Method and system for predicting 4D reachable area of hypersonic aircraft

Abstract

The invention discloses a 4D reachable area prediction method and system of a hypersonic aircraft, and belongs to the field of aircraft trajectory planning. According to the method, firstly, initial flight conditions, any control effect and complex flight constraints are considered, an expression of a four-dimensional reachable area is constructed, and key features of the four-dimensional reachable area are described based on an approximate fitting scheme of a three-dimensional irregular central curved surface and a two-dimensional curve boundary. For reconstruction of a four-dimensional dynamic flight envelope, an online intelligent prediction model based on a BP neural network is provided. In order to verify the effectiveness of the proposed model, a correct detection probability, a false alarm probability and a missed alarm probability are defined for a flight drop point set. The algorithm is expected to be migrated and applied to reachable area prediction of hypersonic cruise aircrafts and air-breathing hypersonic aircrafts and calculation of attack areas and escape areas of the aircrafts.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft trajectory planning, and in particular relates to a method and system for predicting a 4D reachable area of ​​a hypersonic aircraft. Background Art

[0002] The reachable area of ​​a hypersonic glide reentry vehicle (HGV) refers to the boundary curve of the reachable range of the vehicle on the earth's surface under certain constraints. As a reflection of the longitudinal and lateral maneuverability and strike area of ​​the vehicle, the calculation of the reachable area is of great significance and is usually used for the trajectory design and performance analysis of the vehicle. Due to the extremely harsh flight environment of the reentry phase and the influence of possible interference, if the vehicle cannot reach the reentry point according to the predetermined orbit, the pre-designed trajectory will no longer be feasible and the trajectory must be regenerated. Therefore, the calculation of the reachable area of ​​the reentry vehicle requires strong real-time and accuracy.

[0003] At present, the calculation of the reachable area of ​​the aircraft reentry mainly stays at the two-dimensional level, which is divided into the calculation of the characteristic points of the reachable area such as the maximum longitudinal and transverse range and the acquisition of the boundary of the reachable area. For the calculation of the maximum longitudinal and transverse range of the aircraft, some scholars have obtained the change law of the roll angle through analytical methods, pseudo-spectral methods, sequential convex optimization methods, optimization principles, drag acceleration profile constraints, etc. For the acquisition of the boundary of the reachable area, the traversal method and elliptic approximation method are currently mainly included. With the development of neural networks, there are more and more studies on the real-time calculation and online prediction of the reachable area. In order to solve the problems of real-time online calculation and solution accuracy of the dynamic attackable area after the air-to-air missile is fired during combat, Ge Luqin et al. proposed a BP neural network fitting method for the dynamic attackable area after the missile is fired based on the improved genetic algorithm.

[0004] It is worth noting that most of the existing literature focuses on the research of low-speed flying objects, without considering the flight characteristics of the aircraft across airspace and speed domains, and most of them remain at the two-dimensional level. There is little research on the real-time and accurate fitting method of the dynamic three-dimensional reachable area of ​​the aircraft. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a 4D reachable area prediction method and system for a hypersonic aircraft to solve the problem in the prior art of lacking a real-time and accurate fitting method for the dynamic three-dimensional reachable area of ​​the aircraft.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for predicting a 4D reachable area of ​​a hypersonic aircraft comprises the following steps:

[0008] S1, constructing a four-dimensional reachable area expression of the aircraft in a generalized equatorial coordinate system, wherein the four-dimensional reachable area is related to the initial flight state and flight time of the aircraft; the four-dimensional reachable area is a time-varying three-dimensional reachable area, and the three-dimensional reachable area is a closed space area composed of six boundaries, wherein the six boundaries include a nearest boundary, a farthest boundary, a left boundary, a right boundary, a bottom boundary and an upper boundary, and each boundary is a curved surface;

[0009] S2, constructing a generalized equatorial coordinate system, obtaining the longitude and latitude of the aircraft in the generalized equatorial coordinate system, and obtaining the reentry flight longitudinal range and reentry flight transverse range of the aircraft based on the longitude and latitude;

[0010] S3, in the generalized equatorial coordinate system, the four-dimensional reachable area is expressed by a three-dimensional irregular central surface in combination with the reentry flight longitudinal range and the reentry flight lateral range of the spacecraft, and the four-dimensional reachable area is approximated by a two-dimensional curve equation to obtain the expression of the four-dimensional reachable area of ​​the spacecraft in the generalized equatorial coordinate system;

[0011] S4, solving the expression of the four-dimensional reachable area through a BP neural network; the input of the BP neural network is the initial parameters of the aircraft, and the output is the key parameters of the four-dimensional reachable area of ​​the aircraft.

[0012] A further improvement of the present invention is:

[0013] Preferably, in S1, the four-dimensional reachable area expression is:

[0014]

[0015] Where: Ad is the initial launch azimuth; V0 is the speed of the aircraft at time t0; θ0 is the ballistic inclination angle of the aircraft at time t0; H0 is the flight altitude of the aircraft at time t0; H f is the altitude at the end of the flight; α(t) is the angle of attack control instruction for the entire flight process; υ(t) is the roll angle control instruction for the entire flight process; Λ1, Λ2, and Λ3 are the maximum heat flux constraint, maximum dynamic pressure constraint, and maximum overload constraint, respectively.

[0016] Preferably, in S1, among the six boundaries, the arc surfaces of the farthest boundary, the left boundary, the right boundary, the bottom boundary and the upper boundary are each composed of four arcs, and two adjacent arc surfaces share a curve; the nearest boundary is composed of two arc surfaces.

[0017] Preferably, in S2, in the generalized equatorial coordinate system, it is assumed that the earth is a homogeneously rotating sphere, and the new geocentric coordinate system O E is the center of the earth, X M The Y axis is the direction of the earth's center vector along the flight starting point; M The axis is perpendicular to the X axis in the reentry arc plane.M The axis points in the direction of the target; Z M Axis and X M Axis, Y M The axes form a right-hand system, pointing to the new pole M.

[0018] Preferably, in S2, the longitude and latitude of the aircraft are:

[0019]

[0020] The calculation expressions of the reentry flight longitudinal distance L and the reentry flight lateral distance W are:

[0021]

[0022] Among them, λ M ,φ M are the longitude and latitude of the aircraft, R e is the average radius of the Earth.

[0023] Preferably, in S3, the expression of the three-dimensional irregular central surface is:

[0024]

[0025] Where:

[0026]

[0027] In formula (11), ι and For the definition in R 5 The coefficient matrix in the space; ξ and ζ are defined in R 4 The coefficient matrix in space; v is defined in R 3 The coefficient matrix in space.

[0028] Preferably, the expression for approximating the four-dimensional reachable area using a two-dimensional curve equation is:

[0029]

[0030] Where:

[0031]

[0032] Where, L is the longitudinal distance of the reentry flight, W is the lateral distance of the reentry flight, and Both are defined in R 3 The coefficient matrix in space is shown in formula (16):

[0033]

[0034] In the formula: g1, g2, g3, a1, a2, a3, q1, q2, q3, b1, b2, b3 are all unknown coefficients.

[0035] Preferably, in S3, the target point (L o ,W o ,H o ) is within the range of the aircraft's strike capability, and both equations (17) and (18) are satisfied:

[0036]

[0037] Where: H δ_max and H δ_min is a constant, which can be obtained from experience; W min and W max Satisfying formula (18):

[0038]

[0039] Among them, W min is the minimum value of the flight range of the aircraft’s accessible area, W max It is the maximum value of the flight range of the aircraft reachable area.

[0040] Preferably, in S4, the initial parameters of the aircraft are the launch azimuth Ad, the initial speed V0, the initial altitude H0, the initial ballistic inclination θ0 and the flight time t; the key parameters of the four-dimensional reachable area of ​​the aircraft are 21 output signals ι1, ι2, ι3, ι4, ι5, ξ1,ξ2,ξ3,ξ4,ζ1,ζ2,ζ3,ζ4 and

[0041] A 4D reachable area prediction system for a hypersonic aircraft, comprising:

[0042] An expression building module is used to build a four-dimensional reachable area expression of the aircraft, wherein the four-dimensional reachable area is related to the initial flight state and flight time of the aircraft; the four-dimensional reachable area is a three-dimensional reachable area that changes with time, and the three-dimensional reachable area is a closed space area composed of six boundaries, wherein the six boundaries include a nearest boundary, a farthest boundary, a left boundary, a right boundary, a bottom boundary and an upper boundary, and each boundary is a curved surface;

[0043] The generalized equatorial coordinate module is used to construct a generalized equatorial coordinate system, obtain the longitude and latitude of the aircraft in the generalized equatorial coordinate system, and obtain the reentry flight longitudinal range and reentry flight transverse range of the aircraft based on the longitude and latitude;

[0044] A new expression module is used to express the four-dimensional reachable area through a three-dimensional irregular central surface in the generalized equatorial coordinate system, combining the reentry flight longitudinal range and reentry flight lateral range of the aircraft, and approximate the four-dimensional reachable area with a two-dimensional curve equation to obtain the expression of the four-dimensional reachable area of ​​the aircraft in the generalized equatorial coordinate system;

[0045] A solution module is used to solve the expression of the four-dimensional reachable area through a BP neural network; the input of the BP neural network is the initial parameters of the aircraft, and the output is the key parameters of the four-dimensional reachable area of ​​the aircraft

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The present invention relates to a method for intelligently predicting the 4D reachable area of ​​a hypersonic glide vehicle, and belongs to the field of aircraft trajectory planning. This invention first considers the initial flight conditions, arbitrary control effects and complex flight constraints, and proposes the definition of the four-dimensional reachable area of ​​"time-longitudinal range-lateral range-height (t-LWH)" of a hypersonic reentry glide vehicle, and adopts an approximate fitting scheme based on "three-dimensional irregular central surface + two-dimensional curve boundary" to describe its key features. Furthermore, for the reconstruction of the four-dimensional dynamic flight envelope, an online intelligent prediction model based on BP neural network is proposed. In order to verify the effectiveness of the proposed model, the correct detection probability, false alarm probability and missed alarm probability are defined for the flight landing point set. The algorithm is expected to be migrated and applied to the prediction of the reachable area of ​​hypersonic cruise aircraft and air-breathing hypersonic aircraft and the calculation of the attack area and escape area of ​​the aircraft.

[0048] Most of the existing predictions of accessible areas are based on fitting elliptical models based on the maximum longitudinal and transverse ranges of aircraft in a two-dimensional plane. This paper proposes the concept of t-λφh four-dimensional accessible area for the first time, and transforms the four-dimensional accessible area into a closed surface fitting problem that changes with time. The zero isosurface of the implicit function represented by the radial basis function is used to fit the surface of the accessible area. Finally, the parameters that can represent the key features of the 4D accessible area are extracted, and the adaptive fuzzy neural network training data set is used to obtain the 4D accessible area intelligent prediction model, which can be applied online. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic diagram of the three-dimensional reachable area;

[0050] Figure 2 It is a schematic diagram of the four-dimensional reachable area;

[0051] Figure 3 is a schematic diagram of the coordinate system;

[0052] Figure 4 It is a schematic diagram of key features of the accessible area;

[0053] Figure 5This is a conceptual diagram of the probability of correct detection, the probability of false alarm, and the probability of missed alarm;

[0054] Figure 6 A BP neural network model for intelligently predicting the four-dimensional reachable area of ​​an aircraft;

[0055] Figure 7 BPNN structure for predicting some parameters of surface equations;

[0056] Figure 8 Compare the predicted reachable area of ​​the aircraft with the actual reachable area;

[0057] Among them, (a) is aircraft No. 1; (b) is aircraft No. 2; (c) is aircraft No. 3; (d) is aircraft No. 4.

[0058] Fig. 9 This is a graph of the correct detection probability and missed alarm probability of the neural network prediction model. DETAILED DESCRIPTION

[0059] In the following, the terms "first", "second", "third", and "fourth" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, a feature defined as "first", "second", "third", and "fourth" may explicitly or implicitly include one or more of the features.

[0060] The co-shooting method provided in the embodiment of the present application can be applied to terminal devices such as mobile phones, tablet computers, wearable devices, vehicle-mounted devices, augmented reality (AR) / virtual reality (VR) devices, laptop computers, ultra-mobile personal computers (UMPC), netbooks, personal digital assistants (PDA), etc. The embodiment of the present application does not impose any restrictions on the specific type of the terminal device.

[0061] It should be noted that the terms "first", "second", etc. in the specification and drawings of the present invention are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0062] A first aspect of the present invention discloses a method for predicting a 4D reachable area of ​​a hypersonic aircraft, the method specifically comprising the following steps:

[0063] Step 1: determine the set of three-dimensional reachable areas of the aircraft at any flight time based on the initial flight time and initial flight state of the aircraft.

[0064] See also Figure 2 In order to construct the four-dimensional reachable area of ​​the hypersonic gliding vehicle in the generalized equatorial coordinate system, it refers to the process of the vehicle flying along its predetermined flight trajectory after re-entering the atmosphere at time t0, based on the initial launch azimuth, current t p (t p ≥t0) time flight speed, t p The inclination angle of the trajectory at time t p The flight altitude at any moment is the range of the four-dimensional space of time, vertical range, horizontal range and height that can hit the target under various constraints and arbitrary control, that is:

[0065]

[0066] Where: t i (t i ≥t p ) is the three-dimensional reachable area of ​​longitudinal range, lateral range and altitude that the aircraft can hit the target at the moment, and its calculation form is shown in formula (2); Ξ is the four-dimensional reachable area of ​​the aircraft, which is the set of three-dimensional reachable areas of the aircraft at any flight time.

[0067]

[0068] Where: {L max (t i )} and {L min (t i)} are respectively the maximum longitudinal range and minimum longitudinal range sets at different height positions at time ti after the aircraft is launched. Among them, the maximum longitudinal range set of the aircraft is also called the farthest reachable boundary, and the minimum longitudinal range set is also called the nearest reachable boundary; {W max (t i )} and {W min (t i )} are respectively the maximum left and right ranges at different heights at time ti after the launch of the aircraft. Among them, the value corresponding to the left range is a positive number, and the value corresponding to the right range is a negative number; {H max (t i )} and {H min (t i )} are respectively the tth i The highest and lowest reachable boundary set at the moment is the reachable area. The aircraft boundary set is related to the initial flight state (Ad, V0, θ0, H0) and the flight time ti, and its calculation formula is as follows:

[0069]

[0070] Where: Ad is the initial launch azimuth; V0 is the speed of the aircraft at time t0; θ0 is the ballistic inclination angle of the aircraft at time t0; H0 is the flight altitude of the aircraft at time t0; H f is the altitude at the end of the flight; α(t) is the angle of attack control instruction for the entire flight process; υ(t) is the roll angle control instruction for the entire flight process; Λ1, Λ2, and Λ3 are the maximum heat flux constraint, maximum dynamic pressure constraint, and maximum overload constraint, respectively.

[0071] Based on the experience of the dataset, the shape of the three-dimensional reachable area is drawn in the longitudinal-lateral-height (LWH) spatial coordinate system as follows: Figure 1 As shown, the shape of the four-dimensional reachable area is drawn in the time-longitudinal-horizontal-height (t-LWH) space coordinate system as shown in Figure 2 shown.

[0072] Figure 1 middle, and It is the nearest boundary of the reachable area. It changes with the initial state of the aircraft and the time it has flown. The nearest boundary can be in the shape of a ginkgo leaf or a sheep horn. and is the farthest boundary of the reachable area; and is the left boundary of the reachable area; and is the right boundary of the reachable area; is the lowest boundary of the reachable area; is the highest boundary of the reachable area.

[0073] Combination Figure 1 In , the three-dimensional reachable area is a closed space composed of six curved surfaces, where the farthest boundary, left boundary, right boundary, bottom boundary and top boundary are all curved surfaces. Among them, the farthest boundary, left boundary, right boundary, bottom boundary and top boundary are all composed of four arcs, and two adjacent arcs share a curve.

[0074] Among them, the nearest boundary is in the shape of a ginkgo leaf or a sheep horn, and the two sides of the boundary are an arc. The upper side is composed of two arcs connected in sequence, and the two arcs have the same bulging direction, both bulging toward the back and upper side; the lower side is composed of two arcs connected in sequence.

[0075] Step 2, obtain the reentry longitudinal range and reentry lateral range of the spacecraft in the generalized equatorial coordinate system.

[0076] Most of the existing aircraft position information is described in the geodetic coordinate system using latitude, longitude and height (λ, φ, H). If the earth is considered to be a homogeneously rotating sphere, the coordinates of the aircraft in the geocentric coordinate system can be described as:

[0077]

[0078] Where: R e is the average radius of the Earth.

[0079] Taking into account the influence of the earth's rotation, when the initial re-entry plane of the aircraft does not coincide with the equatorial plane, the reachable zone established in the longitude and latitude geodetic coordinate system is irregular. However, in the longitudinal x-lateral y plane, it can be basically considered that the two-dimensional reachable zone is symmetrical about the x-axis. Transferring this theory, it can be seen that the three-dimensional reachable zone in the longitudinal-lateral-altitude spatial coordinate system is also symmetrical. In order to facilitate the description of the longitudinal re-entry and transverse re-entry of the aircraft, the present invention adopts the scheme of Xie Y, Liu L, Liu J, et al. Rapid generation of entry trajectories with waypoint and no-fly zone constraints [J]. Acta Astronautica to construct a new M coordinate system, such as Figure 3 Assume that the earth is a homogeneous rotating sphere with an average radius of R e In the figure, O E is the center of the earth, N is the North Pole, O E X E , O E Y E , O E Z EThe X-axis, Y-axis and Z-axis of the Earth-centered Earth-fixed coordinate system are defined respectively. A reentry great circle plane is determined according to the reentry starting point and azimuth as the new "equatorial" plane, and a new generalized equatorial coordinate system O is defined. E -X M Y M Z M :X M The Y axis is along the direction of the earth's center vector at the flight starting point; M The axis is perpendicular to the X axis in the reentry arc plane. M Axis points in the target direction; Z M Axis and X M Axis, Y M The axes form a right-hand system, pointing to the new pole M. In the M coordinate system, the longitude and latitude of the starting point I of the aircraft are zero, and the longitude of the landing point F is λ. M and latitude φ M The reentry longitudinal angle and reentry lateral angle of the spacecraft are described respectively. In this new M coordinate system, no matter what the initial flight conditions are, the reachable area is symmetrical about the x-axis, which is convenient for predicting the reachable area and avoiding the influence of the earth's rotation.

[0080] Assume that the latitude and longitude coordinates of the starting point I of the aircraft glide in the geodetic coordinate system are (λ0, φ0, H0), and the initial launch azimuth is A0. Then the transformation matrix between the Earth-centered Earth-fixed coordinate system E and the M coordinate system is The expression is as follows:

[0081]

[0082] Where:

[0083]

[0084] Assume that the position information of the aircraft in the Earth-centered Earth-fixed coordinate system E is (λ E ,φ E ,H E ), then the position information of the aircraft in the M coordinate system (λ M ,φ M ,H M ) can be calculated according to formula (6):

[0085]

[0086] Where: H M =H E .

[0087] Substituting formula (5) into formula (6), we can obtain:

[0088]

[0089] Therefore, in the given M coordinate system, the new latitude and longitude information of the aircraft (λ M ,φ M ) is calculated as follows:

[0090]

[0091] Then the calculation form of the reentry flight longitudinal distance L and the reentry flight lateral distance W is as follows:

[0092]

[0093] Step 3, based on the longitudinal flight range L and the reentry flight lateral range W, mathematically model the four-dimensional reachable area of ​​the aircraft in the new M coordinate system.

[0094] Let P = {(L i ,W i ,H i )}, i=1,…,n is R 3 Point model in space, Γ is defined on R 3 The physical meaning of the surface in space is the surface of the three-dimensional reachable area of ​​the aircraft at a certain moment. Based on the point model P, the implicit function f(L, W, H) shown in equation (10) is generated so that its zero level set approaches the target surface Γ.

[0095] f(L i ,W i ,H i )=0,i=1,…,n (10)

[0096] When the target point (L o ,W o ,H o ) is within the strike capability of the aircraft, the condition f(L o ,W o ,H o )<0.

[0097] When the number of points in the point model is not large, Gaussian elimination can be used to solve the coefficients of the radial basis function representing the implicit surface. However, sometimes, in order to obtain a more accurate reachable area boundary, a large number of experiments may be performed to generate a large number of boundary points. At this time, the set of equations for solving the coefficients continues to expand, and the amount of calculation increases to exceed the solution capability of Gaussian elimination. Moreover, the coefficients obtained by fitting using Gaussian elimination are too many, which is not conducive to generating an online intelligent prediction model for the reachable area. Therefore, an approximate fitting scheme based on "three-dimensional irregular central surface + two-dimensional curve boundary" is proposed. The key features of the reachable area are as follows: Figure 4 As shown:

[0098] The new four-dimensional reachable area center surface is The form of the S fitting equation of the enclosed surface is shown in formula (11):

[0099]

[0100] Where:

[0101]

[0102] In formula (11): ι and For the definition in R 5 The coefficient matrix in the space; ξ and ζ are defined in R 4 The coefficient matrix in space; v is defined in R 3 The coefficient matrix in space. Its form is shown in formula (13):

[0103]

[0104] In the formula: ι1, ι2, ι3, ι4, ι5, ι6, ξ1,ξ2,ξ3,ξ4,ζ1,ζ2,ζ3, All are unknown coefficients.

[0105] The two-dimensional curve equation is used to approximate the near and far boundaries of the four-dimensional reachable area, that is, Figure 4 middle The resulting boundary is as follows:

[0106]

[0107] Where:

[0108]

[0109] In formula (14): and Both are defined in R 3 The coefficient matrix in space is shown in formula (16):

[0110]

[0111] In the formula: g1, g2, g3, a1, a2, a3, q1, q2, q3, b1, b2, b3 are all unknown coefficients.

[0112] When the target point (L o ,W o ,H o ) is within the strike capability of the aircraft and satisfies both of the following conditions:

[0113]

[0114] Where: H δ_max and H δ_min is a constant, which can be obtained from experience; W min and W max Satisfying formula (18):

[0115]

[0116] To verify the effectiveness of the proposed prediction model, the radar target detection method is defined as follows: Figure 5 The concepts of correct detection probability, false alarm probability and missed alarm probability are shown in the figure. The correct detection probability is defined as the probability of correctly detecting whether the landing point is covered when the proposed prediction model is used to calculate the reachable area; due to the existence of fitting errors, the missed alarm probability is defined as the probability of judging that there is no feasible landing point in the actual reachable area but there is no feasible landing point; the false alarm probability is defined as the probability of judging that there is a landing point in the actual reachable area but there is no feasible landing point.

[0117] Step 4: Prediction of reachable area based on BP neural network

[0118] From the above analysis, we can see that the key parameters of the aircraft's four-dimensional reachable area are related to the aircraft's initial state and flight time. The mapping relationship is established as follows:

[0119]

[0120]

[0121] It can be seen from equations (19) and (20) that the relationship between the initial conditions of the aircraft and the key parameters of the accessible area is complex and highly nonlinear, and cannot be expressed by explicit functions, which makes it difficult to quickly predict the accessible area of ​​the aircraft. Neural networks have the ability to approximate the complex relationship between replacement parameters and can quickly approximate equations (19) and (20); the improved chaotic particle swarm optimization algorithm can use the hyperparameters in the neural network as independent variables in the optimization algorithm and the neural network fitting effect as the objective function in the optimization algorithm. It can be trained offline to obtain an intelligent prediction model of the four-dimensional accessible area and realize online application.

[0122] Taking the mapping relationship shown in the approximation formula (19) as an example, the neural network model is established as follows Figure 6 As shown:

[0123] Figure 6 The neural network in the above example includes an input layer (M), a hidden layer (L1), a hidden layer (L2), and an output layer (N). X = [x1, x2, ..., x5] is five input signals, representing the launch azimuth Ad, initial velocity V0, initial altitude H0, initial trajectory inclination θ0, and flight time t of the aircraft; Y = [y1, y2, ..., y 21] are 21 output signals, representing the key parameters of the four-dimensional reachable area of ​​the aircraft, namely the key parameters shown in formula (19) and the key coefficients in formula (13); is the weight matrix from the input layer to the hidden layer L1, is the weight matrix from hidden layer L1 to hidden layer L2, is the weight matrix from hidden layer L2 to output layer N; the nonlinear function obtained by combining sigmoid function and tanh function is used as the activation function of BP neural network, so the output of neural network can be expressed as

[0124] Y=h ω,b (X) = h(ωX T +b) (21)

[0125] Where: ω is the weight matrix; b is the bias term.

[0126] The network training process is trained with reference to the content disclosed in publication number CN114936531A, which will not be repeated here. In order to objectively evaluate the accuracy and effectiveness of the neural network prediction results, the root mean square error, mean absolute error and mean absolute percentage error are used to evaluate and analyze the neural network model. The specific calculation formula is as follows:

[0127]

[0128]

[0129] Where: is the root mean square error; is the mean absolute error; is the mean absolute percentage error; y i is the true coefficient; is the coefficient of the model output; N is the number of samples in the test set.

[0130] Simulation Example

[0131] The following is an analysis and explanation of the effectiveness verification of the four-dimensional reachable area prediction model in conjunction with a specific simulation example.

[0132] The effectiveness of the improved four-dimensional reachable area prediction model of supersonic gliding aircraft is simulated and verified. The X-33 aircraft is used to verify the feasibility, considering the initial flight state and flight constraints as shown in Table 1 and Table 2, the publication number is CN115903878A, and traversing different initial states and control instructions to generate a data set containing sufficient trajectory landing points offline.

[0133] Table 1 Initial flight status

[0134]

[0135] Table 2 Flight constraints

[0136]

[0137] In order to verify the accuracy and real-time performance of the BP neural network prediction model parameters, training samples are first generated. The input samples used for BP network training are formed by different flight condition combinations. The value range of each flight condition is shown in Table 3. 100,000 samples are generated by random value combinations.

[0138] Table 3 Flight condition value table in BP neural network training samples

[0139]

[0140] Taking the prediction of the surface equation parameter ζ1 as an example, simulation is performed based on the aircraft mathematical model to obtain the parameter ζ1 of the four-dimensional reachable area under the corresponding conditions as the network output sample. These input and output data are used to train the BP network.

[0141] To verify the effectiveness of BP neural network in predicting the four-dimensional reachable area, four groups of aircraft were selected from the 10,000 data sets of the validation set as simulation examples. Their initial flight states and flight times are shown in Table 4. The fitting results of the dynamic attackable area of ​​the aircraft after launch are compared with the actual results. Figure 8 shown.

[0142] Table 4 Initial flight status and flight time of the validation set aircraft

[0143]

[0144] According to the flight conditions of the four aircrafts shown in Table 4, 11011 landing points are generated according to the control instruction calculation method shown in the publication number CN115903878A. Let h s =2.5, and the correct detection probability and missed alarm probability of the neural network prediction model are calculated according to formula (17). The simulation results are shown in Fig. 9 As shown:

[0145] From the analysis of simulation results, the probability of correct warning of the reachable area is greater than 95%, which proves that the trained neural network can accurately and intelligently predict the four-dimensional reachable area.

[0146] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A 4D reachable area prediction method for a hypersonic vehicle, characterized in that: The following steps are involved: S1, constructing a four-dimensional reachable area expression of the aircraft in a generalized equatorial coordinate system, wherein the four-dimensional reachable area is related to the initial flight state and flight time of the aircraft; the four-dimensional reachable area is a time-varying three-dimensional reachable area, and the three-dimensional reachable area is a closed space area composed of six boundaries, wherein the six boundaries include a nearest boundary, a farthest boundary, a left boundary, a right boundary, a bottom boundary and an upper boundary, and each boundary is a curved surface; S2, constructing a generalized equatorial coordinate system, obtaining the longitude and latitude of the aircraft in the generalized equatorial coordinate system, and obtaining the reentry flight longitudinal range and reentry flight transverse range of the aircraft based on the longitude and latitude; S3, in the generalized equatorial coordinate system, the four-dimensional reachable area is expressed by a three-dimensional irregular central surface in combination with the reentry flight longitudinal range and the reentry flight lateral range of the spacecraft, and the four-dimensional reachable area is approximated by a two-dimensional curve equation to obtain the expression of the four-dimensional reachable area of ​​the spacecraft in the generalized equatorial coordinate system; S4, solving the expression of the four-dimensional reachable area through a BP neural network; the input of the BP neural network is the initial parameters of the aircraft, and the output is the key parameters of the four-dimensional reachable area of ​​the aircraft.

2. The method for predicting a 4D reachable area of ​​a hypersonic vehicle according to claim 1, characterized in that: In S1, the four-dimensional reachable area expression is: Where: Ad is the initial launch azimuth; V0 is the speed of the aircraft at time t0; θ0 is the ballistic inclination angle of the aircraft at time t0; H0 is the flight altitude of the aircraft at time t0; H f is the altitude at the end of the flight; α(t) is the angle of attack control instruction for the entire flight process; υ(t) is the roll angle control instruction for the entire flight process; Λ1, Λ2, and Λ3 are the maximum heat flux constraint, maximum dynamic pressure constraint, and maximum overload constraint, respectively.

3. The method for predicting a 4D reachable area of ​​a hypersonic flight according to claim 2, characterized in that: In S1, among the six boundaries, the arc surfaces of the farthest boundary, the left boundary, the right boundary, the bottom boundary and the top boundary are each composed of four arcs, and two adjacent arc surfaces share a curve; the nearest boundary is composed of two arc surfaces.

4. The 4D reachable area prediction method of a hypersonic aircraft according to claim 1, characterized in that: In S2, in the generalized equatorial coordinate system, it is assumed that the earth is a homogeneously rotating sphere, and the new geocentric coordinate system O E is the center of the earth, X M The Y axis is the direction of the earth's center vector along the flight starting point; M The axis is perpendicular to the X axis in the reentry arc plane. M The axis points in the direction of the target; Z M Axis and X M Axis, Y M The axes form a right-hand system, pointing to the new pole M.

5. The method for predicting a 4D reachable area of ​​a hypersonic vehicle according to claim 4, characterized in that: In S2, the longitude and latitude of the aircraft are: The calculation expressions of the reentry flight longitudinal distance L and the reentry flight lateral distance W are: Among them, λ M ,φ M are the longitude and latitude of the aircraft, R e is the average radius of the Earth.

6. The method for predicting a 4D reachable area of ​​a hypersonic vehicle according to claim 1, characterized in that: In S3, the expression of the three-dimensional irregular central surface is: Where: In formula (11), ι and For the definition in R 5 The coefficient matrix in the space; ξ and ζ are defined in R 4 The coefficient matrix in space; v is defined in R 3 The coefficient matrix in space.

7. The method for predicting a 4D reachable area of ​​a hypersonic vehicle according to claim 1, characterized in that: The expression for approximating the four-dimensional reachable area using the two-dimensional curve equation is: Where: Where, L is the longitudinal distance of the reentry flight, W is the lateral distance of the reentry flight, and Both are defined in R 3 The coefficient matrix in space is shown in formula (16): In the formula: g1, g2, g3, a1, a2, a3, q1, q2, q3, b1, b2, b3 are all unknown coefficients.

8. The method for predicting a 4D reachable area of ​​a hypersonic vehicle according to claim 1, characterized in that: In S3, the target point (L o ,W o ,H o ) is within the range of the aircraft's strike capability, and both equations (17) and (18) are satisfied: Where: H δ_max and H δ_min is a constant, which can be obtained from experience; W min and W max Satisfying formula (18): Among them, W min is the minimum value of the flight range of the aircraft’s accessible area, W max It is the maximum value of the flight range of the aircraft reachable area.

9. The method for predicting a 4D reachable area of ​​a hypersonic vehicle according to claim 1, characterized in that: In S4, the initial parameters of the aircraft are the launch azimuth Ad, the initial speed V0, the initial altitude H0, the initial ballistic inclination θ0 and the flight time t; the key parameters of the four-dimensional reachable area of ​​the aircraft are 21 output signals ι1, ι2, ι3, ι4, ι5, ξ1,ξ2,ξ3,ξ4,ζ1,ζ2,ζ3,ζ4 and 10. A 4D reachable area prediction system for a hypersonic aircraft, characterized in that: include: An expression building module is used to build a four-dimensional reachable area expression of the aircraft, wherein the four-dimensional reachable area is related to the initial flight state and flight time of the aircraft; The four-dimensional reachable area is a time-varying three-dimensional reachable area, and the three-dimensional reachable area is a closed space area composed of six boundaries, the six boundaries include a nearest boundary, a farthest boundary, a left boundary, a right boundary, a bottom boundary and an upper boundary, and each boundary is a curved surface; The generalized equatorial coordinate module is used to construct a generalized equatorial coordinate system, obtain the longitude and latitude of the aircraft in the generalized equatorial coordinate system, and obtain the reentry flight longitudinal range and reentry flight transverse range of the aircraft based on the longitude and latitude; A new expression module is used to express the four-dimensional reachable area through a three-dimensional irregular central surface in the generalized equatorial coordinate system, combining the reentry flight longitudinal range and reentry flight lateral range of the aircraft, and approximate the four-dimensional reachable area with a two-dimensional curve equation to obtain the expression of the four-dimensional reachable area of ​​the aircraft in the generalized equatorial coordinate system; The solution module is used to solve the expression of the four-dimensional reachable area through a BP neural network; the input of the BP neural network is the initial parameters of the aircraft, and the output is the key parameters of the four-dimensional reachable area of ​​the aircraft.

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