Cross-medium aircraft water strike bounce trajectory generation method based on proxy model prediction

Abstract

The invention discloses a cross-medium aircraft water strike bounce trajectory generation method based on proxy model prediction, and belongs to the field of aircraft trajectory planning. According to the method, a cross-medium aircraft trajectory generation problem is modeled into a nonlinear programming problem with constraint conditions, solving is carried out based on a pseudo-spectral method, a feasible air section flight trajectory meeting constraints is obtained, and the reliability of cross-medium aircraft trajectory generation is improved. Latin hypersquare design is used as a sampling method, input distribution can be accurately reconstructed through sampling comparison with limited iteration times, samples with higher space coverage rate are provided for construction of an agent model, modeling errors caused by the fact that a simplified model is used by a cross-medium aircraft are reduced, and the modeling accuracy is improved. And the prediction result of the state quantity of the aircraft after the water striking section has relatively high accuracy. According to the method, nonlinear mapping is carried out on the state quantities before and after the water striking section through the proxy model constructed through finite element software simulation, an accurate water striking section kinetic equation does not need to be deduced, and the calculation complexity caused by modeling is remarkably reduced.

Description

Technical Field

[0001] The invention relates to a method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction, and belongs to the technical field of aircraft trajectory planning. Background Art

[0002] A cross-medium aircraft is a special aircraft with both sea and air amphibious operation capabilities. It not only has the characteristics of an aircraft and an underwater vehicle, but can also break through the medium isolation between water and air, improve the reliability of successful cross-water and air missions, and has huge application potential. Trajectory planning for cross-medium aircraft is one of the key technologies to achieve its autonomous flight. Near-water ski jumping, as a special flight mode of cross-medium aircraft, has better maneuverability and accuracy than high-altitude projection, and can effectively improve the flight range and survivability of the aircraft.

[0003] The generation of mission trajectories for cross-medium aircraft needs to be designed considering the characteristics of different flight phases. The entire flight phase can be divided into an air flight phase and a water-striking phase. The generation of trajectories for the air flight phase needs to consider constraints such as the flight performance and state boundaries of the cross-medium aircraft, and generate a feasible optimal trajectory for the aircraft with the shortest time or the shortest flight range as performance indicators. For the water-striking phase, the existing methods for generating water-striking bounce trajectories for cross-medium aircraft mainly consider the forces between the fluid and the aircraft, accurately model the cross-medium aircraft, and solve the corresponding results, or abstract the aircraft into a flat plate or cylinder for dynamic modeling. However, since the water-striking process includes the interaction between air, water and the aircraft, the movement of the cross-medium aircraft is random and unknown, and it is difficult to obtain a display expression for the relevant forces. At the same time, there are many types of cross-medium aircraft with different shapes, and their simulation models are difficult to calculate and time-consuming. Therefore, it is necessary to carry out a fusion study of cross-medium aircraft and proxy models, which can reduce the cost of model research while meeting reliability.

[0004] In view of the above problems, the present invention proposes a method for generating a water-hitting bounce trajectory of a cross-media aircraft based on a proxy model, which is used to plan the water-hitting flight trajectory of the whole process of the cross-media aircraft. The proxy model is constructed by simulating and collecting state quantity samples of the cross-media aircraft before and after the water-hitting under different working conditions, and nonlinear mapping is performed on the state quantity before and after the water-hitting section, and then the state after the water-hitting in the real situation is predicted, which solves the problem of the difficulty in deriving the accurate dynamic model of the water-hitting section of the cross-media aircraft and the low accuracy of the simplified modeling, and provides reliable technical support for the completion of the multi-stage flight mission of the cross-media aircraft. Summary of the invention

[0005] In order to solve the problems of difficulty in deriving an accurate dynamic model of a cross-media aircraft hitting the water and low precision of simplified modeling, the present invention provides a method for generating a cross-media aircraft hitting the water bounce trajectory based on proxy model prediction. The method simulates and samples different working conditions of the hitting water section, constructs a proxy model to perform nonlinear mapping of state quantities before and after hitting the water, and then models the cross-media aircraft flight trajectory generation problem as an optimal control problem; the pseudo-spectral method is used to iteratively solve the nonlinear optimal control problem until all trajectory constraints are met, and the flight trajectory of the cross-media aircraft during the whole process of hitting the water is generated. The present invention can predict the state of the aircraft after hitting the water, avoid the problem of high calculation difficulty and long time consumption caused by the real aircraft simulation model, and has the advantages of high precision and high reliability.

[0006] The purpose of the present invention is achieved through the following technical solutions.

[0007] A method for generating a water-hitting bounce trajectory of a cross-medium aircraft based on proxy model prediction is characterized by comprising the following steps:

[0008] Step 1: Generate a set of Latin hypercube sampling points, the four dimensions are velocity inclination θ sample , speed V sample , angle of attack α sample With mass m sample , and the response value corresponding to the Latin hypercube sampling point set is obtained by finite element software simulation, that is, the position of the cross-medium aircraft before and after hitting the water [x res ,y res ], speed V res , Pitch angle Angle of attack α res ; Construct several groups of response values ​​into a sample point database;

[0009] Step 2: Use the sample point database in step 1 to construct a radial basis function RBF proxy model;

[0010]

[0011] In the formula,

[0012]

[0013] Among them, z is the input value, n s To construct the sample size of the radial basis function surrogate model, is the weight coefficient, calculated by equation (2)-(3). φ is the radial function; c i represents the sample point set constructed in step 1, and w represents the response value of the sample point in step 1; The output value of the proxy model is the flight state of the cross-medium aircraft after hitting the water;

[0014] Step 3: Set the initial simulation parameters of the cross-medium aircraft; the initial simulation parameters include: the cross-medium aircraft thrust P(t), the flight time of each stage t i (i=phase1,phase2,phase3), initial position [x0,y0], initial velocity V0, initial mass m0, initial ballistic inclination θ0, initial angle of attack α0, state boundary s min ,s max , control boundary u min ,u max and the maximum allowable error ε d ;

[0015] Step 4: Based on performance indicators, dynamic constraints, state constraints and control quantity constraints, establish the optimal control model of the cross-medium aircraft's air gliding segment and low-altitude flight segment;

[0016] The performance index J of the cross-medium aircraft trajectory generation is the maximum flight range:

[0017] J=-x (4)

[0018] x is the horizontal position of the cross-medium vehicle;

[0019] The dynamic constraints of the cross-medium aircraft are expressed as:

[0020]

[0021] Where s = [V, θ, x, y, m, α] is the state of the cross-medium aircraft, V is the velocity, θ is the ballistic inclination, x is the horizontal position, y is the vertical position, m is the mass, and α is the angle of attack; P represents the thrust of the aircraft, X represents the aerodynamic drag, Y represents the aerodynamic lift, and m c represents the mass flow rate, is the rate of change of angle of attack; g is the acceleration due to gravity;

[0022] The state constraints of the high-altitude flight stage, low-altitude flight stage and post-water-striking stage of the cross-medium aircraft include: initial state constraints such as formula (6), terminal state constraints such as formula (7) and state boundary constraints such as formula (8);

[0023]

[0024] θ(t f )=θ f , y(t f )=y f (7)

[0025]

[0026] Among them, t0 represents the initial time, t frepresents the terminal time, V(t) represents the value of V at time t, and the rest of the variables are similar; s0=[V0,θ0,x0,y0,m0,α0] represents the initial state of each stage, [θ f ,y f ] represents the terminal state of each stage state quantity, s min =[V min ,θ min ,x min ,y min ,m min ,α min ] and s max =[V max ,θ max ,x max ,y max ,m max ,α max ] represent the lower and upper boundaries of the states of each stage respectively;

[0027] Considering the ability of the actuator, to avoid the instability of the control system due to high-frequency changes in the control quantity, it is necessary to limit the range of change of the control quantity, that is,

[0028]

[0029] Among them, the control amount is the rate of change of angle of attack, represents the minimum rate of change of angle of attack, Indicates the maximum value of the rate of change of the angle of attack; indicates the upper and lower boundaries of the control quantity in each stage respectively;

[0030] According to equations (4) to (9), the optimal control problem model for the air segment trajectory generation of a cross-medium aircraft is established.

[0031]

[0032] Among them, u is the control quantity, that is, is the rate of change of the angle of attack of the i-th segment; x i is the horizontal position of the aircraft in the i-th phase; phase1 represents the high-altitude flight phase, phase2 represents the low-altitude flight phase, and phase3 represents the post-water impact phase, all of which are aerial flight phases of cross-medium aircraft; this problem requires finding a set of control quantities that minimize the performance index under the condition that each phase satisfies the constraints;

[0033] Step 5: The optimal control problem established in step 4 is converted into a nonlinear programming problem through discretization and numerical approximation;

[0034] Step 5.1: The discretization process is as follows:

[0035] The interval [t0,tf ] is evenly divided into K grid sub-intervals, and the time step of each grid sub-interval is △t=(t f -t0) / K, and then each grid subinterval [t k-1 ,t k The state and control quantities on the ] are discretized at discrete points and approximated by constructing interpolation polynomials, thereby transforming the differential equation into algebraic equation constraints;

[0036] The time domain t∈[t k-1 ,t k ] is transformed to the variable τ∈[-1,1] through equation (11);

[0037]

[0038] Assume that the state and control variables of the kth grid subinterval are s (k) (τ) and u (k) (τ), in order to ensure the continuity of the state between each grid sub-interval, the internal grid point constraint condition shown in formula (12) is added, that is,

[0039] s (k) (+1) = s (k+1) (-1), k=0,1,...,K-1 (12)

[0040] By transforming equations (11) and (12), the optimal control problem is Transformed into a multi-interval optimal control problem, the performance index shown in formula (4) is transformed into minimizing the multi-interval Bolza type cost function:

[0041]

[0042] Among them, Φ represents the Mayer type cost function and G represents the Lagrange type cost function.

[0043] In summary, after the transformation of equations (11) to (13), the optimal control problem of multi-interval Bolza-type performance index with added internal grid point constraints is considered: It is expressed as follows:

[0044]

[0045] Among them, f and They are dynamic constraints and initial and final constraints of state quantities respectively;

[0046] Step 5.2: Use numerical approximation to approximate the dynamic equations, boundary conditions and process constraints of the cross-medium aircraft and transform them into the general solution form of the pseudo-spectral method, thereby converting the solution established in step 5.1 into Transformed into a nonlinear programming problem;

[0047] Assume (k) (τ) and u (k) (τ) respectively represent the kth subinterval [t k-1 ,t k ] state quantity and control quantity within;

[0048] Take N k LGR point and end point As a node, N k +1 Lagrange interpolation polynomial for the state quantity s (k) (τ) and control quantity u (k) (τ) is approximated by:

[0049]

[0050] Among them, S (k) (τ) and U (k) (τ) are the approximated state quantity and control quantity, S i (k) Indicates that the state quantity is in the interval [t k-1 ,t k ] the value of the i-th collocation point, U i (k) Indicates that the control quantity is in the interval [t k-1 ,t k ] the value of the i-th collocation point; L i (τ)i=1,...,N k +1 for N k The Lagrange interpolation polynomial is:

[0051]

[0052] In the formula, τ i and τ j It means that Radau pseudospectral method is used in the interval [t k-1 ,t k ] any two non-repeating points in .

[0053] Differentiate equation (15) and we get

[0054]

[0055] Then the dynamic differential equation constraints at the LGR point are transformed into algebraic equation constraints:

[0056]

[0057] In the formula, is the pseudo-spectral differential matrix of the kth subinterval.

[0058] Each grid subinterval has N k The boundary constraints on the collocation points are:

[0059]

[0060] The state constraints on the network nodes are:

[0061]

[0062] The integral term in the multi-interval Bolza performance index (13) is approximated by the multi-interval Gauss integral, and we get

[0063]

[0064] In the formula, is the Lagrange cost function in the kth subinterval; is the Legendre-Gauss-Radau weight in the kth subinterval, expressed as:

[0065]

[0066] After the numerical approximation process of equations (15) to (22), we finally get Transformed into a nonlinear programming problem with constraints

[0067]

[0068] Step 6: Use pseudospectral method to Solve and obtain The solution of is the flight trajectory of the high-altitude flight segment and the low-altitude flight segment of the cross-medium aircraft;

[0069] Step 7: Judge according to formula (25). If the result of step 6 satisfies formula (25), then output If the solution is not satisfied, execute step 8; if not satisfied, add discrete points through equation (26) and go to step 5;

[0070]

[0071] in, is the kth subinterval [t k-1 ,t k ] is the sth sampling point selected from the s sampling point, ceil(·) is the upward rounding function, N d is a positive integer used to adjust the number of newly added discrete nodes; It is expressed as the maximum error in the kth subinterval;

[0072] Step 8: Output The solution results are used to obtain the flight trajectories of the high-altitude flight segment and the low-altitude flight segment, and the flight state of the cross-medium aircraft after hitting the water is obtained through the proxy model constructed in step 2;

[0073] The velocity inclination angle θ in the final state of the trajectory of the solution is f , speed V f , angle of attack α f 、Mass m f As an independent variable, it is input into the proxy model (1) to obtain the initial state of the cross-medium aircraft after hitting the water, namely:

[0074] x input =[θ f ,V f ,α f ,m f ] (27)

[0075]

[0076] Among them, x input represents the final state of the trajectory to be solved, x output represents the state of the aircraft after hitting the water, and also represents the initial state x after hitting the water 0,phase3 ;

[0077] Step 9: Based on the initial state x of the rear part of the water strike obtained in step 8 0,phase3 , establish the optimal control model for the latter part of the water striking, go to step 5 to solve, and obtain the flight trajectory for the latter part of the water striking;

[0078] Step 10: Output and splice the high-altitude flight segment trajectory, the low-altitude flight segment trajectory, and the post-water-hitting flight segment trajectory obtained in step 6, and obtain all the trajectories, which is the result of generating the cross-medium aircraft water-hitting bounce trajectory based on the proxy model prediction;

[0079] It also includes step eleven: based on the aircraft water-hitting bounce trajectory generation result obtained in step ten, the entire flight trajectory of the cross-medium aircraft in the multi-task stage can be obtained, so that the cross-medium aircraft can reach the target position range from a given position through one or more water-hitting bounces while satisfying the constraints of each stage, thereby realizing high-precision and low-computation cross-medium aircraft water-hitting flight.

[0080] Beneficial effects:

[0081] 1. The method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction disclosed in the present invention models the cross-medium aircraft trajectory generation problem as a nonlinear programming problem with constraints, and solves it based on the pseudo-spectral method to obtain a feasible air segment flight trajectory that meets the constraints, thereby improving the reliability of the cross-medium aircraft trajectory generation.

[0082] 2. The method for generating the water-hitting bounce trajectory of a cross-media aircraft based on proxy model prediction disclosed in the present invention uses Latin hypersquare design as a sampling method. It can reconstruct the input distribution more accurately through sampling with a limited number of iterations, provide samples with higher spatial coverage for the construction of the proxy model, reduce the modeling error caused by the use of simplified models for cross-media aircraft, and have a higher accuracy in the prediction results of the aircraft state quantities after the water-hitting segment.

[0083] 3. The method for generating the water-hitting bounce trajectory of a cross-media aircraft based on proxy model prediction disclosed in the present invention uses a proxy model constructed by finite element software simulation to perform nonlinear mapping of state quantities before and after the water-hitting segment. There is no need to derive an accurate dynamic equation for the water-hitting segment, which significantly reduces the computational complexity caused by modeling and improves the efficiency of generating the water-hitting bounce trajectory of a cross-media aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a flow chart of a method for generating a water-hitting and bouncing flight trajectory of an aircraft based on proxy model prediction of the present invention;

[0085] Figure 2 The flight trajectory of the cross-medium aircraft obtained by the method of the present invention in a specific implementation example;

[0086] Figure 3 It is a partial enlarged view of the water-hitting section of a cross-medium aircraft obtained by the method of the present invention in a specific implementation example;

[0087] Figure 4 is a cross-medium aircraft velocity curve obtained by the method of the present invention in a specific implementation example;

[0088] Figure 5 is a curve of the change of the attitude angle in the result obtained by the method of the present invention in a specific implementation example;

[0089] Figure 6 It is a curve of the rate of change of angle of attack in the results obtained by the method of the present invention in a specific implementation example. DETAILED DESCRIPTION

[0090] In order to better illustrate the purpose and advantages of the present invention, the present invention is further described below through an example of generating a water-hitting bouncing trajectory of a cross-medium aircraft, in combination with drawings and tables, and the comprehensive performance of the present invention is verified and analyzed.

[0091] Known conditions: The cross-medium aircraft starts flying from an altitude of y0=150m, and after a high-altitude flight of t1=20s and a low-altitude flight of t2=20s, it begins to touch the water, leaves the water surface after a water-hitting bounce, and then reaches the specified position range after a water-hitting flight of t3=10s, completing the mission.

[0092] like Figure 1 As shown, the method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction disclosed in this embodiment has the following specific implementation steps:

[0093] Step 1: Randomly generate a set of Latin hypercube sampling points and obtain their response values.

[0094] Generate a set of Latin hypercube sampling points, X = lhsdesign (50, 4), and use ANSYS software to simulate and obtain the velocity inclination angle θ of the Latin hypercube sampling point set. sample , speed V sample , angle of attack α sample 、Mass m sample The position of the down-span medium vehicle before and after hitting the water [x res ,y res ], speed V res , pitch angle θ res , angle of attack α res Equal response value.

[0095] Step 2: Construct the RBF proxy model using the state quantities before and after water impact in the sample point database.

[0096]

[0097] Among them, the weight coefficient It can be solved by the following formula

[0098]

[0099] In this example, n s The sample size for constructing the RBF proxy model is taken as 4; φ(|| ||) takes a multi-quadratic function, that is, φ(r)=(r 2 +1) 1 / 2

[0100] Step 3: Input the initial state, mission parameters, state constraints and algorithm parameter settings of the cross-medium aircraft.

[0101] In this example, the initial thrust of the trans-medium aircraft is set to P0 = 361.3N, and the initial mass flow rate is The initial time is t0=0s, the high-altitude flight time is t1=20s, the low-altitude flight time is t2=20s, and the flight time after hitting the water is t3=10s.

[0102] The initial position of the cross-medium aircraft is [x0, y0] = [0km, 150m] T , initial velocity V0=500m / s, initial ballistic inclination angle θ0=0°, initial mass m0=280kg, initial angle of attack α0=0°.

[0103] The boundary constraint values ​​of the state and control quantities in the high-altitude flight phase are shown in formula (31):

[0104]

[0105] The boundary constraint values ​​of the state and control quantities in the low-altitude flight segment are shown in formula (32):

[0106]

[0107] The boundary constraint values ​​of the state quantity and control quantity in the latter stage of water striking are shown in formula (33):

[0108]

[0109] Step 4: For the trajectory generation problem of the cross-medium aircraft's gliding segment and low-altitude flight segment, establish the optimal control problem of performance indicators, dynamic constraints, state constraints, and control quantity constraints, as shown in formula (34).

[0110]

[0111] in, represents the derivative of the state quantity s with respect to time t, f(s,t) represents the dynamic differential equation, s(t i,0 ) represents the value of the state quantity at time 0 (initial time) of the i-th segment, s(t i,f ) represents the value of the state quantity at the terminal time of the i-th segment, s i,min Indicates the minimum value of the state quantity in the i-th segment, s i,max Indicates the maximum value of the state quantity in the i-th segment.

[0112] Step 5: The optimal control problem established in step 4 is transformed into a nonlinear programming problem through discretization and numerical approximation.

[0113] Step 5.1: Discretize the problem and transform the continuous problem into a discrete problem.

[0114] Select the number of discrete intervals K = 100 and divide the interval [t0,t f ] is evenly divided into 100 grid sub-intervals, and the time step of each interval is △t=(t f -t0) / 100, and then each subinterval [t k-1 ,t k ]The state quantities and control quantities on it are discretized at discrete points.

[0115] In summary, the optimal control problem of multi-interval Bolza-type performance index with added internal network point constraints is considered. It is expressed as follows:

[0116]

[0117] Among them, f and They are dynamic constraints and initial and final constraints of state quantities respectively.

[0118] Step 5.2: Convert the discrete problem into the general solution form of the pseudospectral method.

[0119] Numerical approximation is performed on equation (35) to establish a nonlinear programming problem with constraints:

[0120]

[0121] Step 6: Use pseudospectral method to Solve and obtain The solution of is the flight trajectory of the high-altitude flight segment and the low-altitude flight segment of the cross-medium aircraft;

[0122] Step 7: Determine whether the approximate error of the result of step 6 is less than the allowable error. If it is satisfied, output the solution trajectory and execute step 8; if not, add discrete points and go to step 4.

[0123] The convergence condition is shown in formula (37), and the method of adding discrete points is shown in formula (38).

[0124]

[0125] in, is the kth subinterval [t k-1 ,t k ] is the sth sampling point selected from the s sampling point, ceil(·) is the upward rounding function, N k is the current number of discrete points, N k,new is the number of discrete points after adjustment, N d It is a positive integer used to adjust the number of newly added discrete nodes.

[0126] Step 8: Output the aerial trajectory of step 6, and obtain the flight state of the cross-medium aircraft after hitting the water through the proxy model.

[0127] Use step 6 to solve the velocity inclination angle θ in the final state of the trajectory f , speed V f , angle of attack α f 、Mass m f As an independent variable, it is input into the proxy model (1) to obtain the initial state of the cross-medium aircraft after hitting the water, namely:

[0128] x input =[θ f ,V f ,α f ,m f ] (39)

[0129]

[0130] Among them, x input represents the final state of the trajectory to be solved, x output represents the state of the aircraft after hitting the water, and also represents the initial state x of the trajectory in the air after hitting the water 0,phase3 .

[0131] Step 9: Based on the initial state after water impact solved in step 8, establish the optimal control model for the post-water impact stage, and go to step 5 to obtain the aerial flight trajectory of the cross-medium aircraft after water impact.

[0132] Step 10: Output and splice the high-altitude flight segment trajectory, the low-altitude flight segment trajectory and the post-water-hitting flight trajectory obtained in step 6, and obtain all the trajectories, which is the result of generating the aircraft water-hitting bouncing flight trajectory based on the proxy model prediction.

[0133] Step 11: Based on the result of the aircraft water-hitting hopping flight trajectory obtained in step 10, the cross-medium aircraft is enabled to reach the target position range from a given position through one or more water-hitting hopping while satisfying the constraints of each stage, thereby realizing high-precision and low-computation cross-medium aircraft water-hitting flight.

[0134] For the above specific example, the trajectory results obtained by the method for generating the trajectory of the aircraft hitting water bounce based on the proxy model prediction of the present invention are as follows: Figure 2 shown. Figure 2 In the figure, the blue diamond line is the trajectory of the aircraft in the high altitude section, the green circular line is the flight trajectory of the aircraft in the low altitude section, and the red square line is the flight trajectory of the aircraft after hitting the water. Figure 2 A partial enlarged view of the water striking section is given. Figure 2 and Figure 3 It can be seen that the trajectory generated by the method proposed in the present invention can guide the cross-medium aircraft to fly from the target position to the target position through one water-hitting bounce. Figure 4 The velocity curve corresponding to the solution result is given to satisfy the upper and lower bound constraints of the velocity in each segment. Figure 5 The attitude angle variation curve of the cross-medium aircraft is given, and it can be seen that the cross-medium aircraft meets the upper and lower bound constraints of the attitude angle of each segment. Figure 6 The rate of change of the angle of attack is given, and it can be seen that the control amount of the cross-medium aircraft is always in the range of [-2° / s, 2° / s], satisfying the control amount constraint.

[0135] According to the simulation results and analysis of the aforementioned cross-medium aircraft water-hitting bounce trajectory generation example, it can be seen that the cross-medium aircraft water-hitting bounce trajectory generation method based on proxy model prediction described in the present invention can enable the cross-medium aircraft to successfully touch the water after flying from the air at an altitude of y0=150m through a high-altitude segment of t1=20s and a low-altitude segment of t2=20s, leave the water surface after a water-hitting bounce, and then reach the specified position range after a post-water-hitting flight of t3=10s, completing the mission. The entire process meets the state constraints and control constraints of each stage, safely completes the entire flight process, and meets the mission requirements. Therefore, the present invention has strong engineering practicality and basically achieves the expected purpose of the invention.

[0136] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for generating a water-hitting bounce trajectory of a cross-medium aircraft based on proxy model prediction, characterized in that: The steps include: Step 1: Generate a set of Latin hypercube sampling points, the four dimensions are velocity inclination θ sample , speed V sample , angle of attack α sample With mass m sample , and the response value corresponding to the Latin hypercube sampling point set is obtained by finite element software simulation, that is, the position of the cross-medium aircraft before and after hitting the water [x res ,y res ], speed V res , Pitch angle Angle of attack α res ; Construct several groups of response values ​​into a sample point database; Step 2: Use the sample point database in step 1 to construct a radial basis function RBF proxy model; Among them, z is the input value, n s To construct the sample size of the radial basis function surrogate model, is the weight coefficient, φ is the radial function; c i represents the sample points constructed in step 1; The output value of the proxy model is the flight state of the cross-medium aircraft after hitting the water; Step 3: Set the initial simulation parameters of the cross-medium aircraft; The initial simulation parameters include: the thrust of the cross-medium aircraft P(t), the flight time of each stage t i (i=phase1,phase2,phase3), initial position [x0,y0], initial velocity V0, initial mass m0, initial ballistic inclination θ0, initial angle of attack α0, state boundary s min ,s max , control boundary u min ,u max and the maximum allowable error ε d ; Step 4: For the trajectory generation problem of the high-altitude flight segment and the low-altitude flight segment of the cross-medium aircraft, establish the optimal control problem model of performance indicators, dynamic constraints, state constraints, and control quantity constraints; Step 5: The optimal control problem established in step 4 is converted into a nonlinear programming problem through discretization and numerical approximation; Step 6: For the nonlinear programming problem with constraints established in step 5, the pseudo-spectral method is used to solve it and obtain the trajectories of the high-altitude flight segment and the low-altitude flight segment of the cross-medium aircraft; Step 7: Determine whether the approximate error of the flight trajectory result obtained in step 6 is less than the allowable error; if satisfied, output the solution trajectory and execute step 8; if not satisfied, add discrete points and go to step 4; Step 8: Output the air segment trajectory obtained in step 7, and obtain the flight state of the cross-medium aircraft after hitting the water through the proxy model; Step 9: Based on the initial state after striking the water solved in step 8, establish the optimal control model for the post-striking stage, and go to step 5 to solve and obtain the flight trajectory of the post-striking stage; Step 10: Output all the trajectories obtained by splicing steps 6 and 9, which is the result of generating the cross-medium aircraft water-hitting bouncing flight trajectory based on the proxy model prediction.

2. The method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction according to claim 1, characterized in that: Step 4 is implemented as follows: The performance index J of the cross-medium aircraft trajectory generation is the maximum flight range, as shown in formula (2): J=-x (2) x is the horizontal position of the cross-medium vehicle; The dynamic constraints of the cross-medium aircraft are expressed as the following differential equations: Where s = [V, θ, x, y, m, α] is the state of the cross-medium aircraft, V is the velocity, θ is the ballistic inclination, x is the horizontal position, y is the vertical position, m is the mass, and α is the angle of attack; P represents the thrust of the aircraft, X represents the aerodynamic drag, Y represents the aerodynamic lift, and m c represents the mass flow rate, is the rate of change of angle of attack; g is the acceleration due to gravity; The state constraints of the high-altitude flight stage, low-altitude flight stage, and post-water-striking stage of the cross-medium aircraft include: initial state constraints such as formula (4), terminal state constraints such as formula (5), and state boundary constraints such as formula (6); θ(t f )=θ f , y(t f )=y f (5) Among them, t0 represents the initial time, t f represents the terminal time, V(t) represents the value of V at time t, and the rest of the variables are similar; s0=[V0,θ0,x0,y0,m0,α0] represents the initial state of each stage, [θ f ,y f ] represents the terminal state of each stage state quantity, s min =[V min ,θ min ,x min ,y min ,m min ,α min ] and s max =[V max ,θ max ,x max ,y max ,m max ,α max ] represent the lower and upper boundaries of the states of each stage respectively; Considering the ability of the actuator, to avoid the instability of the control system due to high-frequency changes in the control quantity, it is necessary to limit the range of change of the control quantity, that is, Among them, the control amount is the rate of change of angle of attack, represents the minimum rate of change of angle of attack, Indicates the maximum rate of change of angle of attack; According to the performance index given by equation (2) and the constraints given by equations (3)-(7), the optimal control problem model for the trajectory generation of the cross-medium aircraft in the air segment is established. Among them, u is the control quantity, that is, is the rate of change of the angle of attack of the i-th segment; x i is the horizontal position of the aircraft in the i-th segment; phase1 represents the high-altitude flight segment, phase2 represents the low-altitude flight segment, and phase3 represents the post-water-striking segment, all of which are aerial flight segments of cross-medium aircraft; this problem requires finding a set of control quantities that minimize the performance index under the condition that each segment satisfies the constraints.

3. The method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction according to claim 2, characterized in that: Step 5 is implemented as follows: Step 5.1: The discretization process is as follows: The interval [t0,t f ] is evenly divided into K grid sub-intervals, and the time step of each grid sub-interval is △t=(t f -t0) / K, and then each grid subinterval [t k-1 ,t k The state and control quantities on the ] are discretized at discrete points and approximated by constructing interpolation polynomials, thereby transforming the differential equation into algebraic equation constraints; The time domain t∈[t k-1 ,t k ] is transformed to the variable τ∈[-1,1] through equation (9); Assume that the state and control variables of the kth grid subinterval are s (k) (τ) and u (k) (τ), in order to ensure the continuity of the state between each grid sub-interval, the internal grid point constraint condition shown in formula (10) is added, that is, s (k) (+1)=s (k+1) (-1), k=0,1,...,K-1 (10) By transforming equations (9) and (10), the optimal control problem is transformed into Transformed into a multi-interval optimal control problem, the performance index shown in formula (2) is transformed into minimizing the multi-interval Bolza type cost function: Among them, Φ represents the Mayer type cost function and G represents the Lagrange type cost function. In summary, according to the transformation of equations (9) to (11), the optimal control problem of multi-interval Bolza-type performance index with added internal grid point constraints is considered: It is expressed as follows: Among them, f and They are dynamic constraints and initial and final constraints of state quantities respectively; Step 5.2: Use numerical approximation to approximate the dynamic equations, boundary conditions and process constraints of the cross-medium aircraft and transform them into the general solution form of the pseudo-spectral method, thereby converting the solution established in step 5.1 into Transformed into a nonlinear programming problem; Assume (k) (τ) and u (k) (τ) respectively represent the kth subinterval [t k-1 ,t k ] state quantity and control quantity within; Take N k LGR point and end point As a node, N k +1 Lagrange interpolation polynomial for the state quantity s (k) (τ) and control quantity u (k) (τ) is approximated by: Among them, S (k) (τ) and U (k) (τ) are the approximated state quantity and control quantity, S i (k) Indicates that the state quantity is in the interval [t k-1 ,t k ] the value of the i-th collocation point, U i (k) Indicates that the control quantity is in the interval [t k-1 ,t k ] the value of the i-th collocation point; L i (τ)i=1,...,N k +1 for N k The Lagrange interpolation polynomial is: In the formula, τ i and τ j It means that Radau pseudospectral method is used in the interval [t k-1 ,t k ] any two non-repeating points in . Differentiate equation (13) and we get Then the dynamic differential equation constraints at the LGR point are transformed into algebraic equation constraints: In the formula, is the pseudo-spectral differential matrix of the kth subinterval. Each grid subinterval has N k The boundary constraints on the collocation points are: The state constraints on the network nodes are: The integral term in the multi-interval Bolza performance index (11) is approximated by the multi-interval Gauss integral, and we get In the formula, is the Lagrange cost function in the kth subinterval; is the Legendre-Gauss-Radau weight in the kth subinterval, expressed as: After the numerical approximation process of equations (13) to (20), we finally get Transformed into a nonlinear programming problem with constraints 4. The method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction according to claim 3, characterized in that: In step six, The pseudo-spectral method is used to solve the nonlinear programming problem shown in formula (22) to obtain the flight trajectories of the high-altitude and low-altitude segments of the cross-medium aircraft.

5. The method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction according to claim 4, characterized in that: In step seven, The convergence condition is shown in formula (23), and the discrete point increase method is shown in formula (24); in, is the kth subinterval [t k-1 ,t k ] is the sth sampling point selected from the s sampling point, ceil(·) is the upward rounding function, N d is a positive integer used to adjust the number of newly added discrete nodes; It is expressed as the maximum error in the kth subinterval.

6. The method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction according to claim 5, characterized in that: The implementation method of step eight is: Use step 6 to solve the velocity inclination angle θ in the final state of the trajectory f , speed V f , angle of attack α f 、Mass m f As an independent variable, it is input into the proxy model (1) to obtain the initial state of the cross-medium aircraft after hitting the water, namely: x input =[θ f ,V f ,a f ,m f ] (25) Among them, x input represents the final state of the trajectory to be solved, x output represents the state of the aircraft after hitting the water, and also represents the initial state x after hitting the water 0,phase3。 7. The method for generating a cross-medium aircraft water-hitting bounce trajectory based on proxy model prediction according to claim 1, 2, 3, 4, 5 or 6, characterized in that: It also includes step eleven: based on the result of the cross-medium aircraft water-hitting bouncing flight trajectory generated in step ten, the entire flight trajectory of the cross-medium aircraft in the multi-task stage can be obtained, so that the cross-medium aircraft can reach the target position range from a given position through one or more water-hitting bouncings while satisfying the constraints of each stage, thereby realizing high-precision and low-computation cross-medium aircraft water-hitting flight.

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