CN112861257B - Aircraft fire control system precision sensitivity analysis method based on neural network - Google Patents

Aircraft fire control system precision sensitivity analysis method based on neural network Download PDF

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CN112861257B
CN112861257B CN202110027414.3A CN202110027414A CN112861257B CN 112861257 B CN112861257 B CN 112861257B CN 202110027414 A CN202110027414 A CN 202110027414A CN 112861257 B CN112861257 B CN 112861257B
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neural network
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高晓光
汪强龙
谭翔元
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Northwestern Polytechnical University
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Abstract

The invention discloses an aircraft fire control system precision sensitivity analysis method based on a neural network, which improves the analysis precision of sensitivity coefficients of precision indexes of an aircraft fire control system by introducing a local sensitivity algorithm and a global sensitivity algorithm into index sensitivity analysis of the aircraft fire control system and comprehensively utilizing an entropy method and a Sobol method according to organic combination of different precision indexes. The BP neural network is added in the airplane fire control system and trained, the accuracy index and the final killing probability of the airplane fire control system are fitted, and the required sample data is expanded quickly and effectively. And the optimal distribution of the precision indexes of the airplane fire control system is realized through a precision optimal distribution algorithm. The method can well solve the analysis and evaluation problem of multi-precision indexes in the airplane fire control system under the condition of insufficient data samples, can quickly expand experimental data based on the learning and analysis of the neural network, and ensures that the airplane fire control system achieves the specified killing rate.

Description

Aircraft fire control system precision sensitivity analysis method based on neural network
Technical Field
The invention belongs to the technical field of airplane fire control, and particularly relates to a fire control precision sensitivity analysis method.
Background
In recent years, with the concern and importance of China on the correlation analysis of the errors and the precision of the airplane fire control system, people put higher requirements on the correlation analysis of the errors and the precision of the airplane fire control system, and therefore the topic of the correlation analysis of the errors and the precision of the airplane fire control system becomes the focus of the concern of the fire control industry. In order to improve the working performance of the aircraft fire control system to the maximum extent, on one hand, the use of the fire control system needs to be improved, and on the other hand, the analysis of the accuracy sensitivity of the aircraft fire control system needs to be emphasized. For various aircraft, whether gunship or fighter or other types of aircraft, the key to the prediction of the effectiveness of a battle is the calculation of the accuracy of the system, and in particular the calculation of the CEP (circular probability deviation: radius of circular area for 50% hit probability) of the selected target effectiveness of the battle. Therefore, it is very important to research and simulation calculation for factors affecting the accuracy of the system. The method has positive significance for improving the shooting precision of the weapon, reasonably distributing the error source indexes of the fire control system and controlling the errors of the whole system.
Aircraft, by virtue of their maneuverability, play an increasingly important role in modern war. The aerial bomb, the aerial bomb and the like put higher requirements on the accuracy of the airplane fire control system, and in actual combat, the accuracy of the fire control system is influenced by various factors due to the complexity of battlefield environment, attack conditions, target motion and the like. Analyzing the influence and the influence degree of the factors on the striking precision is very important for improving the performance of the fire control system. The influence of different error sources on the accuracy of the airplane fire control system is researched and analyzed at home and abroad, and measures for reducing errors and improving the accuracy are provided. However, each error source does not act on the fire control system independently, and multiple errors often exist simultaneously and have strong mutual coupling effect. Therefore, it is necessary to analyze the sensitivity of the fire control system to find out the main error sources and the influence of the interaction between the error sources on the final accuracy.
In the military industry field, the related precision of an existing aircraft system is difficult to evaluate due to the cost problem and the operation difficulty problem, and for a complex system, the precision analysis of a plurality of influence factors of hit probability of the complex system is difficult, so that the development, development and test of weaponry are limited to a certain extent. Meanwhile, the fire control system is complex in system and difficult in data acquisition, and how to utilize the existing data to perform effective precision analysis also becomes a key problem for improving the performance of the aircraft fire control system.
The artificial neural network simulates neurons in the human brain, each neuron is regarded as a node, the nodes are connected, and the neurons of each layer transmit information along one direction through weighting. And a directed graph model is constructed. The artificial neural network has the following remarkable characteristics that firstly, the adaptive capacity is strong, and secondly, large-scale mass data can be processed. The BP network can learn and store a large number of input-output pattern mappings without prior disclosure of mathematical equations describing such mappings. The neural network can fit any complex mathematical relationship, and the characteristic plays an important role in expanding the application of the neural network.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an aircraft fire control system precision sensitivity analysis method based on a neural network, which improves the analysis precision of the sensitivity coefficient of the precision index of the aircraft fire control system by introducing a local sensitivity algorithm and a global sensitivity algorithm into index sensitivity analysis of the aircraft fire control system and comprehensively utilizing an entropy method and a Sobol method according to organic combination of different precision indexes. The BP neural network is added in the airplane fire control system and trained, the accuracy index and the final killing probability of the airplane fire control system are fitted, and the required sample data is expanded quickly and effectively. And the optimal distribution of the precision indexes of the airplane fire control system is realized through a precision optimal distribution algorithm. The method can well solve the analysis and evaluation problem of multi-precision indexes in the airplane fire control system under the condition of insufficient data samples, can quickly expand experimental data based on the learning and analysis of the neural network, and ensures that the airplane fire control system can reach the specified killing probability.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: constructing a simulation verification system based on an airplane fire control system, and acquiring a sample of the accuracy index of the airplane fire control system and a corresponding killing probability accuracy value by adopting the simulation verification system;
step 2: adopting a BP neural network, taking a sample of the accuracy index of the airplane fire control system as the input of the BP neural network, taking the precision value of the killing probability obtained in the step 1 as the output of the BP neural network, learning the BP neural network, and fitting the precision index and the precision value of the killing probability of the airplane fire control system by the BP neural network to generate an analysis sample;
and step 3: analyzing local sensitivity;
step 3-1: determining a precision local sensitivity analysis index;
obtaining a killing probability precision value matrix corresponding to m sample points under all n precision indexes by the BP neural network learned in the step 2:
Figure BDA0002890823590000021
wherein x isi,jRepresenting the killing probability precision value of the ith sample point under the jth precision index;
step 3-2: carrying out nonnegative treatment on the precision value of the killing probability;
precision value x of assumed killing probabilityi,j∈[c,d]Taking a threshold value Qq＝(d-c)*p+c,p∈(0,1)；
When x isi,j≥QqThe method comprises the following steps:
Figure BDA0002890823590000031
when x isi,j<QqThe method comprises the following steps:
Figure BDA0002890823590000032
wherein, x'ijThe killing probability precision value after nonnegative treatment is obtained;
step 3-3: calculating the entropy of the jth precision index:
Figure BDA0002890823590000033
wherein
Figure BDA0002890823590000034
Representing the weight of the ith sample point under the jth precision index;
calculating the sensitivity of the jth precision index:
Figure BDA0002890823590000035
step 3-4: to sensitivity SjSorting from big to small, reserving the first r sensitivities, taking the precision indexes corresponding to the first r sensitivities as sensitivity indexes, and recording as x1,x2,x3,…,xrR is less than or equal to n; the sample points become t;
and 4, step 4: analyzing global sensitivity;
step 4-1: determining a global sensitivity analysis index;
defining a combat effectiveness model as follows:
Y＝f(x1,x2,x3,…,xr) In the formula (1), Y is the precision of an airplane fire control system;
calculating an input matrix:
Figure BDA0002890823590000036
wherein the content of the first and second substances,
Figure BDA0002890823590000037
indicating the killing probability precision value plus the sampling interval of the ith sample point under the jth precision index,
Figure BDA0002890823590000038
is the sampling interval;
the ith column of the matrix B is replaced by the ith column of the matrix A, and the obtained matrix is marked as MiThe matrix obtained by replacing the ith column of the matrix A with the ith column of the matrix B is recorded as M_i(ii) a Remember YA,YB,
Figure BDA0002890823590000041
Respectively is A, B, Mi,M_iAn output corresponding to the input of equation (1);
step 4-2: calculating by using a Sobol index method:
Figure BDA0002890823590000042
Figure BDA0002890823590000043
wherein, V (.) represents the variance;
and memorize:
Figure BDA0002890823590000044
Figure BDA0002890823590000045
Figure BDA0002890823590000046
step 4-3: calculating a global sensitivity index;
input variable xiIndex of main effect of
Figure BDA0002890823590000047
The estimation of (d) is:
Figure BDA0002890823590000048
input variable xiAnd xjSecond order interaction effect index of
Figure BDA0002890823590000049
The estimation of (d) is:
Figure BDA00028908235900000410
and 5: optimizing and distributing the precision;
step 5-1: the main effect values of each sensitivity index obtained by the global sensitivity analysis in the step 4 are respectively as follows:
Figure BDA00028908235900000411
carrying out normalization processing on the main effect value:
Figure BDA00028908235900000412
step 5-2: let the sensitivity index x1,x2,x3,…,xrRespectively is [ a ]1,b1],…[ar,br]And calculating the value upper limit corresponding to each sensitivity index:
Figure BDA00028908235900000413
preferably, the method for learning the BP neural network is as follows:
setting M to represent the number of nodes of the BP neural network input layer; q is used for representing the number of hidden layer nodes of the BP neural network, L is used for representing the number of output layer nodes of the BP neural network,
Figure BDA0002890823590000051
a threshold representing the jth neuron in the hidden layer of the BP neural network,
Figure BDA0002890823590000052
threshold, w, representing the g-th neuron in the output layer of the BP neural networkijRepresenting the connection weight, w, between the input layer and hidden layer nodes of the BP neural networkjgRepresenting the connection weight between the hidden layer and the output layer node of the BP neural network, wherein the input of the hidden layer and the output layer node of the BP neural network is the weighted sum of the output of the node of the previous layer; the specific mapping procedure is calculated as follows:
(1) randomly initializing each weight and threshold of the BP neural network;
(2) inputting a sample of the precision index of the airplane fire control system to a BP neural network input layer; defining the iteration number n as 1;
(3) calculating the output of each layer of BP neural network, and the output of the jth node of the hidden layer
Figure BDA0002890823590000053
Comprises the following steps:
Figure BDA0002890823590000054
in the formula:
Figure BDA0002890823590000055
an input for the jth node of the hidden layer;
Figure BDA0002890823590000056
is the output of the ith node of the input layer;
Figure BDA0002890823590000057
is a Sigmoid function.
Output to the g-th node of the output layer
Figure BDA0002890823590000058
Comprises the following steps:
Figure BDA0002890823590000059
in the formula:
Figure BDA00028908235900000510
is the input of the g-th node of the output layer;
(4) the error of each layer is calculated:
output layer error:
Figure BDA00028908235900000511
Figure BDA00028908235900000512
representing a desired output;
implicit layer error:
Figure BDA00028908235900000513
(5) and (4) correcting the weight and the threshold:
Figure BDA00028908235900000514
Figure BDA00028908235900000515
Figure BDA00028908235900000516
Figure BDA00028908235900000517
in the formula: eta is the learning rate, eta belongs to (0, 1); alpha is a momentum factor, and alpha belongs to (0, 1);
(6) when the training error is smaller than a given training error threshold value, ending the iteration; otherwise, adding 1 to n, and returning to the step (3) to execute repeatedly.
The invention has the following beneficial effects:
1. the invention establishes a plurality of main error sources of the precision of the airplane fire control system, and considers a plurality of subsystems such as a radar subsystem, a photoelectric subsystem, a navigation subsystem, a cockpit display control subsystem and the like, so that the analysis result has practical significance.
2. The invention creatively combines the neural network and the airplane fire control system, leads the neural network to have the capability of fitting precision influence indexes and killing probability through training and learning, and expands a large amount of training sample data so as to lead the subsequent sensitivity analysis to be more accurate.
3. The invention adopts the precision sensitivity analysis based on the neural network, utilizes the thought of an entropy value method to carry out local sensitivity analysis in the specific implementation process, utilizes the thought of Sobol exponential method variance decomposition to carry out global sensitivity analysis, and finally reversely distributes the value of each precision index, so that the analysis result is more comprehensive.
Drawings
FIG. 1 is a schematic diagram of the attack simulation of the present invention.
Fig. 2 is a schematic diagram of the neural network structure of the present invention.
FIG. 3 is a block diagram of the local sensitivity analysis of the present invention.
FIG. 4 is a line graph of the results of the local sensitivity analysis of the present invention.
FIG. 5 is a block diagram of a global sensitivity analysis of the present invention.
FIG. 6 is a line graph of the results of the global sensitivity analysis of the present invention.
FIG. 7 is a histogram of the results of entropy analysis of the present invention.
FIG. 8 is a histogram of the results of entropy sensitivity analysis based on neural networks.
FIG. 9 is a histogram of the BPSobol method sensitivity analysis based on 5-layer neural network of the present invention.
FIG. 10 is a histogram of the BPSobol method sensitivity analysis based on 3-layer neural network.
FIG. 11 is a histogram of the Sobol method sensitivity analysis based on the regression model of the present invention.
FIG. 12 is a histogram of the sensitivity analysis of the Bayesian-based BNSobol method of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
As shown in fig. 1, the accuracy sensitivity analysis of the aircraft fire control system is a basis for determining the development and construction emphasis of the aircraft, and is an important content for optimizing the fire control system. The main methods for analyzing the accuracy of the system include two main categories: local sensitivity analysis and global sensitivity analysis. The local sensitivity analysis method is an analysis method in which only the input of a variable to be researched is controlled to change and the rest variables are controlled to be fixed during each analysis. Common methods include direct derivation, finite difference, entropy, and the like, wherein the first two methods are mainly used in system models with simpler mathematical expressions, fewer uncertain factors, and easier derivation of sensitive differential equations. Because the precision analysis of the fire control system of the airplane is a system with a complex nonlinear model, the method introduces an entropy method to carry out local sensitivity analysis. The global sensitivity method is mainly used for testing the influence of simultaneous change of a plurality of input variables on the system output. Compared with a local sensitivity analysis method, the global sensitivity analysis method has the advantages that the model input space explored is larger, and the analysis result is more sufficient. The method for analyzing the global sensitivity mainly comprises a regression analysis method, a response surface method, a Sobol index method and the like, and the Sobol method is selected to analyze the global sensitivity according to the nonlinear characteristics of the fire control system.
An aircraft fire control system precision sensitivity analysis method based on a neural network comprises the following steps:
step 1: constructing a simulation verification system based on an airplane fire control system, and acquiring a sample of the accuracy index of the airplane fire control system and a corresponding killing probability accuracy value by adopting the simulation verification system;
step 2: adopting a BP neural network, taking a sample of the accuracy index of the airplane fire control system as the input of the BP neural network, taking the precision value of the killing probability obtained in the step 1 as the output of the BP neural network, learning the BP neural network, and fitting the precision index and the precision value of the killing probability of the airplane fire control system by the BP neural network to generate an analysis sample;
and step 3: analyzing local sensitivity;
step 3-1: determining a precision local sensitivity analysis index;
obtaining a killing probability precision value matrix corresponding to m sample points under all n precision indexes by the BP neural network learned in the step 2:
Figure BDA0002890823590000071
wherein x isi,jRepresenting the killing probability of the ith sample point under the jth precision indexAn accuracy value;
step 3-2: carrying out nonnegative treatment on the precision value of the killing probability; the entropy method quantifies and integrates inherent information of each scheme to be selected of multi-objective decision evaluation and subjective information judged by experience of a decision maker according to the concept and the property of entropy. The entropy method adopts the ratio of a certain index of each scheme to the sum of the same index value, so that the method has no dimensional influence, does not need to carry out standardization processing, and needs to carry out nonnegativity processing on data if the data has negative numbers. In addition, in order to avoid meaningless logarithms when entropy is obtained, data translation is required;
precision value x of assumed killing probabilityi,j∈[c,d]Taking a threshold value Qq＝(d-c)*p+c,p∈(0,1)；
When x isi,j≥QqThe method comprises the following steps:
Figure BDA0002890823590000081
when x isi,j<QqThe method comprises the following steps:
Figure BDA0002890823590000082
wherein, x'ijThe killing probability precision value after nonnegative treatment is obtained;
step 3-3: calculating the entropy of the jth precision index:
Figure BDA0002890823590000083
wherein
Figure BDA0002890823590000084
Representing the weight of the ith sample point under the jth precision index;
calculating the sensitivity of the jth precision index:
Figure BDA0002890823590000085
step 3-4: to sensitivity SjSorting from big to small, reserving the first r sensitivities, taking the precision indexes corresponding to the first r sensitivities as sensitivity indexes, and recording as x1,x2,x3,…,xrR is less than or equal to n; the sample points become t; and excluding non-sensitivity indexes, and reducing the sample space for next index optimization decomposition. And further analyzing the precision sample data of the selected sensitivity index, analyzing the sensitivity interval, and reducing the sample space for carrying out global sensitivity analysis for the next step.
And 4, step 4: analyzing global sensitivity;
step 4-1: determining a global sensitivity analysis index;
defining a combat effectiveness model as follows:
Y＝f(x1,x2,x3,…,xr) In the formula (1), Y is the precision of an airplane fire control system;
calculating an input matrix:
Figure BDA0002890823590000086
wherein the content of the first and second substances,
Figure BDA0002890823590000087
indicating the killing probability precision value plus the sampling interval of the ith sample point under the jth precision index,
Figure BDA0002890823590000088
is the sampling interval;
the ith column of the matrix B is replaced by the ith column of the matrix A, and the obtained matrix is marked as MiThe matrix obtained by replacing the ith column of the matrix A with the ith column of the matrix B is recorded as M_i(ii) a Remember YA,YB,
Figure BDA0002890823590000091
Are respectively provided withA,B,Mi,M_iAn output corresponding to the input of equation (1);
step 4-2: the Sobol sensitivity analysis method is a variance-based Monte Carlo method, and the basic idea is to analyze the influence of input on output variance and evaluate the sensitivity of single or multiple input interaction effects by calculating the contribution of single or multiple inputs to the output variance. Calculating by using a Sobol index method:
Figure BDA0002890823590000092
Figure BDA0002890823590000093
wherein, V (.) represents the variance;
and memorize:
Figure BDA0002890823590000094
Figure BDA0002890823590000095
Figure BDA0002890823590000096
step 4-3: calculating a global sensitivity index;
input variable xiIndex of main effect of
Figure BDA0002890823590000097
The estimation of (d) is:
Figure BDA0002890823590000098
input variable xiAnd xjSecond order interaction effect index of
Figure BDA0002890823590000099
The estimation of (d) is:
Figure BDA00028908235900000910
and 5: optimizing and distributing the precision;
step 5-1: the main effect values of each sensitivity index obtained by the global sensitivity analysis in the step 4 are respectively as follows:
Figure BDA00028908235900000911
carrying out normalization processing on the main effect value:
Figure BDA00028908235900000912
step 5-2: and reallocating each precision index. The precision optimization distribution is a method for realizing the optimization distribution of precision indexes of the airplane fire control system on the basis of index sensitivity analysis. Let the sensitivity index x1,x2,x3,…,xrRespectively is [ a ]1,b1],…[ar,br]And calculating the value upper limit corresponding to each sensitivity index:
Figure BDA0002890823590000101
preferably, the method for learning the BP neural network is as follows:
setting M to represent the number of nodes of the BP neural network input layer; q is used for representing the number of hidden layer nodes of the BP neural network, L is used for representing the number of output layer nodes of the BP neural network,
Figure BDA0002890823590000102
representing the jth nerve in the hidden layer of BP neural networkThe threshold of the element is set to be,
Figure BDA0002890823590000103
threshold, w, representing the g-th neuron in the output layer of the BP neural networkijRepresenting the connection weight, w, between the input layer and hidden layer nodes of the BP neural networkjgRepresenting the connection weight between the hidden layer and the output layer node of the BP neural network, wherein the input of the hidden layer and the output layer node of the BP neural network is the weighted sum of the output of the node of the previous layer; the specific mapping procedure is calculated as follows:
(1) randomly initializing each weight and threshold of the BP neural network;
(2) inputting a sample of the precision index of the airplane fire control system to a BP neural network input layer; defining the iteration number n as 1;
(3) calculating the output of each layer of BP neural network, and the output of the jth node of the hidden layer
Figure BDA0002890823590000104
Comprises the following steps:
Figure BDA0002890823590000105
in the formula:
Figure BDA0002890823590000106
an input for the jth node of the hidden layer;
Figure BDA0002890823590000107
is the output of the ith node of the input layer;
Figure BDA0002890823590000108
is a Sigmoid function.
Output to the g-th node of the output layer
Figure BDA0002890823590000109
Comprises the following steps:
Figure BDA00028908235900001010
in the formula:
Figure BDA00028908235900001011
is the input of the g-th node of the output layer;
(4) the error of each layer is calculated:
output layer error:
Figure BDA00028908235900001012
Figure BDA00028908235900001013
representing a desired output;
implicit layer error:
Figure BDA00028908235900001014
(5) and (4) correcting the weight and the threshold:
Figure BDA00028908235900001015
Figure BDA00028908235900001016
Figure BDA00028908235900001017
Figure BDA0002890823590000111
in the formula: eta is the learning rate, eta belongs to (0, 1); alpha is a momentum factor, and alpha belongs to (0, 1);
(6) when the training error is smaller than a given training error threshold value, ending the iteration; otherwise, adding 1 to n, and returning to the step (3) to execute repeatedly.
The specific embodiment is as follows:
the method for analyzing the precision sensitivity of the airplane fire control system based on the neural network is simulated through computer simulation, and the simulation environment is set as follows: the simulation step length is 0.1 second, and the simulation time is less than 45 seconds; the current situation is assumed to be: the enemy plane moves linearly at a constant speed and invades the airspace of one party, the manned plane of one party is intercepted, and the manned plane of one party is detected and struck by using radar equipment. Specific intended contents and comments are shown in table 1:
TABLE 1 XML battle scenario content
Figure BDA0002890823590000112
Figure BDA0002890823590000121
The selected indexes comprise an inertial navigation positioning precision index, an inertial navigation course precision index, an inertial navigation attitude precision index, an inertial navigation speed precision index, an atmospheric aircraft data system height measurement precision index, a radar detection distance precision index and a radar detection range precision index, and specific aircraft fire control system index values are shown in the following table 2:
TABLE 2 aircraft fire control System indicators
Figure BDA0002890823590000122
Figure BDA0002890823590000131
Stage one: model building and neural network learning
1. And (5) building a model. Firstly, a network platform is built through computer simulation based on an airplane fire control system. The simulation verification system comprises subsystems such as a planning file, a planning analysis engine, a database file, a database engine, a general simulation model, an object assembly engine, a red and blue object pilot tone, a data center, a two-dimensional situation engine, a performance evaluation engine and the like on the framework composition. The subsystems are interdependent and matched with each other, so that the system has a general combat simulation function. And (4) carrying out experimental simulation to obtain a sample corresponding to the precision influence index and a corresponding killing probability by loading the set combat scenario.
2. And (4) learning a neural network. The operation of the airplane is a complex process, the simulation experiment is divided into five stages in total in order to achieve a vivid reduction operation process as much as possible, and the five stages are respectively a preparation stage, a target detection stage, a weapon-target distribution stage, a fire control calculation stage and a weapon operation control stage. In order to overcome the defect of overlong simulation time, the invention introduces the neural network for learning after the simulation is finished, the forward neural network is learned through simulated data and a BP algorithm, and more analysis samples are generated by the learned neural network. The large number of samples analyzed will make the sensitivity analysis more convincing and accurate.
The neural network may perform learning of any function. This conclusion holds even for neural networks with only one hidden layer. There are two important preconditions for the neural network to be able to implement a function of any function: first, it is to be understood that the neural network is not capable of accurately computing the value of the primitive function, but can approximate the primitive function by adding hidden layer neuron values. That is, for any function f that needs to be implemented, precision error >0 is required, and enough hidden layer neurons are needed so that the neural network output g satisfies | f-g | < error for all inputs. The second premise is that the function being modeled is a continuous function, although sometimes the continuous approximation obtained by the neural network is already substantially satisfactory for non-continuous functions. The output of the simplest single-layer neuron is determined by weight and bias, the parameter weight and bias are changed, a standard sigmoid function can be obtained, and the function of the output can be infinitely close to any step function by changing the weight and the bias. Single layer neurons can learn any form of step function.
The invention adopts the BP neural network to learn the precision analysis data model, and realizes the precision analysis function of the airplane fire control system. The commonly used precision evaluation model mainly comprises a simulation model, an expert evaluation model, an analytic calculation model and the like. The subjective factors of expert models are too many, and it is difficult to obtain an accurate analytic model for a nonlinear complex system such as multi-person/unmanned plane cooperation, so that the efficiency value is difficult to accurately describe through expert evaluation or analytic calculation. Therefore, the invention adopts the simulation model to carry out the precision analysis of the airplane fire control system.
The simulation model takes the index values of all subsystems as input, and corresponding system precision values are obtained through calculation of a simulation system. In theory, the accuracy corresponding to any input combination can be obtained by using the Monte Carlo method, however, because the simulation and simulation process is time-consuming, the time overhead of the method is unacceptable when the simulation times of the Monte Carlo method are increased. Based on the reasons, the precision analysis data model is learned by adopting the BP neural network, and then precision analysis is carried out on the basis of the data model. The structure of the neural network and the accuracy index used by the invention is shown in figure 2. Learning precision index and sample precision value (missile miss amount De/killing probability P) by using neural networkkillRound probability error CEP) is the core model of the entire module. The module takes each precision index value as input, takes the corresponding precision value obtained by the calculation of a simulation system as output, and obtains the relation between each precision index and the corresponding precision value, namely an aircraft platform air combat precision analysis model Deky＝fky(σ, μ, ε, δ, λ, ρ, τ) and CEPkw＝fkw(sigma, mu, epsilon, delta, lambda, rho and tau), and an airplane platform ground attack precision analysis model
Figure BDA0002890823590000141
And CEPdw＝fdw(sigma, mu, epsilon, delta, lambda, rho and tau), and cross-platform collaborative combat accuracy analysis model of manned aircraft/unmanned aerial vehicle
Figure BDA0002890823590000142
Figure BDA0002890823590000143
And CEPww＝fww(σ, μ, ε, δ, λ, ρ, τ), more accurate analysis sample data is generated by the learned neural network, thereby providing sufficient sample data for sensitivity analysis.
And a second stage: analyzing local sensitivity;
the local sensitivity analysis module is mainly used for researching the influence degree and range of the change of a single precision index on the precision of the avionic system, further screening out the sensitivity index from a large number of precision index sets and determining the sensitivity interval of the sensitivity index, and reducing the sample space for carrying out 'global sensitivity analysis of the precision index' in the next step. The local sensitivity analysis module is composed as shown in fig. 3.
3. Determining precision local sensitivity analysis index precision value xij：
4. And nonnegativity processing of the precision index. The entropy method quantifies and integrates inherent information of each scheme to be selected of multi-objective decision evaluation and subjective information judged by experience of a decision maker according to the concept and the property of entropy. The entropy method adopts the ratio of a certain index of each scheme to the sum of the same index value, so that the method has no dimensional influence, does not need to carry out standardization processing, and needs to carry out nonnegativity processing on data if the data has negative numbers. In addition, in order to avoid meaningless logarithms when entropy is obtained, data translation is required;
5. calculating the local sensitivity of each index;
aiming at all precision indexes, carrying out sensitivity SjAnd sorting, eliminating non-sensitivity indexes, and reducing the sample space for the next step of index optimization decomposition. And further analyzing the precision sample data of the selected sensitivity index, analyzing the sensitivity interval, and reducing the sample space for carrying out global sensitivity analysis for the next step. The local sensitivity results analyzed by the present embodiment are shown in fig. 4 in the form of a line graph, and it can be seen that the difference of the local sensitivity analysis results is not large, and the sensitivity individual change difference of each index is not large. The local sensitivity coefficients for each accuracy index are shown in table 3 below:
table 3: local coefficient of sensitivity
Figure BDA0002890823590000151
And a third stage: global sensitivity analysis
The global sensitivity analysis is performed on the basis of the local sensitivity analysis module, mainly performs combined multidimensional analysis on the sensitivity indexes, and explores the influence degree of the combined action of the multiple indexes on the system precision, as shown in fig. 5. Aiming at the nonlinear characteristics of the combat simulation system, a Sobol analysis method is selected to complete the global sensitivity analysis research of the precision index, and the scheme can generally obtain a relatively accurate optimization result.
6. And determining the precision global sensitivity analysis index.
The efficiency model is an airplane single-platform air combat mission model (controlled weapon) Deky＝fky(σ, μ, ε, δ, λ, ρ, τ), aircraft Single platform air combat mission model (uncontrolled weapons) CEPkw＝fkw(sigma, mu, epsilon, delta, lambda, rho, tau), model of the aircraft single-platform ground-attack mission (weapon in control) Pkilldy＝fdy(σ, μ, ε, δ, λ, ρ, τ), aircraft platform-to-ground attack mission model (uncontrolled weapons) CEPdw＝fdw(σ, μ, ε, δ, λ, ρ, τ), manned/unmanned cooperative cross-platform combat mission model analysis model (weapon controlled)
Figure BDA0002890823590000152
CEP (unmanned weapon) model analysis model for cooperative cross-platform combat mission of manned aircraft/unmanned aerial vehicleww＝fww(σ,μ,ε,δ,λ,ρ,τ)。
7. And calculating relevant parameters of the Sobol index method. The Sobol sensitivity analysis method is a variance-based Monte Carlo method, and the basic idea is to analyze the influence of input on output variance and evaluate the sensitivity of single or multiple input interaction effects by calculating the contribution of single or multiple inputs to the output variance.
8. A global sensitivity index is calculated.
The local sensitivity result analyzed by the embodiment is shown in fig. 6, and is displayed in a line graph form, so that the result difference of the global sensitivity analysis is large, and the sensitivity difference of each index is large, wherein the indexes, namely the inertial navigation positioning error (Y azimuth), the inertial navigation positioning error (Z azimuth), the inertial navigation speed measurement error (X azimuth), the inertial navigation speed measurement error (Y azimuth), the inertial navigation speed measurement error (Z azimuth), the atmospheric machine height measurement error (H), and the radar detection distance error (d), have large influences, and the sensitivity coefficient is high. The influence of the indexes of the inertial navigation positioning error (X azimuth), the inertial navigation detection attitude error (Y), the inertial navigation detection pitch error (P), the radar detection azimuth angle error (a) and the radar detection pitch angle error (b) is small, and the sensitivity coefficient is small. The global sensitivity coefficients for the various accuracy indicators are shown in table 4 below:
table 4: global coefficient of sensitivity
Figure BDA0002890823590000161
And a fourth stage: precision optimized allocation
9. And determining the main effect value of each index and normalizing. The main effect value of each index (corresponding to each battle task precision index ((sigma)) obtained by global sensitivity analysis is set1,σ2,…,…)/(μ1,μ2,…,…)/(ε1,ε2,…,…)/(δ1,δ2,…,…)/(λ1,λ2,…,…)/(ρ1,ρ2,…,…)/(τ1,τ2,…,…))。
10. And reallocating each precision index. The precision optimization distribution is a method for realizing the optimization distribution of precision indexes of the airplane fire control system on the basis of index sensitivity analysis.
The result of the precision assignment of this example is shown in table 5 below:
table 5: precision optimization allocation algorithm allocation scheme
Figure BDA0002890823590000162
The simulation system constructed by the invention takes the precision index value influencing the airplane fire control system as input, changes different precision index values by executing different combat scenarios, performs actual combat simulation by fusing various complex combat simulation modules, such as a multi/unmanned aerial vehicle cooperative combat module, an avionic system precision analysis module and the like, and takes the final killing probability of the airplane of an enemy as a final analysis index. In this embodiment, the average killing probability of one inverse distribution of the local sensitivity accuracy index without any operation is only 53%, and after the local sensitivity analysis and the global sensitivity analysis based on the neural network of the present invention are performed, the average killing probability of one inverse distribution of the experiment after the return to the combat system can reach 78% and 94% respectively. Illustrating the effectiveness of the present invention.
In order to further verify the effectiveness of the method for analyzing the precision sensitivity of the airplane fire control system based on the neural network, the advantages of the method are explained from the following two aspects:
1) airplane fire control system precision local sensitivity analysis based on neural network
Under the condition that the system has more inputs, the global sensitivity analysis is difficult to calculate and takes long time, the local sensitivity analysis method is simple, the rapid calculation capability of the local sensitivity analysis method can be utilized to screen the first round of indexes, factors behind the sensitivity ranking are removed, and factors before the sensitivity ranking are mainly analyzed, so that the difficulty of the global sensitivity analysis can be greatly reduced. In order to verify the effectiveness of the partial sensitivity analysis based on the neural network, the following control group experiment is designed, and after the model is built, the neural network learning stage of the patent is not carried out in the control group experiment, and the entropy method analysis is directly carried out. The results of the entropy method and the neural network-based entropy method of the present invention are shown in fig. 7 and fig. 8, respectively, and the effectiveness of the neural network-based entropy method of the present invention is demonstrated from the following two aspects: 1) the index value of the sensitivity result analyzed by the entropy value method and the method is reversely distributed once is brought into the fire control system again, the experiment is repeated, and average results of the killing probability of 77.76% and the killing probability of 53.93% are respectively obtained. 2) The target killing probability is set to be 90%, local sensitivity coefficients obtained by an entropy method and the neural network-based entropy method of the patent are substituted into the precision optimization distribution formula of the patent, experiments are repeated, the traditional entropy method needs 22 times of average iteration to meet the requirement of 90%, and the neural network-based entropy method of the patent can meet the requirement of the killing probability only by 10 times of average iteration operation. The effectiveness of the method is further verified. The relative merits of the two experimental methods are shown in table 6 below:
table 6: comparison table of local sensitivity analysis advantages and disadvantages of patent and contrast formula method
Figure BDA0002890823590000171
2) Aircraft fire control system precision global sensitivity analysis based on neural network
In order to compare and prove the effectiveness of the global sensitivity analysis based on the neural network, the following two groups of experiments of a control group are designed, the experiment of the control group 1 does not carry out the learning of the neural network in the step 2 of the patent, but adopts the most basic linear regression model to fit a complex fire control system after the model is built, and then carries out the sensitivity analysis, wherein the global sensitivity method of the control group experiment is a Sobol exponential method based on the regression model. The experiment of the control group 2 and the experiment of the control group 1 have the same steps at the early stage, the neural network learning expansion data of the patent is not carried out, but in the subsequent analysis part, the general sensitivity analysis is carried out by combining a naive Bayesian network and a Sobol index method, and the experimental method of the control group 2 is derived from a BNSobol method for helicopter fire control system precision sensitivity analysis in the patent. In the global sensitivity analysis stage, two innovative methods are designed, one is a BPSobol method based on a 5-layer neural network, the other is a BPSobol method based on a 3-layer neural network, and the results of experiments 1 and 2 and a control group are respectively shown in the attached figures 9, 10, 11 and 12. Similar to the local sensitivity analysis, the following two aspects prove the effectiveness of the global sensitivity analysis of the Sobol method based on the neural network in the patent: 1) firstly, the sensitivity results of the method of the patent and the methods of the control group experiments 1 and 2 are only subjected to one-time reverse distribution of index values and are re-introduced into a fire control system, the experiments are repeated, and average results of killing probabilities of 94.30%, 87.22%, 41.00% and 82.02% are respectively obtained. 2) Setting the target killing probability to be 90%, respectively substituting the global sensitivity coefficients obtained by the two methods and the two groups of comparison formula methods into the precision optimization distribution formula of the method, repeating the experiment, and finding that the Sobol method based on the 5-layer neural network and the Sobol method based on the 3-layer neural network can meet the requirement only by carrying out average iteration for 1 time and 3 times, the BNSobol method based on the Bayesian network needs 8 iterations on average, and the Sobol method based on the regression model can not reach the specified 90% killing probability by an iteration algorithm in the experiment, thereby further verifying the effectiveness of the global sensitivity analysis method based on the neural network. The relative merits of the four experimental methods are shown in table 7 below:
table 7: the patent compares table with the overall sensitivity analysis of the contrast group
Figure BDA0002890823590000191
To summarize: the aircraft fire control system precision sensitivity analysis method based on the neural network can effectively utilize the excellent characteristic extraction and data generation capacity of the neural network, when the complex fire control system is analyzed, the neural network can be used for fitting a complex fire control system model, a large amount of effective data are generated in an expansion mode, and the local sensitivity analysis and global sensitivity analysis result precision of the fire control system precision is greatly improved.

Claims (2)

1. An aircraft fire control system precision sensitivity analysis method based on a neural network is characterized by comprising the following steps:
step 1: constructing a simulation verification system based on an aircraft fire control system, and acquiring a sample of tactical indexes of the aircraft fire control system and a corresponding killing probability accuracy value by adopting the simulation verification system;
step 2: adopting a BP neural network, taking a sample of the tactical indexes of the airplane fire control system as the input of the BP neural network, taking the precision value of the killing probability obtained in the step 1 as the output of the BP neural network, learning the BP neural network, fitting the tactical indexes and the precision value of the killing probability of the airplane fire control system by the BP neural network, and generating an analysis sample;
and step 3: analyzing local sensitivity;
step 3-1: determining a precision local sensitivity analysis index;
and (3) obtaining a killing probability precision value matrix corresponding to m sample points under all n tactical indexes by the BP neural network after learning in the step (2):
Figure FDA0002890823580000011
wherein x isi,jRepresenting the killing probability precision value of the ith sample point under the jth tactical index;
step 3-2: carrying out nonnegative treatment on the precision value of the killing probability;
precision value x of assumed killing probabilityi,j∈[c,d]Taking a threshold value Qq＝(d-c)*p+c,p∈(0,1)；
When x isi,j≥QqThe method comprises the following steps:
Figure FDA0002890823580000012
when x isi,j<QqThe method comprises the following steps:
Figure FDA0002890823580000013
wherein, x'ijThe killing probability precision value after nonnegative treatment is obtained;
step 3-3: calculating the entropy of the jth tactical index:
Figure FDA0002890823580000014
wherein
Figure FDA0002890823580000015
Representing the weight of the ith sample point under the jth tactical index;
calculate the sensitivity of the jth tactical index:
Figure FDA0002890823580000021
step 3-4: to sensitivity SjSorting from big to small, reserving the first r sensitivities, which correspond to tactical indexes as sensitivity indexes and are marked as x1,x2,x3,…,xrR is less than or equal to n; the sample points become t;
and 4, step 4: analyzing global sensitivity;
step 4-1: determining a global sensitivity analysis index;
defining a combat effectiveness model as follows:
Y＝f(x1,x2,x3,…,xr) (1)
in the formula, Y is the precision of the airplane fire control system;
calculating an input matrix:
Figure FDA0002890823580000022
wherein the content of the first and second substances,
Figure FDA0002890823580000023
indicating the killing probability precision value plus the sampling interval of the ith sample point under the jth tactical index,
Figure FDA0002890823580000024
is the sampling interval;
the ith column of the matrix B is replaced by the ith column of the matrix A, and the obtained matrix is marked as MiThe matrix obtained by replacing the ith column of the matrix A with the ith column of the matrix B is recorded as M_i(ii) a Remember YA,YB,
Figure FDA0002890823580000025
Respectively is A, B, Mi,M_iAn output corresponding to the input of equation (1);
step 4-2: calculating by using a Sobol index method:
Figure FDA0002890823580000026
Figure FDA0002890823580000027
wherein, V (.) represents the variance;
and memorize:
Figure FDA0002890823580000028
Figure FDA0002890823580000029
Figure FDA00028908235800000210
step 4-3: calculating a global sensitivity index;
input variable xiIndex of main effect of
Figure FDA0002890823580000031
The estimation of (d) is:
Figure FDA0002890823580000032
input variable xiAnd xjSecond order interaction effect index of
Figure FDA0002890823580000033
The estimation of (d) is:
Figure FDA0002890823580000034
and 5: optimizing and distributing the precision;
step 5-1: the main effect values of each sensitivity index obtained by the global sensitivity analysis in the step 4 are respectively as follows:
Figure FDA0002890823580000035
carrying out normalization processing on the main effect value:
Figure FDA0002890823580000036
step 5-2: let the sensitivity index x1,x2,x3,…,xrRespectively is [ a ]1,b1],…[ar,br]Calculating the value corresponding to each sensitivity indexLimiting:
Figure FDA0002890823580000037
2. the method for analyzing the accuracy and the sensitivity of the fire control system of the airplane based on the neural network as claimed in claim 1, wherein the method for learning the BP neural network is as follows:
setting M to represent the number of nodes of the BP neural network input layer; q is used for representing the number of hidden layer nodes of the BP neural network, L is used for representing the number of output layer nodes of the BP neural network,
Figure FDA0002890823580000038
a threshold representing the jth neuron in the hidden layer of the BP neural network,
Figure FDA0002890823580000039
threshold, w, representing the g-th neuron in the output layer of the BP neural networkijRepresenting the connection weight, w, between the input layer and hidden layer nodes of the BP neural networkjgRepresenting the connection weight between the hidden layer and the output layer node of the BP neural network, wherein the input of the hidden layer and the output layer node of the BP neural network is the weighted sum of the output of the node of the previous layer; the specific mapping procedure is calculated as follows:
(1) randomly initializing each weight and threshold of the BP neural network;
(2) inputting a sample of tactical indexes of the airplane fire control system to a BP neural network input layer; defining the iteration number n as 1;
(3) calculating the output of each layer of BP neural network, and the output of the jth node of the hidden layer
Figure FDA00028908235800000310
Comprises the following steps:
Figure FDA00028908235800000311
in the formula:
Figure FDA0002890823580000041
an input for the jth node of the hidden layer;
Figure FDA0002890823580000042
is the output of the ith node of the input layer;
Figure FDA0002890823580000043
is a Sigmoid function;
output to the g-th node of the output layer
Figure FDA0002890823580000044
Comprises the following steps:
Figure FDA0002890823580000045
in the formula:
Figure FDA0002890823580000046
is the input of the g-th node of the output layer;
(4) the error of each layer is calculated:
output layer error:
Figure FDA0002890823580000047
Figure FDA0002890823580000048
representing a desired output;
implicit layer error:
Figure FDA0002890823580000049
(5) and (4) correcting the weight and the threshold:
Figure FDA00028908235800000410
Figure FDA00028908235800000411
Figure FDA00028908235800000412
Figure FDA00028908235800000413
in the formula: eta is the learning rate, eta belongs to (0, 1); alpha is a momentum factor, and alpha belongs to (0, 1);
(6) when the training error is smaller than a given training error threshold value, ending the iteration; otherwise, adding 1 to n, and returning to the step (3) to execute repeatedly.
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