Improved Bayesian network-based reconnaissance and attack integrated unmanned aerial vehicle use safety assessment method

Abstract

In order to solve the problems that combat missions of the reconnaissance and attack integrated unmanned aerial vehicle are complex and diverse, test data are difficult to obtain, and the safety assessment subjectivity is high, the invention provides the reconnaissance and attack integrated unmanned aerial vehicle use safety assessment method based on the improved Bayesian network, and aims to assess the use safety of the reconnaissance and attack integrated unmanned aerial vehicle through the model. The method mainly comprises the following steps: step 1, constructing a reconnaissance and attack integrated unmanned aerial vehicle use safety evaluation index system; and step 2, improving the Bayesian network evaluation model. According to the method, the prior probability of the root node is obtained by improving the G1 method through the entropy method, and the conditional probability of the child node is obtained through the EM algorithm for the first time. The improved Bayesian network significantly enhances the adaptability and accuracy of the model in an incomplete data environment by means of the unique advantages of processing complexity and multivariable conditional probability distribution, and can be applied to wider application scenarios.

Description

Technical Field

[0001] The present invention relates to the technical field of the safety assessment of the use of unmanned aerial vehicles, and particularly to the application of an improved Bayesian network assessment method in the field of the safety assessment of the use of reconnaissance and strike integrated unmanned aerial vehicles. Background Art

[0002] The reconnaissance and strike integrated unmanned aerial vehicle integrates a variety of mission functions and has a high system complexity, which makes it necessary to coordinate multiple subsystems when performing tasks, increasing the operation difficulty and potential risks. The complexity of this system causes the reconnaissance and strike integrated unmanned aerial vehicle to be vulnerable to interference in a strong confrontation environment, making the unmanned aerial vehicle face safety threats such as out of control, crashing, and forced landing during use. In the face of potential safety threats, effectively assessing the use safety of the reconnaissance and strike integrated unmanned aerial vehicle and guiding its combat decision-making and safe use according to the assessment results are the key to ensuring the effective exertion of the combat effectiveness of the reconnaissance and strike integrated unmanned aerial vehicle.

[0003] Some tasks usually need to be performed in a complex and changeable environment, and the real environment is often difficult to be completely tested or simulated by a test platform, which leads to certain difficulties in obtaining the test data of the reconnaissance and strike integrated unmanned aerial vehicle, making it highly dependent on the experience and subjective judgment of experts in the process of use safety assessment, thus affecting the fairness and objectivity of the assessment. Therefore, it is crucial to select a use safety assessment method that conforms to the mission characteristics of the reconnaissance and strike integrated unmanned aerial vehicle. Summary of the Invention

[0004] In view of the current situation that the combat missions of the reconnaissance and strike integrated unmanned aerial vehicle are complex and diverse, the test data is difficult to obtain, and the safety assessment is highly subjective, the present invention provides a method for assessing the use safety of a reconnaissance and strike integrated unmanned aerial vehicle by improving the Bayesian network, which specifically includes the following steps:

[0005] Step 1. Construct an index system for assessing the use safety of a reconnaissance and strike integrated unmanned aerial vehicle;

[0006] The combat stage of the reconnaissance and strike integrated unmanned aerial vehicle is specifically divided into 5 stages: 1. Airport preparation; 2. Takeoff and climb; 3. Entering the battlefield; 4. Performing tasks; 5. Returning to the airport;

[0007] Based on the basic principles and methods of constructing the index system and combining the insights of experts in related fields, the index system is designed as a four-layer structure; 32 key indicators are selected, namely: the command and control ability, emergency handling ability, and health and fatigue level of ground station operators; the safety of anti-interference devices, reconnaissance payloads, and weapon payloads; the safety of power systems, sensing systems, and flight platforms; the endurance time, cruising speed, and endurance altitude of the UAV; the adaptability of the UAV to harsh terrain, weather, and electromagnetic environments; the anti-data link spoofing, anti-electromagnetic interference, anti-information attack, anti-satellite navigation spoofing, and anti-sound wave interference capabilities of the UAV; the data encryption, information transmission, and radar detection security capabilities of the UAV; the networking communication, trajectory tracking, and collaborative strike security among multiple UAVs; the target positioning, strike, and anti-interception capabilities of the UAV; the fault detection and self-repair capabilities of the UAV;

[0008] Step 2. Improve the Bayesian network evaluation model;

[0009] (1) Bayesian network;

[0010] If the observed data D is known, and let φ be the parameter to be estimated, then we have:

[0011]

[0012] In the formula, P(φ|D,ζ) is the posterior probability, P(φ|ζ) is the prior probability, P(D|φ,ζ) is the likelihood function, P(D|ζ) is the total probability of the observed data D under all possible parameters, D represents the observed data, and ζ represents the context content;

[0013] Equation (1) is transformed into:

[0014]

[0015] In the formula, if the context content ζ is ignored, the parameter φ to be estimated is denoted as A, and the observed data D is denoted as B, representing the conditional probability of inferring the occurrence of event B under the condition that event A has occurred;

[0016] The Bayesian network is represented as:

[0017] G = <x, g, p> (3)

[0018] In the formula, G represents the Bayesian network, <> represents the set of Bayesian networks, x = {x1, x2,..., x n} is the set of nodes, n is the number of nodes; g represents the dependence relationship between nodes, which is an n×n matrix; p is the conditional probability table, representing the conditional probability of each node x i i, where i is an integer taking values from 1 to n;

[0019] By the chain rule, the joint probability is:

[0020]

[0021] Wherein, P(X1, X2, …, X n ) represents the joint probability, P(X1) represents the probability of the occurrence of event X1, and P(X n |X1, γ, X n-1 ) represents the probability of the occurrence of X n-1 under the condition that events X1, …, X n occur;

[0022] A Bayesian network is composed of a set of variables X = {X1, X2,..., X n}, and each node corresponds to one variable in the set of variables; the joint probability is written as the product of local probabilities:

[0023]

[0024] Wherein, P(X) represents the joint probability, P(X i |P ai ) is the conditional probability of the child node X ai under the parent node P i , and P ai is the parent node of node X i ;

[0025] (2) Determine the prior probability by using the G1 method of order relation analysis improved based on entropy value;

[0026] Specifically as follows:

[0027] Step1: Let the evaluation object be A, corresponding to n evaluation indexes O = (O1, O2,..., O n ), and there are m experts M = (M1, M2, ···, M m ) participating in the evaluation, where M1, M2, ···, M m respectively represent m experts, and M represents the set of experts; if the evaluation importance degree of evaluation index O i is greater than that of O j , it is recorded as O i > O j , and > is the standard symbol, and its meaning is that the importance degree is greater than;

[0028] Step2: The expert selects the most important index from the index set and records it as O1 * ;

[0029] Step3: The expert then selects the most important index from the remaining n - 1 indexes and records it as O * 2;

[0030] Step 4: Repeat the previous step until the last index; obtain the order relationship after re - sorting all the indices:

[0031]

[0032] Step 5: Calculate the proportion of the j - th index under the i - th expert:

[0033]

[0034] In the formula:

[0035] ω ij is the proportion of the j - th index by the i - th expert. The larger this value is, the more important the index is and the greater its importance to the evaluation. Here, i = 1, 2,..., m, j = 1, 2,..., n;

[0036] o ij is the evaluation of the j - th index by the i - th expert;

[0037] is the sum of the evaluations of all experts on the j - th index;

[0038] Step 6: Calculate the entropy value e j of the j - th index:

[0039]

[0040] Step 7: Judge the ratio of the importance degrees of adjacent indices:

[0041]

[0042] In the formula, r k is the ratio of the entropy values of adjacent indices, k = n, n - 1,..., 2;

[0043] Step 8: Calculate the index weights. The weight v n of the last index is:

[0044]

[0045] Then, according to:

[0046]

[0047] back - calculate to obtain the weights of all indices;

[0048] Step 9: Assume that all levels of the index are divided into s levels, L=(L1, L2, ··· L s ), L1, L2, ··· L sThey respectively represent the levels of the indicators. Let \(L\) represent the set of indicator levels, and determine the membership degree of each indicator with respect to the levels:

[0049]

[0050] In the formula, \(\mu\) ij is the membership degree of the \(j\)-th indicator belonging to level \(i\), \(N\) is the total number of evaluators, and \(k\) is the number of evaluators whose scoring results of the \(j\)-th indicator belong to level \(i\);

[0051] Step10: Calculate the prior probability that the root node belongs to each level:

[0052]

[0053] In the formula, \(P\) represents the prior probability of the root node, \(v\) j is the weight of the \(j\)-th indicator among \(n\) indicators, and \(\mu\) ij is the membership degree of the \(j\)-th indicator belonging to level \(i\);

[0054] (3) Determine the conditional probability based on the EM algorithm;

[0055] E step - Expectation step: Under the current estimation of the Bayesian model parameters \(\theta\), calculate the posterior probability of the latent variable \(z\) (i) , that is, the expectation of the latent variable, as the current estimated value of the latent variable:

[0056] \(Q\) i (z (i) ) = p(z (i) |x (i) ; \(\theta\)) (14)

[0057] Among them, \(x\) (i) represents the observed variable in the \(i\)-th sample, corresponding to the observed node in the Bayesian network; \(z\) (i) represents the latent variable in the \(i\)-th sample, corresponding to the unobserved node in the Bayesian network; p(z (i) |x (i) ; \(\theta\)) represents the posterior distribution of the latent variable \(z\) (i) under the known observed data and the current parameters;

[0058] M step - Maximization step: According to the expected value \(Q\) i (z (i) ) calculated in the E step, update the parameter \(\theta\) to maximize the log-likelihood function:

[0059]

[0060] In the formula, p(x (i) ,z (i); θ) represents the maximum likelihood estimation function under the current parameters, where i is each sample; in the M-step, using the posterior probability calculated in the E-step, the model parameters θ are re-estimated to maximize the maximum likelihood estimation function;

[0061] In the M-step, the latent variable z needs to be considered (i) for all possible values, and according to their posterior probability Q i (z (i) ) to calculate the expected value by weighting; this means that for each sample i, not only the actually observed data x (i) needs to be considered, but also the influence of all possible values of the latent variable needs to be comprehensively considered;

[0062] The M-step decomposes the objective function into the sum of the logarithms of the conditional probabilities of each node, independently updates the parameters of each node, and the E-step and M-step processes are repeatedly iterated until the parameters converge; through the above corresponding relationship, the EM algorithm can transform the uncertainty of the latent variable into the update basis of the conditional probability parameters, gradually optimize the Bayesian network model, and finally approximate the true distribution of the data.

[0063] The advantages of the present invention are as follows:

[0064] (1) According to the combat characteristics of the reconnaissance and strike integrated UAV, it is divided into 5 combat stages, the safety risk factors in the use process of different stages are identified, and a safety evaluation index system for the use of the reconnaissance and strike integrated UAV in a strong confrontation environment is constructed;

[0065] (2) Based on the index system, the topological structure of the Bayesian network is determined. It is first proposed to use the entropy value method to improve the G1 method to obtain the prior probability of the root node, and it is first proposed to use the EM algorithm to obtain the conditional probability of the child node; only by calculating these two probabilities can the Bayesian network be used to evaluate the use safety of the UAV;

[0066] (3) Simulation verification shows that the improved Bayesian network significantly enhances the adaptability and accuracy of the model in an incomplete data environment and can be applied to a wider range of application scenarios. Brief Description of the Drawings

[0067] Figure 1 is the combat stage of the reconnaissance and strike integrated UAV;

[0068] Figure 2 is the combat execution process of the reconnaissance and strike integrated UAV;

[0069] Figure 3 is the safety evaluation index system for the use of the reconnaissance and strike integrated UAV;

[0070] Figure 4 is the flow chart of the safety evaluation;

[0071] Figure 5 It is a local Bayesian network for C3 nodes;

[0072] Figure 6 It is a simulation result graph, where Figure 6 (a) shows the use of the safety assessment result graph, Figure 6 (b) shows the result of reverse inference, Figure 6 (a) shows the result of influence strength analysis;

[0073] Figure 7 It is a comparison of evaluation results. Specific implementation manner

[0074] The present invention will be further described below in conjunction with examples and drawings.

[0075] The present invention evaluates the use safety of reconnaissance and strike integrated UAVs based on an improved Bayesian network. Specifically: Based on the combat characteristics of reconnaissance and strike integrated UAVs, it is divided into 5 combat stages, and a use safety evaluation index system for reconnaissance and strike integrated UAVs in a strong confrontation environment is constructed; Based on the index system, the topological structure of the Bayesian network is determined, and the entropy method is used to improve the G1 method to obtain the prior probability of the root nodes, and the EM algorithm is used to obtain the conditional probability of the child nodes. Specifically as follows.

[0076] Step 1. Construct a use safety evaluation index system for reconnaissance and strike integrated UAVs;

[0077] A scientific and systematic index system is the basis for the use safety evaluation of reconnaissance and strike integrated UAVs and plays a decisive role in the entire evaluation process. The present invention focuses on reconnaissance and strike integrated UAVs, integrates their combat mission characteristics and the structural characteristics of large and medium-sized UAVs, and constructs a use safety evaluation index system for reconnaissance and strike integrated UAVs in a strong confrontation environment according to the division of combat stages.

[0078] The combat stage refers to the division of the entire combat process into a series of relatively independent but interrelated stages according to different requirements and goals of the mission during the operation. These stages help to systematically manage and execute combat missions and improve combat efficiency and success rate. Further dividing the combat stages of reconnaissance and strike integrated UAVs, the following 5 stages can be obtained, as Figure 1 shown.

[0079] 1. Airport preparation.

[0080] During this stage, the reconnaissance and strike integrated UAV is mainly involved in comprehensively inspecting the UAV to ensure it is in good condition, and loading corresponding weapons and sensors (such as high-definition optoelectronic / infrared cameras, synthetic aperture radars, air-to-ground missiles, guided bombs, etc.) according to the mission requirements, and setting the flight route and combat plan.

[0081] 2. Takeoff and climb

[0082] The takeoff and climb phase is the first step for a reconnaissance and strike integrated UAV to enter the battlefield, and multiple aspects such as endurance time, speed, altitude, and environmental factors need to be comprehensively considered. By reasonably planning the flight route and endurance time, reasonably adjusting the flight speed and altitude, and comprehensively evaluating environmental factors and other measures, it can be ensured that the reconnaissance and strike integrated UAV can have the best performance and safety during the takeoff and climb phase.

[0083] 3. Entering the battlefield

[0084] The battlefield environment adaptation phase is a process in which a reconnaissance and strike integrated UAV dynamically senses and adapts to the battlefield environment during the mission execution. A reconnaissance and strike integrated UAV usually integrates advanced reconnaissance, strike, and defense systems and needs to execute tasks in a more complex combat environment. To ensure the safe execution of reconnaissance and strike tasks, a series of advanced technical means and measures need to be taken to improve its anti-interference, anti-deception, and anti-strike capabilities.

[0085] 4. Executing the mission

[0086] The mission command and control phase refers to the link of real-time command and control during the mission execution of a reconnaissance and strike integrated UAV to ensure the smooth progress of the mission. A reconnaissance and strike integrated UAV needs to obtain battlefield information in real time, including the positions and dynamics of enemy targets, etc., adjust the strike strategy according to the battlefield information to ensure accurate strikes, and transmit reconnaissance information to the ground command center in real time to provide support for decision-making.

[0087] 5. Returning to the airport

[0088] The return phase is the process for the UAV to safely return to the base after completing the mission. Since a reconnaissance and strike integrated UAV faces a more complex battlefield environment during mission execution, its return process needs to pay more attention to safety. The task processes corresponding to each phase are as Figure 2 shown.

[0089] In Figure 2 the combat execution process of the reconnaissance and strike integrated UAV shown, since the UAV enters the battlefield and executes the mission basically simultaneously, and the anti-countermeasure ability of the UAV in a strong confrontation environment is difficult to reflect in the execution flow chart, the battlefield environment adaptation phase and the mission execution phase are combined into one phase. However, in the safety assessment index system, these are two phases that need to be evaluated separately, and they evaluate the performance and safety of the UAV from different perspectives. Therefore, they are divided into two phases as independent assessment indicators.

[0090] Based on the analysis of the combat use process of the reconnaissance and strike integrated UAV, each combat phase is divided, the risk factors in its use process are identified, and based on the basic principles and methods of index system construction, combined with the insights of experts in related fields, 32 key indicators are finally selected to evaluate the use safety of the reconnaissance and strike integrated UAV. AsFigure 3 As shown, the index system is designed as a four - layer structure, and each index is numbered according to the principle of top - down and left - right order. These indexes are respectively the command and control ability, emergency handling ability, and health and fatigue degree of ground station operators; the safety of anti - interference devices, reconnaissance payloads, and weapon payloads; the safety of power systems, sensing systems, and flight platforms; the endurance time, cruising speed, and endurance altitude of the UAV; the adaptability of the UAV to harsh terrains, weather, and electromagnetic environments; the anti - data - link spoofing, anti - electromagnetic interference, anti - information - attack, anti - satellite - navigation spoofing, and anti - acoustic - interference abilities of the UAV; the data encryption, information transmission, and radar detection security abilities of the UAV; the networking communication, track tracking, and cooperative strike security among multiple UAVs; the target positioning, strike, and anti - interception abilities of the UAV; the fault detection and self - repair abilities of the UAV. The use safety of the reconnaissance - strike integrated UAV is evaluated based on these 32 indexes. The subsequent Bayesian network is also constructed according to these indexes.

[0091] The preparation stage covers three major elements. First is the professional ability and health status of ground control personnel; second is the safety of equipment configuration, specifically involving reconnaissance ability, weapon payload configuration, and the effectiveness of anti - interference equipment; finally is the ability to ensure basic flight safety, which includes the stability of the power system, the accuracy of the sensing system, the reliability of the flight platform, and the security performance of software and hardware systems.

[0092] The take - off stage includes two major dimensions. One is the flight performance of the reconnaissance - strike integrated UAV, covering its endurance time, flight speed, and altitude; the other is the environmental adaptability of the UAV, specifically referring to its performance in bad weather, complex terrains, and electromagnetic environments.

[0093] The battlefield environment adaptation stage includes three aspects. First is communication security, that is, the ability of the reconnaissance - strike integrated UAV to resist electromagnetic interference, spoofed information, and information attacks; second is navigation security, including the ability to resist navigation spoofing and acoustic interference; finally is information security, covering data encryption technology, the robustness of signal transmission, and radar detection effectiveness.

[0094] Regarding the mission execution stage, it mainly involves two major fields: multi - UAV cooperative operation and command and control of the reconnaissance - strike integrated UAV. For multi - UAV cooperation, the reliability of networking communication, the accuracy of track tracking, and the effectiveness of cooperative strikes need to be considered; for command and control, the accuracy of target positioning, strike effectiveness, and anti - interception ability need to be concerned.

[0095] Finally is the return stage. In this stage, the possible faults of the reconnaissance - strike integrated UAV during flight need to be monitored in real - time, and it should have a certain self - repair ability to ensure a safe return.

[0096] Step 2. Improve the Bayesian network evaluation model;

[0097] (1) Principle of Bayesian network. A Bayesian network (BN for short) is a statistical inference tool based on probabilistic graphical models, used to represent the conditional dependence relationships between variables. It formally depicts the causal relationships between variables in the form of directed acyclic graphs (DAGs), where nodes represent random variables and edges represent the dependence relationships between variables.

[0098] Bayes' theorem is a fundamental theorem in probability theory, which describes how to update the probability of an event after observing new evidence. Given the observed data D, let θ be the parameter to be estimated, then we have:

[0099]

[0100] In the formula, P(θ|D,ζ) is the posterior probability, P(θ|ζ) is the prior probability, P(D|θ,ζ) is the likelihood function, D represents the observed data, and ζ represents the context. Bayes' formula shows that when one conditional probability is difficult to obtain while the other is relatively easy to get, the reverse conditional probability can be calculated from one conditional probability.

[0101] Equation (1) can be transformed into:

[0102]

[0103] represents the conditional probability of event B occurring given that event A has occurred. It can be used to infer the probability of event A occurring given that event B has occurred.

[0104] A Bayesian network can be represented as:

[0105] G = <x, g, p> (3)

[0106] In the formula, G represents the Bayesian network, <> represents the set of Bayesian networks, x = {x1, x2,..., x n} are all the nodes; g represents the dependence relationships between the nodes, which is an n×n matrix; p is the conditional probability table, representing the conditional probability of each node x i , where i is an integer taking values from 1 to n (n is the number of nodes).

[0107] Through the chain rule, the joint probability can be known as:

[0108]

[0109] In the formula, P(X1, X2, γ, X n ) represents the joint probability, P(X1) represents the probability of event X1 occurring, P(X n |X1, c, X n-1)Denotes the probability of X occurring under the condition that the event occurs at X1, γ, X n-1 under the condition that the event occurs n of X occurring.

[0110] The Bayesian network consists of a set of variables X = {X1, X2,..., X n}, and each node corresponds to one variable in the set of variables. Since each node is independent of the nodes other than its parent node, conditional independence can be used to greatly reduce the computational amount, that is, the joint probability can be written as the product of local probabilities:

[0111]

[0112] where P ai is the parent node of node X i .

[0113] (2) Determine the prior probability based on the improved G1 method using entropy value. The order relation analysis method, also known as the G1 method, belongs to a kind of subjective weighting method. It is an ordinal evaluation method that determines the importance degree between two indicators through experts, so as to determine the weights of the indicators. The order relation is easy to understand, can be applied to various types of quantitative or qualitative data, can clearly show the relative order between objects, and is convenient for further analysis. However, the G1 method is often affected by the subjective biases of evaluators, while the entropy value method is an objective calculation based on the data itself. Combining the entropy value method with the order relation analysis method can reduce the influence of human factors on the analysis results and improve the objectivity of the results. The main operation steps are as follows:

[0114] The following 10 steps are the steps after improving the G1 method and used for the Bayesian network. The present invention first proposes to use the entropy value method to improve the G method, and then uses the membership degree weighting method to obtain the prior probability of the root node of the Bayesian network.

[0115] Step1: Let the evaluation object be A, corresponding to n evaluation indicators O = (O1, O2,..., O n ), and there are m experts M = (M1, M2, ···, M m ) participating in the evaluation, where M1, M2, ···, M m respectively represent m experts, and M represents the set of experts. If the evaluation importance degree of evaluation indicator O i is greater than that of O j , it is denoted as O i > O j , and > is the standard symbol, whose meaning is that the importance degree is greater than.

[0116] Step2: The expert selects the most important indicator from the set of indicators and denotes it as O1 * .

[0117] Step 3: The expert then selects the most important indicator from the remaining n - 1 indicators, denoted as

[0118] Step 4: Repeat the previous step (i.e., Step 3) until the last indicator. In this way, the order relationship of all indicators after re - sorting is obtained:

[0119]

[0120] Step 5: Calculate the proportion of the j - th indicator under the i - th expert (assuming there are 5 experts and 5 indicators. The j - th indicator under the i - th expert means: the proportion of the evaluation of the 3rd indicator by the 2nd expert. At this time, i = 2, j = 3):

[0121]

[0122] In the formula:

[0123] ω ij is the proportion of the j - th indicator under the i - th expert (the proportion represents the degree of importance of a certain indicator). The larger this value, the more important the indicator and the greater its importance to the evaluation. (i = 1, 2,..., m, j = 1, 2,..., n);

[0124] o ij is the evaluation of the j - th indicator by the i - th expert. (i = 1, 2,..., m, j = 1, 2,..., n);

[0125] is the sum of the evaluations of all experts on the j - th indicator.

[0126] Step 6: Calculate the entropy value e j of the j - th indicator:

[0127]

[0128] Step 7: Judge the ratio of the importance degrees of adjacent indicators:

[0129]

[0130] In the formula, r k is the ratio of the entropy values of adjacent indicators, also known as the tone operator. (k = n, n - 1,..., 2)

[0131] In the order relation method, the tone operator is an important concept, which is mainly used to express the degree of affirmation in language. At present, the 9 - level operator method is commonly used in China. It divides the evaluation or decision - making object into 9 levels, and each level corresponds to an operator or fuzzy set.

[0132] The traditional order relation method often relies on subjective judgment when determining the tone operator, resulting in subjectivity and inconsistency in the evaluation results. The introduction of the entropy value method determines the weights through the information of the data itself, avoiding the drawbacks of subjective weight assignment.

[0133] Step8: Calculate the index weights, and the weight v of the last index n is:

[0134]

[0135] Then according to:

[0136]

[0137] the weights of all indexes can be inversely deduced.

[0138] Step9: Assume that all levels of the index are divided into s, L=(L1, L2, ··· L s ), L1, L2, ··· L s respectively represent the levels of the index, L represents the set of index levels, and determine the membership degree of each index relative to the level:

[0139]

[0140] In the formula, μ ij is the membership degree of the j-th index belonging to the i-th level, N is the total number of evaluators, and k is the number of evaluators whose scoring results of the j-th index belong to the i-th level;

[0141] Step10: Calculate the prior probability that the root node belongs to each level:

[0142]

[0143] In the formula, P represents the prior probability of the root node, v j is the weight of the j-th index among n indexes, and μ ij is the membership degree of the j-th index belonging to the i-th level.

[0144] (3) The EM algorithm is a method for parameter estimation of models containing hidden variables. This algorithm is mainly used in the case of missing data and optimizes the model parameters through an iterative method. The EM algorithm provides a powerful tool for dealing with missing data and hidden variables. Especially in Bayesian networks, by effectively estimating conditional probabilities, it improves the prediction ability and application effect of the model. The EM algorithm includes two main steps:

[0145] Step1: Expectation Step (E-step): In a Bayesian network, the conditional probability of a child node is represented by the parameters in its Conditional Probability Table (CPT). Specifically, these parameters are part of the set of model parameters, usually denoted by the symbol θ. Under the current estimation of the Bayesian model parameters θ, calculate the posterior probability of the latent variable z (i) as the expectation of the latent variable, which serves as the current estimate of the latent variable:

[0146] Q i (z (i) ) = p(z (i) |x (i) ; θ) (14)

[0147] where z (i) represents the latent variable, x (i) represents the observed variable, θ is the model parameter, and Q i (z (i) ) represents the expected value of the latent variable z (i) , and p(z (i) |x (i) ; θ) represents the posterior distribution of the latent variable given the observed data and the current parameters.

[0148] Step2: Maximization Step (M-step): According to the expected value Q i (z (i) ) calculated in the E-step, update the parameter θ to maximize the log-likelihood function.

[0149]

[0150] The E-step mainly focuses on calculating the expected value Q i (z (i) ), while the M-step focuses on re-estimating the model parameter θ based on these expected values. These two steps are performed alternately until the algorithm converges to a local optimal solution θ.

[0151] 3. Case Analysis

[0152] This invention selects a reconnaissance-strike integrated UAV. Before performing a mission, the overall safety level of the UAV is first evaluated to infer the possibility of successful mission execution. In addition, there are many uncertain factors during the mission execution, and at this time, the strategy also needs to be adjusted. Referring to GJB900A "General Requirements for Equipment Safety Work", the severity levels of hazards are divided into four levels, namely catastrophic, severe, minor, and slight. Therefore, the safety of the reconnaissance-strike integrated UAV is correspondingly divided into four levels. The use safety level A indicates a very high safety level with only slight risks; the use safety level B indicates an average safety level, but small accidents may still occur; the use safety level C indicates a relatively low safety level, and relatively serious accidents may occur; the use safety level D indicates an extremely low safety level, and serious losses and irreversible injuries will occur once problems arise.

[0153] Taking the basic guarantee factor C3 of the reconnaissance-strike integrated UAV in the index system as an example, as a root node of the Bayesian network, C3 has four parent nodes at this time, namely the power system safety D7, the sensing system safety D8, the flight platform safety D9, and its own software and hardware failures D10. Five experts in the field of UAV safety were invited for this evaluation, and the scoring range for each index is [0, 100]. After discussion, it is stipulated that the scoring range [90, 100] is good, denoted as Good; the scoring range [80, 90) is average, denoted as Medium; and the score below 80 is poor, denoted as Bad. The expert scoring results are shown in Table 1.

[0154] Table 1 Expert Scoring Table for Key Guarantee Factors

[0155]

[0156] The calculation results are as Figure 5 shown. The probabilities that the C3 index belongs to Good, Medium, and Bad are 28.6%, 51.4%, and 20% respectively. Using the BNT toolbox in MATLAB, the parameters of the Bayesian network can be obtained using the EM algorithm. Table 2 is the conditional probability table of B1 in the preparation stage, and it has three parent nodes, namely the human factor safety C1, the equipment deployment safety C2, and the basic guarantee safety C3. Taking this as an example, the conditional probability distributions of all child nodes in the Bayesian network can be obtained.

[0157] Table 2 Conditional Probability Table in the Preparation Stage

[0158]

[0159]

[0160] (1) Simulation results.

[0161] Common Bayesian network simulation software includes GeNIe, Netica, Hugin, BayesiaLab, etc. Compared with other software, the advantages of GeNIe lie in its ease of use, powerful functions, flexibility, open source nature, and cross-platform support. Therefore, GeNIe is selected for simulation calculation. The obtained parameters are passed into the Bayesian network, and the simulation results are as shown in Figure 6 (a). It can be seen from the figure that the probabilities of the UAV using safety levels A, B, C, and D are 35%, 43%, 13%, and 9% respectively (the actual results are 35.1%, 43.3%, 13.1%, and 8.5%, and the figure is accurate to the units digit of the percentage). The overall use safety level is B, that is, the use safety is average. The probabilities of being excellent in the preparation stage (B1), takeoff stage (B2), battlefield environment adaptation stage (B3), mission command and control stage (B4), and return stage (B5) are 51%, 44%, 45%, 50%, and 52% respectively, and the probabilities of being average are 33%, 33%, 35%, 31%, and 36% respectively. The differences between the Good and Medium values in the B1, B2, B3, B4, and B5 nodes are calculated and represented by a, b, c, d, and e. a = 18%, b = 11%, c = 10%, d = 19%, e = 16%. The larger the difference, the better the performance. The values of b and c are relatively small, indicating that the safety of the UAV in the takeoff stage and the battlefield environment adaptation stage needs to be improved.

[0162] (2) Simulation analysis.

[0163] By setting the LevelA probability of A to 100%, the model can be updated, and the obtained results are as shown in Figure 6 (b). It can be seen from the figure that the Good values of all nodes have increased. For several nodes of A, the value of B1 being Good has increased from 51% to 56%, an increase of 5 percentage points; the value of B2 being Good has increased from 44% to 47%, an increase of 3 percentage points; the value of B3 being Good has increased from 45% to 52%, an increase of 7 percentage points; the value of B4 being Good has increased from 50% to 54%, an increase of 4 percentage points. This phenomenon further illustrates that the battlefield environment adaptation stage has a relatively large impact on the use safety of the reconnaissance and strike integrated UAV. The safety ability of the battlefield environment adaptation stage is mainly affected by C6 (communication security), C7 (navigation security), and C8 (information security), indicating that to improve the safety ability of the UAV, it is necessary to ensure the security ability of the UAV's communication link.

[0164] The influence intensity represents the degree of dependence between nodes. The thicker the connection line between two nodes, the greater the influence intensity. The analysis results of the influence intensity are as shown in Figure 6(as shown in (c)). It can be seen from the figure that the node paths with the greatest influence intensity in the above risk network are: ① C3 → B1; ② C5 → B2; ③ C10 → B4; ④ C11 → B5. In the preparation stage, the basic guarantee function of the reconnaissance-strike integrated UAV will have a greater impact on it; environmental factors account for a larger proportion in the takeoff stage; when the UAV is performing tasks, if the target positioning failure rate is high, it will lead to an increase in the usage time, thereby increasing the probability of safety risks. Finally, in the return stage, the reconnaissance-strike integrated UAV needs to monitor possible faults in real time and have a certain repair ability to ensure a safe return.

[0165] In the preparation stage, the basic guarantee function of the reconnaissance-strike integrated UAV should be checked, and the corresponding weapons and sensors should be loaded. It can be seen from the simulation results that the safety of the basic guarantee function is relatively low, and all key equipment and systems need to be thoroughly checked before performing tasks; in the takeoff stage, it can be seen that the flight performance of the reconnaissance-strike integrated UAV is poor, but its environmental adaptability is good. This requires more refined mission planning to ensure that the reconnaissance-strike integrated UAV can complete tasks efficiently and safely; after the reconnaissance-strike integrated UAV enters the battlefield environment, interference such as suppression and deception by the enemy will pose a threat to its use safety, and this stage has a greater impact on the use safety of the reconnaissance-strike integrated UAV. It can be seen from the simulation results that the influence degrees of the communication safety, navigation safety, and information safety of the UAV are similar, but the safety of the navigation system is relatively low, and more advanced navigation technologies and equipment need to be adopted to improve the positioning accuracy and anti-interference ability of the UAV; the command and control stage and the return stage of the reconnaissance-strike integrated UAV have relatively little impact on its overall use safety, and the use safety in both stages is relatively high. Therefore, the UAV is relatively stable and safe in the command and control stage and the return stage.

[0166] In summary, the safety of the basic guarantee function of the reconnaissance-strike integrated UAV is relatively low, its flight performance is limited, and the anti-interference ability of its navigation system is weak. Before performing tasks, all key equipment needs to be thoroughly checked, more advanced navigation technologies and equipment need to be adopted, and more refined mission planning is required during the execution of tasks to ensure the use safety of the reconnaissance-strike integrated UAV.

[0167] (3) Comparison of evaluation results.

[0168] The traditional Bayesian network directly determines the network parameter values through expert scoring and statistics. The improved Bayesian network calculates the parameters through the entropy method to optimize the G1 method and the EM algorithm. The comparison between the two is as Figure 7 shown. It can be seen that although the evaluation results obtained by the two methods are the same, compared with the traditional one, the improved Bayesian network improves the efficiency and flexibility through automated calculation and optimization algorithms, making the grade difference more obvious. It can be applied to reconnaissance-strike integrated UAVs with similar use safety, reducing the ambiguity of the evaluation results and being applicable to a wider range of application scenarios.

[0169] According to the combat characteristics of reconnaissance and strike integrated UAVs, they are divided into 5 combat stages, the safety risk factors in the use process of different stages are identified, and a safety assessment index system for the use of reconnaissance and strike integrated UAVs in a strong confrontation environment is constructed. Based on the index system, the topological structure of the Bayesian network is determined, the entropy value method is used to improve the G1 method to obtain the prior probability of the root nodes, and the EM algorithm is used to obtain the conditional probability of the child nodes. Finally, the data is imported into GeNie software for simulation to obtain the probability distribution of different use safety levels of reconnaissance and strike integrated UAVs, and reverse reasoning and influence strength analysis are carried out on the model to clarify the key factors leading to safety accidents of reconnaissance and strike integrated UAVs. The simulation results show that: the improved Bayesian network, with its unique advantages in dealing with complexity and multi-variable conditional probability distributions, significantly enhances the adaptability and accuracy of the model in an incomplete data environment and can be applied to a wider range of application scenarios.

Claims

1. A method for evaluating the safety of using an integrated reconnaissance and strike UAV based on an improved Bayesian network, characterized in that: The specific steps include: Step 1. Construct a safety assessment indicator system for the use of reconnaissance and strike drones; The combat phase of the reconnaissance and strike UAV is specifically divided into five stages:

1. Airport preparation; 2. Take-off and climb; 3. Enter the battlefield; 4. Carry out tasks; 5. Return to the airport; Based on the basic principles and methods of indicator system construction and combined with the insights of experts in related fields, the indicator system is designed as a four-layer structure; 32 key indicators are selected, namely: the command and control capability, emergency handling capability and health fatigue level of ground station operators; the safety of anti-interference devices, reconnaissance payloads and weapon payloads; the safety of power systems, sensor systems and flight platforms; the endurance time, cruising speed and endurance altitude of drones; the adaptability of drones to harsh terrain, weather and electromagnetic environments; the ability of drones to resist data link deception, electromagnetic interference, information attacks, satellite navigation deception and sound wave interference; the data encryption, information transmission and radar detection security capabilities of drones; the security of networking communication, track tracking and coordinated strikes between multiple drones; the target positioning, strike and anti-interception capabilities of drones; the fault detection and self-repair capabilities of drones; Step 2. Improve the Bayesian network evaluation model; (1) Bayesian network; If the observed data D is known, let φ be the parameter to be estimated: Where P(φ|D,ζ) is the posterior probability, P(φ|ζ) is the prior probability, P(D|φ,ζ) is the likelihood function, P(D|ζ) is the total probability of the observed data D under all possible parameters, D represents the observed data, and ζ represents the context content; Formula (1) is transformed into: In the formula, if the context content ζ is ignored, the parameter to be estimated φ is recorded as A, and the observed data D is recorded as B, which means the conditional probability of event B occurring under the condition that event A is known to occur; The Bayesian network is represented as: G=<x,g,p> (3) In the formula, G represents the Bayesian network, <> represents the Bayesian network set, x = {x1, x2, ..., x n } is a node set, n is the number of nodes; g represents the dependency relationship between nodes, which is an n×n matrix; p is a conditional probability table, indicating that each node x i The conditional probability of , i is an integer ranging from 1 to n; By chain method, we know that the joint probability is: In the formula, P(X1,X2,…,X n ) represents the joint probability, P(X1) represents the probability of event X1 occurring, P(X n |X1,γ,X n-1 ) means that in X1,…,X n-1 Under the condition that the event occurs X n Probability of occurrence; The Bayesian network consists of a set of variables X = {X1, X2, ..., X n }, each node corresponds to a variable in a set of variables; the joint probability is written as the product of local probabilities: In the formula, P(X) represents the joint probability, P(X i |P ai ) is the parent node P ai Next child node X i The conditional probability, P ai is node X i The parent node of (2) Determine the prior probability based on the G1 method of order relationship analysis improved by entropy value; The details are as follows: Step 1: Let the evaluation object be A, corresponding to n evaluation indicators O = (O1, O2, ..., O n ), there are m experts M=(M1,M2,···,M m ) participated in the evaluation, among which M1,M2,···,M m Represent m experts respectively, M represents the set of experts; if the evaluation index O i The evaluation importance is greater than O j , then record it as O i >O j , > is the standard symbol, meaning the degree of importance is greater than; Step 2: Experts select the most important indicator from the indicator set, denoted as Step 3: The expert then selects the most important indicator from the remaining n-1 indicators, denoted as Step 4: Repeat the previous step until the last indicator; get the order relationship after all indicators are reordered: Step 5: Calculate the weight of the jth indicator under the i-th expert: Where: ω ij is the weight of the i-th expert on the j-th indicator. The larger the value, the more important the indicator is and the greater its importance to the evaluation. i = 1, 2, ..., m, j = 1, 2, ..., n; o ij is the evaluation of the jth indicator by the i-th expert; is the sum of all experts’ evaluations on the jth indicator; Step 6: Calculate the entropy value e of the jth indicator j : Step 7: Determine the importance ratio of adjacent indicators: In the formula, r k is the ratio of the entropy values ​​of adjacent indicators, k = n, n-1, ..., 2; Step 8: Calculate the indicator weight, the weight of the last indicator v n for: Based on: Reverse the process to get the weights of all indicators; Step 9: Assume that all levels of the indicators are divided into s, L = (L1, L2, ···L s ), L1, L2, · · · L s They represent the levels of the indicators respectively, L represents the set of indicator levels, and the degree of membership of each indicator relative to the level is determined: In the formula, μ ij is the degree of membership of the jth indicator to level i, N is the total number of evaluators, and k is the number of evaluators whose scoring results of the jth indicator belong to level i; Step 10: Calculate the prior probability that the root node belongs to each level: In the formula, P represents the prior probability of the root node, v j is the weight of the jth indicator among n indicators, μ ij is the degree of membership of the jth indicator to level i; (3) Determine conditional probability based on the EM algorithm; E-step - expectation step: Under the current Bayesian model parameter θ estimation, calculate the latent variable z (i) The posterior probability, that is, the expectation of the latent variable, is the current estimated value of the latent variable: Q i (z (i) )=p(z (i) |x (i) ;θ) (14) Among them, x (i) represents the observed variable in the i-th sample, corresponding to the observed node in the Bayesian network; z (i) represents the hidden variable in the i-th sample, corresponding to the unobserved node in the Bayesian network; p(z (i) |x (i) ; θ) represents the hidden variable z under known observation data and current parameters (i) The posterior distribution of M-step - maximization step: the expected value Q calculated according to the E-step i (z (i) ), update the parameters θ to maximize the log-likelihood function: In the formula, p(x (i) ,z (i) ; θ) represents the maximum likelihood estimation function under the current parameters, i is each sample; in the M step, the posterior probability calculated in the E step is used to re-estimate the model parameter θ so that the maximum likelihood estimation function is maximized; In the M step, the hidden variable z needs to be considered (i) All possible values, and according to their posterior probability Q under the current parameters i (z (i) ) to calculate the expected value; this means that for each sample i, not only the actual observed data x (i) , but also need to consider the impact of all possible values ​​of the hidden variables; The M step decomposes the objective function into the sum of the logarithms of the conditional probabilities of each node, independently updates the parameters of each node, and iterates the E step and M step processes repeatedly until the parameters converge. Through the above correspondence, the EM algorithm can transform the uncertainty of hidden variables into the basis for updating the conditional probability parameters, gradually optimize the Bayesian network model, and ultimately approach the true distribution of the data.

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