Aircraft combat effectiveness sensitivity analysis based on Bayesian network and deep learning

Abstract

The present invention relates to an aircraft combat effectiveness sensitivity analysis integrating Bayesian network and deep learning. By combining the modeling advantages of Bayesian network under a small amount of sample data and the excellent high-dimensional data processing ability of deep learning, an aircraft combat system proxy model is constructed, creating perfect conditions for sensitivity analysis using the Sobol index method, and improving the accuracy of aircraft combat effectiveness sensitivity analysis. The high-dimensional data used for aircraft combat effectiveness sensitivity analysis is preliminarily processed based on a mutual information hierarchical clustering method, and then an autoencoder is used to extract features from the preliminarily processed data to achieve dimensionality reduction, and then a model is established through a Bayesian network. At this point, the aircraft combat system proxy model is successfully established through the fusion of deep learning and Bayesian network models, and a high-precision sensitivity analysis of aircraft combat effectiveness is achieved through the proxy model. The problem that a proxy model with a small sample size is difficult to establish in the problem of aircraft combat effectiveness sensitivity analysis is effectively solved.

Description

Technical Field

[0001] The present invention belongs to the field of aircraft combat effectiveness research and relates to an aircraft combat effectiveness sensitivity analysis integrating a Bayesian network and a deep learning model. Background Art

[0002] In modern warfare, air power has gradually replaced the traditional army and navy to become the protagonist of war. Therefore, it is very necessary to evaluate the combat effectiveness of aircraft, which can provide a more reliable basis for the development strategy of aircraft weapons and equipment, and also provide a scientific reference for the guiding ideology and tactics of war.

[0003] In actual combat, the battlefield environment has many factors that affect all aspects of the aircraft, which makes the analysis of aircraft combat effectiveness more complicated. Analyzing the impact of these factors and the degree of influence is the sensitivity analysis of aircraft combat effectiveness. Through sensitivity analysis, the degree of influence of each influencing factor on the aircraft combat effectiveness can be calculated. The degree of influence of each factor is called their sensitivity coefficient. The sensitivity coefficients of each influencing factor are sorted by size, and the factors that have the greatest impact on the aircraft combat effectiveness can be found and paid attention to. At the same time, ignoring factors with smaller sensitivity coefficients can greatly reduce the blindness of effectiveness analysis and greatly improve the efficiency of aircraft combat effectiveness analysis.

[0004] Aircraft combat effectiveness sensitivity analysis methods are mainly divided into two categories: local sensitivity analysis methods and global sensitivity analysis methods. Local sensitivity analysis method refers to analyzing the influence of a single input on the model each time, and other inputs are fixed in the process. The sensitivity index of this type of method is generally the differential of the model output to the input or the output change caused by a single input. When the model input and output are in a linear relationship, it has high accuracy. The global sensitivity analysis method analyzes the total impact of multiple input changes on the output at the same time, and analyzes the impact of a single input or the interaction between multiple inputs on the model output. The global sensitivity analysis method takes into account the changes in other input parameters when analyzing and calculating the sensitivity of a single input. Compared with the local sensitivity analysis method, the model input space explored is larger, and the analysis results obtained are also more robust. It is suitable for aircraft combat effectiveness sensitivity analysis with nonlinear relationships between input and output.

[0005] Regression analysis, mutual information index method, Fourier amplitude sensitivity test method and Sobol index method are several commonly used global sensitivity analysis methods. Regression analysis is to apply mathematical statistics to study the uncertain relationship between input and output. It can analyze the impact of a single input on the output when multiple inputs change at the same time. However, regression analysis requires an advance assumption of the functional relationship between input and output, and the sensitivity analysis results are highly dependent on the selected functional relationship. In addition, if the input parameters are not independent of each other, the accuracy of the algorithm is difficult to guarantee. The core of the mutual information index method is to construct a measure of the contribution of a specific input to the output, and to rank the sensitivity of each input based on the measure of each input. It also considers the impact of other inputs when calculating the sensitivity of a single input, but cannot analyze the interaction effect of multiple inputs. The Fourier amplitude sensitivity test method selects a special spatial curve in the multidimensional input space to construct an exploration of each parameter at different frequencies. This method can quantitatively analyze the contribution of a single input to the output variance, but the accuracy of the result is poor in the case of discrete inputs. The input parameters of the aircraft combat system are not independent of each other and have strong interaction effects. In most cases, the input is a discrete variable, so the above methods are difficult to apply to the sensitivity analysis of aircraft combat effectiveness. The Sobol index method is a global sensitivity analysis method based on variance for sensitivity analysis. Its core idea is variance decomposition, which decomposes the model into a single input and a function of multiple inputs combined with each other, and then calculates the influence of a single input and multiple inputs on the output variance. It can analyze the influence of a single input or multiple inputs on the output, and does not affect the accuracy when the data is discrete. Therefore, it is suitable for application in the sensitivity analysis of aircraft combat effectiveness.

[0006] Due to the complexity of the combat environment and the particularity of the military field, sensitivity analysis of aircraft combat effectiveness often faces the situation of small sample size and high data dimension, which makes it difficult to establish the proxy model required for sensitivity analysis. Summary of the invention

[0007] Technical issues to be solved

[0008] In order to avoid the shortcomings of the prior art, the present invention proposes an aircraft combat effectiveness sensitivity analysis that integrates Bayesian networks and deep learning, which can well solve the problem of aircraft combat effectiveness sensitivity analysis. Combining Bayesian networks and deep learning, it can quickly establish an aircraft combat system agent model, ensure the efficiency and accuracy of sensitivity analysis, and play a supporting role in the development of aircraft weapons and equipment.

[0009] Technical Solution

[0010] An aircraft combat effectiveness sensitivity analysis integrating Bayesian network and deep learning is characterized by the following steps:

[0011] Establishment of Agent Model for Aircraft Combat System

[0012] Step 1: Data clustering based on mutual information hierarchical clustering algorithm: The aircraft combat simulation data to be analyzed is m-dimensional. First, the m-1-dimensional data except the missile hit probability is clustered based on the mutual information hierarchical clustering algorithm to obtain the m-1-dimensional data x = (x1, x2, ..., x m-1 ) into k data clusters x * =(x1 * ,x2 * ,…,x k * ); k is the number of clusters;

[0013] Step 2: Feature extraction based on deep autoencoder: The autoencoder model in deep learning is used to extract features from each cluster of data. The data dimension is reduced from m-1 to k, and the overall data dimension is reduced from m to k+1.

[0014] Step 3: Use Bayesian network to build a Bayesian network model for the data whose dimension has been reduced from m dimension to k+1 dimension after clustering and feature extraction, and obtain the entire proxy model, that is, the aircraft-to-ground combat system proxy model Y=f(x1,x2,x3,...,x 32 ), where Y is the missile hit probability of the aircraft, x1,x2,x3,...,x 32 It is the various factors in the index system that affect the probability of aircraft missiles hitting the target;

[0015] Sensitivity Analysis of Aircraft Combat Effectiveness

[0016] Step 4: Calculate the relevant parameters of the Sobol index method

[0017] Random sampling is used to sample two input matrices A and B from the input space. Each row in the two matrices is a set of input combinations of the model under study, and each combination is calculated by the proxy model to obtain the corresponding output:

[0018]

[0019] Then construct the matrix AB i , the construction method is to replace the i-th column of matrix A with the i-th column of matrix B. Similarly, the i-th column of matrix A can be replaced with the i-th column of matrix B to obtain matrix A i B:

[0020]

[0021]

[0022] Substitute the matrix into the proxy model to get the output vector, which is denoted as y A ,y B , and The following results are obtained based on the Monte Carlo algorithm:

[0023]

[0024]

[0025]

[0026] In the formula

[0027] Step 5: Calculate the global sensitivity coefficient

[0028] Input variable X i The main effect index Total Effect Index The estimate is:

[0029]

[0030]

[0031] Based on the main effect index Total Effect Index The global sensitivity coefficient is calculated, the values ​​of various indicators are calculated, and the aircraft combat effectiveness is analyzed and evaluated.

[0032] The data clustering process based on the mutual information hierarchical clustering algorithm in step 1 is as follows: the aircraft combat simulation data to be analyzed is m-dimensional, and the m-1-dimensional data except the missile hit probability is firstly clustered based on the mutual information hierarchical clustering algorithm;

[0033] Any two error sources x i ,x j The mutual information is: i≠j,1,2,3,m-1

[0034]

[0035] x i ,x j The inverse of the mutual information is

[0036]

[0037] Where: D(x i ;x j ) and x i and x j The similarity between them is inversely proportional;

[0038] Select the number of clusters to be k, and set the m-1-dimensional data x = (x1, x2, ..., x m-1 ) into k data clusters

[0039] The process of extracting features from each cluster of data using the autoencoder model in deep learning in step 2 is as follows: for the clustered data set with dimension k, x * ∈R The autoencoder maps the data to the feature space and obtains the encoding z of each set of data (n) And reconstruct the sample with the help of this set of encodings:

[0040] z (k) =f encode (x *(k) )

[0041] x' (19) =g decode (z (19) ) = g decode f encode (x *(19) )

[0042] For the sample x * , the activation function uses the Sigmoid function, and the activation value of the hidden layer is the encoding of x:

[0043] z=Sigmoid(W (1) x * +b (1) )

[0044] The output of the autoencoder is:

[0045] x'=Sigmoid(W (2) z+b (2) )

[0046] Where W (1) ,W (2) ,b (1) ,b (2) is the network parameter;

[0047] The original input x is measured using mean square error (n) and reconstruct the output x' (n) The error between:

[0048]

[0049] Where λ is the coefficient of the regularization term;

[0050] When the autoencoder network training is completed, the decoder is removed and only the encoder is retained. The output of the encoder is the feature of the data cluster; the data dimension is reduced from m-1 dimension to k dimension, and the overall data dimension is reduced from m dimension to k+1 dimension.

[0051] The process of obtaining the aircraft-to-ground combat system proxy model by Bayesian network modeling in step 3 is as follows: first, the Bayesian network structure is learned by the A* algorithm, and each node in the network structure is the feature extracted from the data cluster after data clustering; then the maximum likelihood method is used to learn the parameters of the Bayesian network, and the Bayesian network is established. The entire proxy model, that is, the aircraft-to-ground combat system proxy model Y=f(x1,x2,x3,...,x 32 ).

[0052] Beneficial Effects

[0053] The present invention proposes a sensitivity analysis of aircraft combat effectiveness that integrates Bayesian networks and deep learning. By combining the modeling advantages of Bayesian networks under a small amount of sample data and the excellent high-dimensional data processing capabilities of deep learning, an aircraft combat system proxy model is constructed, creating perfect conditions for sensitivity analysis using the Sobol index method, thereby improving the accuracy of sensitivity analysis of aircraft combat effectiveness. In the present invention, the high-dimensional data used for sensitivity analysis of aircraft combat effectiveness is preliminarily processed by a mutual information hierarchical clustering method, and then an autoencoder is used to extract features from the preliminarily processed data to achieve dimensionality reduction, and then a model is established through a Bayesian network. At this point, the aircraft combat system proxy model is successfully established through the fusion of deep learning and the Bayesian network model, and finally a high-precision sensitivity analysis of aircraft combat effectiveness is achieved through the proxy model.

[0054] The beneficial effects of the present invention are:

[0055] (1) The present invention uses a mutual information clustering algorithm and an autoencoder to reduce the dimensionality of high-dimensional sample data composed of multiple influencing factors that affect the effectiveness of aircraft during combat, and then performs Bayesian network modeling on the reduced-dimensional data, effectively solving the problem of difficulty in establishing a proxy model with a small sample size in the problem of sensitivity analysis of aircraft combat effectiveness.

[0056] (2) The present invention creatively combines the modeling advantages of the Bayesian network under a small amount of sample data and the excellent high-dimensional data processing capabilities of deep learning, and improves the accuracy of the proxy model to a certain extent in the face of a data environment with a small number of samples and high dimensions.

[0057] (3) The present invention adopts a proxy model established by integrating deep learning and Bayesian network to calculate the Sobol index, which saves a lot of time cost and improves the accuracy of aircraft combat effectiveness sensitivity analysis to a certain extent.

[0058] In summary, the present invention proposes a method for analyzing the sensitivity of aircraft combat effectiveness by integrating Bayesian networks and deep learning, which can accurately and effectively analyze the many factors that affect the aircraft combat effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 :Schematic diagram of the basic process of hierarchical clustering algorithm

[0060] Figure 2 : Clustering tree

[0061] Figure 3 :The basic structure of deep autoencoder

[0062] Figure 4 :The learning process of the autoencoder

[0063] Figure 5 :The basic process of establishing a Bayesian network model integrating deep learning

[0064] Figure 6 :Indicator system in the example

[0065] Figure 7 :The hidden layer of the autoencoder in the implementation process of the present invention

[0066] Figure 8 :Global sensitivity analysis results using the fusion model as a proxy model under 2000 samples

[0067] Fig. 9 : Benchmark results with 5000 samples

[0068] Fig.10 :Global sensitivity analysis results using neural network as surrogate model under 2000 samples DETAILED DESCRIPTION

[0069] The present invention will now be further described with reference to the embodiments and the accompanying drawings:

[0070] The present invention adopts the Sobol index method to perform sensitivity analysis. When there is a specific expression of the original system When the original system model is used, the analytical method can be used directly for calculation. However, in most cases, the specific expression of the original system model cannot be obtained. Therefore, the Monte Carlo method is usually used for calculation in engineering applications. It does not rely on specific function expressions, but still needs to obtain data output through model operation. When there are many combinations of variables to be considered, the amount of calculation of this method will increase sharply, and sometimes it is impossible to substitute the sampled data back into the original system. The sensitivity analysis of complex nonlinear relationships such as aircraft combat effectiveness faces such a dilemma. At this time, we need to build a proxy model that reflects the input-output relationship of the original system. The quality of the proxy model will directly affect the accuracy of the sensitivity analysis results. The traditional proxy model is a linear regression model, which is easy to calculate and has a fast running time, but the model has low accuracy and cannot fit complex models. The neural network proxy model can fit complex nonlinear relationships and has a higher model accuracy, but it requires a large amount of sample data support. Due to the complexity of the aircraft combat environment and the particularity of the military field, the sensitivity analysis of aircraft combat effectiveness often faces the situation of small sample size and high data dimension. At this time, it is particularly important to seek new methods to establish proxy models.

[0071] Bayesian networks can express the correlation between variables very well, so we use Bayesian networks to model the original system. Existing studies have shown that Bayesian networks have obvious advantages in modeling a small amount of sample data, but the difficulty of Bayesian network modeling will increase significantly with the increase of data dimensions, resulting in a sharp decrease in its ability to model high-dimensional data. Currently available Bayesian network structure learning algorithms can be divided into two types: approximate algorithms and exact algorithms. Although the approximate algorithm has a high learning efficiency, it is easy to fall into the local optimum and it is difficult to obtain an accurate network structure, so the present invention selects an exact algorithm to learn the structure of the Bayesian network. The next step is to find a method to improve the Bayesian network's ability to model high-dimensional data.

[0072] Deep learning involves multiple layers of nonlinear transformations, and therefore has superior high-dimensional data processing capabilities. After years of development, it has become one of the hottest research directions in the field of computer science and is widely used in facial recognition, text and speech processing, automatic control, bioinformatics, autonomous driving, and machine translation. In terms of its essential characteristics, deep learning first obtains low-dimensional features through training, and then classifies or predicts the given data. The training process of deep learning mostly uses gradient descent to fit a large amount of sample data. It is impossible to explain the training process of the network and the learned network parameters, and it can only be understood as a "black box model". Therefore, in areas involving the safety of life and property, such as decision-making in battlefield environments and security assessments of financial systems, deep learning still cannot replace some traditional modeling methods (such as decision tree methods, Bayesian methods, etc.).

[0073] The Bayesian network is simple in form and requires less data for modeling, but the difficulty of modeling increases significantly with the increase of data dimension. Deep learning is very good at processing high-dimensional data, but it is difficult to explain the relationship between variables and requires a large amount of data for learning. If we can combine the characteristics of the two and integrate deep learning into the modeling process of the Bayesian network, we will hopefully get a Bayesian model that can model high-dimensional data, especially high-dimensional data with a small number of samples.

[0074] The technical solution adopted by the present invention to solve its technical problem is:

[0075] In establishing the aircraft combat system agent model, the following algorithm is used:

[0076] 1. Data clustering based on mutual information hierarchical clustering algorithm:

[0077] The hierarchical clustering algorithm first needs to set a similarity measurement criterion, and then use this criterion to evaluate the similarity between data points. Then, according to the size of the calculated similarity value, the two most similar data points among all current data points are combined, and the combined data becomes one class. Then, this operation is repeated, and finally a nested clustering tree can be created based on the similarity measurement criterion and the size of the similarity. In this clustering tree, the bottom layer is all the original data points (at this time, each original data point belongs to a different class), and a large class node containing all the original data points is at the top of the tree. The following is an introduction to the merging method in the hierarchical clustering algorithm. The meaning of the merging method is to complete the clustering process from the bottom up. The basic steps are as follows:

[0078] (1) Initialization: Classify each sample point of the original data into one category, and calculate the similarity between each two categories, that is, the similarity between each two samples, according to the pre-defined similarity measurement criteria;

[0079] (2) normalize the two most recent categories;

[0080] (3) Recalculate the similarity between all classes at this time according to the method in (1);

[0081] (4) Repeat (2) and (3) until the algorithm ends.

[0082] Attached Figure 1 The basic process of hierarchical clustering algorithm is demonstrated.

[0083] In addition to the merging method, the implementation of the hierarchical clustering algorithm also includes a top-down splitting method, which has the opposite idea to the merging method.

[0084] This algorithm has four main advantages:

[0085] There is no need to pre-specify the number of clusters, which is very useful for the problem to be studied in this invention;

[0086] The similarity metric between two classes is easier to define and has fewer restrictions.

[0087] ·You can discover the hierarchical relationship of classes;

[0088] The clustering tree can be obtained at one time. If classification is required later, there is no need to repeat the calculation. You only need to "cross-cut" along the clustering tree to get the clustering result.

[0089] For attachment Figure 1 The clustering process shown in the figure, the clustering tree obtained by the hierarchical clustering algorithm is shown in the attached Figure 2 shown.

[0090] From the above introduction to the hierarchical clustering algorithm, we can know that the definition of the similarity measurement criterion between two samples or two variables is the key to hierarchical clustering. Considering that the present invention needs to cluster the attributes of the sample data, we consider using mutual information as the measurement criterion for the similarity of sample data points.

[0091] Mutual information is defined as follows, where R and T are random variables

[0092]

[0093] According to the mutual information, we can get

[0094] I(R;T)=H(R)-H(R|T)=H(T)-H(T|R) (2)

[0095] If I(R;T) between variables R and T is zero, then variables R and T are independent. Therefore, it is feasible to use mutual information to measure the similarity between data. Using mutual information as a similarity measure can also satisfy properties such as non-negativity and symmetry. The greater the mutual information between data, the greater the similarity between data. However, when using a hierarchical clustering algorithm, the two classes with the closest "distance" are clustered into one class, so it is inappropriate to directly use mutual information as a measurement criterion. So here we define the inverse of mutual information as

[0096]

[0097] Indicates data similarity. The smaller D(R; T), the higher the similarity between R and T, and the smaller the "distance". Conversely, the smaller the similarity between R and T, the larger the "distance". This is how the clustering algorithm used in this article is derived.

[0098] 2. Feature extraction based on deep autoencoder

[0099] The deep autoencoder in deep learning is used to extract features from the data clusters obtained by the hierarchical clustering algorithm based on mutual information. The difference between the autoencoder and the general neural network is that the dimension of the output layer is consistent with the input layer, and the dimension of the intermediate hidden layer is generally lower than the input layer. Its purpose is to convert high-dimensional input data into low-dimensional features. In terms of functional composition, the autoencoder consists of two parts: the encoder and the decoder. The encoder transforms the input sample data into the feature space, and the decoder restores the features in the feature space. Figure 3 The basic structure of the autoencoder is given.

[0100] For a set of sample data, the dimension is D, that is, x (n) ∈R D ,1≤n≤N, the autoencoder maps this set of data to the feature space and obtains the encoding z of each set of data (n) ∈R M ,1≤n≤N, and reconstruct the samples with the help of this set of codes, that is,

[0101] z (n) =f encode (x (n) ) (4)

[0102] x' (n) =g decode (z (n) ) = g decode f encode (x (n) ) (5)

[0103] For sample x, the activation value of the hidden layer is the encoding of x, that is:

[0104] z=σ(W (1) x+b (1) ) (6)

[0105] The output of the autoencoder is:

[0106] x'=σ(W (2) z+b (2) ) (7)

[0107] Where W (1) ,W (2) ,b (1) ,b (2) is the network parameter, and σ(·) is the activation function.

[0108] The learning goal of the autoencoder is to make the error between input and output as small as possible, usually using the mean square error to measure the original input x (n) and reconstruct the output x' (n) The error between them is:

[0109]

[0110] Where λ is the coefficient of the regularization term.

[0111] By minimizing the error between input and output, the parameters in the network structure can be effectively learned. If the error is trained to be small enough, it can be considered that the information of the original data is contained in the feature space. In order to obtain low-dimensional features of high-dimensional input data, the number of nodes in the hidden layer of the autoencoder is usually smaller than the dimension of the input data. That is, if the original input data is reconstructed with fewer nodes within the allowable error range, it is considered that the autoencoder has learned the low-dimensional features of the high-dimensional data. However, the number of hidden layer nodes of the autoencoder does not have to be less than the number of input layer nodes (that is, the dimension of the original sample data). For example, the number of hidden layer nodes of a sparse autoencoder is higher than the dimension of the input data. This type of model can also have a good training effect. Appendix Figure 4 The learning process of the autoencoder is given.

[0112] Once an autoencoder network is trained, the decoder can be removed and only the encoder can be retained. The output of the encoder can be used as input for subsequent related tasks.

[0113] 3. Bayesian network modeling

[0114] The Bayesian network model is established using the features obtained by the autoencoder feature extraction and isolated variable nodes (some data clusters may have only one variable, so feature extraction is not required). In the present invention, the Bayesian network structure learning algorithm adopts the A* algorithm, and the parameter learning algorithm adopts the maximum likelihood estimation method. After obtaining the model, the established Bayesian network model can be used to complete specific application tasks such as reasoning.

[0115] Bayesian networks have the following advantages and are well suited for aircraft combat effectiveness sensitivity analysis:

[0116] (1) The representation of the Bayesian network is very simple. It uses directed edges between nodes to represent the relationship between variables, which is intuitive and easy to understand.

[0117] (2) Bayesian networks have a good mathematical foundation and the relevant derivation process is very rigorous. Unlike some "black box" tools, the reasoning results of Bayesian networks have good theoretical support;

[0118] (3) Bayesian networks are very flexible when dealing with problems. They can add prior information or expert experience and combine it with sample data to improve the accuracy of modeling. At the same time, they can reduce the complexity of learning problems. They can also adjust the network structure and parameters according to new data or the knowledge of domain experts to make them more reasonable.

[0119] (4) Bayesian networks have a good ability to handle small sample data sets and incomplete data sets. The accuracy of Bayesian network reasoning results is less affected by the accuracy of network parameters. Moreover, by fusing qualitative and quantitative information, it can effectively solve problems in various scenarios.

[0120] So far, the proxy model has been successfully established by integrating the autoencoder and the Bayesian network. The basic process is as follows: Figure 5 shown.

[0121] In the sensitivity analysis of aircraft combat effectiveness:

[0122] 1. Calculate the relevant parameters of the Sobol index method.

[0123] The Sobol index method is a global sensitivity analysis method based on variance. It focuses on decomposing the variance, decomposing the model to be studied into a single independent variable and a function of multiple independent variables coupled with each other, and then calculating the influence of a single independent variable and multiple independent variables on the output variance, so as to calculate the sensitivity of a single independent variable or the sensitivity of the coupled effect of multiple independent variables. Figure 5 The surrogate model established by the process shown is used for sensitivity analysis.

[0124] Assume that the aircraft combat system agent model is

[0125] Y=f(x1,x2,x3,...,x n ) (9)

[0126] Where Y can be the hit probability, kill probability or penetration probability of the weapon, etc., x1,x2,x3,...,x n To analyze the error factors that affect the analysis index Y, such as radar error, inertial navigation error, etc. First, the random sampling method is used to sample from the input space of the model under study to obtain two input matrices A and B. Each row in the two matrices is a set of input combinations of the model under study, and each combination can be calculated by model (9) to obtain the corresponding output. Then construct the matrix AB i , the construction method is to replace the i-th column of matrix A with the i-th column of matrix B. Similarly, the i-th column of matrix A can be replaced with the i-th column of matrix B to obtain matrix A i B.

[0127]

[0128]

[0129] Substituting these matrices into the agent model under study, we can get the output vectors, which are denoted as y A ,y B, and According to the Monte Carlo algorithm, the following results can be obtained:

[0130]

[0131]

[0132]

[0133] 2. Calculate the global sensitivity coefficient.

[0134] Input variable X i , main effect index of 1≤i≤n Total Effect Index The estimate is:

[0135]

[0136]

[0137] In the formula Specific embodiment:

[0139] Combined with the accompanying drawings, the data obtained by the established aircraft-to-ground combat simulation system is taken as an example, and the aircraft missile hit probability is taken as the effectiveness analysis indicator to further illustrate the specific implementation process of the aircraft combat effectiveness sensitivity analysis of the present invention.

[0140] In this example, the error sources of the aircraft-to-ground combat simulation system are inertial navigation speed measurement error (north, east, celestial), inertial navigation positioning error (north, east, celestial), inertial navigation angle measurement error (yaw, pitch, roll), photoelectric speed measurement error (north, celestial, east), photoelectric positioning error (north, celestial, east), photoelectric angle measurement error (yaw, pitch, roll), photoelectric installation position error (north, celestial, east), photoelectric installation angle error (yaw, pitch, roll), target position binding error, target speed binding error, missile positioning error, missile speed measurement error, missile angle measurement error, initial alignment error, fire control solution position error and fire control solution speed error, involving a total of 32 error indicators, represented by x1, x2,…, x 31 ,x 32 The indicator system is shown in the attached Figure 6 As shown, with the addition of a hit probability indicator, the dimension of the data to be analyzed is 33 dimensions, and the sample size is set to 2000. Next, based on this data, the present invention is applied to perform a sensitivity analysis on the missile hit probability during an aircraft-to-ground attack.

[0141] Phase 1: Establishment of the Agent Model of Aircraft-to-Ground Combat System

[0142] Step 1: Data clustering based on mutual information hierarchical clustering algorithm

[0143] The aircraft combat simulation data to be analyzed is 33-dimensional, and it is difficult to model it using only the Bayesian network. Therefore, the 32-dimensional data except the missile hit probability is first clustered based on the mutual information hierarchical clustering algorithm.

[0144] Any two error sources x i ,x j The mutual information is:

[0145]

[0146] x i ,x j The inverse of the mutual information is

[0147]

[0148] D(x i ;x j ) is smaller, it means x i and x j The higher the similarity between them, the lower the similarity between them. i and x j The smaller the similarity between them, the smaller the similarity between them. Here we choose to set the number of clusters to 19, that is, the 32-dimensional data x = (x1, x2, ..., x 32 ) are clustered into 19 data clusters The clustering results are shown in Table 1.

[0149] Table 1 Clustering results of each indicator

[0150]

[0151] Step 2: Feature extraction based on deep autoencoder

[0152] After obtaining 19 data clusters using the mutual information-based hierarchical clustering algorithm, the next step is to extract features for each cluster of data. Here, the autoencoder model in deep learning is used for feature extraction.

[0153] The difference between an autoencoder and a general neural network is that the dimension of the output layer is consistent with the input layer, and the dimension of the intermediate hidden layer is generally lower than the input layer. Its purpose is to convert high-dimensional input data into low-dimensional features. Because each clustered data cluster contains 1 to 3 indicators (data clusters containing only 1 indicator do not require feature extraction), the number of hidden layers is set to 3, with dimensions of 2, 1, and 2, respectively, as shown in the attached figure. Figure 7 shown.

[0154] In terms of functional composition, the autoencoder consists of two parts: the encoder and the decoder. The encoder transforms the input sample data into the feature space, and the decoder restores the features in the feature space.

[0155] For the clustered data set, the dimension is 19, that is, x * ∈R The autoencoder maps this set of data to the feature space and obtains the encoding z of each set of data (n) And with the help of this set of codes, the samples are reconstructed, that is,

[0156] z (19) =f encode (x *(19) ) (18)

[0157] x' (19) =g decode (z (19) ) = g decode f encode (x *(19) ) (19)

[0158] For the sample x * , the activation function uses the Sigmoid function, and the activation value of the hidden layer is the code of x, that is

[0159] z=Sigmoid(W (1) x * +b (1) ) (20)

[0160] The output of the autoencoder is

[0161] x'=Sigmoid(W (2) z+b (2) ) (twenty one)

[0162] Where W (1) ,W (2) ,b (1) ,b (2) is the network parameter.

[0163] The learning goal of the autoencoder is to make the error between input and output as small as possible, usually using the mean square error to measure the original input x (n) and reconstruct the output x' (n) The error between

[0164]

[0165] Where λ is the coefficient of the regularization term.

[0166] By minimizing the error between input and output, the parameters in the network structure can be effectively learned. If the error is trained small enough, it can be considered that the information of the original data is contained in the feature space. When the autoencoder network is trained, the decoder can be removed and only the encoder is retained. The output of the encoder is the feature of the data cluster. In this way, the data dimension is reduced from 32 dimensions to 19 dimensions, and the overall data dimension is reduced from 33 dimensions to 20 dimensions.

[0167] Step 3: Bayesian network modeling

[0168] The data dimension obtained through the aircraft-to-ground combat simulation system is too high to be directly modeled using the Bayesian network. However, after clustering and feature extraction, the data dimension has been reduced from 33 dimensions to 20 dimensions. At this time, using these features and isolated variable nodes (some data clusters may have only one variable, so feature extraction is not required) can establish the Bayesian network model more accurately and efficiently. First, the Bayesian network structure is learned through the A* algorithm, and each node in the network structure is the feature extracted from the data cluster after data clustering. Next, the maximum likelihood method is used to learn the parameters of the Bayesian network. In this way, the Bayesian network is established, and the entire proxy model is successfully established by fusing the autoencoder and the Bayesian network. In subsequent calculations, the Bayesian network inference algorithm is used to infer the results for sensitivity analysis.

[0169] Phase 2: Sensitivity Analysis of Aircraft Ground Combat Effectiveness

[0170] Step 4: Calculate the relevant parameters of the Sobol index method.

[0171] Taking the aircraft's missile hit probability as an indicator, the established aircraft-to-ground combat system agent model is

[0172] Y=f(x1,x2,x3,...,x 32 ) (25)

[0173] Where Y is the missile hit probability of the aircraft, x1,x2,x3,...,x 32 It refers to the various factors in the index system that affect the probability of aircraft missile hitting.

[0174] First, we use random sampling to sample from the input space to obtain two input matrices A and B. Each row in the two matrices is a set of input combinations of the model under study, and each combination is calculated by the proxy model to obtain the corresponding output. Then we construct the matrix AB i , the construction method is to replace the i-th column of matrix A with the i-th column of matrix B. Similarly, the i-th column of matrix A can be replaced with the i-th column of matrix B to obtain matrix A i B.

[0175]

[0176]

[0177]

[0178] Substituting these matrices into the proxy model, we can get the output vectors, which are denoted as y A ,y B , and According to the Monte Carlo algorithm, the following results can be obtained:

[0179]

[0180]

[0181]

[0182] In the formula

[0183] Step 5: Calculate the global sensitivity coefficient.

[0184] Input variable X i The main effect index Total Effect Index The estimate is:

[0185]

[0186]

[0187] The global sensitivity analysis results of this example are shown in Table 2. Figure 8 The results are displayed in the form of a bar graph. It can be seen that error sources such as indicator 2 (inertial navigation eastward speed error), indicator 23 (photoelectric installation angle error (pitch angle)), indicator 27 (missile positioning error), and indicator 32 (fire control solution speed error) have a greater impact. When evaluating the aircraft's combat effectiveness, we can focus on studying these indicators with greater influence.

[0188] Table 2 Global sensitivity coefficients

[0189]

[0190] In the above example, when the sample size is 5000, the surrogate model is established using a neural network. The number of iterations is limited. The error between the surrogate model output and the original system output can reach 0.001. At this time, the neural network fits the original system very accurately. Therefore, the results of the sensitivity analysis using the surrogate model (see attached) are shown in Figure 2. Fig. 9 As shown) is used as a benchmark to further illustrate the advantages of the present invention:

[0191] 1. The sensitivity analysis results of using the fusion model and neural network to build the proxy model under 2000 samples (see attached) Fig.10 Compared with the benchmark results, the 10 factors with the highest global sensitivity coefficients in the analysis results of the proxy model constructed using the fusion model have a similarity of 80% with the benchmark results, while the 10 factors with the highest global sensitivity coefficients in the analysis results of the proxy model constructed using the neural network have a similarity of only 40% with the benchmark results. This shows that the fusion Bayesian network and deep learning model proposed in the present invention still has a high accuracy rate in the sensitivity analysis of aircraft combat effectiveness in the face of a data environment with fewer samples and higher dimensions.

[0192] 2. When the aircraft-to-ground combat simulation system in the example of the present invention is used for simulation, the average simulation time can reach more than 2 minutes each time. If the Sobol index calculation is performed directly through the original aircraft-to-ground combat simulation system, it will take more than 2130 hours to obtain the results of the sensitivity analysis of the aircraft-to-ground combat effectiveness. However, after establishing the fusion model as the proxy model, the Sobol index calculation of the example can obtain the results of the sensitivity analysis of the aircraft-to-ground combat effectiveness within 2 to 3 minutes. It can be seen that the present invention significantly improves the efficiency of the sensitivity analysis of the aircraft combat effectiveness.

Claims

1. An aircraft combat effectiveness sensitivity analysis integrating Bayesian network and deep learning, characterized by Here are the steps: Establishment of Agent Model for Aircraft Combat System Step 1: Data clustering based on mutual information hierarchical clustering algorithm: The aircraft combat simulation data to be analyzed is m-dimensional. First, the m-1-dimensional data except the missile hit probability is clustered based on the mutual information hierarchical clustering algorithm to obtain the m-1-dimensional data x=(x1,x2,···,x m-1 ) into k data clusters The k is the number of clusters; Step 2: Feature extraction based on deep autoencoder: The autoencoder model in deep learning is used to extract features from each cluster of data. The data dimension is reduced from m-1 to k, and the overall data dimension is reduced from m to k+1. Step 3: Use Bayesian network to build a Bayesian network model for the data whose dimension has been reduced from m dimension to k+1 dimension after clustering and feature extraction, and obtain the entire proxy model, that is, the aircraft-to-ground combat system proxy model Y=f(x1,x2,x3,...,x 32 ), where Y is the missile hit probability of the aircraft, x1,x2,x3,...,x 32 It is the various factors in the index system that affect the probability of aircraft missiles hitting the target; Sensitivity Analysis of Aircraft Combat Effectiveness Step 4: Calculate the relevant parameters of the Sobol index method Random sampling is used to sample two input matrices A and B from the input space. Each row in the two matrices is a set of input combinations of the model under study, and each combination is calculated by the proxy model to obtain the corresponding output: Then construct the matrix AB i , the construction method is to replace the i-th column of matrix A with the i-th column of matrix B. Similarly, the i-th column of matrix A can be replaced with the i-th column of matrix B to obtain matrix A i B: Substitute the matrix into the proxy model to get the output vector, which is denoted as y A ,y B , and The following results are obtained according to the Monte Carlo algorithm: Step 5: Calculate the global sensitivity coefficient Input variable X i The main effect index Total Effect Index The estimate is: In the formula Based on the main effect index Total Effect Index The global sensitivity coefficient is calculated, the values ​​of various indicators are calculated, and the aircraft combat effectiveness is analyzed and evaluated.

2. The aircraft combat effectiveness sensitivity analysis integrating Bayesian network and deep learning according to claim 1 is characterized by: The data clustering process based on the mutual information hierarchical clustering algorithm in step 1 is as follows: the aircraft combat simulation data to be analyzed is m-dimensional, and the m-1-dimensional data except the missile hit probability is firstly clustered based on the mutual information hierarchical clustering algorithm; Any two error sources x i ,x j The mutual information is: i≠j,1,2,3,m-1 x i ,x j The inverse of the mutual information is Where: D(x i ;x j ) and x i and x j The similarity between them is inversely proportional; Set the number of clusters to k and transform the m-1 dimensional data x=(x1,x2,···,x m-1 ) into k data clusters 3. The aircraft combat effectiveness sensitivity analysis integrating Bayesian network and deep learning according to claim 1 is characterized by: The process of extracting features from each cluster of data using the autoencoder model in deep learning in step 2 is as follows: for the clustered data set with dimension k, x * ∈R The autoencoder maps the data to the feature space and obtains the encoding z of each set of data (n) And reconstruct the sample with the help of this set of encodings: z (k) =f encode (x *(k) ) x' (19) =g decode (z (19) )=g decode f encode (x *(19) ) For the sample x * , the activation function uses the Sigmoid function, and the activation value of the hidden layer is the encoding of x: z=Sigmoid(W (1) x * +b (1) ) The output of the autoencoder is: x'=Sigmoid(W (2) z+b (2) ) Where W (1) ,W (2) ,b (1) ,b (2) is the network parameter; The original input x is measured using mean square error (n) and reconstruct the output x' (n) The error between: Where λ is the coefficient of the regularization term; When the autoencoder network training is completed, the decoder is removed and only the encoder is retained. The output of the encoder is the feature of the data cluster. The data dimension is reduced from m-1 dimension to k dimension, and the overall data dimension is reduced from m dimension to k+1 dimension.

4. The aircraft combat effectiveness sensitivity analysis integrating Bayesian network and deep learning according to claim 1 is characterized by: The process of obtaining the aircraft-to-ground combat system proxy model by Bayesian network modeling in step 3 is as follows: first, the Bayesian network structure is learned by the A* algorithm, and each node in the network structure is the feature extracted from the data cluster after data clustering; then the maximum likelihood method is used to learn the parameters of the Bayesian network, and the Bayesian network is established. The entire proxy model, that is, the aircraft-to-ground combat system proxy model Y=f(x1,x2,x3,...,x 32 ).

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