Interception rendezvous condition analysis method and system based on binary decision tree

Abstract

The application provides an intercept rendezvous condition analysis method and system based on a binary decision tree, comprising: establishing a rendezvous condition mathematical model; setting intervals of a rendezvous angle, an initial relative distance and a target speed ratio of a spacecraft in the rendezvous condition mathematical model according to random distribution characteristics of measurement noise, target inclination and radial maneuver noise of a spacecraft detection device, and generating training data through a relative motion model; training a binary decision tree model by using the labeled training data, evaluating the obtained binary decision tree model according to a receiver operating characteristic (ROC) curve, and obtaining a trained binary decision tree model when the evaluation meets preset requirements; and extracting rendezvous condition rules from the binary decision tree according to constraint conditions and bifurcation endpoint data of each layer node of the trained binary decision tree model, and obtaining set-form rendezvous condition rules with interpretability through set intersection and union operations of intervals of each element in the rendezvous condition.

Description

Technical Field

[0001] This invention relates to the fields of aircraft guidance and control technology and statistical machine learning technology. Specifically, it relates to an interception and rendezvous condition analysis method and system based on binary decision trees, which is mainly used to provide a method for analyzing nonlinear models of aircraft and establishing the relationship between initial rendezvous conditions and guidance accuracy. Background Technology

[0002] Intercepting high-speed, highly maneuverable targets has always been a difficult problem in the field of aircraft guidance. Under different rendezvous conditions, the target's maneuvering mode, maneuvering magnitude, and the seeker's ability to adapt to detection noise are different. Therefore, in order to ensure guidance accuracy requirements, the analysis of rendezvous conditions is necessary.

[0003] The relative motion model of the missile and target during the interception process is a complex model with nonlinear random inputs. Methods for directly analyzing such models are scarce and often fail to yield satisfactory results. Currently, the main methods for analyzing nonlinear systems include the Monte Carlo method, the analysis of covariance describing function method (CADET), and the adjoint system analysis method. The analysis of covariance can statistically analyze the error characteristics caused by random factors in the system and is suitable for analyzing complex nonlinear systems. Compared with the Monte Carlo method, its computational cost is lower. However, when analyzing nonlinear systems, the linearization process reduces the accuracy of the analysis results. It still cannot obtain the relationship between the desired rendezvous conditions and the interception miss distance. The adjoint method is mainly applied to the influence of various random factors and disturbances on the accuracy of the guidance system; its advantage lies in the accuracy analysis of the guidance system. Monte Carlo statistical analysis typically seeks certain statistical regularities through extensive simulations. Theoretically, it can obtain statistical analysis results of intersection conditions. However, the results are usually given as indicators such as mathematical expectation or standard deviation. The analysis results cannot directly reveal the relationship between the expected intersection conditions and the miss quantity, and are not easy to apply to design problems.

[0004] Machine learning methods are a commonly used tool for problems seeking relationships between model inputs and outputs. For example, neural networks and decision trees can both fit or approximate the desired model to some extent. Decision trees are another commonly used method, showing good learning performance for regression and classification problems of nonlinear models, and the results are intuitive, directly reflecting the relationship between inputs and outputs, facilitating further analysis. Therefore, this invention applies decision tree theory to provide an effective and feasible method for analyzing intersection conditions. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for analyzing interception and intersection conditions based on a binary decision tree.

[0006] The interception and intersection condition analysis method based on binary decision tree provided by the present invention includes:

[0007] Step S1: Establish a mathematical model of handover conditions based on the relative motion relationship between the aircraft and the target;

[0008] Step S2: Based on the random distribution characteristics of the noise measured by the aircraft detection device, the target tendency and radial maneuver noise, set the intervals of the rendezvous angle, initial relative distance and the ratio of aircraft to target speed in the handover condition mathematical model, and generate and store training data through the relative motion model of the aircraft and target in the inertial line of sight frame.

[0009] Step S3: Label the training data and use the labeled training data to train the binary decision tree model, establish the relationship between the initial handover conditions and the terminal guidance miss distance, evaluate the obtained binary decision tree model according to the receiver operating characteristic (ROC) curve, and obtain the trained binary decision tree model when the evaluation meets the preset requirements; otherwise, continue training.

[0010] Step S4: Based on the trained binary decision tree model, extract the handover condition rules according to the constraints of each node and the data of the branch endpoints. By performing the intersection and union operation of the intervals of each element in the handover condition, the handover condition rules in the form of an interpretable set are obtained.

[0011] Preferably, step S1 involves: constructing a mathematical model of handover conditions based on the terminal guidance interception process of a high-speed aircraft against a target, consisting of the rendezvous angle, the initial relative distance, and the speed ratio between the aircraft and the target;

[0012] The mathematical model for the handover conditions adopts:

[0013] φ=[ψ0 r0 k v ] T

[0014] Where ψ0 represents the initial rendezvous angle, r0 represents the initial relative distance between the aircraft and the target, and k v This indicates the ratio of the aircraft's speed to the target speed.

[0015] Preferably, step S3 adopts the following method: using a preset value as the quantitative standard for the precise guidance miss amount, selecting the miss amount at the moment of interception terminal as the classification label, data with a miss amount higher than the preset value as negative samples, and data with a miss amount less than or equal to the preset value as positive samples, and labeling the training data.

[0016] The miss distance of the intercepting terminal at any given time is calculated as follows:

[0017]

[0018] Where r represents the relative distance, t f Indicates the terminal time. Indicates the line-of-sight angular rate. "Approach speed" indicates the speed of approach, and "zem" indicates the distance of miss.

[0019] Preferably, the relationship between the initial handover conditions and the terminal guidance miss distance is as follows:

[0020] zem(t f )~f(φ,X,u)

[0021] Where f(φ,u) represents the state-space model; X represents the state variables of the state-space model; and u represents the input vector of the state-space model, including: the target's measured maneuvering acceleration a Tn axial acceleration a Tt and the measurement noise of the seeker. φ represents the initial handover conditions.

[0022] Preferably, step S3 involves evaluating the obtained binary decision tree model based on the receiver operating characteristic (ROC) curve, including global classification accuracy, area under the curve (AUC), and binary decision tree sensitivity.

[0023] Preferably, step S4 involves: based on the trained binary decision tree model, extracting corresponding handover condition rules according to the leaf nodes, branch relationships, intersection angle, initial relative distance, and aircraft-target speed ratio; and obtaining several rules that meet the precision guidance requirements through intersection and union operations of sets consisting of intersection angle intervals, speed ratio intervals, and relative distance intervals.

[0024] ψ∈[ψ a ,ψ b ]∧k v ∈[k va ,k vb ]∧r∈[r a ,r b ].

[0025] An interception and intersection condition analysis system based on a binary decision tree, provided by the present invention, includes:

[0026] Module M1: Establishing a mathematical model of handover conditions based on the relative motion relationship between the aircraft and the target;

[0027] Module M2: Based on the random distribution characteristics of noise measured by the aircraft detection device, target tendency and radial maneuver noise, the range of rendezvous angle, initial relative distance and aircraft-target velocity ratio in the handover condition mathematical model is set, and training data is generated and stored through the relative motion model of the aircraft and target in the inertial line of sight frame;

[0028] Module M3: Labels the training data and uses the labeled training data to train the binary decision tree model, establishes the relationship between the initial handover conditions and the terminal guidance miss distance, evaluates the obtained binary decision tree model based on the receiver operating characteristic (ROC) curve, and obtains the trained binary decision tree model when the evaluation meets the preset requirements; otherwise, training continues.

[0029] Module M4: Based on the trained binary decision tree model, the module extracts handover condition rules from the binary decision tree according to the constraints of each node and the data of the branch endpoints. Through the intersection and union operation of the intervals of each element in the handover condition, the module obtains the handover condition rules in the form of an interpretable set.

[0030] Preferably, module M1 employs the following approach: based on the terminal guidance interception process of a high-speed aircraft against a target, a mathematical model of handover conditions is constructed, consisting of the rendezvous angle, the initial relative distance, and the speed ratio between the aircraft and the target.

[0031] The mathematical model for the handover conditions adopts:

[0032] φ=[ψ0 r0 k v ] T

[0033] Where ψ0 represents the initial rendezvous angle, r0 represents the initial relative distance between the aircraft and the target, and k v This indicates the ratio of the aircraft's speed to the target speed.

[0034] Preferably, module M3 adopts the following method: using a preset value as the quantitative standard for the precise guidance miss amount, selecting the miss amount at the moment of interception terminal as the classification label, data with a miss amount higher than the preset value as negative samples, and data with a miss amount less than or equal to the preset value as positive samples, and labeling the training data.

[0035] The miss distance of the intercepting terminal at any given time is calculated as follows:

[0036]

[0037] Where r represents the relative distance, t f Indicates the terminal time. Indicates the line-of-sight angular rate. The approach velocity is represented by zem, and the miss distance is represented by zem.

[0038] The relationship between the initial handover conditions and the terminal guidance miss distance is as follows:

[0039] zem(t f )~f(φ,X,u)

[0040] Where f(φ,u) represents the state-space model; X represents the state variables of the state-space model; and u represents the input vector of the state-space model, including: the target's measured maneuvering acceleration a Tn axial acceleration a Tt and the measurement noise of the seeker. φ represents the initial handover conditions;

[0041] The obtained binary decision tree model was evaluated based on the receiver operating characteristic (ROC) curve, including: global classification accuracy, area under the curve (AUC), and binary decision tree sensitivity.

[0042] Preferably, module M4 employs the following method: based on the trained binary decision tree model, it extracts corresponding handover condition rules according to the leaf nodes, branch relationships, intersection angle, initial relative distance, and aircraft-target speed ratio. Through intersection and union operations of sets consisting of intersection angle intervals, speed ratio intervals, and relative distance intervals, it obtains several rules that meet the requirements of precision guidance.

[0043] ψ∈[ψ a ,ψ b ]∧k v ∈[k va ,k vb ]∧r∈[r a ,r b ].

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. Transform the handover condition analysis problem into a classification problem, and extract the rules of intersection conditions from the trained tree model to obtain the desired analysis results;

[0046] 2. Combining decision tree theory from machine learning with aircraft guidance theory provides an effective approach to analyzing nonlinear models;

[0047] 3. Fully utilize the "black box effect" between machine learning input and output to simplify the need for nonlinear models in the design process. The training results obtained can directly yield mathematical set rules for design.

[0048] 4. The algorithm has strong scalability. The design of the shift change condition model can be set manually, and the target's maneuvering form can be set arbitrarily. Thus, it can cover flight conditions in multiple airspaces and speed ranges, and can widely analyze the relative motion between various aircraft and targets. Attached Figure Description

[0049] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0050] Figure 1 This is a flowchart of the interception and intersection condition analysis method based on binary decision trees.

[0051] Figure 2 This is a schematic diagram of a binary decision tree model.

[0052] Figure 3 This is a schematic diagram of the ROC curve corresponding to the binary decision tree model. Detailed Implementation

[0053] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0054] The problem to be solved by this invention is the analysis of handover conditions during the interception process of a high-speed aircraft. The technical solution adopted by this invention to solve the technical problem is: to provide an interception handover condition analysis method based on a binary decision tree, to establish a nonlinear model of the aircraft and a decision tree model to establish the relationship between the initial rendezvous conditions and the guidance accuracy, and to analyze and extract a set of rules that can be applied to the design of handover conditions.

[0055] Example 1

[0056] An interception and intersection condition analysis method based on a binary decision tree, provided by the present invention, includes:

[0057] Step S1: Establish a mathematical model of handover conditions based on the relative motion relationship between the aircraft and the target;

[0058] Step S2: Based on the random distribution characteristics of the noise measured by the aircraft detection device, the target tendency and radial maneuver noise, set the intervals of the rendezvous angle, initial relative distance and the ratio of aircraft to target speed in the handover condition mathematical model, and generate and store training data through the relative motion model of the aircraft and target in the inertial line of sight frame.

[0059] Step S3: Label the training data and use the labeled training data to train the binary decision tree model, establish the relationship between the initial handover conditions and the terminal guidance miss distance, evaluate the obtained binary decision tree model according to the receiver operating characteristic (ROC) curve, and obtain the trained binary decision tree model when the evaluation meets the preset requirements; otherwise, continue training.

[0060] Step S4: Based on the trained binary decision tree model, extract the handover condition rules according to the constraints of each node and the data of the branch endpoints. By performing the intersection and union operation of the intervals of each element in the handover condition, the handover condition rules in the form of an interpretable set are obtained.

[0061] Specifically, step S1 involves: constructing a handover condition mathematical model based on the terminal guidance interception process of a high-speed aircraft against a target, consisting of the rendezvous angle, the initial relative distance, and the speed ratio between the aircraft and the target.

[0062] The mathematical model for the handover conditions adopts:

[0063] φ=[ψ0 r0 k v ] T

[0064] Where ψ0 represents the initial rendezvous angle, r0 represents the initial relative distance between the aircraft and the target, and k v This indicates the ratio of the aircraft's speed to the target speed.

[0065] Specifically, step S3 adopts the following approach: using a preset value as the quantitative standard for the precise guidance miss amount, selecting the miss amount at the moment of interception terminal as the classification label, data with a miss amount higher than the preset value as negative samples, and data with a miss amount less than or equal to the preset value as positive samples, and labeling the training data.

[0066] The miss distance of the intercepting terminal at any given time is calculated as follows:

[0067]

[0068] Where r represents the relative distance, t f Indicates the terminal time. Indicates the line-of-sight angular rate. "Approach speed" indicates the speed of approach, and "zem" indicates the distance of miss.

[0069] Specifically, the relationship between the initial handover conditions and the terminal guidance miss distance is as follows:

[0070] zem(t f )~f(φ,X,u)

[0071] Where f(φ,u) represents the state-space model; X represents the state variables of the state-space model; and u represents the input vector of the state-space model, including: the target's measured maneuvering acceleration a Tn axial acceleration a Tt and the measurement noise of the seeker. φ represents the initial handover conditions.

[0072] Specifically, step S3 involves evaluating the obtained binary decision tree model based on the receiver operating characteristic (ROC) curve, including global classification accuracy, area under the curve (AUC), and binary decision tree sensitivity.

[0073] Specifically, step S4 employs the following approach: Based on the trained binary decision tree model, according to the leaf nodes, branch relationships, intersection angle, initial relative distance, and aircraft-target speed ratio, corresponding handover condition rules are extracted. Through intersection and union operations of sets consisting of intersection angle intervals, speed ratio intervals, and relative distance intervals, several rules that meet the requirements of precision guidance are obtained.

[0074] ψ∈[ψ a ,ψ b ]∧k v ∈[k va ,k vb ]∧r∈[r a ,r b ].

[0075] An interception and intersection condition analysis system based on a binary decision tree, provided by the present invention, includes:

[0076] Module M1: Establishing a mathematical model of handover conditions based on the relative motion relationship between the aircraft and the target;

[0077] Module M2: Based on the random distribution characteristics of noise measured by the aircraft detection device, target tendency and radial maneuver noise, the range of rendezvous angle, initial relative distance and aircraft-target velocity ratio in the handover condition mathematical model is set, and training data is generated and stored through the relative motion model of the aircraft and target in the inertial line of sight frame;

[0078] Module M3: Labels the training data and uses the labeled training data to train the binary decision tree model, establishes the relationship between the initial handover conditions and the terminal guidance miss distance, evaluates the obtained binary decision tree model based on the receiver operating characteristic (ROC) curve, and obtains the trained binary decision tree model when the evaluation meets the preset requirements; otherwise, training continues.

[0079] Module M4: Based on the trained binary decision tree model, the module extracts handover condition rules from the binary decision tree according to the constraints of each node and the data of the branch endpoints. Through the intersection and union operation of the intervals of each element in the handover condition, the module obtains the handover condition rules in the form of an interpretable set.

[0080] Specifically, module M1 adopts the following approach: based on the terminal guidance interception process of a high-speed aircraft against a target, a mathematical model of handover conditions is constructed, consisting of the rendezvous angle, the initial relative distance, and the speed ratio of the aircraft to the target.

[0081] The mathematical model for the handover conditions adopts:

[0082] φ=[ψ0 r0 k v ] T

[0083] Where ψ0 represents the initial rendezvous angle, r0 represents the initial relative distance between the aircraft and the target, and k v This indicates the ratio of the aircraft's speed to the target speed.

[0084] Specifically, module M3 adopts the following approach: using a preset value as the quantitative standard for the precise guidance miss amount, selecting the miss amount at the moment of interception terminal as the classification label, data with a miss amount higher than the preset value as negative samples, and data with a miss amount less than or equal to the preset value as positive samples, and labeling the training data.

[0085] The miss distance of the intercepting terminal at any given time is calculated as follows:

[0086]

[0087] Where r represents the relative distance, t f Indicates the terminal time. Indicates the line-of-sight angular rate. The approach velocity is represented by zem, and the miss distance is represented by zem.

[0088] The relationship between the initial handover conditions and the terminal guidance miss distance is as follows:

[0089] zem(t f )~f(φ,X,u)

[0090] Where f(φ,u) represents the state-space model; X represents the state variables of the state-space model; and u represents the input vector of the state-space model, including: the target's measured maneuvering acceleration a Tn axial acceleration a Tt and the measurement noise of the seeker. φ represents the initial handover conditions;

[0091] The obtained binary decision tree model was evaluated based on the receiver operating characteristic (ROC) curve, including: global classification accuracy, area under the curve (AUC), and binary decision tree sensitivity.

[0092] Specifically, module M4 employs the following approach: Based on the trained binary decision tree model, it extracts corresponding handover condition rules according to the leaf nodes, branch relationships, intersection angle, initial relative distance, and aircraft-target speed ratio. Through intersection and union operations of sets consisting of intersection angle intervals, speed ratio intervals, and relative distance intervals, it obtains several rules that meet the requirements of precision guidance.

[0093] ψ∈[ψ a ,ψ b ]∧k v ∈[k va ,k vb ]∧r∈[r a ,r b ].

[0094] Example 2

[0095] Example 2 is a preferred example of Example 1.

[0096] The interception and intersection condition analysis method based on a binary decision tree provided by the present invention, such as... Figure 1 As shown, it includes:

[0097] Step 1: Examine the terminal guidance interception process of a high-speed aircraft against a target, construct a handover condition mathematical model consisting of the rendezvous angle, initial relative distance, and the speed ratio between the aircraft and the target, and use it as input to the relative motion model between the aircraft and the target in the inertial line-of-sight frame;

[0098] φ=[ψ0 r0 k v ] T

[0099] Step 2: Given the random distribution characteristics of the noise measured by the aircraft detection device and the target lateral and radial maneuvering noise, set the intervals of the rendezvous angle, initial relative distance and aircraft-target velocity ratio in the handover condition mathematical model, generate training data through relative motion simulation and store it;

[0100] Step 3: Using 0.3m as the quantitative standard for the miss distance of precision guidance, the miss distance at the interception terminal is selected as the classification label. Data with a miss distance greater than 0.3m are negative samples, and data with a miss distance less than or equal to 0.3m are positive samples. The training data is then labeled.

[0101] Step 4: Train the binary decision tree model based on the labeled training data, and set the number of leaf nodes and branches of the binary decision tree to complete the pruning.

[0102] Step 5: Evaluate the classifier model of the obtained binary decision tree based on the receiver operating characteristic (ROC) curve, and assess the global classification accuracy, area under the curve (AUC), and sensitivity of the binary decision tree.

[0103] Step 6: Extract the handover condition rules from the binary decision tree based on the constraints of each node and the data of the branch endpoints. By performing the intersection and union operations on the intervals of each element in the handover condition, the handover condition rules in the form of an interpretable set are obtained.

[0104] like Figure 3 As shown, starting from the child nodes at all the endpoints of the tree, we want to extract the handover rules that meet the accuracy requirements. We can see that the first "yes" is located on the leftmost side. Starting from this child node, we search upwards. The condition for fy is less than 0.270526. Continuing upwards, we reach the parent node of the tree, where the condition is fy less than 0.39. These two conditions regarding fy represent two sets or two ranges of numbers. In other words, both conditions must be satisfied simultaneously to satisfy "yes," which is equivalent to finding the intersection of the intervals. That is, starting from the terminal child node that satisfies either "yes" or "no," we traverse upwards along the branches of the tree until we reach the top parent node, finding the intersection of the intervals of each mathematical variable along the way. This yields the rule reflecting the change pattern of a particular branch.

[0105] Specifically, based on the interception process, a handover condition vector is introduced, consisting of the initial rendezvous angle ψ0, the initial relative distance r0 between the aircraft and the target, and the velocity ratio k. v Composition; a state-space model of the relative motion between the interceptor and the target during the terminal guidance phase, taking the relative distance r and the approach velocity as... line-of-sight angle q, line-of-sight angular rate Rendezvous angle ψ, aircraft overload a Mn Let X be the state variable of the model, and select the target's measured maneuvering acceleration a. Tn axial acceleration a Tt and the measurement noise of the seeker. As the input vector u of the model, the target maneuver model can adopt CA maneuver or Singer maneuver model, the random distribution of noise can be regarded as normal distribution, and the guidance law of the aircraft can adopt generalized proportional guidance. Based on the relative motion equation and the vector composition theorem, the complete state-space model f(φ,u) can be obtained, which is the object of the terminal guidance motion under study. Generally, the relative motion model reflects the relationship between the miss distance and the state and input. This method introduces the handover condition vector to seek the relationship between the miss distance and the state, input, and handover conditions, that is,

[0106] zem(t f )~f(φ,X,u) (1)

[0107] Among them, the miss distance at the terminal guidance moment can be expressed as equation (2):

[0108]

[0109] Specifically, initial values ​​for the model and rendezvous conditions are set, and simulations are performed based on the relative motion model to generate training data for analysis. By using the CART model in a decision tree for training, the relationship between initial rendezvous conditions and terminal guidance miss distance is established, providing an interpretable model different from neural network classifiers. Leaf nodes in the decision tree represent category labels, i.e., whether they meet the requirements for precision guidance. Each branch represents the combined effect of various input features, and the weight of each input feature needs to be defined, such as prioritizing the rendezvous angle, followed by the velocity ratio, etc. All input features collectively guide the nodes to the terminal leaf nodes. The CART tree, based on certain classification rules and partitioning attributes, partitions the input features, i.e., the observed values. The partitioning process terminates at a leaf node according to the set constraints. Considering the performance envelope of the aircraft, the method provides a range of parameter values ​​for each input feature, randomly selects initial rendezvous conditions within this range for simulation, and obtains and stores the relevant data.

[0110] Specifically, by training the selected decision tree model based on training data samples, an accurate model of the decision tree and a receiver operating characteristic (ROC) curve to evaluate the model's classification results can be obtained. The closer the points of the decision tree trained by this method are to the upper left corner of the curve, the better. Figure 2 The point shown is (0.14, 0.94); the higher its global classification accuracy, the better the classifier performance; the area under the ROC curve can measure the sensitivity of the trained decision tree model and its predictive ability on the data.

[0111] Specifically, the trained binary decision tree classification model can extract the corresponding handover condition rules based on the leaf nodes, branch relationships, and input features of the tree. Since the classification process of the binary decision tree is equivalent to dividing the data according to complex relationships and input features, it ultimately leads to each leaf node. Therefore, each leaf node obtained is a rule. By performing intersection and union operations on the sets composed of intersection angle intervals, velocity ratio intervals, and relative distance intervals, several rules that meet the requirements of precision guidance can be obtained. The form of these rules is the set of interval intersections that satisfy equation (3):

[0112] ψ∈[ψ a ,ψ b ]∧k v ∈[k va ,k vb ]∧r∈[r a ,r b (3)

[0113] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0114] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for analyzing interception and intersection conditions based on a binary decision tree, characterized in that, include: Step S1: Establish a mathematical model of handover conditions based on the relative motion relationship between the aircraft and the target; Step S2: Based on the random distribution characteristics of the noise measured by the aircraft detection device, the target tendency and radial maneuver noise, set the intervals of the rendezvous angle, initial relative distance and the ratio of aircraft to target speed in the handover condition mathematical model, and generate and store training data through the relative motion model of the aircraft and target in the inertial line of sight frame. Step S3: Label the training data and use the labeled training data to train the binary decision tree model, establish the relationship between the initial handover conditions and the terminal guidance miss distance, evaluate the obtained binary decision tree model according to the receiver operating characteristic (ROC) curve, and obtain the trained binary decision tree model when the evaluation meets the preset requirements; otherwise, continue training. Step S4: Based on the trained binary decision tree model, extract the handover condition rules according to the constraints of each node and the data of the branch endpoints. By performing the intersection and union operation of the intervals of each element in the handover condition, the handover condition rules in the form of an interpretable set are obtained.

2. The interception and intersection condition analysis method based on binary decision tree according to claim 1, characterized in that, Step S1 adopts the following approach: based on the terminal guidance interception process of a high-speed aircraft against a target, a mathematical model of handover conditions is constructed, consisting of the rendezvous angle, the initial relative distance, and the speed ratio of the aircraft to the target. The mathematical model for the handover conditions adopts: in, Indicates the initial intersection angle. This indicates the initial relative distance between the aircraft and the target. This indicates the ratio of the aircraft's speed to the target speed.

3. The interception and intersection condition analysis method based on binary decision tree according to claim 1, characterized in that, Step S3 adopts the following approach: using a preset value as the quantitative standard for the precise guidance miss amount, selecting the miss amount at the moment of interception terminal as the classification label, data with a miss amount higher than the preset value as negative samples, and data with a miss amount less than or equal to the preset value as positive samples, and labeling the training data. The miss distance of the intercepting terminal at any given time is calculated as follows: in, Indicates relative distance. Indicates the terminal time. Indicates the line-of-sight angular rate. Indicates the approximate speed. This indicates the amount of data that missed the target.

4. The interception and intersection condition analysis method based on binary decision tree according to claim 1, characterized in that, The relationship between the initial handover conditions and the terminal guidance miss distance is as follows: in, Representing a state-space model; Represents the state variables of a state-space model; The input vector representing the state-space model includes: the target's measured maneuver acceleration. Axial acceleration and the measurement noise of the seeker. ; This indicates the initial handover conditions.

5. The interception and intersection condition analysis method based on binary decision tree according to claim 1, characterized in that, Step S3 involves evaluating the obtained binary decision tree model based on the receiver operating characteristic (ROC) curve, including global classification accuracy, area under the curve (AUC), and binary decision tree sensitivity.

6. A system for analyzing interception and intersection conditions based on a binary decision tree, characterized in that, include: Module M1: Establishing a mathematical model of handover conditions based on the relative motion relationship between the aircraft and the target; Module M2: Based on the random distribution characteristics of noise measured by the aircraft detection device, target tendency and radial maneuver noise, the range of rendezvous angle, initial relative distance and aircraft-target velocity ratio in the handover condition mathematical model is set, and training data is generated and stored through the relative motion model of the aircraft and target in the inertial line of sight frame; Module M3: Labels the training data and uses the labeled training data to train the binary decision tree model, establishes the relationship between the initial handover conditions and the terminal guidance miss distance, evaluates the obtained binary decision tree model based on the receiver operating characteristic (ROC) curve, and obtains the trained binary decision tree model when the evaluation meets the preset requirements; otherwise, training continues. Module M4: Based on the trained binary decision tree model, the module extracts handover condition rules from the binary decision tree according to the constraints of each node and the data of the branch endpoints. Through the intersection and union operation of the intervals of each element in the handover condition, the module obtains the handover condition rules in the form of an interpretable set.

7. The interception and intersection condition analysis system based on a binary decision tree according to claim 6, characterized in that, The module M1 adopts the following approach: based on the terminal guidance interception process of a high-speed aircraft against a target, a mathematical model of handover conditions is constructed, consisting of the rendezvous angle, the initial relative distance, and the speed ratio of the aircraft to the target. The mathematical model for the handover conditions adopts: in, Indicates the initial intersection angle. This indicates the initial relative distance between the aircraft and the target. This indicates the ratio of the aircraft's speed to the target speed.

8. The interception and intersection condition analysis system based on a binary decision tree according to claim 6, characterized in that, The module M3 adopts the following approach: using a preset value as the quantitative standard for the precise guidance miss amount, selecting the miss amount at the moment of interception terminal as the classification label, data with a miss amount higher than the preset value as negative samples, and data with a miss amount less than or equal to the preset value as positive samples, and labeling the training data. The miss distance of the intercepting terminal at any given time is calculated as follows: in, Indicates relative distance. Indicates the terminal time. Indicates the line-of-sight angular rate. Indicates the approximate speed. Indicates the amount of data that missed the target; The relationship between the initial handover conditions and the terminal guidance miss distance is as follows: in, Representing a state-space model; Represents the state variables of a state-space model; The input vector representing the state-space model includes: the target's measured maneuver acceleration. Axial acceleration and the measurement noise of the seeker. ; Indicates the initial handover conditions; The obtained binary decision tree model was evaluated based on the receiver operating characteristic (ROC) curve, including: global classification accuracy, area under the curve (AUC), and binary decision tree sensitivity.

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