CN112800082A - Air target identification method based on confidence rule base inference - Google Patents

Air target identification method based on confidence rule base inference Download PDF

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CN112800082A
CN112800082A CN202110197690.4A CN202110197690A CN112800082A CN 112800082 A CN112800082 A CN 112800082A CN 202110197690 A CN202110197690 A CN 202110197690A CN 112800082 A CN112800082 A CN 112800082A
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rule base
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CN112800082B (en
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黄健
刘嘉迪
郝建国
龚建兴
周葱
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National University of Defense Technology
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Abstract

The invention discloses an aerial target identification method based on confidence rule base inference, which is characterized in that a confidence rule base model which takes aerial target attribute information as input and takes an aerial target type as output is established in a linear combination mode, the classification number of a target identification problem is associated with the rule number of a confidence rule base, the rule number is set to be equal to an identification classification number, an initial confidence rule base is established, parameter optimization is carried out on the confidence rule base through a local particle swarm algorithm, multi-source information is inferred and fused, then the confidence level is mapped into an identification result, and the aerial target is identified. The recognition method provided by the invention effectively enhances the recognition precision of the aerial target recognition model based on the confidence rule base inference, solves the problem of low recognition accuracy of the initial confidence rule base, and meanwhile, the confidence rule base is set as a white box system, the fusion inference process is visible, experts can participate, and the result has traceability and interpretability.

Description

Air target identification method based on confidence rule base inference
Technical Field
The invention belongs to the field of target identification of multi-source information fusion, and particularly relates to an aerial target identification method based on confidence rule base reasoning.
Background
The rapid development of the target recognition technology enables the target recognition technology to be widely applied to civil fields such as face recognition and license plate recognition, and plays a significant role in military fields. In the modern war, especially for the air and space battlefield, the war has the characteristics of burstiness, rapidity, large depth, omnibearing, and short duration. The battlefield is very variable, and it is very difficult to require a ground commander to make an accurate command decision in a very short time, so that it is very important to quickly, accurately and reliably identify a battlefield target, and whether the type of an aerial target is accurately identified or not directly influences the deployment, distribution and effective attack of air-defense fire.
However, relying only on information evidence obtained by a single sensor, it is difficult to distinguish the real target to be attacked from various false targets and random disturbances. For this reason, a multi-sensor system is generally used to integrate different detection information of various sensors to identify the target. In the process of target identification, information from a plurality of sensors has various expression forms and complex relations, and due to the complex environment of a battlefield, the information has a plurality of uncertainties, and the traditional methods such as Bayesian inference, support vector machines and the like can not effectively process the uncertainty information, so that the type of the aerial target can not be effectively and accurately identified. Therefore, it is necessary to provide an air target identification method capable of better processing multiple types of messages under the condition of fusion uncertainty.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an air target identification method based on confidence rule base reasoning.
In order to achieve the purpose, the invention adopts the technical scheme that:
an air target identification method based on confidence rule base reasoning comprises the following steps:
s1, constructing a confidence rule base for aerial target recognition based on a linear combination mode
S11, input and output variable definition and aerial target recognition model establishment
Firstly, defining air target characteristic information as input of a confidence rule reasoning method, and then defining an air target type as output of the confidence rule reasoning method to obtain a confidence rule base model for air target identification;
s12, assuming that the number of the precondition attributes in the identification problem is T, the number of the training data groups is H, and the number of the known target classifications is C, the matrix form of the aerial target identification problem data set is as follows:
Figure BDA0002947694400000021
wherein, PiThe ith row of the matrix is represented, namely a row vector formed by the ith group of input data; u shapejRepresenting the jth column of the matrix, namely a column vector formed by the jth attribute of all input data; x is the number ofi,jRepresenting the j attribute value of the ith group of classified data as an element of the matrix;
because the target classification number is known to be C, each precondition attribute is correspondingly provided with C reference values, the utility grade number is set to be C, the rule number in the confidence rule base of the aerial target identification is known to be C according to the linear combination mode, and the rule number is used as the basis of the inference of the confidence rule base;
s13, setting the parameter value of the confidence rule base according to the data set
Setting the initial weight value of the kth rule in the confidence rule base as:
θk＝1
setting the initial weight value of the ith precondition attribute in the confidence rule base as:
σi＝1
setting the initial values of all reference values corresponding to the ith precondition attribute in the kth rule in the confidence rule base as:
Figure BDA0002947694400000031
wherein the content of the first and second substances,
Figure BDA0002947694400000032
an initial value x representing each reference value corresponding to the ith precondition attribute in the kth ruleh,iThe ith attribute value representing the h-th group of classified data,
Figure BDA0002947694400000033
represents the initial value of each reference value corresponding to the ith precondition attribute in the C rule,
Figure BDA0002947694400000034
representing initial values of all reference values corresponding to the ith precondition attribute in the 1 st rule, wherein L represents the number of confidence rules, and H represents the group number of training data;
the evaluation grade D in the confidence rule basenThe method comprises the following steps:
Dn＝n,1≤n≤N
setting the confidence corresponding to the nth evaluation level in the kth rule in the confidence rule base as:
Figure BDA0002947694400000035
wherein, betan,kRepresenting the confidence, rand, corresponding to the nth evaluation level in the kth rule in the confidence rule basei() Represents the ith value, rand, in a random number sequence of length L between 0 and 1n() Representing the nth value in a random number sequence with the length of L between 0 and 1, wherein N represents the dimension of a conclusion vector, and L represents the number of confidence rules;
s2, parameters of confidence rule base constructed based on local particle swarm optimization training
Carrying out optimization training on parameters of the belief rule base, wherein the optimization algorithm is a local particle swarm algorithm, and a motion function of the optimization algorithm is defined as:
Vi(t+1)＝ωVi(t)+c1r1(pbest-xi(t))+c2r2(lbest-xi(t))
xi(t+1)＝xi(t)+vi(t+1)
wherein, Vi(t) is the velocity of the particles, xi(t) is the current position of the particle, t is the number of iterations, ω is the inertial weight, c1And c2Is a learning factor, r1And r2Is [0,1 ]]Random number between,/bestFor a neighborhood optimum, pbestAn individual optimum value;
the symbolic expression of the confidence rule base parameter optimization model is as follows:
min{ξ(V)}
s.t.A(V)＝0,B(V)≥0
wherein V represents a group consisting of
Figure BDA0002947694400000041
The composed parameter vector, xi (V) represents the inference error; a (V) represents an equality constraint; b (P) represents an inequality constraint condition, inputs historical observation data into a confidence rule base to generate aerial target confidence output, obtains parameters according to optimization model optimization training, and finally obtains the confidence rule base after parameter optimization training;
s3, reasoning and outputting the result based on evidence reasoning and realizing confidence rule base
S31, calculating activation weight
First, input information xiConversion to relative reference value
Figure BDA0002947694400000042
The matching degree of (2):
Figure BDA0002947694400000043
wherein the content of the first and second substances,
Figure BDA0002947694400000044
indicates the matching degree, x, of the ith input attribute in the jth ruleiAn input representing an attribute of the object is entered,
Figure BDA0002947694400000045
represents the initial value of each reference value corresponding to the ith precondition attribute in the kth rule,
Figure BDA0002947694400000046
representing the initial value of each reference value corresponding to the ith precondition attribute in the (k + 1) th rule;
in finding the degree of matching
Figure BDA0002947694400000047
Then, the rules are fused, calculated and output by an evidence reasoning algorithm; when the system has input, some principle based on the confidence rule base is activated, and the activation weight calculation formula of the k-th rule is as follows:
Figure BDA0002947694400000051
wherein the content of the first and second substances,
Figure BDA0002947694400000052
representing the ith input x in the kth ruleiRelative to a reference value
Figure BDA0002947694400000053
The degree of matching of (a) to (b),
Figure BDA0002947694400000054
representing the ith input x in the ith ruleiRelative to a reference value
Figure BDA0002947694400000055
The matching degree of (1), L is the total rule number, and M is the number of the precondition attributes; thetakIs the weight of the kth rule;
s32 and ER algorithm fusion
After the activation degree of the rules is calculated, the rules in the confidence rule base are fused by utilizing an ER algorithm, and the formula is as follows:
Figure BDA0002947694400000056
Figure BDA0002947694400000057
wherein the content of the first and second substances,
Figure BDA0002947694400000058
indicates the corresponding output evaluation grade D under the kth rulejN denotes the dimensionality of the conclusion vector, L denotes the number of confidence rules, βj,kIndicates the confidence coefficient, omega, of the jth evaluation level in the kth rule in the rule basekThe activation weight of the kth rule;
s33, outputting the result
Selecting the output grade corresponding to the highest confidence as the final target recognition result:
Figure BDA0002947694400000059
preferably, in step S2, the inference error ξ (V) can be represented by a mean square error, and the formula is as follows:
Figure BDA0002947694400000061
preferably, said EiThe set values are:
Figure BDA0002947694400000062
wherein, ymFor the actual recognition result of the ith set of input data in object recognition,
Figure BDA0002947694400000063
and identifying the model of the ith group of input data in the target identification.
Preferably, in step S2, the equality constraint a (v) and the inequality constraint b (v) are:
(1) attribute weight normalized to the kth reference value of the ith attribute
Figure BDA0002947694400000064
The following constraints must be satisfied:
Figure BDA0002947694400000065
wherein, lbiAnd ubiRespectively representing the minimum value and the maximum value of the ith attribute in the training data, wherein L represents the number of confidence rules, and M is the number of precondition attributes;
(2) the confidence level of the initial rule output needs to satisfy:
0≤βj,k≤1，j＝1,2,…,N，k＝1,2,…,L
Figure BDA0002947694400000066
wherein, L represents the number of confidence rules, and N represents the dimension of the conclusion vector;
(3) the rule weight, after the rule weight is standardized, the value of the rule weight should be between 0 and 1, namely:
0≤θk≤1，k＝1,2,…,L
wherein L represents the number of confidence rules.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides an air target recognition method based on confidence rule base inference, which establishes a confidence rule base model taking air target attribute information as input and air target type as output by adopting a linear combination mode, associates classification numbers of target recognition problems with rule numbers of a confidence rule base, sets the rule numbers to be equal to recognition classification numbers, infers and fuses multi-source information, then maps confidence levels to recognition results and recognizes air targets, thereby improving the calculation method of individual matching degree in the traditional confidence rule base, effectively overcoming the 'combination explosion' problem of the rule numbers and the 'zero activation' problem of the rules, optimizing parameters of the confidence rule base by local particle swarm algorithm, effectively enhancing the recognition accuracy of the air target recognition model based on the confidence rule base inference, solving the problem of low recognition accuracy of an initial confidence rule base, meanwhile, the confidence rule base is set as a white box system, the fusion reasoning process is visible, experts can participate, and the result has traceability and interpretability.
Drawings
FIG. 1 is a diagram illustrating a linear combination method used in constructing a confidence rule base according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating a traversal assembly used in the prior art to construct a confidence rule base;
FIG. 3 is a diagram of a model for optimizing confidence rule base parameters according to an embodiment of the present invention;
FIG. 4 is a flowchart of an air target recognition method based on belief rule base inference according to an embodiment of the present invention;
FIG. 5 is a diagram of an aerial target recognition model of a confidence rule base in an embodiment of the present invention;
fig. 6 is a flowchart of local particle swarm optimization in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 4, the air target identification method based on confidence rule base inference provided in the embodiment of the present invention specifically includes the following steps:
s1, constructing a confidence rule base for aerial target recognition based on a linear combination mode
S11, input and output variable definition and aerial target recognition model establishment
Firstly, defining air target characteristic information as input of a confidence rule reasoning method, and then defining an air target type as output of the confidence rule reasoning method to obtain a confidence rule base model for air target identification;
as the Air targets are various, there are Tactical Ballistic Missiles (TBM), Air-to-Ground missiles (AGM), Early Warning monitors (EWA), Stealth Aircrafts (SA), anti-radiation missiles, fighters, bombers, armed helicopters and transporters, and the TBM, AGM, EWA and SA are four typical Air targets, and the others are Common Targets (CT), therefore, the embodiment of the invention selects four typical Air targets as the output of the confidence rule inference method, and the target characteristic information thereof is described from the following five aspects including radar scanning area sigma (m2), horizontal velocity V (horizontal velocity)H(m/s) vertical velocity VV(m/s), the flying height H (m), the flying acceleration a (m/s2), and more than 5 parameters are selected as the input of the aerial target recognition model, so that the structure of the aerial target recognition model of the confidence rule base (BRB) can be obtained as shown in FIG. 5.
For the characteristics of the aerial target identification problem, the embodiment of the present invention does not use the conventional way of traversing all candidate values of each antecedent attribute when constructing the BRB, as shown in fig. 2, but constructs each rule in the BRB by a linear combination way, as shown in fig. 1.
S12, assuming that the number of the precondition attributes in the identification problem is T, the number of the training data groups is H, and the number of the known target classifications is C, the matrix form of the aerial target identification problem data set is as follows:
Figure BDA0002947694400000091
wherein, PiThe ith row of the matrix is represented, namely a row vector formed by the ith group of input data; u shapejRepresenting the jth column of the matrix, namely a column vector formed by the jth attribute of all input data; x is the number ofi,jRepresenting the j attribute value of the ith group of classified data as an element of the matrix;
c reference values are set for each premise attribute, the number of utility grades is set as C, the rule number in the confidence rule base of the aerial target identification is known according to a linear combination mode, and the rule number is C and serves as the basis of the inference of the confidence rule base;
it can be known from the design of the embodiment S11 of the present invention that the number of the prerequisite attributes in the problem identification in the embodiment of the present invention is 5, which are the radar scanning area, the horizontal velocity, the vertical velocity, the flying height, and the flying acceleration, that is, the number of the prerequisite attributes is 5
{A1,A2,A3,A4,A5The identification result is tactical ballistic missile, air-to-ground missile, anti-radiation missile and stealth airplane, namely D ═ TBM (D) } (D)1),AGM(D2),EWA(D3),SA(D4)}
Since the recognition result is 4 types, the number of rules of the initial BRB recognition model is 4 according to the linear combination method.
S13, setting the parameter value of the confidence rule base according to the data set
Setting the initial weight value of the kth rule in the confidence rule base as:
θk＝1
setting the initial weight value of the ith precondition attribute in the confidence rule base as:
σi＝1
setting the initial values of all reference values corresponding to the ith precondition attribute in the kth rule in the confidence rule base as:
Figure BDA0002947694400000101
wherein L represents the number of BRB system rules, xiRepresenting the value of the ith attribute in the data;
according to data measured by a historical data set, the minimum maximum value of each attribute data of the target can be known, the boundary data of each attribute of the target is shown in the following table 1, and then the initial values of each reference value corresponding to the ith precondition attribute in the kth rule are obtained by uniformly distributing the upper and lower bounds of the corresponding data;
TABLE 1 boundary data for various attributes of an airborne target
Serial number σ(m2) VH(m/s) VV(m/s) H(m) a(m/s2) Object type
1 1.5 2180 370 28500 40 TBM
2 1.7 1650 250 5000 22 AGM
3 1.6 560 12 300 1.8 SA
4 0.22 1700 500 650 25 AGM
5 0.11 450 27 570 2.1 AGM
6 0.33 150 18 700 5 EWA
Will trust the rule baseMiddle evaluation grade DnThe method comprises the following steps:
Dn＝n,1≤n≤N
setting the confidence corresponding to the nth evaluation level in the kth rule in the confidence rule base as:
Figure BDA0002947694400000102
wherein, randi() Represents the ith value in a random number sequence with the length of L between 0 and 1;
thus, the initial confidence rule base established is shown in table 2 below;
TABLE 2 initial confidence rule base
Figure BDA0002947694400000103
Figure BDA0002947694400000111
S2, parameters of confidence rule base constructed based on local particle swarm optimization training
As shown in fig. 3, the parameters of the belief rule base are optimally trained, the optimization algorithm is a local particle swarm algorithm, and the motion function is defined as:
Vi(t+1)＝ωVi(t)+c1r1(pbest-xi(t))+c2r2(lbest-xi(t))
xi(t+1)＝xi(t)+vi(t+1)
where ω is the inertial weight, c1And c2Is a learning factor, r1And r2Is [0,1 ]]Random number between,/bestFor a neighborhood optimum, pbestAn individual optimum value;
the optimization flow chart of the local particle swarm algorithm is shown in fig. 6, and the specific process is realized as follows:
step 1: initializing the particle swarm. And randomly initializing the speed and the position of each particle in the population within the range of the constraint condition, wherein each particle comprises parameters needing to be trained in the BRB optimization model.
Step 2: a particle fitness value is calculated. And calculating the fitness value of each particle according to the fitness function, namely the MSE value output by the system.
And step 3: and searching individual optimal solution. For each particle, its fitness value is compared with its own recorded individual optimal solution pbestIf the fitness is better, the information of the current particle is used for updating the individual optimal solution pbest(ii) a Otherwise, no processing is performed.
And 4, step 4: and searching a neighborhood optimal solution. For each particle, its fitness value is compared to the best solution l recorded in its neighborhoodbestIf the fitness is better, updating the local optimal solution l of the neighborhood by using the information of the current particlebest(ii) a Otherwise, no processing is performed.
And 5: and continuously and iteratively updating the speed and the position of each particle through the motion function of the algorithm.
Step 6: when the preset maximum iteration number G is reachedmaxThe search is stopped, at which time the domain-optimal solution l isbestAs an output result, assigning the position of the BRB to the corresponding BRB parameter to obtain an optimized BRB system; otherwise, returning to the step 3.2 to continue searching.
The symbolic expression of the confidence rule base parameter optimization model is as follows:
min{ξ(V)}
s.t.A(V)＝0,B(V)≥0
wherein V represents a group consisting of
Figure BDA0002947694400000121
The composed parameter vector, xi (V) represents the inference error; a (V) represents an equality constraint; b (P) represents an inequality constraint condition, inputs historical observation data into a confidence rule base to generate aerial target confidence output, obtains parameters according to optimization model optimization training, and finally obtains the confidence rule base after parameter optimization training;
the inference error ξ (V) may be represented as the mean square error, and the formula is as follows:
Figure BDA0002947694400000122
wherein E isiThe set values are:
Figure BDA0002947694400000123
wherein, ymFor the actual recognition result of the ith set of input data in object recognition,
Figure BDA0002947694400000124
for the model recognition result of the ith group of input data in the target recognition, when the actual recognition result is consistent with the model recognition result, EiThe value is 0, when the actual recognition result is inconsistent with the model recognition result, EiThe value is 1.
The above equality constraint a (v) and inequality constraint b (v) are:
(1) attribute weight normalized to the kth reference value of the ith attribute
Figure BDA0002947694400000125
The following constraints must be satisfied:
Figure BDA0002947694400000131
wherein, lbiAnd ubiRespectively representing the minimum value and the maximum value of the ith attribute in the training data;
(2) the confidence level of the initial rule output needs to satisfy:
0≤βj,k≤1，j＝1,2,…,N，k＝1,2,…,L
Figure BDA0002947694400000132
(3) the rule weight, after the rule weight is standardized, the value of the rule weight should be between 0 and 1, namely:
0≤θk≤1，k＝1,2,…,L。
s3, reasoning and outputting the result based on evidence reasoning and realizing confidence rule base
S31, calculating activation weight
First, input information xiConversion to relative reference value
Figure BDA0002947694400000133
The matching degree of (2):
Figure BDA0002947694400000134
wherein the content of the first and second substances,
Figure BDA0002947694400000135
indicates the matching degree, x, of the ith input attribute in the jth ruleiAn input representing an attribute of the object is entered,
Figure BDA0002947694400000136
represents the initial value of each reference value corresponding to the ith precondition attribute in the kth rule,
Figure BDA0002947694400000137
representing the initial value of each reference value corresponding to the ith precondition attribute in the (k + 1) th rule;
in finding the degree of matching
Figure BDA0002947694400000141
Then, the rules are fused, calculated and output by an evidence reasoning algorithm; when the system has input, some principle based on the confidence rule base is activated, and the activation weight calculation formula of the k-th rule is as follows:
Figure BDA0002947694400000142
wherein the content of the first and second substances,
Figure BDA0002947694400000143
representing the ith input x in the kth ruleiRelative to a reference value
Figure BDA0002947694400000144
The degree of matching of (a) to (b),
Figure BDA0002947694400000145
representing the ith input x in the ith ruleiRelative to a reference value
Figure BDA0002947694400000146
The matching degree of (1), L is the total rule number, and M is the number of the precondition attributes; thetakIs the weight of the kth rule;
s32 and ER algorithm fusion
After the activation degree of the rules is calculated, the rules in the confidence rule base are fused by utilizing an ER algorithm, and the formula is as follows:
Figure BDA0002947694400000147
Figure BDA0002947694400000148
wherein the content of the first and second substances,
Figure BDA0002947694400000149
indicates the corresponding output evaluation grade D under the kth rulejN denotes the dimensionality of the conclusion vector, L denotes the number of confidence rules, βj,kIndicates the confidence coefficient, omega, of the jth evaluation level in the kth rule in the rule basekThe activation weight of the kth rule;
s33, outputting the result
Selecting the output grade corresponding to the highest confidence as the final target recognition result:
Figure BDA0002947694400000151
randomly selecting 100 groups of measured data as training data, and training parameters by using a local particle swarm algorithm to obtain the rule of the optimized BRB system as shown in the following table 3:
TABLE 3 optimized confidence rule base
Figure BDA0002947694400000152
The remaining 20 sets of data were tested using the parameter optimized model, and the recognition results are shown in table 4 below.
TABLE 4 target identification results
Figure BDA0002947694400000153
Figure BDA0002947694400000161
As can be seen from table 4, with the identification method of the present invention, 19 sets of targets in 20 sets of test data are correctly identified (group 16 is incorrectly identified), and the identification accuracy is 95%, which fully illustrates the effectiveness of the proposed identification model.
To verify the robustness of the proposed model, 10 tests were performed, with training data and test data randomly selected each time, and the test results obtained are shown in table 5 below,
TABLE 5 test results
Figure BDA0002947694400000162
The results in table 5 show that the aerial target identification method provided by the embodiment of the invention has better robustness, and the average identification accuracy is 95.5% after 10 tests.
In summary, in the air target identification method based on confidence rule base inference provided in the embodiments of the present invention, an initial confidence rule base is first constructed in a linear combination manner according to an index relationship of a target identification problem and air target situation historical data, and the confidence rule base reflects a complex nonlinear mapping relationship between an input parameter variable and a target type output; and then, optimizing the parameters of a confidence rule base through a local particle swarm algorithm to improve the identification precision of the model target, finally inputting the attribute information of the aerial target, calculating the rule weight, performing fusion reasoning on the activated multiple rules by using an evidence reasoning method, and finally obtaining the possible type of the aerial target, so as to realize the identification of the aerial target and further provide a reliable basis for battlefield situation analysis and command decision.
The above-mentioned embodiments only express the specific embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.

Claims (5)

1. An air target identification method based on confidence rule base reasoning is characterized by comprising the following steps:
s1, constructing a confidence rule base for aerial target recognition based on a linear combination mode
S11, input and output variable definition and aerial target recognition model establishment
Firstly, defining air target characteristic information as input of a confidence rule reasoning method, and then defining an air target type as output of the confidence rule reasoning method to obtain a confidence rule base model for air target identification;
s12, assuming that the number of the precondition attributes in the identification problem is T, the number of the training data groups is H, and the number of the known target classifications is C, the matrix form of the aerial target identification problem data set is as follows:
Figure FDA0002947694390000011
wherein, PiThe ith row of the matrix is represented, namely a row vector formed by the ith group of input data; u shapejRepresenting the jth column of the matrix, namely a column vector formed by the jth attribute of all input data; x is the number ofi,jIs an element of the matrix, represents the j attribute value of the ith group of classified data,
because the target classification number is known to be C, each precondition attribute is correspondingly provided with C reference values, the utility grade number is set to be C, the rule number in the confidence rule base of the aerial target identification is known to be C according to the linear combination mode, and the rule number is used as the basis of the inference of the confidence rule base;
s13, setting the parameter values of the confidence rule base according to the data set;
s2, parameters of confidence rule base constructed based on local particle swarm optimization training
Carrying out optimization training on parameters of the belief rule base, wherein the optimization algorithm is a local particle swarm algorithm, and a motion function of the optimization algorithm is defined as:
Vi(t+1)＝ωVi(t)+c1r1(pbest-xi(t))+c2r2(lbest-xi(t))
xi(t+1)＝xi(t)+vi(t+1)
wherein, Vi(t) is the velocity of the particles, xi(t) is the current position of the particle, t is the number of iterations, ω is the inertial weight, c1And c2Is a learning factor, r1And r2Is [0,1 ]]Random number between,/bestFor a neighborhood optimum, pbestAn individual optimum value;
the symbolic expression of the confidence rule base parameter optimization model is as follows:
min{ξ(V)}
s.t.A(V)＝0,B(V)≥0
wherein V represents a group consisting of
Figure FDA0002947694390000021
The composed parameter vector, xi (V) represents the inference error; a (V) represents an equality constraint; b (P) represents an inequality constraint condition, inputs historical observation data into a confidence rule base to generate aerial target confidence output, obtains parameters according to optimization model optimization training, and finally obtains the confidence rule base after parameter optimization training;
s3, reasoning and outputting the result based on evidence reasoning and realizing confidence rule base
S31, calculating activation weight
First, input information xiConversion to relative reference value
Figure FDA0002947694390000022
The matching degree of (2):
Figure FDA0002947694390000023
wherein the content of the first and second substances,
Figure FDA0002947694390000024
indicates the matching degree, x, of the ith input attribute in the jth ruleiAn input representing an attribute of the object is entered,
Figure FDA0002947694390000025
represents the initial value of each reference value corresponding to the ith precondition attribute in the kth rule,
Figure FDA0002947694390000026
representing the initial value of each reference value corresponding to the ith precondition attribute in the (k + 1) th rule;
in finding the degree of matching
Figure FDA0002947694390000027
Then, the rules are fused, calculated and output by an evidence reasoning algorithm; based on certain principles of the confidence rule base when the system has inputActivated, the activation weight ω of the kth rulekThe calculation formula is as follows:
Figure FDA0002947694390000031
wherein the content of the first and second substances,
Figure FDA0002947694390000032
representing the ith input x in the kth ruleiRelative to a reference value
Figure FDA0002947694390000033
The degree of matching of (a) to (b),
Figure FDA0002947694390000034
representing the ith input x in the ith ruleiRelative to a reference value
Figure FDA0002947694390000035
The matching degree of (1), L is the total rule number, and M is the number of the precondition attributes; thetakIs the weight of the kth rule;
s32 and ER algorithm fusion
After the activation degree of the rules is calculated, the rules in the confidence rule base are fused by utilizing an ER algorithm, and the formula is as follows:
Figure FDA0002947694390000036
Figure FDA0002947694390000037
wherein the content of the first and second substances,
Figure FDA0002947694390000038
indicates the corresponding output evaluation grade D under the kth rulejN denotes the direction of the conclusionDimension of the quantity, L representing the number of confidence rules, βj,kIndicates the confidence coefficient, omega, of the jth evaluation level in the kth rule in the rule basekThe activation weight of the kth rule;
s33, outputting the result
Selecting the output grade corresponding to the highest confidence as the final target recognition result:
Figure FDA0002947694390000039
2. the air target recognition method based on confidence rule base inference as claimed in claim 1, wherein in step S13, the parameter values of the confidence rule base are specifically:
setting the initial weight value of the kth rule in the confidence rule base as:
θk＝1
setting the initial weight value of the ith precondition attribute in the confidence rule base as:
σi＝1
setting the initial values of all reference values corresponding to the ith precondition attribute in the kth rule in the confidence rule base as:
Figure FDA0002947694390000041
wherein the content of the first and second substances,
Figure FDA0002947694390000042
an initial value x representing each reference value corresponding to the ith precondition attribute in the kth ruleh,iThe ith attribute value representing the h-th group of classified data,
Figure FDA0002947694390000043
represents the initial value of each reference value corresponding to the ith precondition attribute in the C rule,
Figure FDA0002947694390000044
representing initial values of all reference values corresponding to the ith precondition attribute in the 1 st rule, wherein L represents the number of confidence rules, and H represents the group number of training data;
the evaluation grade D in the confidence rule basenThe method comprises the following steps:
Dn＝n,1≤n≤N
setting the confidence corresponding to the nth evaluation level in the kth rule in the confidence rule base as:
Figure FDA0002947694390000045
wherein, betan,kRepresenting the confidence, rand, corresponding to the nth evaluation level in the kth rule in the confidence rule basei() Represents the ith value, rand, in a random number sequence of length L between 0 and 1n() And the nth value in the random number sequence with the length of L between 0 and 1 is represented, N represents the dimension of the conclusion vector, and L represents the number of the confidence rules.
3. The air target recognition method based on confidence rule base inference as claimed in claim 1, wherein in step S2, the inference error ξ (V) can be represented as the mean square error, and the formula is as follows:
Figure FDA0002947694390000051
4. the air target recognition method based on belief rule base inference as claimed in claim 3, wherein E isiThe set values are:
Figure FDA0002947694390000052
wherein, ymFor the actual recognition result of the ith set of input data in object recognition,
Figure FDA0002947694390000053
and identifying the model of the ith group of input data in the target identification.
5. The air target recognition method based on belief rule base inference as claimed in claim 1, wherein in step S2, the equality constraint a (v) and the inequality constraint b (v) are:
(1) attribute weight normalized to the kth reference value of the ith attribute
Figure FDA0002947694390000056
The following constraints must be satisfied:
Figure FDA0002947694390000054
wherein, lbiAnd ubiRespectively representing the minimum value and the maximum value of the ith attribute in the training data, wherein L represents the number of confidence rules, and M is the number of precondition attributes;
(2) the confidence of the initial rule output needs to satisfy the following constraints:
0≤βj,k≤1，j＝1,2,…,N，k＝1,2,…,L
Figure FDA0002947694390000055
wherein, L represents the number of confidence rules, and N represents the dimension of the conclusion vector;
(3) the rule weight, after the rule weight is standardized, the value of the rule weight should be between 0 and 1, namely:
0≤θk≤1，k＝1,2,…,L
wherein L represents the number of confidence rules.
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