[0018] Based on a high-order Shapley model and setting linear attribution conditions, the present invention constructs a high-order linear model that encompasses first-order and second-order Shapley value additive models. This model can more comprehensively consider the interactions between various factors and their combined impact on the response results. In addition, based on the high-order linear model, the least squares method is used to calculate the Shapley value of each factor. This allows for rapid calculation of the Shapley value without relying on the internal structure of the model, improving the flexibility and efficiency of the radar anti-interference system, allowing for the rapid assessment of the influence of factors in complex systems, and enabling analysis of the interaction between factors in the radar anti-interference system, thereby optimizing the global sensitivity index of the radar anti-interference system. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0020] Figure 1 1 is a flow chart of a method for optimizing a global sensitivity index for radar anti-interference in one embodiment;

[0021] Figure 2 A schematic diagram of a radar anti-interference test scenario under false target interference in one embodiment;

[0022] Figure 3 1 is a bar diagram of a global sensitivity index of a radar anti-interference factor in one embodiment;

[0023] Figure 4 This is a structural block diagram of a global sensitivity index optimization device for radar anti-interference in one embodiment;

[0024] Figure 5 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment.

[0025] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0026] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0027] It should be noted that 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 this field can implement it. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0028] The following describes the embodiments of the present invention in detail with reference to the accompanying drawings.

[0029] Example 1

[0030] Radar anti-interference testing refers to a test of the performance and stability of a radar system when facing various interference sources. Its main purpose is to evaluate the anti-interference performance of the radar system under complex interference patterns, so that the radar can maintain its ability to detect and track the correct target. These performance indicators mainly include indicators such as the suppressive interference self-defense range, anti-deceptive interference success rate, effective interference sector, tracking error, and anti-range dragging success rate. They need to be calculated through continuous or typed parameters obtained from experimental tests. For example, the anti-deceptive interference success rate is calculated by the number of times the real target is identified through multiple tests under false target interference. The radar tracking error indicators under different interference conditions can be obtained by superimposing different tail pulses on the target echo.

[0031] The jamming methods used in radar anti-jamming tests mainly include deception jamming, active suppression jamming, and electromagnetic jamming. Multiple false target jamming is a common radar jamming method. Within the radar monitoring range, false targets with similar characteristics to the real target, such as distance, angle, speed, and RCS, sometimes appear. This interferes with radar judgment and causes the radar to mistakenly track the false target or even lose the target.

[0032] Radar anti-jamming performance testing is plagued by significant uncertainty due to strong nonlinearities and interactions within the system, complex external environmental constraints, insufficient prior knowledge, and insufficient manually collected information. The performance indicator of interest is called the response, the factors influencing the response are called factors, and the values ​​of the factors are called levels. Due to uncertainty, the impact of input factors on the system is unclear. As the number of such factors increases, the sample space explodes. To achieve statistically significant results, the number of samples required for testing often increases significantly, resulting in inestimable testing costs. Therefore, the pervasive uncertainty demands effective methods to reduce risk and improve efficiency to ensure the stability and reliability of radar anti-jamming systems.

[0033] This embodiment discloses a global sensitivity index optimization method for radar anti-interference. By building on a high-order Shapley model and setting linear attribution conditions, a high-order linear model that encompasses first-order and second-order Shapley value additive models is constructed. This allows for a more comprehensive consideration of the interactions between factors and their combined impact on the response results. Furthermore, based on the high-order linear model, the least squares method is used to calculate the Shapley value of each factor, enabling rapid calculation of the Shapley value without relying on the internal structure of the model. This improves the flexibility and efficiency of the radar anti-interference system, allows for rapid assessment of the influence of factors in complex systems, and enables analysis of the interaction between factors in the radar anti-interference system, thereby optimizing the global sensitivity index of the radar anti-interference system.

[0034] It is worth noting that, in order to facilitate understanding of the present invention, this embodiment illustrates the solution of the present invention through a radar performance test of a typical interference pattern of false target interference, with the aim of addressing complex and diverse interference patterns. However, this does not constitute a specific limitation of the present invention.

[0035] refer to Figure 1 As shown, a global sensitivity index optimization method for radar anti-interference is provided, including the following steps:

[0036] Step 201: obtain simulation sample data under a radar anti-interference test, and construct a proxy model between factors and response results based on the simulation sample data.

[0037] As can be understood, the interference pattern in the radar anti-interference test is first determined, the radar anti-interference factors that may occur under the current interference pattern are determined, and the corresponding level values ​​of each factor are set. Then, simulation tests are performed to obtain the corresponding response results. The factors, corresponding level values ​​of each factor, and the response results of each simulation test are used as a set of simulation sample data. By constructing a surrogate model with multiple sets of simulation sample data, the relationship between factors and response results can be more accurately captured, a more precise surrogate model can be constructed, and the accuracy of the optimization process can be improved.

[0038] Step 202: Based on the surrogate model, a high-order Shapley model of the relationship between the response result and each factor is constructed; a linear attribution condition is set for the high-order Shapley model to obtain a high-order linear model.

[0039] As can be understood, the constructed high-order Shapley model can more comprehensively consider the interactions between various factors and their combined impact on the response, which is superior to a simple linear model. By setting linear attribution conditions, the complexity of the model can be simplified. The resulting high-order linear model not only maintains an accurate assessment of factor contributions, but also enables rapid calculation and analysis, enhancing the robustness of the system.

[0040] Step 203: Based on the high-order linear model, the Shapley value of each factor is calculated using the least squares method.

[0041] It can be understood that the traditional SHAP tool relies on a tree structure model to calculate the second-order Shapley value. However, in a complex nonlinear system such as radar anti-interference, the phenomenon of multi-factor coupling will be very obvious, and the traditional SHAP tool relying on the tree structure model cannot handle the calculation of higher-order Shapley values. Therefore, this embodiment uses the least squares method to calculate the Shapley value of each factor, which can analyze the factor interaction relationship in the radar anti-interference system, thereby fully understanding the interaction between each factor in a complex nonlinear environment, and then more effectively identifying key factors, providing a more in-depth global sensitivity analysis.

[0042] Step 204 : determining the influence of each factor on the response result based on the Shapley value, and optimizing the radar anti-interference system by taking the influence of each factor on the response result as a global sensitivity index.

[0043] It can be understood that the present invention calculates the Shapley values ​​of all possible factors from a global perspective, which can provide a comprehensive understanding of the impact of each factor and ensure the comprehensiveness and effectiveness of the optimization scheme; then, based on the Shapley value, the degree of influence of each factor on the response result is determined, which can effectively identify the key factors, thereby providing a clear direction for the optimization of the radar anti-interference system and improving the anti-interference capability of the radar anti-interference system.

[0044] During the specific implementation of step 201, possible radar anti-interference factors are first determined and the corresponding levels of each factor are set. A radar anti-interference simulation system is then established. Based on the corresponding levels of each factor, simulation calculations are performed on the factors to obtain the corresponding response results. The factors, their corresponding levels, and the corresponding response results are used as simulation sample data. Several simulation calculations are performed to obtain several sets of simulation sample data.

[0045] Then, a surrogate model is constructed based on the factors in the simulation sample data and the response results corresponding to each factor. The expression of the surrogate model is:

[0046] f(X sample )=y sample ;

[0047] Where, f represents the agent model of the radar anti-interference simulation system; X sample =[x1,x2,…,x n ] represents a factor set consisting of n factors in any set of simulation sample data; y sample Represents the response results corresponding to each factor in any set of simulation sample data.

[0048] Specifically, if Figure 2 The figure shows a schematic diagram of the radar anti-interference test scenario under false target interference. The radar Radar is turned on to detect the target at a certain distance from the real target Target. The real target Target is in a moving state. When conducting the radar anti-interference test, multiple groups of false targets fake-Target with a signal-to-noise ratio (SNR) close to the real target Target are released at a certain lateral distance D from the real target Target. Since there is a certain time gap before and after the release, the movement of the real target Target during this period can be represented by the time T or the distance moved. There is a certain number of false targets fake-Target Num, and there is a certain interval Interval between each two. According to Figure 1 The experimental scenario is used to determine the interference factors and levels. The relevant factors and levels of the radar anti-interference test are set as shown in Table 1.

[0049] Table 1 Correlation factors and level settings of radar anti-interference test

[0050] Factor name Release Timing Dry-to-signal ratio Horizontal distance interval quantity symbol T(s) SNR D(m) Interval(km) Num level [0,100] [20,100] (0,20) (0,1) {2,4,6}

[0051] Then the response results are obtained through simulation. Under the interference of false targets, the response results have only two possibilities: tracking the real target or tracking the false target.

[0052] For example, in the radar anti-interference system F, N groups of simulation sample data are obtained through the radar anti-interference system F test. Then the N groups of simulation sample data include n factors and m response results. The agent model f is constructed based on the n factors and m response results. Define an n-dimensional input space That is, the input simulation sample data space can be defined as X={X1,X2,…,X n}; Define an m-dimensional response space Then Y can be defined as the response vector of model f, that is, Y = f(X), where Y = (y1, y2, ..., y m ).

[0053] In the radar anti-interference test scenario under false target interference, each set of simulation sample data has factor X n ={T,SNR,D,Interval,Num}, Then, for any set of simulation sample data, there is X sample =[x1,x2,…,x n ], proxy model f(X sample )=y sample , where x n represents the nth factor.

[0054] In the specific implementation process of step 202, based on the surrogate model, a high-order Shapley model of the relationship between the response result and each factor is constructed, and the expression is:

[0055]

[0056] Where,

[0057] |S l | = l;

[0058]

[0059] In the formula, l represents the order of the Shapley value to be calculated; represents the Shpaley value of each factor at the l-th order; p represents the number of factor subsets; S l represents the set of factor subsets of all possible d factors, where d is numerically equal to l and d < n; q represents the possible elements in S l that is val(p ∪ q) represents the value of the factors in p and q; n represents the number of factors in any set of simulation sample data; represents the marginal effect under different factor subset sets.

[0060] For example, when the order of the Shapley value l = 2 and the number of factors n = 3, there is a calculation process shown in Table 2.

[0061] Table 2

[0062]

[0063] Set the linear attribution condition for the high-order Shapley model, which is expressed as:

[0064]

[0065] Where,

[0066]

[0067] In the formula, y sample represents the response result corresponding to each factor in any set of simulation sample data; represents the mean performance of the system without factor input; E represents the mean calculation rule; f(X) represents the response result of the surrogate model f to the input X.

[0068] Then a high-order linear model can be obtained, and the expression is:

[0069]

[0070] When the highest order of the high-order linear model is 1, the linear model is expressed as:

[0071]

[0072] When the highest order of the high-order linear model is 2, the linear model is expressed as:

[0073]

[0074] As can be seen, the high-order linear model constructed in this embodiment encompasses the traditional first-order and second-order Shapley value models. It not only retains the fairness and interpretability of the basic Shapley value, but also enhances the ability to describe complex collaborative scenarios by introducing higher-order interaction effects.

[0075] In the specific implementation process of step 203, according to the above steps, for any set of simulation sample data, there are X sample =[x1,x2,…,x n ],f(X sample )=y sample , then the Shapley value corresponding to each factor As the parameters to be estimated; for N groups of simulation sample data, there are a total of parameters to be estimated.

[0076] According to the marginal contribution idea of ​​Shapley value, for any set of simulation sample data, if X is fixed, sample Any factor x in n Or the value of a factor subset p, and change the value of other factors, then the response after the change is y' sample , the estimated value is obtained by averaging different samples So The increment from φ0 is determined only by the fixed factor X k Or factor subset q, assuming its true value is Then the high-order linear model can be transformed into:

[0077]

[0078] Where, Indicates the true value of the response result corresponding to each factor; Represents the factor subset set S l Are all the factors in fixed? This is expressed as:

[0079] Obtain all possible fixed factor combinations by full permutation Z n is a A two-dimensional matrix. Since the full permutation needs to consider every possible fixed factor combination Z n The weight W n =[w1,w2,…,w 2n-2 ] T , W n is a (2 n -2)×1 column vector. n The value of each row is mapped to Z n The fixed factor combination under the same row of where h(z s ) represents the fixed factor combination Z n The number of fixed factors in the sth row, that is, the number of 1s in the sth row. Based on this, the normalized weight is obtained by normalization. Therefore, the fixed factor combination Z n With normalized weight W' n It can be determined before estimating the Shapley value φ.

[0080] According to the fixed factor combination Z n With normalized weight W' n , perform secondary deformation on the deformed high-order linear model, the expression is:

[0081]

[0082] For any set of simulation sample data X sample =[x1,x2,…,x n ], the fixed factor combination Z is known n And the original data X is Combining Z by fixed factors n Fixed factor information in, determine the factor set X sample The index and value of the fixed factor are located in the original factor set X according to the index, and all the values ​​in the original factor set X are updated to X sample The value of the fixed factor in ; for example, for z 1 , X sample The constant factor in is X1, and its value is x1, then the updated Bringing it into the proxy model f, we can get Calculate the mean value as

[0083] Consider the fixed factor portfolio Z n For each possibility in , a new factor set can be obtained The new factor set X newBring it into the proxy model and get a new set of response results where X new is a [(2 n -2)*N]×n two-dimensional matrix, Y new is a (2 n -2)×1 column vector.

[0084] Based on the linear attribution condition, first eliminate the last factor x n The influence of factor x n If Y is fixed, new The factor x is also included n Contribution of Y new with y sample The difference represents X new The degree of influence of the other unfixed factors on the response results; on the contrary, if the factor x n If not fixed, then Y new The factor x is not included in n The contribution of Y new It represents X new The degree of influence of the remaining unfixed factors on the response results. Based on this, the least squares method is used to calculate the Shapley value of each factor, and the expression is:

[0085]

[0086] Where, represents the Shapley value of the factor to be estimated; Z n represents a fixed factor combination; W' n Represents every possible fixed factor combination Z when all permutations are performed n Normalized weight of Y new Denote the new factor set X new The new set of response results in the proxy model f; ° represents the corresponding multiplication of each row of the matrix; (·) T Represents vector transpose; Indicates elimination factor X n The factor change of , where · is a replaceable state variable. Eliminate the factor x n The specific process of factor changes is shown in Table 3.

[0087] Table 3 Elimination factor x n The changes in factors.

[0088]

[0089] Furthermore, consider the nth factor x n , you can directly obtain

[0090] The method proposed in the present invention is verified by a specific example below.

[0091] Under false target interference, simulation calculations were performed based on the radar anti-interference simulation system to obtain 25 sets of simulation sample data, that is, N = 25, and then the SVM model was used to construct the proxy model f; it can be understood that SVM is a supervised learning algorithm that can find an optimal hyperplane to classify samples by maximizing the distance between categories and minimizing the classification error.

[0092] The 25 groups of simulation sample data are shown in Table 4.

[0093] Table 4 Radar anti-interference simulation sample data

[0094]

[0095]

[0096] The above simulation sample data are normalized, and the highest order is set to l = 3. The high-order Shapley value is calculated using the least squares method to obtain the first-order, second-order, and third-order contribution results of each factor in the 25 data, as shown in Table 5.

[0097] Table 5 High-order Shapley values ​​of radar anti-interference (l=3, N=25)

[0098]

[0099]

[0100]

[0101]

[0102] The absolute value of each Shapley value of the 25 data is averaged, and the result is as follows: Figure 3 The global sensitivity bar chart of the radar anti-interference factor clearly shows the presence of second-order and higher-order contributions. Furthermore, the higher-order contributions can be quantified for different sample points. Based on this, the corresponding parameters of the radar anti-interference system are optimized to improve its anti-interference performance.

[0103] Although this embodiment Figure 2 The steps in the diagram are shown in the order indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 2At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0104] Example 2

[0105] Based on the global sensitivity index optimization method for radar anti-interference in Example 1, this embodiment discloses a global sensitivity index optimization device for radar anti-interference, such as Figure 4 As shown, the global sensitivity index optimization device for radar anti-interference includes: an agent model construction module 401, a high-order linear model construction module 402, a Shapley value calculation module 403 and an optimization module 404, wherein:

[0106] The proxy model construction module 401 is used to obtain simulation sample data under the radar anti-interference test and construct a proxy model between factors and response results based on the simulation sample data.

[0107] The high-order linear model construction module 402 is used to construct a high-order Shapley model of the relationship between the response results and various factors based on the surrogate model; set linear attribution conditions for the high-order Shapley model to obtain a high-order linear model.

[0108] The Shapley value calculation module 403 is used to calculate the Shapley value of each factor using the least squares method based on a high-order linear model.

[0109] The optimization module 404 is used to determine the influence of each factor on the response result based on the Shapley value, and use the influence of each factor on the response result as a global sensitivity index to optimize the radar anti-interference system.

[0110] In this embodiment, the specific working process and working principle of the proxy model construction module 401, the high-order linear model construction module 402, the Shapley value calculation module 403 and the optimization module 404 are the same as those in the method of Example 1, and therefore will not be described in detail in this embodiment. Each unit module can be implemented in whole or in part by software, hardware or a combination thereof. Each unit module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in the form of software in a computer device so that the processor can call and execute the operations corresponding to each of the above unit modules.

[0111] Example 3

[0112] like Figure 5The terminal device disclosed in this embodiment includes a transmitter, a receiver, a memory, and a processor. The transmitter is used to send instructions and data, the receiver is used to receive instructions and data, the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions stored in the memory to implement the method in the above-mentioned embodiment 1.

[0113] It should be noted that the above memory can be independent or integrated with the processor. When the memory is independently provided, the terminal device further includes a bus for connecting the memory and the processor.

[0114] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0115] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] The above-described embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that a person skilled in the art would be able to make numerous modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A global sensitivity index optimization method for radar anti-interference, characterized in that: The method comprises: Acquire simulation sample data under a radar anti-interference test, and construct a proxy model between factors and response results based on the simulation sample data; Based on the surrogate model, a high-order Shapley model of the relationship between the response result and each factor is constructed; a linear attribution condition is set for the high-order Shapley model to obtain a high-order linear model; Based on the high-order linear model, the Shapley value of each factor is calculated using the least squares method; Determine the influence of each factor on the response result based on the Shapley value, and use the influence of each factor on the response result as a global sensitivity index to optimize the radar anti-interference system; The high-order Shapley model of the relationship between the response results and each factor is expressed as follows: ； The linear attribution condition is set as follows: ； in, ； The high-order linear model expression is: ； Where, Indicates the order of the Shapley value to be calculated; Indicates the Shpaley value of each factor at the order; represents the number of factor subsets; Indicates all possible A set of factor subsets of factors, where Numerically equal to ,and < n ; represents the number of factors in any set of simulation sample data; Represents the marginal effects under different factor subsets; Represents the response results corresponding to each factor in any set of simulation sample data; represents the mean performance of the system when there is no factor input; represents the mean calculation rule; Representing a proxy model Input Response result.

2. The global sensitivity index optimization method for radar anti-interference according to claim 1 is characterized in that: Acquire simulation sample data under radar anti-interference test, including: Determine possible radar anti-interference factors and set the corresponding levels of each factor; Establish a radar anti-interference simulation system, simulate and calculate the factors according to their corresponding levels, and obtain the response results corresponding to each factor; The factors, the levels corresponding to the factors, and the response results corresponding to the factors are used as simulation sample data; Perform several simulation calculations to obtain several sets of simulation sample data.

3. The global sensitivity index optimization method for radar anti-interference according to claim 2 is characterized in that: Constructing a proxy model between factors and response results based on the simulation sample data, including: A proxy model is constructed based on the factors in the simulation sample data and the response results corresponding to each factor. The expression of the proxy model is: ； Where, An agent model representing the radar anti-jamming simulation system; Indicates any set of simulation sample data A factor set consisting of factors; Represents the response results corresponding to each factor in any set of simulation sample data.

4. The global sensitivity index optimization method for radar anti-interference according to claim 1 is characterized in that: Based on the high-order linear model, the least squares method is used to calculate the Shapley value of each factor, including: According to the marginal contribution idea of ​​Shapley value, for any set of simulation sample data, one of the factors is fixed. , changing the values ​​of other factors, the high-order linear model can be transformed into: ； Where, Indicates the true value of the response result corresponding to each factor; Represents a set of factor subsets Are all the factors in fixed? Obtain all possible fixed factor combinations by full permutation ; Consider every possible combination of fixed factors when all permutations are considered Weight , since the weight of each possible combination The value of each row is mapped The fixed factor combination under the same row is normalized based on this to obtain the normalized weight ; According to the fixed factor combination With the normalized weight , perform secondary deformation on the deformed high-order linear model, and the expression is: For any of the above simulation sample data, by combining fixed factors Fixed factor information in, determining the factor set The index and value of the fixed factor, and the original factor set is located according to the index The fixed factors in the original factor set All values ​​in are updated to The fixed factor values ​​in ; then consider the fixed factor combination For each possibility in , we get a new factor set , the new factor set Bring it into the proxy model and get a new set of response results ; Based on the linear attribution condition, the last factor is eliminated first. The influence of Fixed, then Also included are factors Contribution, and The difference represents The degree of influence of the other unfixed factors on the response results; on the contrary, if the factors If not fixed, Factors not included The contribution of It represents The least squares method is used to calculate the Shapley value of each factor based on the influence of the other unfixed factors on the response results.

5. The global sensitivity index optimization method for radar anti-interference according to claim 1 is characterized in that: The least squares method is used to calculate the Shapley value of each factor, and the expression is: ； Where, Represents the Shapley value of the factor to be estimated; represents a fixed factor combination; Represents every possible fixed factor combination when all permutations are performed The normalized weight of Represents a new set of factors In the proxy model The new response result set in ; Indicates that each row of the matrix is ​​multiplied; Represents vector transpose; Elimination factor The factor changes of A replaceable state variable.

6. A global sensitivity index optimization device for radar anti-interference, characterized in that: The method for optimizing the global sensitivity index for radar anti-interference according to any one of claims 1 to 5 is adopted, wherein the device comprises: An agent model construction module is used to obtain simulation sample data under the radar anti-interference test and construct an agent model between factors and response results according to the simulation sample data; A high-order linear model construction module is used to construct a high-order Shapley model of the relationship between the response result and each factor based on the surrogate model; a linear attribution condition is set on the high-order Shapley model to obtain a high-order linear model; A Shapley value calculation module, configured to calculate the Shapley value of each factor using the least squares method based on the high-order linear model; The optimization module is used to determine the influence of each factor on the response result based on the Shapley value, and optimize the radar anti-interference system by taking the influence of each factor on the response result as a global sensitivity index.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the global sensitivity index optimization method for radar anti-interference according to any one of claims 1 to 5 are implemented.

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