A local approximation method for quantitative analysis of combat effectiveness index

Abstract

This patent introduces a local approximation method for quantitative analysis of combat effectiveness index, with the following specific steps: S1: experts select the influencing indicators of the object to be evaluated, collect and generate training sample data, and then evaluate and normalize the combat effectiveness index and influencing indicators of the target to be evaluated; S2: construct RBF neural network using fuzzy logic theory; S3: establish a combat effectiveness index calculation model using RBF neural network; S4: after training, save the model. The present invention uses RBF neural network or fuzzy neural network as the basic framework to train mathematical models and realize accurate and efficient calculation of combat effectiveness index; the local approximation method of the present invention has a low error rate, is insensitive to small changes in input data, and shows stronger robustness; the method of the present invention is not only suitable for combat effectiveness index calculation in the military field, but can also be migrated to other fields that require high-precision fitting of complex functions, and has broad application prospects.

Description

Technical Field

[0001] The present invention relates to the technical field of combat effectiveness analysis of military systems, and in particular to a local approximation method for quantitative analysis of combat effectiveness index. Background Art

[0002] The combat effectiveness index is greatly affected by the internal mechanism, external influence environment and corresponding constraints. The rules of engagement, strategic weapons, advanced military theories, etc. may play a decisive role. There may also be complex and deep coupling relationships between the various influencing indicators of the combat effectiveness index. To accurately measure it, we should first consider the important constraints, and then consider how to learn its complex internal mechanisms.

[0003] At present, there are more qualitative research results on the theory of combat effectiveness index, but fewer quantitative research results. The few studies involving quantification have low scientific and systematic methods and are difficult to be popularized and applied to various military fields. Judging from the existing results collected, the existing combat effectiveness index analysis methods mostly use hierarchical analysis method, rule association method, construction of Lanchester equation, design of a certain prediction indicator and other methods to evaluate the combat effectiveness index. However, these methods are affected by many subjective factors and are mainly qualitative analysis, which makes it difficult to provide decision makers with objective and simple quantitative data. Especially for complex, high-dimensional and nonlinear combat effectiveness index functions, existing methods are difficult to fit accurately, resulting in large errors in analysis results and difficult to apply in actual military decision-making. Therefore, studying the quantitative analysis method of combat effectiveness and building a systematic calculation model are key problems that need to be solved urgently.

[0004] According to the universal approximate theorem, a feedforward neural network, with only a single hidden layer and a finite number of neural units, can fit functions of arbitrary complexity with arbitrary precision. In recent years, with the rapid development of artificial intelligence technology and the rapid increase in hardware computing power, using the self-derivation ability of neural networks to learn the internal rules of the target has become the choice of many engineering practitioners. Under certain conditions, its performance is not only far better than the rules designed based on prior and expert knowledge, but also has the characteristics of fast calculation and good generalization.

[0005] A typical example from the perspective of global approximation is the BP neural network. The upper and lower layers of the BP neural network are fully connected. Each sample will affect the overall performance during training. Adjusting any weight value in the BP neural network will have an impact on the overall performance. Therefore, the fitting of the BP neural network is also called "global approximation". In addition, there is no connection between neurons in each layer of the BP neural network. If the relationship between neurons is to be expressed, it can only be done by adjusting the weights before and after. Therefore, the BP neural network cannot express the relationship between neurons well. It can be found that: (1) the global approximation strategy and the shortcomings of the BP neural network itself will greatly limit the model's learning of constraint rules; (2) BP neural networks are good at learning the overall influence mechanism of various influencing indicators on the combat effectiveness index, but are not very good at learning the complex relationship between various influencing indicators. According to the research of Freitas et al., a single rule is highly modular, and the rule-based processing method is a method based on the principle of "local mode". The rules that can usually be encoded and processed are "if-then" rules. The fuzzy logic theory developed from this has been proven to be effective in solving a wide range of complex system modeling and control problems. Summary of the invention

[0006] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a local approximation method for quantitative analysis of combat effectiveness index, which can meet the requirements of accurate calculation of the combat effectiveness of complex military systems.

[0007] The technical solution adopted by the present invention is:

[0008] A local approximation method for quantitative analysis of combat effectiveness index, the specific steps are:

[0009] S1: Experts select the impact indicators of the object to be evaluated, collect and generate training sample data, and then evaluate and normalize the combat effectiveness index and impact indicators of the target to be evaluated;

[0010] S2: Use fuzzy logic theory to construct radial basis function RBF neural network,

[0011] S3: Utilizing the self-learning and self-derivation capabilities of the RBF neural network, the training sample data is used to train the RBF neural network to achieve accurate fitting of the combat effectiveness index function, thereby establishing a combat effectiveness index calculation model;

[0012] S4: After training is completed, save the model.

[0013] Specifically, the RBF neural network is a single hidden layer feedforward neural network, and the main construction steps are:

[0014] a. Define the network structure

[0015] The RBF neural network consists of an input layer, a hidden layer, and an output layer. The input layer is responsible for receiving external input data, the hidden layer transforms the input data through a nonlinear function, namely the radial basis function, and the output layer outputs the final prediction result.

[0016] b. Determine the number of input layer nodes

[0017] The number of input layer nodes is equal to the number of input features; assuming that the number of target features is N1, the number of input neurons of the RBF neural network is N1, and the data information of the i-th input sample is a vector, which can be expressed as:

[0018]

[0019] c. Design hidden layer

[0020] The hidden layer is the core part of the RBF neural network, which is composed of multiple RBF neurons. Each RBF neuron has a center vector and a width parameter. The activation function of the RBF neuron usually uses a radial basis function such as a Gaussian function, and its output depends on the distance between the input vector and the center vector and the width parameter.

[0021] Assuming that the number of training samples is N and the number of hidden neurons is N2, the Euclidean distance d from all input data information to the center point of the jth hidden neuron is j It can be expressed as:

[0022]

[0023] In the formula, c j Represents the center point vector of the jth hidden neuron, which can be expressed as:

[0024] c j =[c j1 , c j2 , …, c N1 ] T

[0025] The activation function of the hidden layer of the RBF neural network also has a width factor, which affects the range of action of the neuron on the input information; the width factor R of the jth hidden neuron j It can be expressed as:

[0026] R j =[r1, r2, …, r N1 ] T

[0027] Where:

[0028]

[0029] In the formula, r fis the width adjustment coefficient, which is less than 1. Its function is to adjust the perception of each hidden layer neuron to local information and realize the local response ability of the RBF neural network. The width vector affects the action range of the neuron on the input information. The smaller the width, the narrower the shape of the corresponding hidden layer neuron action function, and the smaller the response of the information near the center of other neurons to the neuron.

[0030] The input value u of the jth hidden neuron H It can be expressed as:

[0031]

[0032] The output value v of the jth hidden neuron H Usually activated by a Gaussian function, which can be expressed as:

[0033] v H =exp(-u H 2 )

[0034] d. Determine the number of hidden layer nodes and width parameters

[0035] The number of hidden layer nodes is the number of RBF neurons and the center vector. After determining the center vector, the width parameter is determined by calculating the average distance from the samples in each cluster to the center, and the width parameter is set to a multiple of this average distance.

[0036] More specifically, the method for determining the number of hidden layer nodes includes:

[0037] Random selection method: randomly select several samples from the training data set as the center of the RBF neuron;

[0038] Clustering algorithm: Divide the training data into K clusters, and the center of each cluster is used as the center of an RBF neuron.

[0039] More specifically, for the deterministic rule, by adjusting the width factor R of the neuron function j , so that it can reach the corresponding excitation intensity; for the strong interactions between the influencing indicators and rules, accurate approximation is achieved by adjusting the distance between the central parameters of each neuron.

[0040] More specifically, in S3, the training process of the RBF neural network uses training sample data to train the network, the training sample data information is transmitted to the output layer, the gradient descent method is used, the error is reversely transmitted to adjust the parameters, and the output layer weights are calculated using the back propagation algorithm; the output layer linearly combines the outputs of the hidden layers to generate the final output; the number of neurons in the output layer depends on the number of targets to be predicted.

[0041] More specifically, in the S4, the network is tested and evaluated before the model is saved; the RBF neural network is tested and evaluated using test data; the performance of the network can be evaluated by calculating the error between the predicted result and the actual result; if the error is large, the network can be further optimized and adjusted, and steps a to d are repeated to adjust the architecture of the RBF neural network.

[0042] A local approximation method for quantitative analysis of combat effectiveness index, the specific steps are:

[0043] S1: Experts select the impact indicators of the object to be evaluated, collect and generate training sample data, and then evaluate and normalize the combat effectiveness index and impact indicators of the target to be evaluated;

[0044] S2: Construct fuzzy neural network using fuzzy logic theory;

[0045] S3: Utilizing the self-learning and self-derivation capabilities of the fuzzy neural network, adopting the error back propagation method, and using training sample data to train the network, the combat effectiveness index function is accurately fitted, thereby establishing a combat effectiveness index calculation model;

[0046] S4: After training is completed, save the model.

[0047] Specifically, the construction process of the fuzzy neural network in S2 is as follows:

[0048] e. Design network structure

[0049] The basic structure of fuzzy neural network includes input layer, fuzzification layer, fuzzy reasoning layer, normalization layer and output layer;

[0050] Input layer: receives raw input data;

[0051] Fuzzification layer: maps the original input data into fuzzy sets and uses membership functions to represent the fuzziness of each input data;

[0052] Fuzzy reasoning layer: reasoning the fuzzified input data according to fuzzy rules to generate fuzzy output results;

[0053] Normalization layer: normalizes the output of the fuzzy inference layer for subsequent calculations;

[0054] Output layer: convert the normalized fuzzy output results into actual numerical output. f. Determine fuzzy rules and membership functions

[0055] Fuzzy rules are formulated based on domain knowledge and expert experience; fuzzy rules are the core of fuzzy neural networks, which define the fuzzy relationship between input and output;

[0056] The membership function is used to describe the degree to which the input data belongs to a fuzzy set;

[0057] g. Parameter initialization

[0058] Before constructing a fuzzy neural network, it is necessary to initialize the parameters in the network, including the center point of the membership function, the width vector, and the connection weights of the output layer; the initial values ​​of the parameters can be randomly generated or set based on prior knowledge;

[0059] More specifically, the membership function in step f includes triangle, trapezoid and Gaussian functions; the selection and parameter setting of the membership function will affect the fuzzification effect and reasoning accuracy of the network.

[0060] More specifically, in S4, network testing and evaluation are performed before saving the model, and the fuzzy neural network is tested and evaluated using test data; the performance of the fuzzy neural network is evaluated by calculating the error or performance index between the predicted result and the actual result; if the performance does not meet the requirements, return to the previous steps to adjust the network structure, optimize the parameters or improve the training method.

[0061] Due to the adoption of the above-mentioned technical solution, the present invention has the following advantages:

[0062] The local approximation method for quantitative analysis of combat effectiveness index of the present invention makes up for the limitation of BP neural network well, and can well learn the constraint rules of combat effectiveness index from the local approximation strategy; the local approximation strategy is good at learning the complex relationship between various influencing indicators and rules; the mathematical model is trained based on RBF neural network or fuzzy neural network to realize accurate and efficient calculation of combat effectiveness index; compared with the global approximation method, the local approximation method of the present invention has a low error rate, is insensitive to small changes in input data, and shows stronger robustness; the method of the present invention is not only suitable for combat effectiveness index calculation in the military field, but also can be migrated to other fields that require high-precision fitting of complex functions, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a combat effectiveness index calculation model diagram of the present invention.

[0064] Figure 2 It is a comparison diagram of the calculation results of the RBF neural network of the present invention and the BP neural network with different structures;

[0065] In the figure, [8] indicates that the BP neural network is used with only one hidden layer and 8 neurons; [14, 6] indicates that there are two hidden layers and 14 and 6 neurons; similarly, [16, 10, 4];

[0066] Figure 3The RBF neural network of the present invention and Figure 2 Comparison of the error rates of BP neural networks with different structures for each sample. DETAILED DESCRIPTION

[0067] The present invention will be further explained below in conjunction with the accompanying drawings and embodiments, which should not be used to limit the protection scope of the present invention. The purpose of disclosing the present invention is to protect all technical improvements within the scope of the present invention.

[0068] Example 1

[0069] Combined with Figure 1-3 A local approximation method for quantitative analysis of combat effectiveness index is shown in FIG. , and the specific steps are as follows:

[0070] S1: Experts select the impact indicators of the object to be evaluated, collect and generate training samples, and then evaluate and normalize the combat effectiveness index and impact indicators of the target to be evaluated; The simulation experiment environment is a computer equipped with AMD Ryzen 55600K CPU, 16GB RAM and RTX 3060GPU hardware functions, and MATLAB 2024a software;

[0071] It is obtained through evaluation, quantification and scoring by the expert group. Specifically, the expert group selects a certain type of weapon, and after expert analysis, determines 7 influencing indicators on the combat effectiveness index, represented by X1 to X7. The determination of the combat effectiveness index value is through two aspects of evaluation. On the one hand, an evaluation value is given based on prior knowledge; on the other hand, through the performance of the weapon in the task in this field, according to the contribution to the result, the expert personnel give a reasonable evaluation value; after normalizing the data, 50 samples are randomly selected as training samples and 20 samples are selected as test samples, as shown in Table 1 and Table 2.

[0072] Table 1 System indicators and corresponding combat effectiveness index (training samples)

[0073]

[0074]

[0075] Table 2 System indicators and corresponding combat effectiveness index (test sample)

[0076]

[0077]

[0078] According to prior knowledge and expert experience, the indicator X1 in the table is a decisive key indicator, similar to the overall influence of the rules, which causes the emergence of a few "singular" samples, such as samples 1, 10, 20, etc. in the training set, and X1 and X4 have a strong coupling relationship. Therefore, the combat effectiveness index function should be a rule-dominated and relatively complex nonlinear function. The calculation model is shown in the attached figure. Figure 1 As shown, the output Z can be expressed as: Z = f(X1, ..., X7).

[0079] S2: Use fuzzy logic theory to construct radial basis neural network RBF;

[0080] RBF neural network is a single hidden layer feedforward neural network, and its main construction steps are:

[0081] a. Define the network structure

[0082] The RBF neural network consists of an input layer, a hidden layer and an output layer. The input layer is responsible for receiving external input data, the hidden layer transforms the input data through a nonlinear function, namely the radial basis function, and the output layer outputs the final prediction result.

[0083] b. Determine the number of input layer nodes

[0084] The number of input layer nodes is equal to the number of input features; assuming that the number of target features is N1, the number of input neurons of the RBF neural network is N1, and the data information of the i-th input sample is a vector, which can be expressed as:

[0085]

[0086] c. Design hidden layer

[0087] The hidden layer is the core part of the RBF neural network, which is composed of multiple RBF neurons. Each RBF neuron has a center vector and a width parameter. The activation function of the RBF neuron usually uses a radial basis function such as a Gaussian function, and its output depends on the distance between the input vector and the center vector and the width parameter.

[0088] Assuming that the number of training samples is N and the number of hidden neurons is N2, the Euclidean distance d from all input data information to the center point of the jth hidden neuron is j It can be expressed as:

[0089]

[0090] In the formula, c j Represents the center point vector of the jth hidden neuron, which can be expressed as:

[0091] c j =[c j1 , cj2 , …, c N1 ] T

[0092] The activation function of the hidden layer of the RBF neural network also has a width factor, which affects the range of action of the neuron on the input information; the width factor R of the jth hidden neuron j It can be expressed as:

[0093] R j =[r1, r2, …, r N1 ] T

[0094] Where:

[0095]

[0096] In the formula, rf is the width adjustment coefficient, which is less than 1. Its function is to adjust the perception ability of each hidden layer neuron to local information and realize the local response ability of the RBF neural network. The width vector affects the action range of the neuron on the input information. The smaller the width, the narrower the shape of the corresponding hidden layer neuron action function, and the smaller the response of the information near the center of other neurons to the neuron.

[0097] The input value u of the jth hidden neuron H It can be expressed as:

[0098]

[0099] The output value v of the jth hidden neuron H Usually activated by a Gaussian function, which can be expressed as:

[0100] v H =exp(-u H 2 ).

[0101] d. Determine the number of hidden layer nodes and width parameters

[0102] The number of hidden layer nodes is the number of RBF neurons and the center vector. After determining the center vector, the width parameter is determined by calculating the average distance from the samples in each cluster to the center. The width parameter is set to a multiple of this average distance.

[0103] Random selection method: randomly select several samples from the training data set as the center of the RBF neuron;

[0104] Clustering algorithm: Divide the training data into K clusters, and the center of each cluster is used as the center of an RBF neuron;

[0105] For the deterministic rule, by adjusting the width factor R of the neuron functionj , so that it can reach the corresponding excitation intensity; for the strong interactions between the influencing indicators and rules, accurate approximation is achieved by adjusting the distance between the central parameters of each neuron.

[0106] S3: Utilizing the self-learning and self-deduction capabilities of the RBF neural network, the network is trained using training sample data. The training sample data information is passed to the output layer, the gradient descent method is used, the error is reversely transferred to adjust the parameters, and the output layer weights are calculated using the back propagation algorithm; the output layer linearly combines the outputs of the hidden layers to achieve accurate fitting of the combat effectiveness index function and generate the final output, thereby establishing a combat effectiveness index calculation model; the number of neurons in the output layer depends on the number of targets to be predicted.

[0107] S4: Perform network testing and evaluation on the trained model; use test data to test and evaluate the RBF neural network; evaluate the performance of the network by calculating the error between the predicted result and the actual result; if the error is large, further optimize and adjust the network by repeating steps a to d to adjust the architecture of the RBF neural network; save the model after completion.

[0108] By the attached Figure 2 It can be seen that BP neural networks with different structures have a great influence on performance, and improper structural selection will cause large errors; the best performing two-layer network has errors 1 and 2 that are 1.66% and 12.02% lower than those of the three-layer network, respectively; compared with the best performing BP neural network, the error rate of the RBF neural network of the present application is about 6.85% and 1.97% lower; this shows that the method based on local approximation has a better fitting effect on the combat effectiveness function under regular conditions, and the combat effectiveness index result calculated by the model constructed according to this method is more accurate; and compared with the tedious work of repetitive structure design required by the BP neural network, the RBF neural network has only a single hidden layer, the structure is simpler, and a lot of time cost can be saved; in addition, the RBF neural network can obtain the global optimal value, avoiding the random problem of the results obtained by the BP neural network.

[0109] In order to further compare the robustness of the method, the error of the proposed method and the best BP neural network in the prior art for all test samples are compared, as shown in the attached figure. Figure 3As shown in the figure, the results obtained by the proposed method are more concentrated with respect to the coordinate axis and have stronger convergence. The method in the prior art has large errors for samples 2, 6, 9, 19, etc., with an error rate of about 20%, which shows that the method in the prior art has not learned the target function well and has a large overfitting problem. Specifically, except for the 4th and 9th samples in the figure, the error rate of the proposed method is reduced, which shows that the proposed method is relatively stable and robust, and is more applicable to the vast majority of data samples without random deviation problems. In addition, the same is true for the learning of singular samples such as test samples 1, 10, and 20. The recognition error rate of the proposed method for these three samples is lower than that of the prior art, which shows that the proposed method is more suitable for learning rules.

[0110] The optimal BP neural network in the prior art described in this embodiment is taken from the literature: Evaluation of cluster equipment combat effectiveness index based on BP neural network [J]. Firepower and Command Control, 2011, 36(11): 87-90. and Research on BP neural network design for combat effectiveness index calculation [J]. Ship Electronic Countermeasures, 2024. 48(3): 456-462.).

[0111] Example 2

[0112] A local approximation method for quantitative analysis of combat effectiveness index, the specific steps are:

[0113] S1: Experts select the impact indicators of the object to be evaluated, collect and generate training sample data, and then evaluate and normalize the combat effectiveness index and impact indicators of the target to be evaluated.

[0114] S2: Use fuzzy logic theory to construct a fuzzy neural network; the construction process is:

[0115] e. Design network structure

[0116] The basic structure of fuzzy neural network includes input layer, fuzzification layer, fuzzy reasoning layer, normalization layer and output layer;

[0117] Input layer: receives raw input data;

[0118] Fuzzification layer: maps the original input data into fuzzy sets and uses membership functions to represent the fuzziness of each input data;

[0119] Fuzzy reasoning layer: reasoning the fuzzified input data according to fuzzy rules to generate fuzzy output results;

[0120] Normalization layer: normalizes the output of the fuzzy inference layer for subsequent calculations;

[0121] Output layer: convert the normalized fuzzy output results into actual numerical output. f. Determine fuzzy rules and membership functions

[0122] Fuzzy rules are formulated based on domain knowledge and expert experience; fuzzy rules are the core of fuzzy neural networks, which define the fuzzy relationship between input and output;

[0123] The membership function is used to describe the degree to which the input data belongs to a fuzzy set; the membership functions include triangle, trapezoidal and Gaussian functions; the selection and parameter setting of the membership function will affect the fuzzification effect and reasoning accuracy of the network.

[0124] g. Parameter initialization

[0125] Before constructing a fuzzy neural network, it is necessary to initialize the parameters in the network, including the center point of the membership function, the width vector, and the connection weights of the output layer; the initial values ​​of the parameters can be randomly generated or set based on prior knowledge.

[0126] S3: Utilizing the self-learning and self-derivation capabilities of fuzzy neural networks, adopting the error back propagation method, and using training sample data to train the network, we can achieve accurate fitting of the combat effectiveness index function, thereby establishing a combat effectiveness index calculation model.

[0127] S4: After the training is completed, the network is tested and evaluated. The performance of the fuzzy neural network is evaluated by calculating the error or performance index between the predicted result and the actual result. If the performance does not meet the requirements, return to the previous steps to adjust the network structure, optimize the parameters or improve the training method. After completion, the model is saved.

[0128] Parts of the present invention not described in detail are prior art.

[0129] The embodiments selected herein for the purpose of disclosing the invention are currently considered to be suitable, but it should be understood that the invention is intended to include all changes and modifications of the embodiments that fall within the scope of the concept and invention.

Claims

1. A local approximation method for quantitative analysis of combat effectiveness index, characterized in that: The specific steps are: S1: Experts select the impact indicators of the object to be evaluated, collect and generate training sample data, and then evaluate and normalize the combat effectiveness index and impact indicators of the target to be evaluated; S2: Construct radial basis function RBF neural network using fuzzy logic theory; S3: Utilizing the self-learning and self-derivation capabilities of the RBF neural network, the training sample data is used to train the RBF neural network to achieve accurate fitting of the combat effectiveness index function, thereby establishing a combat effectiveness index calculation model; S4: After training is completed, save the model.

2. The local approximation method for quantitative analysis of combat effectiveness index according to claim 1, characterized in that: The RBF neural network is a single hidden layer feedforward neural network, and the main construction steps are: a. Define the network structure The RBF neural network consists of an input layer, a hidden layer, and an output layer. The input layer is responsible for receiving external input data, the hidden layer transforms the input data through a nonlinear function, namely the radial basis function, and the output layer outputs the final prediction result. b. Determine the number of input layer nodes The number of input layer nodes is equal to the number of input features; assuming that the number of target features is N1, the number of input neurons of the RBF neural network is N1, and the data information of the i-th input sample is a vector, which can be expressed as: c. Design hidden layer The hidden layer is the core part of the RBF neural network, which is composed of multiple RBF neurons. Each RBF neuron has a center vector and a width parameter. The activation function of the RBF neuron usually uses a radial basis function such as a Gaussian function, and its output depends on the distance between the input vector and the center vector and the width parameter. Assuming that the number of training samples is N and the number of hidden neurons is N2, the Euclidean distance d from all input data information to the center point of the jth hidden neuron is j It can be expressed as: In the formula, c j Represents the center point vector of the jth hidden neuron, which can be expressed as: c j =[c j1 ,c j2 ,…,c N1 ] T The activation function of the hidden layer of the RBF neural network also has a width factor, which affects the range of action of the neuron on the input information; the width factor R of the jth hidden neuron j It can be expressed as: R j ＝[r1，r2，…，r N1 ] T Where: In the formula, r f is the width adjustment coefficient, which is less than 1. Its function is to adjust the perception of each hidden layer neuron to local information and realize the local response ability of the RBF neural network. The width vector affects the action range of the neuron on the input information. The smaller the width, the narrower the shape of the corresponding hidden layer neuron action function, and the smaller the response of the information near the center of other neurons to the neuron. The input value u of the jth hidden neuron H It can be expressed as: The output value v of the jth hidden neuron H Usually activated by a Gaussian function, which can be expressed as: v H =exp(-u H 2 ) d. Determine the number of hidden layer nodes and width parameters The number of hidden layer nodes is the number of RBF neurons and the center vector. After determining the center vector, the width parameter is determined by calculating the average distance from the samples in each cluster to the center, and the width parameter is set to a multiple of this average distance.

3. The local approximation method for quantitative analysis of combat effectiveness index according to claim 2, characterized in that: The method for determining the number of hidden layer nodes includes: Random selection method: randomly select several samples from the training data set as the center of the RBF neuron; Clustering algorithm: Divide the training data into K clusters, and the center of each cluster is used as the center of an RBF neuron.

4. The local approximation method for quantitative analysis of combat effectiveness index according to claim 3 is characterized in that: For the deterministic rule, by adjusting the width factor of the neuron function R j, so that it can reach the corresponding excitation intensity; for the strong interactions between the influencing indicators and rules, accurate approximation is achieved by adjusting the distance between the central parameters of each neuron.

5. The local approximation method for quantitative analysis of combat effectiveness index according to claim 3, characterized in that: In S3, the training process of the RBF neural network uses training sample data to train the network, the training sample data information is transmitted to the output layer, the gradient descent method is used, the error is reversely transmitted to adjust the parameters, and the output layer weight is calculated using the back propagation algorithm; The output layer linearly combines the outputs of the hidden layers to produce the final output; the number of neurons in the output layer depends on the number of targets to be predicted.

6. The local approximation method for quantitative analysis of combat effectiveness index according to claim 5, characterized in that: In the above-mentioned S4, testing and evaluation are performed before the model is saved; the RBF neural network is tested and evaluated using test data; the performance of the network can be evaluated by calculating the error between the predicted result and the actual result; if the error is large, the network can be further optimized and adjusted, and steps a to d are repeated to adjust the architecture of the RBF neural network.

7. A local approximation method for quantitative analysis of combat effectiveness index, characterized in that: The specific steps are: S1: Experts select the impact indicators of the object to be evaluated, collect and generate training sample data, and then evaluate and normalize the combat effectiveness index and impact indicators of the target to be evaluated; S2: Construct fuzzy neural network using fuzzy logic theory; S3: Utilizing the self-learning and self-derivation capabilities of the fuzzy neural network, adopting the error back propagation method, and using training sample data to train the network, the combat effectiveness index function is accurately fitted, thereby establishing a combat effectiveness index calculation model; S4: After training is completed, save the model.

8. The local approximation method for quantitative analysis of combat effectiveness index according to claim 7, characterized in that: The construction process of the fuzzy neural network is as follows: e. Design network structure The basic structure of fuzzy neural network includes input layer, fuzzification layer, fuzzy reasoning layer, normalization layer and output layer; Input layer: receives raw input data; Fuzzification layer: maps the original input data into fuzzy sets and uses membership functions to represent the fuzziness of each input data; Fuzzy reasoning layer: reasoning the fuzzified input data according to fuzzy rules to generate fuzzy output results; Normalization layer: normalizes the output of the fuzzy inference layer for subsequent calculations; Output layer: Convert the normalized fuzzy output results into actual numerical outputs. f. Determine fuzzy rules and membership functions Fuzzy rules are formulated based on domain knowledge and expert experience; fuzzy rules are the core of fuzzy neural networks, which define the fuzzy relationship between input and output; The membership function is used to describe the degree to which the input data belongs to a fuzzy set; g. Parameter initialization Before constructing a fuzzy neural network, it is necessary to initialize the parameters in the network, including the center point of the membership function, the width vector, and the connection weights of the output layer; the initial values ​​of the parameters can be randomly generated or set based on prior knowledge.

9. The local approximation method for quantitative analysis of combat effectiveness index according to claim 8, characterized in that: The membership functions in step f include triangle, trapezoid and Gaussian functions; the selection and parameter setting of the membership function will affect the fuzzification effect and reasoning accuracy of the network.

10. The local approximation method for quantitative analysis of combat effectiveness index according to claim 9, characterized in that: In the above S4, before saving the model, network testing and evaluation are performed, and the performance of the fuzzy neural network is evaluated by calculating the error or performance index between the predicted result and the actual result; If the performance does not meet the requirements, return to the previous steps to adjust the network structure, optimize parameters, or improve the training method.

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