A method to simplify the radar seeker jamming effectiveness evaluation index system based on RS-PCA

Abstract

The present invention discloses a method for simplifying the radar seeker interference effectiveness evaluation index system based on RS‑PCA, and belongs to the technical field of interference effectiveness evaluation. The present invention combines rough sets and principal component analysis to simplify the evaluation index system; firstly, the index system is simplified by using rough sets to obtain several groups of index system simplified sets; then, the principal component analysis method is used to select a group of attribute simplified sets with the largest contribution rate to obtain the final simplified result. The present invention makes full use of the advantages of rough sets in processing uncertain, imprecise and incomplete information, and the objectivity of principal component analysis in evaluating the simplified set through contribution value, designs an index system simplification method, realizes the generation of the optimal simplified set of the interference effectiveness evaluation index system, effectively solves the problems of weak representativeness and strong correlation of the index system, and significantly improves the objectivity, scientificity and operability of the interference effectiveness evaluation.

Description

Technical Field

[0001] The invention belongs to the technical field of interference effectiveness evaluation, and relates to a method for simplifying an interference effectiveness evaluation index system of an anti-ship missile radar seeker based on RS-PCA. Background Art

[0002] With the application of various new technologies, the performance of anti-ship missile radar seekers has been greatly improved, posing greater challenges to surface ship air defense and anti-missile. In order to effectively respond to anti-ship missile attacks, surface ships have also focused on developing soft-kill methods such as active jamming and passive jamming from the perspective of electronic countermeasures. Under the circumstance that the anti-ship missile radar seeker adopts a new system and anti-interference measures, whether the electronic countermeasures and jamming methods are capable of effectively interfering with it has become an urgent problem to be solved in the field of shipborne electronic countermeasures.

[0003] In a complex electromagnetic environment, the evaluation of the interference effectiveness of shipborne radar countermeasure equipment on the radar seeker of anti-ship missiles is a multi-index comprehensive evaluation problem. However, there has been no unified and authoritative evaluation index system and method for the evaluation of the interference effectiveness of anti-ship missile radar seekers.

[0004] A lot of work has been done on jamming effectiveness evaluation at home and abroad. For example, the United States mainly uses probability criteria to evaluate the effectiveness of missile weapon systems, making the evaluation results simple and intuitive. The famous Aegis system analyzes the entire process of the missile and uses interception probability as the evaluation indicator. my country initially selected self-defense distance, detection probability and suppression coefficient as evaluation indicators based on actual combat scenarios. Subsequently, many indicators emerged to measure the jamming effectiveness against radars. Although the existing jamming effectiveness evaluation indicator system has been continuously improved, it still has the following shortcomings: (1) A few indicators are simply combined to form an effectiveness evaluation indicator system, ignoring the internal connection between the indicators; (2) Some indicators are cumbersome to calculate, and some indicators are unmeasurable. When constructing the indicator system, in order to more comprehensively evaluate the jamming effect on the terminal guidance radar, as many indicators as possible will be selected, resulting in information redundancy, increasing the difficulty of making correct decisions, and affecting the accuracy of the evaluation results. Therefore, it is necessary to simplify the indicators and remove unimportant and irrelevant redundant indicators without affecting the classification ability of the information system to improve the evaluation efficiency.

[0005] The rough set (RS) simplification method is highly logical and applicable to both quantitative and qualitative indicators. However, the simplification results of a decision information system are often not unique. If a group is selected from the final simplification results based on experience, there will be subjective arbitrariness. Principal component analysis (PCA) is a feature screening method based on statistical data analysis. The evaluation results are completely dependent on statistical data and cannot solve the problem of information uncertainty. Based on this, the present invention combines the rough set and the principal component analysis method to simplify the evaluation index system. First, the rough set is used to simplify the index system to obtain several groups of index system simplification sets; then the principal component analysis method is used to select a group of attribute simplification sets with the largest contribution rate to obtain the final simplification result. The outstanding advantage of the present invention is that it effectively solves the problems of weak representativeness and strong correlation of the index system in the interference effectiveness evaluation process, and improves the objectivity, scientificity and operability of the evaluation. Summary of the invention

[0006] The purpose of the present invention is to make full use of the advantages of the rough set method and the principal component analysis method, and simplify a more reasonable interference effectiveness evaluation index system by processing the radar seeker interference effectiveness evaluation index system. The result will directly affect the comparison of the effects of different interference measures in the terminal guidance radar, and indirectly affect the objective evaluation and improvement of the combat effectiveness of shipborne radar countermeasure equipment, as well as how to enhance the combat capability of anti-ship missiles in complex electromagnetic environments.

[0007] The technical solution of the present invention is:

[0008] A method for simplifying a radar seeker jamming effectiveness evaluation index system based on RS-PCA comprises the following steps:

[0009] The first step is to construct the original data table of the indicator system.

[0010] Select indicators that can effectively measure the interference effectiveness and determine the indicator set C = (c1, c2, ..., c n ), and collect data to form n indicator data as the object to be evaluated, that is, the domain is U = (u1,u2,…,u n ). The original data table of the indicator system is constructed by integrating the indicator set, domain and sample data.

[0011] The second step is to discretize the sample data.

[0012] Since the rough set method cannot directly process continuous indicators, the continuous indicator data needs to be discretized before the rough set method is used to simplify the indicators.

[0013] For a given information system S = (U, A, V, f), where A is an attribute set and f is an information function, Let its range be V a =[l a ,r a ], then in the range V a Take any set of breakpoints l a <C1 a <C2 a <C3 a <… <r a , divide the range into m+1 intervals, namely V a =[l a <C1 a )∪[C1 a <C2 a )∪…[C m a <r a ],make f w represents the discretized function, then the new information system after discretization S=(U,A,V w ,f w ).

[0014] Data discretization is to divide the value range of attributes by selecting split points, replace continuous attribute values ​​with a small number of interval markers, and reduce and simplify the original data. Commonly used data discretization methods mainly include equal distance division method, equal frequency division method and cluster analysis method. The present invention mainly uses K-means discretization, which is widely used. The numerical value and specific distribution of the attribute are considered in the process of cluster analysis. Therefore, the discretization result obtained by the K-means discretization algorithm has a higher quality. However, the algorithm also needs to give the number of divided intervals in advance. The specific process of sample data discretization of the present invention is as follows:

[0015] The number of division intervals k is determined according to the empirical formula k=1+lgn / lg2 (round the result to the nearest integer), where n is the number of sample data. The K-means algorithm is used to discretize the sample data of quantitative indicators to obtain the discretization results of indicator data; for qualitative indicators, the sample discretization data of each indicator is generally obtained by experts according to the evaluation level.

[0016] The specific process of the K-means discretization algorithm is as follows:

[0017] The K-means discretization algorithm randomly selects k data from n samples as the centroids of the initial clustering according to the given number of intervals k (k < n), and then uses the Euclidean distance to cluster all the remaining data, dividing the data into k clusters. Then, the centroids are reselected as the initial clustering centroids for the next round of iteration, and clustering operations are performed according to the new centroids. This process is continuously looped until the clustering results no longer change, and the final discretization result is obtained. The K-means discretization algorithm makes the data within the clusters highly similar, while the data between the clusters is less similar.

[0018] Step 3: Remove duplicate indicators.

[0019] Observe and compare the discretization result table of the indicator data, remove the completely identical duplicate columns of indicators, and preliminarily simplify the indicator system.

[0020] Step 4: Use rough sets for reduction.

[0021] Use the rough set discernibility function to reduce the indicator system to obtain the core set and multiple indicator reduction sets of the indicator system. The specific steps are as follows:

[0022] Step 1: Calculate the discernibility matrix according to formula (1): Let S = (U, A, V, f) be an information system, the universe of discourse U = {x1, x2,..., x n}, let the discernibility matrix of the information system S be M, |U| = n, then M n×n =(m ij ) n×n (i, j = 1, 2,..., n) Each item is defined as:

[0023]

[0024] Since the discernibility matrix is a symmetric matrix and the diagonal element values are empty, when calculating the discernibility matrix, only the lower triangular elements need to be stored.

[0025] Step 2: The core set of the information system S = (U, A, V, f) is the set composed of all single indicators in the discernibility matrix M, and thus the core set is obtained.

[0026] Step 3: Use the discernibility matrix M to calculate the discernibility function, and obtain the corresponding inner disjunctive outer conjunctive logical expression according to the discernibility function.

[0027] Step 4: Perform logical operations on the result of Step 3 to obtain a logical expression in the form of inner conjunction and outer disjunction.

[0028] Step 5: In the logical expression obtained in Step 4, each conjunctive term is an attribute reduction set of this information system. If the reduction result is not unique, the optimal reduction result needs to be determined according to the principal component analysis.

[0029] The index reduction method based on the rough set discriminant function can easily obtain the core set of the information system and the simplification of all attributes. However, if the amount of data is large, it will consume a lot of time and space. Therefore, this method is often used for theoretical analysis.

[0030] The fifth step is to use principal component analysis to determine the optimal simplification result.

[0031] The principle of principal component analysis is to convert multiple variables with certain correlation into a set of unrelated factors through linear transformation while ensuring the minimum loss of original data information, select several factors with the largest variance contribution rate, and use a few variables to reflect the information in the original variables to achieve dimensionality reduction of high-dimensional variable sets. At the same time, principal component analysis can objectively determine the weight of each indicator by evaluating the attribute contribution rate, avoid subjective arbitrariness, and provide an effective reference for attribute selection. The simplified steps of principal component analysis are:

[0032] Step 1: Standardize the raw data.

[0033] If the original data set contains n samples and p indicator variables, the sample data set X is represented as an n×p matrix:

[0034]

[0035] The original data is standardized using formula (3) so that the mean of the standardized data is 0 and the variance is 1:

[0036]

[0037] Among them, x it is the original data of the tth indicator of the ith sample, z it is the tth index value of the ith sample after standardization, is the sample mean of the tth indicator, σ t is the sample standard deviation of the tth indicator.

[0038] Step 2: Calculate the correlation coefficient matrix.

[0039] According to the standardized data, the correlation coefficient matrix R between the indicators is calculated:

[0040]

[0041] in,

[0042]

[0043] Step 3: Calculate the eigenvalues ​​and eigenvectors of the correlation coefficient matrix R.

[0044] According to |R-λI|=0, the characteristic root λ is calculated t , and sort them by size: λ1≥λ2≥…≥λ p , the corresponding unit eigenvectors are μ1,μ2,…,μ p .

[0045] Step 4: Calculate the variance contribution rate and cumulative variance contribution rate of the principal components.

[0046] The variance contribution rate of the tth principal component is:

[0047]

[0048] The cumulative variance contribution rate of the first t principal components is:

[0049]

[0050] Step 5: Determine the number of principal components.

[0051] In practice, it is generally required that the eigenvalues ​​corresponding to each principal component are greater than 1, and the minimum m0, which satisfies the cumulative variance contribution rate of 70%, is the number of principal components.

[0052] Step 6: Determine the principal component functions.

[0053] According to formula (8), the principal component functions are obtained:

[0054] F i =μ i1 x1+μ i2 x2+…+μ ip x p (i=1,2,…,m0) (8)

[0055] Among them, μ i =(μ i1 ,μ i2 ,…,μ ip ),i=1,2,…,m0 is the eigenvector corresponding to the eigenvalue of each principal component.

[0056] Step 7: Calculate the comprehensive principal component evaluation value.

[0057] Based on the obtained principal component functions and corresponding weights (i.e. variance contribution rates), the comprehensive principal component evaluation expression is obtained as follows:

[0058]

[0059] According to the comprehensive principal component evaluation expression, the contribution value of each index reduction set is calculated, and the reduction set with the largest contribution value is selected as the best result of index reduction.

[0060] Beneficial effects of the present invention: The RS-PCA-based interference effectiveness evaluation index system simplification method described in the present invention fully utilizes the ability of rough sets to effectively analyze and process uncertain, imprecise and incomplete information, and the principal component analysis method to evaluate the objectivity of the simplified set through contribution values, thereby achieving the generation of the optimal simplified set, effectively solving the problems of weak representativeness and strong correlation of the index system in the interference effectiveness evaluation process, and improving the objectivity, scientificity and operability of the evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is the flow chart of the indicator reduction algorithm based on RS-PCA. DETAILED DESCRIPTION

[0062] The present invention is a method for simplifying the interference effectiveness evaluation index system based on RS-PCA. The input data is the initially established interference effectiveness evaluation index system, and the output data is the simplified interference effectiveness evaluation index system. The process flowchart of the method is as follows: Figure 1 The implementation process of the present invention is described below by taking the simplified method of the anti-ship missile radar seeker jamming effectiveness evaluation index system as an example.

[0063] When evaluating the jamming effectiveness of radar seekers, there are many factors that affect the performance of radar seekers. According to the working properties of the seeker itself and the parameter changes during the confrontation process, the jamming effectiveness is evaluated from three aspects: the ability to detect, identify and capture targets, the ability to track targets and the ability to strike targets. Table 1 is the initial evaluation index system for the jamming effectiveness of radar seekers.

[0064] Table 1

[0065]

[0066] First, taking the composite interference of chaff dilution interference, broadband blocking noise and centimeter chaff center of mass on anti-ship missiles as an example, the simplified original data of the index system is obtained through simulation. At the same time, the qualitative indicators are quantified, that is, {good, relatively good, relatively poor, poor} = {4, 3, 2, 1}. The specific original data of the interference effectiveness evaluation index system are shown in Table 2.

[0067] Table 2

[0068]

[0069]

[0070] The first step is to simplify the indicators of the detection, identification and capture target capability subsystem. The K-means algorithm in SPSS is used to discretize the quantitative indicator data in Table 2. Since 10 sample data are selected for analysis, the data is divided into 4 intervals. The discretization results of the indicator data are shown in Table 3.

[0071] Table 3

[0072] <![CDATA[C 11 (a)]]> <![CDATA[C 12 (b)]]> <![CDATA[C 13 (c)]]> <![CDATA[C 14 (d)]]> <![CDATA[C 15 (e)]]> <![CDATA[C 16 (f)]]> 1 1 3 1 3 4 1 2 4 4 2 2 2 4 3 3 2 3 3 3 3 4 4 3 4 1 1 1 5 3 1 3 4 3 1 6 4 4 2 2 2 2 7 1 3 1 4 4 1 8 3 3 3 3 2 4 9 2 1 1 4 4 3 10 4 2 2 2 3 4

[0073] The second step is to simplify the radar seeker jammer effectiveness evaluation index system according to Table 3 and obtain the discrimination matrix as shown in Table 4.

[0074] Table 4

[0075]

[0076]

[0077] The third step is to calculate the discrimination matrix in Table 4 and obtain the core set of the index system as core(B1)={d,f}, and there are two reduced sets as {b,d,f} or {d,e,f}.

[0078] The fourth step is to use principal component analysis to select the optimal index system reduction set because the reduction result is not unique. The specific process is:

[0079] 1) The original data is standardized according to formula (3), and the standardized results are shown in Table 5.

[0080] Table 5

[0081] <![CDATA[C 11 ]]> <![CDATA[C 12 ]]> <![CDATA[C 13 ]]> <![CDATA[C 14 ]]> <![CDATA[C 15 ]]> <![CDATA[C 16 ]]> 1 -0.787 0.283 -0.609 0.194 1.162 0.764 2 1.115 1.227 0.834 -0.775 -0.775 -0.453 3 -0.159 -0.661 0.338 0.194 0.194 1.170 4 1.672 0.283 1.060 -1.743 -1.743 -0.030 5 -0.677 -1.605 -0.113 1.162 0.194 0.409 6 0.420 1.227 0.654 -0.775 -0.775 -1.569 7 -1.101 0.283 -1.240 1.162 1.162 0.037 8 -0.236 0.283 0.113 0.194 -0.775 -1.146 9 -1.214 -1.605 -1.962 1.162 1.162 1.542 10 0.969 0.283 0.925 -0.775 0.194 -0.723

[0082] 2) According to formula (5), the correlation coefficients between the indicators are calculated, and the correlation coefficient matrix R is obtained as follows:

[0083]

[0084] 3) According to the correlation coefficient matrix R, the characteristic roots and variance contribution rates corresponding to each indicator are calculated, and the characteristic roots are sorted from large to small. The results are shown in Table 6.

[0085] Table 6

[0086] Characteristic root Numeric Variance contribution rate (%) Cumulative variance contribution rate (%) <![CDATA[λ1]]> 4.640 77.325 77.325 <![CDATA[λ2]]> 0.771 12.856 90.181 <![CDATA[λ3]]> 0.313 5.222 95.403 <![CDATA[λ4]]> 0.168 2.802 98.204 <![CDATA[λ5]]> 0.075 1.251 99.455 <![CDATA[λ6]]> 0.033 0.545 100

[0087] 4) According to Table 6, the number of principal components m0 = 1, and the eigenvector corresponding to the characteristic root λ1 is: μ1 = [-0.442, -0.357, -0.434, 0.440, 0.414, 0.352].

[0088] 5) According to equations (8) and (9), the comprehensive principal component evaluation expression of the detection, recognition and capture target capabilities is: F = -0.330x1-0.267x2-0.325x3+0.329x4+0.310x5+0.241x6. From the comprehensive principal component evaluation expression, it can be seen that the index C 12 and C 15 The contribution rate, i.e. the weight, is C 15 >C 12 Therefore, {d, e, f} is selected as the reduced set of the optimal indicator system, namely, the target detection capability, the interference availability and the target capture probability loss.

[0089] Similarly, the indicators of the target tracking capability and target strike capability subsystems are simplified, and the simplified interference effectiveness evaluation indicator system is shown in Table 7.

[0090] Table 7

[0091]

[0092] In summary, for the initially established anti-ship missile radar seeker jamming effectiveness evaluation index system, combining the rough set method and the principal component analysis method, the designed index system simplification method is used to simplify the optimal jamming effectiveness evaluation index system, which effectively solves the problems of weak representativeness and strong correlation of the index system, and significantly improves the objectivity, scientificity and operability of the jamming effectiveness evaluation.

Claims

1. A method for simplifying the radar seeker jamming effectiveness evaluation index system based on RS-PCA, characterized in that: The method comprises the following steps: The first step is to build the original data table of the indicator system Select indicators that can effectively measure the interference effectiveness and determine the indicator set C = (c1, c2, ..., c n ), and collect data to form n indicator data as the object to be evaluated, that is, the domain is U = (u1,u2,…,u n );Construct the original data table of the indicator system by integrating the indicator set, domain and sample data; The second step is to discretize the sample data. The number of division intervals k is determined according to the empirical formula k=1+lgn / lg2, where n is the number of sample data; the K-means algorithm is used to discretize the sample data of quantitative indicators to obtain the discretization results of indicator data; for qualitative indicators, experts score according to the evaluation level to obtain the sample discretization data of each indicator; The third step is to remove duplicate indicators Observe and compare the discretization result table of indicator data, remove duplicate columns of completely identical indicators, and make a preliminary simplification of the indicator system; Step 4: Use rough sets to simplify The index system is simplified by using the rough set distinguishing function, and the core set of the index system and multiple index reduction sets are obtained. Step 5: Use principal component analysis to determine the optimal reduction result The steps of selecting the optimal reduction result by principal component analysis are as follows: Step 1: Standardize the raw data If the original data set contains n samples and p indicator variables, the sample data set X is represented as an n×p matrix: The original data is standardized using formula (3) so that the mean of the standardized data is 0 and the variance is 1: Among them, x it is the original data of the tth indicator of the ith sample, z it is the tth index value of the ith sample after standardization, is the sample mean of the tth indicator, σ t is the sample standard deviation of the tth indicator; Step 2: Calculate the correlation coefficient matrix According to the standardized data, the correlation coefficient matrix R between the indicators is calculated: in, Step 3: Calculate the eigenvalues ​​and eigenvectors of the correlation coefficient matrix R According to |R-λI|=0, the characteristic root λ is calculated t , and sort them by size: λ1≥λ2≥…≥λ p , the corresponding unit eigenvectors are μ1,μ2,…,μ p ; Step 4: Calculate the variance contribution rate and cumulative variance contribution rate of the principal components: The variance contribution rate of the tth principal component is: The cumulative variance contribution rate of the first t principal components is: Step 5: Determine the number of principal components It is required that the eigenvalues ​​corresponding to each principal component are greater than 1, and the minimum m0 that satisfies the cumulative contribution rate of 70% is the number of principal components; Step 6: Determine the principal component functions According to formula (8), the principal component functions are obtained: F i =μ i1 x1+μ i2 x2+…+μ ip x p ,i=1,2,…,m0 (8) Among them, μ i =(μ i1 ,μ i2 ,…,μ ip ), i = 1, 2, ..., m0 is the eigenvector corresponding to the eigenvalue of each principal component; Step 7: Calculate the comprehensive principal component evaluation value Based on the obtained principal component functions and corresponding weights, the comprehensive principal component evaluation expression is obtained as follows: According to the comprehensive principal component evaluation expression, the contribution value of each index reduction set is calculated, and the reduction set with the largest contribution value is selected as the best result of index reduction.

2. The method for simplifying the radar seeker jamming effectiveness evaluation index system based on RS-PCA according to claim 1, characterized in that: In the second step, the specific process of the K-means discretization algorithm is as follows: The K-means discretization algorithm randomly obtains k data from n samples as the centroid of the initial cluster according to the given interval number k, and then clusters all the remaining data using the Euclidean distance to divide the data into k clusters; then reselects the centroid as the initial clustering centroid for the next round of iteration, and performs clustering operations according to the new centroid, and continuously repeats this process until the clustering result no longer changes, and the final discrete result is obtained.

3. The method for simplifying the radar seeker jamming effectiveness evaluation index system based on RS-PCA according to claim 1 or 2, characterized in that: In the fourth step, the specific steps of using rough sets for simplification are as follows: Step 1: Calculate the discriminability matrix according to formula (1); let S = (U, A, V, f) be an information system, and the domain U = {x1, x2, …, x n }, let the distinguishing matrix of information system S be M, |U| = n, then M n×n =(m ij ) n×n Each term of is defined as follows, where i,j=1,2,…,n: Since the difference matrix is ​​a symmetric matrix and the diagonal element values ​​are empty, it is sufficient to store the lower triangular elements when calculating the difference matrix; Step 2: The core set of the information system S = (U, A, V, f) is the set of all the individual indicators in the discrimination matrix M, and the core set is obtained from this; Step 3: Use the discriminant matrix M to calculate the discriminant function, and obtain the corresponding inner disjunction and outer conjunction logical expressions according to the discriminant function; Step 4: Perform logical operations on the results of step 3 to obtain a logical expression in the form of inner conjunction and outer disjunction; Step 5: In the logical expression obtained in step 4, each conjunction is a reduced attribute set of the information system; if the reduced result is not unique, the optimal reduced result needs to be determined based on principal component analysis.

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