CN112800082B - An aerial target recognition method based on belief rule base reasoning - Google Patents

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

An aerial target recognition method based on belief rule base reasoning

technical field

The invention belongs to the target identification field of multi-source information fusion, and particularly relates to an aerial target identification method based on a belief rule base reasoning.

Background technique

The rapid development of target recognition technology makes it not only widely used in civil fields such as face recognition and license plate recognition, but also plays a pivotal role in the military field. In modern warfare, especially for the air and space battlefield, the war has the characteristics of suddenness, rapidity, great depth, all-round and short duration. With the ever-changing battlefield, it is very difficult for ground commanders to make accurate command decisions in a very short period of time. Therefore, it is very important to identify battlefield targets quickly, accurately and reliably. It directly affects the deployment, distribution and effective strike of air defense firepower.

However, relying only on the information evidence obtained by a single sensor, it is difficult to distinguish the real target to be attacked from various false targets and random interference. To this end, people usually use a multi-sensor system to fuse the different detection information of various sensors to identify the target. In the process of target recognition, the information from multiple sensors has various forms and complex relationships, and due to the complex environment of the battlefield, there are many uncertainties in the information, and traditional methods such as Bayesian reasoning and support vector machines cannot be effective. The above-mentioned uncertainty information is processed, resulting in the inability to effectively and accurately identify the type of air targets. Therefore, it is necessary to provide an aerial target recognition method that can better handle multiple types of messages under the condition of fusion uncertainty.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art and provide an aerial target recognition method based on the belief rule base reasoning.

For achieving the above object, the technical scheme adopted in the present invention is:

An aerial target recognition method based on belief rule base reasoning, comprising the following steps:

S1. Build a confidence rule base for aerial target recognition based on linear combination

S11. Definition of input and output variables and establishment of air target recognition model

First define the air target feature information as the input of the confidence rule inference method, and then define the air target type as the output of the confidence rule inference method, and obtain the confidence rule base model of the air target recognition;

S12. Assuming that the number of prerequisite attributes in the recognition problem is T, the number of training data groups is H, and the number of known target classifications is C, the matrix form of the air target recognition problem dataset is:

Among them, Pi represents the i-th row of the matrix, that is, the row vector formed by the i-th group of input data; U _j represents the _j -th column of the matrix, that is, the column vector formed by the j-th attribute of all input data; x _i,j is An element of the matrix, representing the value of the jth attribute of the ith group of categorical data;

Since the number of known target classifications is C, C reference values are set corresponding to each prerequisite attribute, and the number of utility levels is set to C. According to the linear combination method, the number of rules in the confidence rule base for aerial target recognition is C. as the basis for the belief rule base reasoning;

S13. Set the parameter values of the confidence rule base according to the data set

Set the initial value of the weight of the kth rule in the confidence rule base as:

θ _k = 1

Set the initial value of the weight of the i-th premise attribute in the confidence rule base as:

σ _i =1

The initial value of each reference value corresponding to the i-th premise attribute in the k-th rule in the confidence rule base is set as:

表示第k条规则中的第i个前提属性所对应的各个参考值的初值x_h,i表示第h组分类数据的第i个属性取值，

表示第C条规则中的第i个前提属性所对应的各个参考值的初值，

表示第1条规则中的第i个前提属性所对应的各个参考值的初值，L表示置信规则的个数，H表示训练数据的组数；in,

Represents the initial value x _{h of each reference value corresponding to the i-th premise attribute in the k-th rule, i} represents the i-th attribute value of the h-th group of categorical data,

Represents the initial value of each reference value corresponding to the i-th premise attribute in the C-th rule,

Represents the initial value of each reference value corresponding to the i-th prerequisite attribute in the first rule, L represents the number of confidence rules, and H represents the number of training data groups;

Set the evaluation level D _n in the confidence rule base as:

D _n =n, 1≤n≤N

The confidence corresponding to the nth evaluation level in the kth rule in the confidence rule base is set as:

Among them, β _n,k represents the confidence level corresponding to the nth evaluation level in the kth rule in the confidence rule base, and rand ⁱ () represents the ith random number sequence of length L between 0 and 1. value, rand ⁿ () represents the nth value in the random number sequence of length L between 0 and 1, N represents the dimension of the conclusion vector, and L represents the number of confidence rules;

S2. Parameters of the confidence rule base constructed based on local particle swarm optimization training

The parameters of the confidence rule base are optimized and trained. The optimization algorithm is the local particle swarm algorithm, and its motion function is defined as:

V _i (t+1)=ωV _i (t)+c ₁ r ₁ (p _{best -xi} (t))+c ₂ r ₂ (l _{best -xi} (t))

x _i (t+1)=x _i (t)+v _i (t+1)

where V _i (t) is the velocity of the particle, _xi (t) is the current position of the particle, t is the number of iterations, ω is the inertia weight, c ₁ and c ₂ are learning factors, and r ₁ and r ₂ are [0 , 1], l _best is the neighborhood optimal value, p _best is the individual optimal 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

组成的参数向量，ξ(V)表示推理误差；A(V)表示等式约束条件；B(P)表示不等式约束条件，输入历史观测数据到置信规则库，产生空中目标置信输出，再根据优化模型优化训练得到参数，最后得出参数优化训练后的置信规则库；where V represents the

The composed parameter vector, ξ(V) represents the inference error; A(V) represents the equality constraint; B(P) represents the inequality constraint, input historical observation data to the confidence rule base, generate the air target confidence output, and then optimize according to the The parameters are obtained through model optimization training, and finally the confidence rule base after parameter optimization training is obtained;

S3. Realize the reasoning of the confidence rule base based on evidence reasoning and output the results

S31. Activation weight calculation

的匹配度：First, convert the input information _xi to relative to the reference value

match:

表示第第j条规则中的第i个输入属性的匹配度，x_i表示属性的输入，

表示第k条规则中的第i个前提属性所对应的各个参考值的初值,

表示第k+1条规则中的第i个前提属性所对应的各个参考值的初值；in,

represents the matching degree of the ith input attribute in the jth rule, x _i represents the input of the attribute,

Represents the initial value of each reference value corresponding to the i-th premise attribute in the k-th rule,

Represents the initial value of each reference value corresponding to the i-th prerequisite attribute in the k+1-th rule;

后用证据推理算法将规则融合计算输出；当系统有输入时，基于置信规则库的某些原则被激活，则第k条规则的激活权重计算公式如下：in finding a match

Then use the evidence inference algorithm to fuse the rules to calculate the output; when the system has input, some principles based on the confidence rule base are activated, and the calculation formula of the activation weight of the kth rule is as follows:

表示第k条规则中第i个输入x_i相对于参考值

的匹配度，

表示第l条规则中第i个输入x_i相对于参考值

的匹配度，L为总的规则数，M为前提属性的个数；θ_k为第k条规则的权重；in,

Represents the i-th input _xi in the k-th rule relative to the reference value

match,

Represents the i-th input _xi in the l-th rule relative to the reference value

The matching degree of , L is the total number of rules, M is the number of prerequisite attributes; θ _k is the weight of the kth rule;

S32, ER algorithm fusion

After calculating the activation degree of the rule, use the ER algorithm to fuse the rules in the confidence rule base. The formula is as follows:

表示第k条规则下对应输出评价等级D_j的置信度，N表示结论向量的维数，L表示置信规则的个数，β_j,k表示规则库中第k条规则中第j个评价等级的置信度，ω_k为第k条规则的激活权重；in,

Represents the confidence of the corresponding output evaluation level D _j under the kth rule, N represents the dimension of the conclusion vector, L represents the number of confidence rules, β _{j, k} represents the jth evaluation level in the kth rule in the rule base The confidence of , ω _k is the activation weight of the k-th rule;

S33. Result output

Select the output level corresponding to the highest confidence as the final target recognition result:

Preferably, in step S2, the inference error ξ(V) can be represented by the mean square error, and the formula is as follows:

Preferably, the E _i setting value is:

为目标识别中第i组输入数据的模型识别结果。Among them, y _m is the actual recognition result of the ith group of input data in target recognition,

It is the model recognition result of the ith group of input data in object recognition.

Preferably, in step S2, the equality constraint A(V) and the inequality constraint B(V) are:

必须满足如下约束：(1) Attribute weight, the kth reference value for the ith attribute after the attribute weight is normalized

The following constraints must be met:

Among them, lb _i and ub _i represent the minimum and maximum values of the i-th attribute in the training data, respectively, L represents the number of confidence rules, and M is the number of prerequisite attributes;

(2) The confidence of the initial rule output must satisfy:

0≤βj _, k≤1, j=1,2,…,N, k=1,2,…,L

Among them, L represents the number of confidence rules, and N represents the dimension of the conclusion vector;

(3) Rule weight. After the rule weight is normalized, the value of the rule weight should be between 0 and 1, that is:

0≤θ _k ≤1, k=1,2,…,L

Among them, L represents the number of confidence rules.

Compared with the prior art, the present invention has the following beneficial effects:

The air target recognition method based on the reasoning of the confidence rule base provided by the present invention adopts a linear combination method to establish a confidence rule base model with the attribute information of the air target as the input and the type of the air target as the output. The number of rules in the confidence rule base is related, the number of rules is set equal to the number of recognition classifications, the multi-source information is reasoned and fused, and then the confidence level is mapped to the recognition result to identify the air target. Therefore, the present invention improves the individual in the traditional confidence rule base. The calculation method of the matching degree effectively overcomes the "combination explosion" problem of the number of rules and the "zero activation" problem of the rules, and the present invention optimizes the parameters of the confidence rule base through the local particle swarm algorithm, which effectively enhances the confidence rule base. The recognition accuracy of the reasoned aerial target recognition model solves the problem of low recognition accuracy of the initial confidence rule base. At the same time, the confidence rule base in the present invention is set as a "white box system", and the fusion reasoning process is visible, experts can participate, and the results Traceable and interpretable.

Description of drawings

1 is a schematic diagram of a linear combination mode adopted for constructing a confidence rule base in an embodiment of the present invention;

Fig. 2 is the schematic diagram of the traversal combination mode adopted by the prior art to construct the confidence rule base;

Fig. 3 is a model diagram of a parameter optimization model of a confidence rule base in an embodiment of the present invention;

4 is a flowchart of an aerial target recognition method based on a belief rule base reasoning provided by an embodiment of the present invention;

5 is a model diagram of an aerial target recognition model of a confidence rule base in an embodiment of the present invention;

FIG. 6 is a flow chart of the optimization of the local particle swarm algorithm in the embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

As shown in FIG. 4 , the aerial target recognition method based on the reasoning of the confidence rule base provided by the embodiment of the present invention specifically includes the following steps:

S1. Build a confidence rule base for aerial target recognition based on linear combination

S11. Definition of input and output variables and establishment of air target recognition model

First define the air target feature information as the input of the confidence rule inference method, and then define the air target type as the output of the confidence rule inference method, and obtain the confidence rule base model of the air target recognition;

Due to the variety of air targets, there are Tactical Ballistic Missile (TBM), Air-to-Ground Missile (AGM), Early Warning Aircraft (EWA), Stealth Aircraft (Stealth Aircraft, SA), anti-radiation missiles, fighter jets, bombers, armed helicopters and transport aircraft, etc., while TBM, AGM, EWA and SA are four typical air targets, and the others are common targets (CT). Therefore, the embodiment of the present invention selects four typical air targets. As the output of the belief rule inference method, aerial targets are described from the following five aspects, including radar scanning area σ (m2), horizontal velocity V _H (m/s), vertical velocity V _V (m/ s), flight height H (m), flight acceleration a (m/s2), and selecting more than 5 parameters as the input of the air target recognition model, the confidence rule base (BRB) air target recognition model structure can be obtained as shown in Figure 5. Show.

In view of the characteristics of the air target recognition problem, the embodiment of the present invention does not use the traditional method of traversing all candidate values of each antecedent attribute when constructing the BRB, as shown in FIG. 2, but constructs each item in the BRB by linear combination rules, as shown in Figure 1.

S12. Assuming that the number of prerequisite attributes in the recognition problem is T, the number of training data groups is H, and the number of known target classifications is C, the matrix form of the air target recognition problem dataset is:

Among them, Pi represents the i-th row of the matrix, that is, the row vector formed by the i-th group of input data; U _j represents the _j -th column of the matrix, that is, the column vector formed by the j-th attribute of all input data; x _i,j is An element of the matrix, representing the value of the jth attribute of the ith group of categorical data;

C reference values are set for each prerequisite attribute, and the number of utility levels is set to C. According to the linear combination method, the number of rules in the confidence rule base for aerial target recognition is C, which is used as the basis for the reasoning of the confidence rule base;

It can be seen from the design of the embodiment S11 of the present invention that the number of prerequisite attributes in the identification problem in the embodiment of the present invention is 5, which are the radar scanning area, the horizontal speed, the vertical speed, the flight height, and the flight acceleration, namely,

{A ₁ , A ₂ , A ₃ , A ₄ , A ₅ } = {radar scanning area, horizontal speed, vertical speed, flight altitude, flight acceleration} Since the identification results are tactical ballistic missiles, air-to-surface missiles, anti-radiation missiles , stealth aircraft, namely D={TBM(D ₁ ), AGM(D ₂ ), EWA(D ₃ ), SA(D ₄ )}

Since the identification results are 4 categories, according to the linear combination method, the number of initial BRB identification model rules is 4.

S13. Set the parameter values of the confidence rule base according to the data set

Set the initial value of the weight of the kth rule in the confidence rule base as:

θ _k = 1

Set the initial value of the weight of the i-th premise attribute in the confidence rule base as:

σ _i =1

The initial value of each reference value corresponding to the i-th premise attribute in the k-th rule in the confidence rule base is set as:

Among them, L represents the number of BRB system rules, and x _i represents the value of the i-th attribute in the data;

According to the data measured in the historical data set, we can know the minimum and maximum value of each attribute data of the target, and the boundary data of each attribute of the target are shown in Table 1 below, and then the value of each reference value corresponding to the i-th premise attribute in the k-th rule is The initial value is obtained according to the uniform distribution of the upper and lower bounds of the corresponding data;

Table 1. The boundary data of each attribute of air targets

serial number σ_(m2) V_H(m/s) V_V(m/s) H_(m) a_(m/s2) target type 1 1.5 2180 370 28500 40 TBM 2 1.7 1650 250 5000 twenty two 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

Set the evaluation level D _n in the confidence rule base as:

D _n =n, 1≤n≤N

The confidence corresponding to the nth evaluation level in the kth rule in the confidence rule base is set as:

Among them, rand ⁱ () represents the ith value in the random number sequence of length L between 0 and 1;

Thus, the established initial confidence rule base is shown in Table 2 below;

Table 2 Initial confidence rule base

S2. Parameters of the confidence rule base constructed based on local particle swarm optimization training

As shown in Figure 3, the parameters of the confidence rule base are optimized and trained. The optimization algorithm is the local particle swarm algorithm, and its motion function is defined as:

V _i (t+1)=ωV _i (t)+c ₁ r ₁ (p _{best -xi} (t))+c ₂ r ₂ (l _{best -xi} (t))

x _i (t+1)=x _i (t)+v _i (t+1)

Among them, ω is the inertia weight, c ₁ and c ₂ are learning factors, r ₁ and r ₂ are random numbers between [0, 1], l _best is the neighborhood optimal value, and p _best is the individual optimal value;

The optimization flow chart of the local particle swarm algorithm is shown in Figure 6, and the specific process is as follows:

Step 1: Initialize the particle swarm. The velocity and position of each particle in the population are randomly initialized within the range of constraints, and each particle contains the parameters that need to be trained in the BRB optimization model.

Step 2: Calculate the particle fitness value. The fitness value of each particle is calculated according to the fitness function, that is, the MSE value output by the system.

Step 3: Search for the individual optimal solution. For each particle, compare its fitness value with the fitness of the individual optimal solution p _best recorded by itself, if it is better, update its individual optimal solution p _best with the information of the current particle; otherwise, do not process.

Step 4: Search for the optimal solution in the neighborhood. For each particle, compare its fitness value with the fitness of the optimal solution l _best recorded in its neighborhood, if it is better, update the neighborhood local optimal solution l _best with the information of the current particle; otherwise, do not process.

Step 5: Iteratively update each particle's velocity and position through the algorithm's motion function.

Step 6: When the preset maximum number of iterations G _max is reached, the search stops, and at this time, the optimal solution l _best in the field is taken as the output result, and its position is assigned to the corresponding BRB parameter to obtain the optimized BRB system; Otherwise, go back to 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

组成的参数向量，ξ(V)表示推理误差；A(V)表示等式约束条件；B(P)表示不等式约束条件，输入历史观测数据到置信规则库，产生空中目标置信输出，再根据优化模型优化训练得到参数，最后得出参数优化训练后的置信规则库；where V represents the

The composed parameter vector, ξ(V) represents the inference error; A(V) represents the equality constraint; B(P) represents the inequality constraint, input historical observation data to the confidence rule base, generate the air target confidence output, and then optimize according to the The parameters are obtained through model optimization training, and finally the confidence rule base after parameter optimization training is obtained;

The inference error ξ(V) can be represented by the mean square error, and the formula is as follows:

Among them, the setting value of E _i is:

为目标识别中第i组输入数据的模型识别结果，当实际识别结果与模型识别结果一致时，则E_i值为0，当实际识别结果与模型识别结果不一致时，则E_i值为1。Among them, y _m is the actual recognition result of the ith group of input data in target recognition,

is the model recognition result of the ith group of input data in target recognition. When the actual recognition result is consistent with the model recognition result, the value of E _i is 0, and when the actual recognition result is inconsistent with the model recognition result, the value of E _i is 1.

The above equality constraints A(V) and inequality constraints B(V) are:

必须满足如下约束：(1) Attribute weight, the kth reference value for the ith attribute after the attribute weight is normalized

The following constraints must be met:

Among them, lb _i and ub _i represent the minimum and maximum values of the i-th attribute in the training data, respectively;

(2) The confidence of the initial rule output must satisfy:

0≤βj _, k≤1, j=1,2,…,N, k=1,2,…,L

(3) Rule weight. After the rule weight is normalized, the value of the rule weight should be between 0 and 1, that is:

0≤θk≤1, _k =1,2,...,L.

S3. Realize the reasoning of the confidence rule base based on evidence reasoning and output the results

S31. Activation weight calculation

的匹配度：First, convert the input information _xi to relative to the reference value

match:

表示第第j条规则中的第i个输入属性的匹配度，x_i表示属性的输入，

表示第k条规则中的第i个前提属性所对应的各个参考值的初值，

表示第k+1条规则中的第i个前提属性所对应的各个参考值的初值；in,

represents the matching degree of the ith input attribute in the jth rule, x _i represents the input of the attribute,

represents the initial value of each reference value corresponding to the i-th premise attribute in the k-th rule,

Represents the initial value of each reference value corresponding to the i-th prerequisite attribute in the k+1-th rule;

后用证据推理算法将规则融合计算输出；当系统有输入时，基于置信规则库的某些原则被激活，则第k条规则的激活权重计算公式如下：in finding a match

Then use the evidence inference algorithm to fuse the rules to calculate the output; when the system has input, some principles based on the confidence rule base are activated, and the calculation formula of the activation weight of the kth rule is as follows:

表示第k条规则中第i个输入x_i相对于参考值

的匹配度，

表示第l条规则中第i个输入x_i相对于参考值

的匹配度，L为总的规则数，M为前提属性的个数；θ_k为第k条规则的权重；in,

Represents the i-th input _xi in the k-th rule relative to the reference value

match,

Represents the i-th input _xi in the l-th rule relative to the reference value

The matching degree of , L is the total number of rules, M is the number of prerequisite attributes; θ _k is the weight of the kth rule;

S32, ER algorithm fusion

After calculating the activation degree of the rule, use the ER algorithm to fuse the rules in the confidence rule base. The formula is as follows:

表示第k条规则下对应输出评价等级D_j的置信度，N表示结论向量的维数，L表示置信规则的个数，β_j,k表示规则库中第k条规则中第j个评价等级的置信度，ω_k为第k条规则的激活权重；in,

Represents the confidence of the corresponding output evaluation level D _j under the kth rule, N represents the dimension of the conclusion vector, L represents the number of confidence rules, β _{j, k} represents the jth evaluation level in the kth rule in the rule base The confidence of , ω _k is the activation weight of the k-th rule;

S33. Result output

Select the output level corresponding to the highest confidence as the final target recognition result:

Randomly select 100 groups of measured data as training data, and after using the local particle swarm algorithm to train the parameters, the rules of the optimized BRB system are obtained as shown in Table 3 below:

Table 3 Optimized confidence rule base

Using the model after parameter optimization, the remaining 20 sets of data are tested, and the identification results are shown in Table 4 below.

Table 4 Target recognition results

It can be seen from Table 4 that using the identification method of the present invention, 19 groups of targets in the 20 groups of test data are correctly identified (the 16th group is not correctly identified), and the identification accuracy rate is 95%, which fully demonstrates the accuracy of the proposed identification model. effectiveness.

In order to verify the robustness of the proposed model, 10 tests were done in this paper, and training data and test data were randomly selected each time. The test results obtained are shown in Table 5 below.

Table 5 Test results

It can be seen from the results in Table 5 that the aerial target recognition method provided by the embodiment of the present invention has good robustness, and the average recognition accuracy rate of 10 tests is 95.5%.

To sum up, the air target recognition method based on the reasoning of the confidence rule base provided by the embodiment of the present invention firstly constructs the initial confidence rule base through a linear combination method according to the index relationship of the target recognition problem and the historical data of the air target situation, and uses the confidence rule The library reflects the complex nonlinear mapping relationship between the input parameter variables and the target type output; then the confidence rule library parameters are optimized by the local particle swarm algorithm to improve the accuracy of the model target recognition, and finally the attribute information of the air target is input to calculate the rule weight, And use the evidence reasoning method to integrate and reason the activated multiple rules, and finally get the possible types of air targets, realize the identification of air targets, and then provide a reliable basis for battlefield situation analysis and command decision-making.

The above-mentioned embodiments only represent specific embodiments of the present invention, and the descriptions thereof are specific and detailed, but should not be construed as limiting the scope of the invention patent. It should be pointed out that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can also be made, which all belong to the protection 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 group number of the training data is H, and the known target classification number is C, the matrix form of the aerial target identification problem data set is as follows:

wherein, P _i The ith row of the matrix is represented, namely a row vector formed by the ith group of input data; u shape _j Representing the jth column of the matrix, namely a column vector formed by the jth attribute of all input data; x is a radical of a fluorine atom _i,j Is 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:

V _i (t+1)＝ωV _i (t)+c ₁ r ₁ (p _best -x _i (t))+c ₂ r ₂ (l _best -x _i (t))

x _i (t+1)＝x _i (t)+v _i (t+1)

wherein, V _i (t) is the velocity of the particles, x _i (t) is the current position of the particle, t is the number of iterations, ω is the inertial weight, c ₁ And c ₂ As a learning factor, r ₁ And r ₂ Is [0,1 ]]Random number between,/ _best For a neighborhood optimum, p _best An 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

The composed parameter vector, xi (V) represents the inference error; a (V) represents an equality constraint; b (P) represents inequality constraint conditions, historical observation data are input into a confidence rule base, air target confidence output is generated, parameters are obtained according to optimization training of an optimization model, and finally the confidence rule base after parameter optimization training is obtained;

s3, reasoning of confidence rule base based on evidence reasoning and outputting result

S31, calculating activation weight

First, input information x _i Conversion to relative reference value

The matching degree of (2):

wherein,

denotes the degree of match, x, of the ith input attribute in the jth rule _i An input representing an attribute of the object is entered,

represents the initial value of each reference value corresponding to the ith precondition attribute in the kth rule,

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

Then, the rules are fused, calculated and output by an evidence reasoning algorithm; when the system has input and some principle based on confidence rule base is activated, the activation weight omega of the k rule _k The calculation formula is as follows:

wherein,

representing the ith input x in the kth rule _i Relative to a reference value

The degree of matching of (a) to (b),

representing the ith input x in the ith rule _i Relative to a reference value

The matching degree of (1), L is the total rule number, and M is the number of the precondition attributes; theta.theta. _k Is 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:

wherein,

indicates the corresponding output evaluation level D under the kth rule _j N denotes the dimensionality of the conclusion vector, L denotes the number of confidence rules, β _j,k The confidence coefficient, omega, of the jth evaluation level in the kth rule in the rule base is represented _k The 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:

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:

θ _k ＝1

setting the initial weight value of the ith precondition attribute in the confidence rule base as:

σ _i ＝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:

wherein,

an initial value x representing each reference value corresponding to the ith precondition attribute in the kth rule _h,i The ith attribute value representing the h-th group of classified data,

represents the initial value of each reference value corresponding to the ith precondition attribute in the C rule,

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;

evaluating grade D in the confidence rule base _n The setting is as follows:

D _n ＝n,1≤n≤N

setting the confidence corresponding to the nth evaluation level in the kth rule in the confidence rule base as:

wherein, beta _n,k Representing the confidence, rand, corresponding to the nth evaluation level in the kth rule in the confidence rule base ⁱ () Represents the ith value, rand, in a random number sequence of length L between 0 and 1 ⁿ () 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:

4. the air target recognition method based on belief rule base inference as claimed in claim 3, wherein E is _i The set values are:

wherein, y _m For the actual recognition result of the ith set of input data in object recognition,

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 toKth reference value of ith attribute

The following constraints must be satisfied:

wherein, lb _i And ub _i Respectively 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≤β _j,k ≤1，j＝1,2,…,N，k＝1,2,…,L

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≤θ _k ≤1，k＝1,2,…,L

wherein L represents the number of confidence rules.

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