CN113076661B - Uncertain data driven radar early warning detection modeling method - Google Patents

Uncertain data driven radar early warning detection modeling method Download PDF

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CN113076661B
CN113076661B CN202110470275.1A CN202110470275A CN113076661B CN 113076661 B CN113076661 B CN 113076661B CN 202110470275 A CN202110470275 A CN 202110470275A CN 113076661 B CN113076661 B CN 113076661B
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胡星辰
李妍
陈超
程光权
吴克宇
黄金才
刘忠
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National University of Defense Technology
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Abstract

The invention discloses an uncertain data driven radar early warning detection modeling method which comprises the steps of converting uncertain description into digital information based on a fuzzy clustering method, generating a fuzzy set relevant to the model action, establishing a clustering center by using fuzzy C mean clustering, combining a spatial structure of training data with the fuzzy set, and further establishing a TS fuzzy rule model based on an IF-THEN rule; according to the invention, from the data perspective, information particles are generated by using a clustering algorithm to capture structural information hidden in a data space, the influence of uncertain factors on data can be reduced, and meanwhile, a TS topological structure combining qualitative knowledge described by an IF-THEN fuzzy rule and quantitative knowledge represented by a local linear model can approach any nonlinear model with any precision, so that the method is beneficial to realizing the fitting of a complex nonlinear model.

Description

Uncertain data driven radar early warning detection modeling method
Technical Field
The invention relates to the technical field of radar early warning detection, in particular to an uncertain data driven radar early warning detection modeling method.
Background
Radar detection is taken as an important means for acquiring information, plays an important role in the fields of target detection, fire hit and the like, in recent years, the technology for researching radar detection performance is rapidly developed, and a radar model detection method and a radar actual measurement correction method are more available, but because the functional relationship between the factors and the actual detection distance of a radar is very complex and a large amount of noise exists in data, a mathematical expression with good universality and accuracy is difficult to construct, in addition, the actual measurement data (sample) is insufficient, an evaluation expert predicts and assigns internal parameters of a model, and the constructed model has artificial traces in different degrees;
due to the characteristics of complexity, variability, dynamics and the like of a real battlefield environment, effective detection of a radar obtained by looking up or expert experience of a traditional radar power diagram has large deviation from an actual detection value, so that the actual requirement is difficult to meet, the data quantity in the countermeasure process is limited and the characteristics are various, the data acquisition and acquisition difficulty is large, a deep learning model depends on a large amount of training data for support, and the existing data quantity is difficult to support the learning and training of the model, so that the invention provides the uncertain data driven radar early warning detection modeling method to solve the problems in the prior art.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide an uncertain data driven radar early warning detection modeling method, which generates information particles by using a clustering algorithm from a data perspective to capture structural information hidden in a data space, so as to reduce the influence of uncertain factors on the data, and meanwhile, a TS topology structure, which is a combination of qualitative knowledge described by an IF-THEN fuzzy rule and quantitative knowledge represented by a local linear model, has a concise and clear form, and can approach any nonlinear model with any precision, thereby facilitating the implementation of the fitting of a complex nonlinear model.
In order to realize the purpose of the invention, the invention is realized by the following technical scheme: an uncertain data driven radar early warning detection modeling method comprises the steps of converting uncertainty description into digital information based on a fuzzy clustering method, generating a fuzzy set relevant to model action, establishing a clustering center by using fuzzy C-means clustering, combining a spatial structure of training data with the fuzzy set, further establishing a TS fuzzy rule model based on an IF-THEN rule, and enabling the TS fuzzy rule model to be used for driving uncertain data to be drivenInput data x k And corresponding output value y k K is 1,2, …, N, where x k ∈R n For n-dimensional data, the following steps are performed:
step one, establishing a relation between mapping input data and output data of 'IF-THEN' rules, wherein each rule represents a subspace of influencing factors of radar effective detection distance, and THEN the subspace has
IFx k isA i (x k ),THENy i isf i (x k ),i＝1,…,c
Where k is 1,2, …, N is the number of input data, x is k Is an n-dimensional input variable, c is the number of fuzzy rules, A i (x k ) Is a multivariate membership function of the ith rule, y, obtained by a clustering algorithm i Is the ith output under a different rule, f i (x k ) Is and the input variable x k A related local linear function;
step two, using the FCM as a structure identification method, and obtaining an input-output space R through the FCM n+1 Cluster center of [ v ] i w i ]From a membership function A i (x k ) To characterize the fuzzy partition matrix in the conditional part of the rule, the calculation formula is as follows (1) and (2):
Figure BDA0003045099400000031
Figure BDA0003045099400000032
wherein m is the fuzzification coefficient;
step three, establishing a local linear function, defining a conclusion part of the rule by the linear function, and expanding the linear function of the conclusion part by a Taylor expansion around a prototype in an input and output space;
step four, establishing a fuzzy rule model and optimizing parameters, summarizing all rules and membership functions related to the rules,obtaining a target output, using the predicted output
Figure BDA0003045099400000033
And the actual output y k As an objective function to calculate the parameter a of the local linear function i . The performance of the model and the sensitivity to noise are measured by the root mean square error, and the calculation formula is as follows:
Figure BDA0003045099400000034
the further improvement lies in that: and in the second step, the number of the rules is equal to the number of the clustering centers.
The further improvement lies in that: the linear function in the third step is
Figure BDA0003045099400000035
Wherein a is i Representing a function f along a local linear i (x k ) A slope parameter of
Figure BDA0003045099400000036
The further improvement lies in that: to the local linear function f in the third step i (x k ) After expansion, it is represented by the following formula:
Figure BDA0003045099400000041
local linear function f located around a prototype in data space i (x k ) The influence of uncertainty factors in the data on the modeling can be reduced to a certain extent.
The further improvement lies in that: for the target output obtained in the fourth step
Figure BDA0003045099400000042
Indicates that there is
Figure BDA0003045099400000043
Derived from a linear function extended in step three
Figure BDA0003045099400000044
The further improvement lies in that: in order to effectively represent the structural characteristics in the local input-output subspace, the sum of the square errors of the predicted output and the actual output is taken as a fitness function:
Figure BDA0003045099400000045
order to
z i ＝A i (x)(x-v i ) (9)
Figure BDA0003045099400000046
And the following formula briefly describes the model
Figure BDA0003045099400000047
Let s be [ y 1 -h 1 ，y 2 -h 2 ，...，y N -h N ] T And Z is ═ Z 11 ，z 12 ，…，z 1c ；z 21 ，z 22 ，…，z 2c ；…，z N1 ，z N2 ，…，z Nc ]Then function writing
Figure BDA0003045099400000048
The further improvement lies in that: using a minimum of twoMultiplying the minimization formula (12) to obtain a parameter slope which is expressed as a opt ＝(Z T Z) -1 Z T s。
The invention has the beneficial effects that: according to the method, from the data perspective, information particles are generated by using a clustering algorithm to capture structural information hidden in a data space, the influence of uncertain factors on data can be reduced, meanwhile, a TS topological structure formed by combining qualitative knowledge described by an IF-THEN fuzzy rule and quantitative knowledge represented by a local linear model has a simple and clear form, and can approach any nonlinear model with any precision, so that the method is favorable for realizing the fitting of a complex nonlinear model.
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FIG. 1 is a modeling flow diagram of the present invention.
Fig. 2 is a schematic diagram of model output and actual output of different data when embodiment c is 3.
Fig. 3 is a schematic diagram of model output and actual output of different data when embodiment c is 5.
Fig. 4 is a schematic diagram of model output and actual output of different data when embodiment c is 7.
Fig. 5 is a schematic diagram of model output and actual output of different data when embodiment c is 9.
Fig. 6 is a schematic diagram of model output and actual output of different data when embodiment c is 11.
FIG. 7 is a boxplot of the RMSE for a training set under different data for an embodiment of the present invention.
FIG. 8 is a box plot of RMSE for a test set under different data for an embodiment of the present invention.
Detailed Description
In order to further understand the present invention, the following detailed description will be made with reference to the following examples, which are only used for explaining the present invention and are not to be construed as limiting the scope of the present invention.
As shown in fig. 1, the embodiment provides an uncertain data driven radar early warning detection modeling method, which includes converting uncertainty description into digital information based on a fuzzy clustering method, and generatingEstablishing a cluster center by using fuzzy C-means clustering, combining the spatial structure of training data with the fuzzy set, further establishing a TS fuzzy rule model based on an IF-THEN rule, and enabling input data x to be input k And corresponding output value y k K is 1,2, …, N, where x k ∈R n For n-dimensional data, the following steps are performed:
step one, establishing a relation between mapping input data and output data of 'IF-THEN' rules, wherein each rule represents a subspace of influencing factors of radar effective detection distance, and THEN the subspace has
IFx k isA i (x k ),THENy i isf i (x k ),i＝1,…,c
Where k is 1,2, …, N, N is the number of input data, x k Is an n-dimensional input variable, c is the number of fuzzy rules, A i (x k ) Is a multivariate membership function of the ith rule, y, obtained by a clustering algorithm i Is the ith output under a different rule, f i (x k ) Is and the input variable x k A related local linear function;
step two, taking the FCM as a structure identification method, and obtaining an input-output space R through the FCM n+1 Cluster center of [ v ] i w i ]Wherein the number of rules is equal to the number of cluster centers, as determined by a membership function A i (x k ) To characterize the fuzzy partition matrix in the conditional part of the rule, the calculation formula is as follows (1) and (2):
Figure BDA0003045099400000061
Figure BDA0003045099400000071
wherein m is the fuzzification coefficient;
step three, establishing a local linear function, and using the linear function as the conclusion part of the ruleNumber f i (x k ) Definition of
Figure BDA0003045099400000072
Wherein a is i Representing a function f along a local linear i (x k ) A slope parameter of
Figure BDA0003045099400000073
And extending the linear function of the conclusion part by a Taylor expansion mode around the prototype in the input and output space to obtain
Figure BDA0003045099400000074
Local linear function f located around a prototype in data space i (x k ) The influence of uncertainty factors in the data on the modeling can be reduced to a certain extent. (ii) a
Step four, establishing a fuzzy rule model and optimizing parameters, summarizing all rules and membership functions related to the rules, and obtaining target output
Figure BDA0003045099400000075
Indicate that then there is
Figure BDA0003045099400000076
According to a linear function f extended in step three i (x k ) To obtain
Figure BDA0003045099400000077
In order to effectively represent the structural characteristics in the local input and output subspace, the sum of the square errors of the prediction output and the actual output is used as a fitness function:
Figure BDA0003045099400000078
order to
z i ＝A i (x)(x-v i ) (9)
Figure BDA0003045099400000081
And the following formula briefly describes the model
Figure BDA0003045099400000082
Let s be [ y 1 -h 1 ，y 2 -h 2 ，...，y N -h N ] T And Z is ═ Z 11 ，z 12 ，…，z 1c ；z 21 ，z 22 ，…，z 2c ；…，z N1 ，z N2 ，…，z Nc ]Then function writing
Figure BDA0003045099400000083
Minimizing the formula (12) by using a least square method to obtain a parameter slope which is expressed as a opt ＝(Z T Z) -1 Z T s, calculating the difference between the model output and the actual output by using the root mean square error to measure the performance of the model and the sensitivity to noise, wherein the calculation formula is as follows:
Figure BDA0003045099400000084
examples
The experimental verification is carried out under the condition that the red and blue parties carry out attack and defense combat under the appointed plan. The forces of both parties are configured to include air combat units (fighter plane and bomber) and ground/sea combat units (ground defense facilities and defense naval vessels). Harvesting machineCollecting radar detection distance information of 10-type radars under different parameter configurations on a military chess deduction platform, screening five characteristics having important influence on effective detection distance of the radars from the radar detection distance information through parameter correlation test, and mapping [0,1 ] of original data by using a discrete standardization method]In the meantime. Respectively taking the influence factors of the normalized radar effective detection distance and the normalized effective detection distance as an input feature vector and a result vector to form a training set X ═ X 1 ,x 2 ,…,x N ]。
The cross-validation method was used to randomly divide 250 groups of data into training samples (90%) and test sets (10%). In order to verify the robustness and effectiveness of the model for uncertain data, noises (the ranges are +/-5%, +/-10% and 20%) with different intensities and obeying normal distribution are sequentially generated, and all training data in the characteristics influencing the effective detection distance of the radar are disturbed.
Noise data and noise-free data with different proportions are respectively substituted into the constructed fuzzy rule model, and the output prediction value is shown in figures 2-6 of the attached drawings of the specification. And testing the predicted detection distance obtained by the model in the set. It can be seen that the results obtained by the fuzzy rule model can be well fitted to the actual output regardless of whether noise is added to the data or not. As c gradually increases, the difference between the predicted output and the actual output gradually decreases.
As shown in fig. 7 and 8 of the drawings according to the specification, RMSE is decreasing as c increases. Adding noise of different strengths in the training set has some effect on the training results, and this effect starts to be significant as the number of clusters increases. In the test set, the RMSE results of different noise intensity data for the same cluster number did not change significantly.
TABLE 1 average RMSE of fuzzy models for different data under different number of rules
Figure BDA0003045099400000091
Table 1 lists the RMSE results calculated by the fuzzy rule model of the feature data affecting radar detection under different noise intensities, and it can be seen that the performance result of the fuzzy rule model for predicting the effective detection distance is improved as the number of the cluster centers increases, regardless of whether the data is added with noise. However, an excessive number of rules may cause an overfitting of the model. In particular, statistical analysis is performed on different data results under the same rule number, and the RMSE change rate is found to be not more than the intensity of the added noise. This demonstrates that the model is robust to interference from uncertain data. The RMSE results were observed after increasing the noise, and in general, the greater the noise intensity, the worse the results of the test set. But partial data produces better results than the original data, which may be that some random noise causes the data to move closer to the prototype, producing occasional results.
According to the radar early warning detection modeling method driven by uncertain data, from the angle of data, information particles are generated by using a clustering algorithm to capture structural information hidden in a data space, the influence of uncertain factors on the data can be reduced, meanwhile, TS topological structures of qualitative knowledge and quantitative knowledge represented by a local linear model and described by an IF-THEN fuzzy rule have a simple and clear form, can approach any nonlinear model with any precision, and are favorable for realizing the fitting of a complex nonlinear model.
The foregoing shows and describes the general principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. An uncertain data driven radar early warning detection modeling method is characterized in that uncertainty description is converted into digital information based on a fuzzy clustering algorithm, and a fuzzy set relevant to model action is generatedEstablishing a clustering center by using fuzzy C-means clustering, combining a spatial structure of training data with a fuzzy set, establishing a TS fuzzy rule model based on an IF-THEN rule, and enabling input data x k And corresponding output value y k K is 1,2, …, N, where x k ∈R n For n-dimensional data, the following steps are performed:
step one, establishing an 'IF-THEN' rule to realize the relation mapping between input data and output data, wherein each rule represents a subspace of influence factors of radar effective detection distance, and THEN the subspace has
IF x k is A i (x k )，THEN y i is f i (x k )，i＝1，…，c
Where k is 1, …, N, N is the number of input data, x k Is an n-dimensional input variable, c is the number of fuzzy rules, A i (x k ) Is a multivariate membership function of the ith rule, y, obtained by a clustering algorithm i Is the ith output under a different rule, f i (x) Is and the input variable x k A related local linear function;
step two, taking the FCM as a structure identification method, and obtaining an input-output space R through the FCM n+1 Cluster center of [ v ] i w i ]From a membership function A i To characterize the fuzzy partition matrix in the rule condition part, the calculation formula is as follows (1) and (2):
Figure FDA0003675352450000011
Figure FDA0003675352450000012
wherein m is the fuzzification coefficient;
step three, establishing a local linear function, wherein a conclusion part of a rule is defined by the linear function, and the linear function of the conclusion part is expanded by a Taylor expansion formula around a prototype in an input and output space;
step four, establishing a fuzzy rule model and optimizing parameters, obtaining target output by summarizing all rules and membership functions related to the rules, and using the target output
Figure FDA0003675352450000021
Indicates that there is
Figure FDA0003675352450000022
Derived from a linear function extended in step three
Figure FDA0003675352450000023
In order to effectively represent the structural characteristics in the local input-output subspace, the sum of the square errors of the predicted output and the actual output is taken as a fitness function:
Figure FDA0003675352450000024
order to
z i ＝A i (x)(x-v i ) (9)
Figure FDA0003675352450000025
And the following formula briefly describes the model
Figure FDA0003675352450000026
Let s be [ y 1 -h 1 ,y 2 -h 2 ,…,y N -h N ] T And Z ═ Z11, Z12, …, Z1 c; z21, z22, …, z2 c; …, zN1，zN2，…，zNc]Then function writing
Figure FDA0003675352450000027
Using prediction output
Figure FDA0003675352450000028
And the actual output y k As an objective function to calculate the parameter a of the local linear function i The performance of the model and the sensitivity to noise are measured by the root mean square error, and the calculation formula is as follows:
Figure FDA0003675352450000031
2. the uncertain data driven radar early warning detection modeling method according to claim 1, wherein the method comprises the following steps: and in the second step, the number of the rules is equal to the number of the clustering centers.
3. The uncertain data driven radar early warning detection modeling method according to claim 1, wherein: the linear function in the third step is
Figure FDA0003675352450000032
Wherein a is i Representing a function f along a local linear i (x) A slope parameter of
Figure FDA0003675352450000033
Figure FDA0003675352450000034
4. The uncertain data driven radar early warning detection modeling method according to claim 1, wherein the method comprises the following steps: to the local linear function f in the third step i (x) After expansion, the formula is shown as follows:
Figure FDA0003675352450000035
the local linear function is located around the prototype in the data space, and when the data is affected by uncertainty factors, the local linear function may have a reduced effect.
5. The uncertain data driven radar early warning detection modeling method according to claim 1, wherein the method comprises the following steps: in the fourth step, a parameter slope is obtained after minimizing the formula (12) by using a least square method and is expressed as a opt ＝(Z T Z) -1 Z T s。
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