Online track planning method for air-breathing hypersonic aircraft with unstarted air inlet channel

Abstract

The invention provides a trajectory online planning method for an air-breathing hypersonic aircraft with an unstarted air inlet, and the method comprises the steps: constructing a mechanism model of the air-breathing hypersonic aircraft, and correcting the mechanism model according to the output of a neural network and in combination with an air inlet / isolation section pressure sensor array; and in the flight process, stability margin prediction is carried out based on the corrected mechanism model, and when the air inlet non-starting margin is lower than a warning value in the future, the trajectory optimization model is called to carry out online trajectory planning. The output error of the corrected mechanism model is obviously reduced, and more accurate dynamic characteristic data supports reduction of the error between the control effect and the preset index; the accuracy of the mechanism model is obviously improved; once it is found that the non-starting margin of the air inlet channel is lower than the warning value in the future, the track optimization model is called to conduct online track planning, and therefore the situation that the air inlet channel is not started is avoided; the method has remarkable effectiveness and robustness in the aspects of trajectory optimization and air inlet non-starting protection.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft control, and in particular to an online trajectory planning method for a scramjet hypersonic vehicle with inlet unstart. Background Art

[0002] Compared with the high cost and insufficient data coverage of flight tests, wind tunnel tests and other methods, the current mechanism modeling considering aerodynamic propulsion coupling shows great development prospects in the modeling process for dynamic characterization and control, because it has fast computational efficiency, excellent convergence and strong scalability. However, due to the insufficient computational accuracy of the mechanism model, it is of great significance to develop a model correction method based on real flight data to improve the computational accuracy of the model and improve the control quality.

[0003] The mechanism-based hypersonic vehicle modeling method is becoming increasingly mature, but there are some environmental parameters in the modeling process, and the accuracy of these parameters significantly affects the accuracy of the mechanism model. The currently widely used modeling method believes that the specific heat ratio γ is only related to temperature. As the inlet temperature increases along the axis, the specific heat ratio should increase accordingly. However, in the actual operation process, the inlet temperature distribution varies greatly, so it is necessary to set the initial γ according to the environmental temperature to calculate the inlet flow field temperature, which leads to certain errors. However, the recent research by Takahashi T T shows that in the hypersonic flight environment, most of the total temperature inherent in the flow exists in the form of kinetic energy. If the airflow decelerates through the inlet, the pressure and temperature increase significantly, resulting in the separation of diatomic gases in the air, causing further changes in γ, and the error of γ fitted with the environmental temperature increases in the hypersonic environment. In the combustion chamber part, the propulsion system of hypersonic vehicles usually designs an active cooling system. After the fuel acts as a coolant, the temperature increases significantly, causing changes in the combustion efficiency in the combustion chamber, that is, the fuel heat release coefficient changes.

[0004] The above reasons lead to inaccurate modeling of the hypersonic vehicle propulsion system. In terms of inlet unstart prediction, it is easy to cause large errors and affect the engineering practicability.

[0005] In order to improve the reliability of the model, in recent years, the fusion of mechanism and data models has become a new development direction. The mechanism-data fusion model combines the generalizability of the mechanism model and the accuracy of the data model, and has been widely recognized in improving the model accuracy and reducing costs. For example, Patent CN 114840914A discloses an intelligent modeling method for the fusion of data-driven and mechanism-driven of hypersonic vehicles. This patent focuses on the relationship between geometric configuration parameters and dynamic characteristics, and carries out the optimal design of geometric configuration parameters. However, it does not pay attention to the empirical parameters existing in the calculation method. In addition, the high-precision data used for comparison comes from a higher-precision modeling method, and there is no model correction method designed to utilize sensor information.

[0006] Patent CN116383957A discloses a multi-source energy optimization method for hypersonic vehicles based on a surrogate model. The surrogate model based on the GA-BP neural network in this patent is used to improve the calculation speed of the mechanism model. It is a method that sacrifices accuracy to a certain extent to improve the calculation speed. In addition, the optimization algorithm is a traditional offline method that does not consider the differences in space-ground consistency and the on-board deployment ability.

[0007] Patent CN118795767A discloses a soft switching method for the main thrust closed-loop - inlet unstart protection control of a scramjet engine. Based on the principle of suppressing switching disturbances, this patent proposes a switching control method to solve the problem of control signal jitter during the switching process of different control laws. However, this method does not consider the model error of the inlet unstart control and does not perform model correction. Summary of the Invention

[0008] Aiming at the deficiencies of the existing technology, the present invention provides an online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart. The output error of the corrected model of the present invention is significantly reduced, and more accurate dynamic characteristic data supports the reduction of the error between the control effect and the preset index. And based on the corrected mechanism model, a trajectory optimization method is used to generate a large number of sample trajectories, a deep neural network is constructed for learning, and the stability margin is predicted based on the corrected mechanism model during the flight process.

[0009] The technical solution of the present invention is as follows: An online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart, comprising the following steps:

[0010] S1). Construct a mechanism model of the air-breathing hypersonic vehicle;

[0011] S2). Construct a neural network, and correct the mechanism model according to the output of the neural network in combination with the inlet / isolation section pressure sensor array;

[0012] S3). During the flight process, predict the stability margin based on the corrected mechanism model. When the future inlet unstart margin is lower than the warning value, call the trajectory optimization model to perform online trajectory planning.

[0013] Preferably, in step S1), constructing a mechanism model of the air-breathing hypersonic vehicle specifically includes the following steps:

[0014] S11). Model the inlet using the shock wave / detachment wave method;

[0015] S12). Model the isolation section combustion chamber;

[0016] S13). Model the nozzle;

[0017] S14), calculating the thrust output of the dual-mode ramjet engine according to the established model;

[0018] S15), constructing a panel model of the aircraft outer surface, and calculating the aerodynamic characteristics according to the pressure vectors on the panels.

[0019] Preferably, in step S11), the inlet duct includes a forebody compression section and a fuselage. When the airflow passes through the internal fold angle, compression occurs to generate an oblique shock wave, and the airflow velocity after the shock wave is obtained through the relationship between the wavefront velocity, the turning angle, and the shock wave angle.

[0020] Preferably, in step S12), the airflow parameters in the isolator and the combustion chamber are calculated through the continuity equation, the energy equation, the momentum equation, the gas state equation, and the equation of the relationship between the sound speed and the gas parameters. And in this process, a combustion mode is assumed for calculation. According to the calculation results, it is judged whether the minimum Mach number in the combustion chamber is less than 1. If it is less than 1, it is in the subsonic combustion mode, and the calculation results of the isolator combustion chamber flow field are corrected according to the subsonic combustion heat release coefficient; if the minimum Mach number is greater than or equal to 1, it is in the supersonic combustion mode, and the calculation results of the isolator combustion chamber flow field are corrected according to the subsonic combustion heat release coefficient; if the judged mode is the same as the constructed mode, no correction is required.

[0021] Preferably, in step S13), the modeling of the nozzle divides the nozzle into two parts: the inner nozzle and the outer nozzle. Among them, the inner nozzle part is modeled using the variable cross-section pipe flow formula considering friction; the flow field parameters of the inner nozzle and the airflow parameters at the outlet of the inner nozzle are obtained;

[0022] The outer nozzle uses plume modeling. The two-dimensional model of the nozzle is divided into small regions along the body axis, and the plume model is established based on the equal air pressure above and below the shear layer.

[0023] Preferably, in step S2), the input of the neural network is the flight state, and the output is the empirical parameters to be corrected; by substituting the empirical parameters output by the neural network into the mechanism model for calculation, the inlet duct outlet pressure and the position of the leading edge of the shock train in the isolator are obtained, and the neural network loss function is constructed in combination with the true value measured by the sensor to correct the empirical parameters.

[0024] Preferably, in step S3), calculating the maximum angle of attack α corresponding to the allowable minimum inlet duct unstart margin and the maximum fuel equivalence ratio under different flight states u and the maximum fuel equivalence ratio and constructing a trajectory optimization model, the maximum angle of attack α u and the maximum fuel equivalence ratio The calculation formulas for are:

[0025] α u (q) = l0 + l1q + l2q 2+l3q 3 ;

[0026]

[0027] where α u (q) represents the maximum angle of attack affected by dynamic pressure; l0, l1, l2, and l3 all represent the fitting coefficients of the maximum angle of attack; q represents the dynamic pressure; represents the maximum fuel equivalence ratio affected by dynamic pressure and angle of attack; p 00 , p 01 , p 10 , p 02 , p 11 , p 20 all represent the fitting coefficients of the maximum fuel equivalence ratio; α represents the angle of attack.

[0028] Preferably, in step S3), a series of optimal trajectories within the range of the initial state and the final state are generated by the Gaussian pseudospectral method as training samples, and a trajectory optimization model is used to learn the optimal trajectories between different two points. After training, the trajectory optimization model is used to replace the optimization algorithm with an overly heavy computational burden for airborne trajectory optimization.

[0029] The beneficial effects of the present invention are as follows:

[0030] 1. The present invention provides an inlet unstart protection method for real-time predicting the inlet unstart margin and online planning a low-risk flight trajectory, which overcomes the inlet unstart protection problem from the underlying mechanism of unstart and the level of trajectory planning;

[0031] 2. The present invention corrects the empirical parameters by combining the empirical parameters output by the neural network and the true values measured by the sensors; the output error of the corrected mechanism model is significantly reduced, and the more accurate dynamic characteristic data supports the reduction of the error between the control effect and the preset index; the accuracy of the mechanism model is significantly improved;

[0032] 3. On the basis of correcting the mechanism model, the present invention uses a trajectory optimization method to generate a large number of sample trajectories, constructs a trajectory optimization model for learning, predicts the stability margin based on the corrected mechanism model during flight, and once it is found that the future inlet unstart margin is lower than the warning value, the trajectory optimization model is called for online trajectory planning, thereby avoiding inlet unstart;

[0033] 4. The present invention formulates the trajectory optimization problem as a highly nonlinear optimal control problem, and extracts the state-action vectors from the optimal trajectories generated under random initial states; it provides a high-quality data basis for the learning of the trajectory optimization model, and designs a trajectory optimization model based on these data to learn the functional relationship between the flight state and the optimal action, thereby realizing the prediction ability of the optimal action;

[0034] 5. The present invention has remarkable effectiveness and robustness in terms of trajectory optimization and inlet unstart protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic flow chart of an embodiment of the present invention;

[0036] Figure 2 It is a flow framework diagram for modifying the mechanism model in an embodiment of the present invention;

[0037] Figure 3 It is an analysis diagram of the influence law of specific heat ratio on the modeling result in an embodiment of the present invention;

[0038] Figure 4 It is an analysis diagram of the influence law of heat release coefficient ratio on the modeling result in an embodiment of the present invention;

[0039] Figure 5 It is an on-line trajectory planning flow chart for inlet unstart protection in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following further describes the specific embodiments of the present invention with reference to the accompanying drawings:

[0041] As Figure 1 shown, this embodiment provides an on-line trajectory planning method for a scramjet hypersonic vehicle with inlet unstart, including the following steps:

[0042] S1). Construct a mechanism model of the scramjet hypersonic vehicle;

[0043] S11). Model the inlet using the shock wave / detonation wave method;

[0044] The inlet described includes a forebody compression section and a fuselage. When the airflow passes through an internal fold angle, an oblique shock wave M a is generated for compression, and the airflow velocity after the shock wave is obtained through the relationship between the wavefront velocity M b , the turning angle δ, and the shock wave angle β, that is:

[0045]

[0046]

[0047] In the formula, γ represents the specific heat ratio; θ represents the airflow direction angle; λ and v are intermediate variables.

[0048] Among them, the intermediate variables λ and χ respectively represent:

[0049]

[0050] In the formula, M1 represents the airflow Mach number at the inlet of the inlet;

[0051] When the air flow passes through the external fold angle, the air flow expands to generate an expansion wave:

[0052]

[0053] In the formula, M represents the Mach number of the air flow;

[0054] After calculating the oblique shock wave M a According to the ideal gas state equation, the state parameters after the wave can be solved; in a two-dimensional flow field, when the wave surfaces intersect, new wave surfaces will be generated. When the wave system of the inlet is complex enough, the average air flow parameters are calculated, and finally the air flow parameters at the outlet of the inlet are obtained: Mach number M2, temperature T2, and pressure P2.

[0055] Combined with the mass conservation equation, the energy conservation equation, and the ideal gas state equation, we can obtain:

[0056]

[0057]

[0058]

[0059] In the formula, M2 and M3 respectively represent the Mach numbers of the air flow at the outlet of the inlet and the outlet of the isolator; T2 and T3 respectively represent the air flow temperatures at the outlet of the inlet and the outlet of the isolator; P2 and P3 respectively represent the air flow pressures at the outlet of the inlet and the outlet of the isolator.

[0060] S12), modeling of the isolator combustion chamber;

[0061] In this embodiment, fuel injection and combustion chamber friction are considered, and heat exchange between the air flow in the flow field and the inner wall of the combustion chamber and the fuel chemical reaction process are ignored. A one-dimensional model of the dual-mode combustion chamber is established:

[0062]

[0063]

[0064]

[0065] In the formula, M represents the Mach number of the air flow; x represents the axial position of the body; ψ th is an intermediate variable, S th represents the cross-sectional area of the internal flow path; T t represents the total temperature; dT t represents the change rate of the total temperature; ε th represents the ratio of the fuel flow velocity on the body axis of the aircraft engine to the air flow velocity in the mainstream field; represents the mass flow rate of fuel added to the combustion chamber; express Indicates the rate of change of the fuel mass flow rate added to the combustion chamber; C f represents the friction coefficient; d th represents hydraulic diameter; P represents airflow pressure; T represents airflow temperature;

[0066] In this embodiment, the total temperature T is determined by using the empirical heat release law. t and its rate of change dT t ; Make the equations solvable; Among them, the total temperature T t Expressed as:

[0067]

[0068] Where, T t2 Indicates the total temperature at the inlet of the isolation section; Q is the empirical heat release coefficient, which is 40-50 in the sub-combustion state and 1-10 in the super-combustion state; represents the dimensionless position, x inj Indicates the injection point position; x4 indicates the combustion chamber outlet position; τ b Indicates the heating ratio.

[0069] In this embodiment, the airflow parameters in the isolation section and the combustion chamber are calculated by the continuity equation, the energy equation, the momentum equation, the gas state equation, and the equation relating the speed of sound to the gas parameters. In this process, a combustion mode is assumed for calculation, and the calculation result is used to determine whether the minimum Mach number in the combustion chamber is less than 1. If it is less than 1, the combustion chamber is in the subcombustion mode, and the calculation result of the flow field in the isolation section combustion chamber is corrected according to the subcombustion heat release coefficient. If the minimum Mach number is greater than or equal to 1, the combustion chamber is in the supercombustion mode, and the calculation result of the flow field in the isolation section combustion chamber is corrected according to the subcombustion heat release coefficient. If the judgment mode and the construction mode are the same, no correction is required.

[0070] In this embodiment, the flow field parameters of the combustion chamber airflow are continuous from supersonic to subsonic. Therefore, there is a sonic point with a Mach number of , which satisfies:

[0071]

[0072] Where A represents the cross-sectional area of the combustion chamber;

[0073] The position of the sonic point is calculated based on the variation law of the combustion chamber cross section in the isolation section, the total temperature distribution law, and the total temperature variation rate of the airflow;

[0074] The Mach numbers before and after the sonic point are:

[0075]

[0076] Wherein, M u represents the Mach number at the sonic point and at certain positions before and after; Δx represents the change in the body axial position;

[0077] The Mach number M4 at the combustor outlet is obtained by integrating backward from the sonic point. In the isolator section, there is a shock train that balances the low-pressure and high-speed airflow in the inlet and the high-pressure and low-speed airflow in the combustor; in the subsonic combustion mode, it exists in the form of a normal shock, and the length L of the shock train s The formula is:

[0078]

[0079] Wherein, R iso represents the isolator height or radius; M3 and M4 are the Mach numbers at the combustor inlet and outlet respectively; Ma3 and Ma4 are the Mach numbers at the isolator inlet and outlet;

[0080] In the supersonic combustion mode, it exists in the form of an oblique shock, and the length formula is:

[0081]

[0082] Wherein, Re represents the Reynolds number; κ represents the momentum thickness of the boundary layer at the isolator inlet; P2 and P3 represent the pressures at the isolator inlet and outlet respectively.

[0083] S13), Modeling of the nozzle;

[0084] In this embodiment, the nozzle modeling divides the nozzle into two parts: the inner nozzle and the outer nozzle. Among them, the inner nozzle part is modeled using the variable cross-section pipe flow formula considering friction; the flow field parameters of the inner nozzle and the airflow parameters at the outlet of the inner nozzle are obtained;

[0085] The outer nozzle uses plume modeling. The two-dimensional model of the nozzle is divided into small regions along the body axis, and the plume model is established based on the equal air pressure above and below the shear layer.

[0086] S14), Calculate the thrust F of the dual-mode ramjet engine according to the constructed model t Output; that is:

[0087]

[0088] Wherein, represents the air mass flow rate; V1 represents the airflow velocity at the inlet of the inlet; represents the fuel equivalence ratio; f st represents the stoichiometric fuel-air ratio; V5 represents the airflow velocity at the outlet of the nozzle; S th5 represents the cross-sectional area at the outlet of the nozzle; P1 represents the pressure at the inlet of the inlet; S th1 represents the cross-sectional area at the inlet of the inlet.

[0089] S15), construct the surface element model of the aircraft outer surface, and calculate the aerodynamic characteristics according to the pressure vectors on the surface elements.

[0090] In this embodiment, the surface elements of the aircraft outer surface include the inlet duct part and the nozzle part. The results of the propulsion system modeling for the inlet duct part and the nozzle part are used as the input conditions for the aerodynamic characteristics modeling, so as to reflect the aircraft-propulsion coupling characteristics. The modified Newton method is used to calculate the pressure on the windward surface elements, as shown in Equations (17) and (18); the Prandtl-Mayer method is used to calculate the pressure on the leeward surface elements, as shown in Equation (19); the pressure vectors on all surface elements are added together to obtain the overall aerodynamic characteristics, that is:

[0091] C p =K m sin 2 δ; (17)

[0092]

[0093]

[0094] In the formula, C p represents the pressure coefficient; K m correction coefficient;

[0095] In this embodiment, the analysis is carried out under the flight conditions of the aircraft at an altitude of 17,000 m, a speed of Ma5.5, and an angle of attack of 3°. Among them, the subsonic combustion mode is simulated and analyzed at a fuel equivalence ratio of 0.6, and the supersonic combustion mode is simulated at a fuel equivalence ratio of 0.4. The analysis of the influence law of the specific heat ratio on the modeling results is as Figure 3 shown; the analysis of the influence law of the heat release coefficient ratio on the modeling results is as Figure 4 shown;

[0096] From Figure 3 it can be seen that when the specific heat ratio γ ∈ [1.3, 1.43], the greater the angle of attack, the more obvious the change in the inlet duct outlet pressure. When the angle of attack is 2.5°, the inlet duct outlet pressures are 235,592 Pa and 261,823 Pa respectively, with a change of 26,231 Pa; the net thrusts are 43,859 N and 73,751.7 N respectively, with a change of 29,892.7 N. The drag is not significantly affected by the specific heat ratio. The pitching moments are 3,250,990 N·m and 3,025,370 N·m respectively, with a change of 225,620 N·m. From Figure 4It can be seen that in the subsonic combustion state, when Q ∈ [40, 50], the angle of attack is 2.8°, the leading edge positions of the shock wave train are 0.3915 m and 0.2789 m respectively, with a change of 0.1126 m. The thrusts are 195255 N and 187237 N respectively, with a change of 8018 N. In the supersonic combustion state, when Q ∈ [1, 10], the angle of attack is 2.8°, the leading edge positions of the shock wave train are 0.3627 m and 0.2973 m respectively, with a change of 0.0654 m. The thrusts are 164924 N and 172792 N respectively, with a change of 7868 N.

[0097] S2), construct a neural network, and correct the mechanism model according to the output of the neural network and in combination with the inlet duct / isolation section pressure sensor array; as Figure 2 described:

[0098] The expression of the neural network constructed in this embodiment is:

[0099]

[0100] In the formula, ψ represents the activation function adopted by the output layer; q represents the number of neurons in the hidden layer; n is the number of neurons in the input layer; ω j is the function weight value between the j-th neuron node in the hidden layer and the only neuron node in the output layer; χ is the activation function of the hidden layer; ω ij represents the function weight value between the j-th neuron node in the hidden layer and the i-th neuron node in the input layer; θ j is the threshold of the j-th neuron node in the hidden layer; x o is the i-th input quantity; a is the threshold of the neuron node in the output layer.

[0101] The input of the described neural network is the flight state, including the altitude H, speed V, angle of attack α and fuel equivalence ratio of the aircraft The output is the empirical parameter to be corrected; by substituting the empirical parameter output by the neural network into the mechanism model for calculation, the inlet duct outlet pressure and the leading edge position of the shock wave train in the isolation section are obtained, and the neural network loss function is constructed in combination with the measured real values by the sensor to correct the empirical parameter. Denote the pressure measured by the inlet duct outlet pressure sensor as p1, and the pressure calculated by the mechanism model as p2, that is, p2 = f M (x, net), f M is the mechanism model; then the constructed neural network loss function is:

[0102]

[0103] In the formula, E represents the loss function value; n represents the number of groups of neural network data sets; P represents the P-th group of neural network data;

[0104] The neuron nodes are corrected by the gradient descent method, and the adjustment amount of the weight value from the hidden layer node to the output layer node is denoted as Δω j , the adjustment amount of the threshold value of the output layer node is denoted as Δa, and the adjustment amount of the weight value from the input layer to the hidden layer node is denoted as Δω ij , the adjustment amount of the threshold value of the j-th node in the hidden layer is denoted as Δθ j , the adjustment formula for the weight value between the hidden layer and the output layer is:

[0105] Δω j =-η(p1 - p2)ψ′n j ; (22)

[0106] In the formula, η is the learning rate; ψ′ represents the derivative of the activation function adopted by the output layer; n j is the input of the output layer node, ω ij represents the weight value of the function between the j-th neuron node in the hidden layer and the i-th neuron node in the input layer; θ j is the threshold value of the j-th neuron node in the hidden layer; x i is the i-th input quantity.

[0107] The adjustment formula for the threshold value of the output layer is:

[0108]

[0109] The adjustment formula for the weight value between the input layer and the hidden layer:

[0110]

[0111] The adjustment formula for the threshold value of the hidden layer:

[0112]

[0113] In the formula, E represents the neural network loss function; represents the partial derivative of the neural network loss function with respect to the threshold value of the output layer neuron node; y j is the output of the j-th neuron in the hidden layer.

[0114] S3), during the flight, based on the corrected mechanism model, the stability margin is predicted. When the future inlet unstart margin is lower than the warning value, the trajectory optimization model is called for online trajectory planning.

[0115] As Figure 5 shown, in this embodiment, during the trajectory optimization process, the angle of attack α and the fuel equivalence ratio are selected As control parameters, the height H, speed V, trajectory inclination angle θ, and vehicle mass m are used as state parameters; during the climbing phase of the vehicle, both the angle of attack and the fuel equivalent ratio are relatively large, so it is easier for the inlet to unstart. The trajectory is optimized as a climbing trajectory, and the optimization goal is to minimize fuel consumption, that is:

[0116] J min =-m(t f ); (26)

[0117] In the formula, J min represents the minimum fuel consumption; m is the vehicle mass; t f represents the maximum allowable time for optimization;

[0118] And it is subject to the boundary conditions and constraints in Table 1;

[0119] Table 1 Trajectory optimization boundary conditions and constraints for inlet unstart

[0120]

[0121] For the control parameters, in order to facilitate the training of the trajectory optimization model, they are designed as quadratic functions of time t:

[0122]

[0123] In the formula, u(t) is the control parameter at time t; T is the optimization operator with respect to time, t f is the maximum allowable time for optimization; a i , b i , i = 0, 1, 2 are the optimization operator coefficients.

[0124] This design avoids the explosion of control variables caused by too long flight time.

[0125] During the climbing process of the vehicle, select the trajectory state points that may detect inlet unstart. Starting from these state points, conduct trajectory planning to obtain the control variable parameters, and then train the trajectory optimization model; the input of the trajectory optimization model is the initial height H0, initial speed V0, initial ballistic angle θ0, the end height H f , the end speed V f , the end ballistic angle θ f , the allowable minimum unstart margin ξ min ; the output of the trajectory optimization model is a i , b i , i = 0, 1, 2, and they are all optimization operator coefficients; input the optimization adjustment and results into the trajectory optimization model for training. If it is predicted during the flight that the inlet unstart margin is lower than a certain specific value, then use the trajectory optimization model to re-plan the trajectory.

[0126] In this embodiment, the Gaussian pseudospectral method is used for parameter optimization. Therefore, the trajectory optimization problem is a single-stage optimal control problem, which can be rewritten in the general form as follows:

[0127]

[0128] where J is the fuel consumption; φ represents the function of fuel consumption related to the aircraft state and time; x represents the aircraft state variable; t f is the maximum allowable time for optimization;

[0129] The dynamic constraint is satisfied as follows:

[0130]

[0131] where represents the rate of change of the aircraft state; f represents the rate of change of the aircraft state related to the aircraft state; x(t) represents the aircraft state; u(t) represents the control parameter at time t; t represents time;

[0132] The path constraint is:

[0133] g L < g(x(t), u(t), t) < g U ; (30)

[0134] where g L represents the lower bound of the path constraint; g represents the path constraint; g U represents the upper bound of the path constraint;

[0135] The control constraint is:

[0136] u L < u(t) < u U ; (31)

[0137] where u L , u U are the minimum and maximum values of the control parameter u(t), respectively.

[0138] If the time range of the optimal control is [t0, t f , and the time range of the Gaussian pseudospectral method is [-1, 1], then the time t is transformed as follows:

[0139]

[0140] where τ represents the transformed time operator; t0 is the initial time of the optimal control; t f is the maximum allowable time for optimization.

[0141] The points obtained by discretizing the Gaussian pseudospectral method are K - order Legendre - Gauss points, which are equivalent to the roots of the K - order Legendre polynomial. Add additional points As the (K + 1)-th interpolation point, and then use (K + 1) Lagrange interpolation polynomials To approximate the state variables:

[0142]

[0143] In the formula, Represents the relationship of the flight state with respect to the time operator; Represents the relationship of the discretized flight state with respect to the time operator; L i Represents the basis function;

[0144] The last point The corresponding state variable Also conforms to the dynamic equation relationship;

[0145] The discrete terminal - state dynamic equation is approximated by Gauss integration, that is:

[0146]

[0147] In the formula, Represents the discrete terminal state; Represents the discrete initial state; w k Represents the Gauss weight coefficient, Represents the control variable at the discrete points; Is the Legendre - Gauss point;

[0148] Similarly, use the Lagrange interpolation polynomial as the basis function to approximate the control variable, where Is the control variable at the discrete points: Is the Legendre - Gauss point. Taking the derivative of Equation (6) to obtain the derivative of the state variable, the dynamic - equation constraint can be transformed into an algebraic constraint, and then substituting it back into the dynamic equation, the algebraic - equation constraint that the state variable should satisfy at the collocation points can be obtained:

[0149]

[0150] In the formula, D ki Represents the constraint of the state variable;

[0151] At this time, the optimal - control problem is transformed into: making the discretized state variable X i The control variable U k And the terminal time tf , solve for the minimum of the J function on the premise of satisfying the constraints of the dynamic equation.

[0152] For the initial altitude H0, initial velocity V0, initial ballistic angle θ0 of the aircraft, and the end altitude H f , end velocity V f , end ballistic angle θ f , allowable minimum non-start margin ξ min Perform offset to form 9,600 sample trajectories. The trajectory optimization model can predict the optimal angle of attack and fuel equivalence ratio according to the input flight state, trajectory objectives, and constraints. Since the prediction only requires simple matrix multiplication and addition operations on the input, the trajectory optimization model has significant real-time performance and stability in airborne applications.

[0153] During flight, predict the non-start of the inlet for a period of time in the future. If the non-start margin of the aircraft inlet is lower than the warning value, call the trajectory optimization model to plan the trajectory online, and the aircraft switches to a safer flight trajectory to reduce the risk of non-start of the inlet while ensuring the completion of the trajectory objectives.

[0154] The above embodiments and descriptions in the specification only illustrate the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.

Claims

1. An online trajectory planning method for a scramjet hypersonic vehicle with inlet unstart, characterized in that It includes the following steps: S1). Construct a mechanism model of an air-breathing hypersonic vehicle; S2). Construct a neural network, and correct the mechanism model according to the output of the neural network and in combination with the inlet duct / isolation section pressure sensor array; S3). During flight, predict the stability margin based on the corrected mechanism model. When the future inlet duct unstart margin is lower than the warning value, call the trajectory optimization model for online trajectory planning.

2. The online trajectory planning method for an airbreathing hypersonic vehicle with inlet unstart according to claim 1, characterized in that: In step S1), to construct a mechanism model of an air-breathing hypersonic vehicle, it specifically includes the following steps: S11). Model the inlet duct using the shock wave / detonation wave method; S12). Model the isolation section combustion chamber; S13). Model the tail nozzle; S14). Calculate the thrust output of the dual-mode ramjet engine according to the constructed model; S15). Construct a surface element model of the vehicle outer surface, and calculate the aerodynamic characteristics according to the pressure vectors on the surface elements.

3. The online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart according to claim 1, characterized in that: In step S2), the expression of the constructed neural network is: In the formula, ψ represents the activation function adopted by the output layer; q represents the number of neurons in the hidden layer; n is the number of neurons in the input layer; ω j is the function weight value between the j-th neuron node in the hidden layer and the only neuron node in the output layer; χ is the activation function of the hidden layer; ω ij represents the weight value of the function between the j-th neuron node in the hidden layer and the i-th neuron node in the input layer; θ j is the threshold of the j-th neuron node in the hidden layer; x i is the i-th input quantity; a is the threshold of the neuron node in the output layer.

4. The online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart according to claim 3, characterized in that: In step S2), the input of the neural network is the flight state, and the output is the empirical parameters to be corrected; by substituting the empirical parameters output by the neural network into the mechanism model for calculation, the inlet duct outlet pressure and the leading edge position of the shock wave train in the isolation section are obtained, and a neural network loss function is constructed in combination with the true values measured by the sensors to correct the empirical parameters.

5. The online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart according to claim 4, wherein: In step S2), denote the pressure measured by the intake port outlet pressure sensor as p1, and the pressure calculated by the mechanism model as p2, that is, p2 = f M (x, net), where f M is the mechanism model; then the loss function of the constructed neural network is: In the formula, E represents the neural network loss function; n represents the number of data groups in the neural network dataset; P represents the Pth group of neural network data.

6. The online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart according to claim 5, characterized in that: In step S2), the neuron nodes are corrected by the gradient descent method. The adjustment amount of the weights from the hidden layer nodes to the output layer nodes is denoted as Δω j , the adjustment amount of the threshold of the output layer nodes is denoted as Δa, and the adjustment amount of the weights from the input layer to the hidden layer nodes is denoted as Δω ij , the adjustment amount of the threshold of the j-th node in the hidden layer is denoted as Δθ j , and the adjustment formula for the weights between the hidden layer and the output layer is as follows: Δω j = -η(p1 - p2)ψ′n j ; (22) where η is the learning rate; ψ ′ represents the derivative of the activation function used in the output layer; n j is the input to the output layer node, ω ij represents the weight of the function between the j-th neuron node in the hidden layer and the i-th neuron node in the input layer; θ j is the threshold of the j-th neuron node in the hidden layer; x i is the i-th input quantity; The adjustment formula for the output layer threshold is: The adjustment formula for the weights between the input layer and the hidden layer: The adjustment formula for the hidden layer threshold: In the formula, E represents the neural network loss function; represents the partial derivative of the neural network loss function with respect to the threshold of the output layer neuron node; y j is the output of the j-th neuron in the hidden layer.

7. An online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart according to claim 1, characterized in that: In step S3), calculate the maximum angle of attack α corresponding to the allowable minimum inlet unstart margin under different flight states u and the maximum fuel equivalence ratio and construct a trajectory optimization model. The calculation formulas for the maximum angle of attack α u and the maximum fuel equivalence ratio are as follows: α u f(q) = l0 + l1q + l2q 2 + l3q 3 ; Where α u (q) represents the maximum angle of attack related to the dynamic pressure; l0, l1, l2, and l3 are all coefficients of the fitting relationship of the maximum angle of attack; q represents the dynamic pressure of the aircraft; represents the maximum fuel equivalent ratio related to the angle of attack and the dynamic pressure; p 00 , p 01 , p 10 , p 02 , p 11 , p 20 respectively represent the coefficients of the fitting relationship of the maximum fuel equivalent ratio; α represents the angle of attack.

8. The online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart according to claim 7, characterized in that: In step S3), a series of optimal trajectories within the range of the initial state and the final state are generated by the Gaussian pseudospectral method as training samples. The trajectory optimization model is used to learn the optimal trajectories between different two points. When the future inlet duct unstart margin is lower than the warning value, the trained trajectory optimization model is used for online trajectory planning.

9. The online trajectory planning method for an airbreathing hypersonic vehicle with inlet unstart according to claim 8, characterized in that: In step S3), during the trajectory optimization process, the angle of attack α and the fuel equivalence ratio are selected as control parameters, and the altitude H, speed V, trajectory inclination angle θ, and aircraft mass m are used as state parameters; the optimized trajectory is designed as a climbing trajectory, and the optimization goal is to minimize fuel consumption, that is: J min = -m(t f ); (26) Where J min represents the minimum fuel consumption; m is the mass of the aircraft; t f represents the maximum time allowed for optimization; For the control parameters, they are designed as quadratic functions of time t: where \(u(t)\) is the control parameter at time \(t\); \(T\) is the optimization operator with respect to time, t f is the maximum time allowed for optimization; \(a\) i , \(b\) i , \(i = 0, 1, 2\) are the optimization operator coefficients; During the climb of the aircraft, select the trajectory state points for detecting the inlet unstart. Starting from these state points, conduct trajectory planning to obtain the control variable parameters, and then train the trajectory optimization model; the input of the trajectory optimization model is the initial height H0, initial velocity V0, initial ballistic angle θ0, and the end height H f , the end velocity V f , the end ballistic angle θ f , and the allowable minimum unstart margin ξ min ; the output of the trajectory optimization model is the optimization operator coefficients a i , b i , i = 0, 1, 2; input the optimization adjustment and results into the trajectory optimization model for training. During the flight, if it is predicted that the inlet unstart margin is lower than a certain specific value, use the trajectory optimization model to re-plan the trajectory.

10. The online trajectory planning method for an air-breathing hypersonic vehicle with inlet unstart according to claim 9, characterized in that: In step S3), the trajectory optimization problem is simplified to a single-stage optimal control problem. Therefore: MinJ = φ(x(t f ), t f ); (28) where J is the fuel consumption; φ represents the function of fuel consumption related to the aircraft state and time; x represents the aircraft state variable; t f is the maximum allowable time for optimization; The dynamic constraints to be satisfied are: In the formula, represents the rate of change of the aircraft state; f represents the functional relationship between the rate of change of the aircraft state, the aircraft state, the control parameters, and time; x(t) represents the aircraft state; u(t) represents the control parameter at time t; t represents time; The path constraints are: g L <g(x(t), u(t), t) < g U ; (30) where g L represents the lower bound of the path constraint; g represents the path constraint; g U represents the upper bound of the path constraint; The control constraints are: u L <u(t) < u U ; (31) where u L and u U are the minimum and maximum values of the control parameter u(t), respectively; If the time horizon of the optimal control is [t0, t f , and the time horizon of the Gaussian pseudospectral method is [-1, 1], then perform a transformation on the time t: In the formula; represents the converted time operator; t0 is the initial time of the optimal control; t f To optimize the maximum allowable time; The points processed by the discrete Gauss pseudospectral method are the K - order Legendre - Gauss points, which are equivalent to the roots of the K - order Legendre polynomial Add additional points As the (K + 1)-th interpolation point, and then use (K + 1) Lagrange interpolation polynomials To approximate the state variables: In the formula, represents the relationship of the flight state with respect to the time operator; represents the relationship of the discretized flight state with respect to the time operator; L i represents the basis function; The last point The corresponding state variable Also conforms to the kinetic equation relationship; The discrete end-state dynamic equation is approximated by Gauss integration, that is: In the formula, represents the discrete end state; represents the discrete initial state; w k represents the Gauss weight coefficient, represents the control variable at the discrete points; is the Legendre-Gauss point; Use the Lagrange interpolation polynomial as the basis function to approximate the control variables, where is the control variable at the discrete points: is the Legendre-Gauss point; Differentiate Equation (6) to obtain the derivative of the state variable. By transforming the dynamic equation constraint into an algebraic constraint and then substituting it back into the dynamic equation, the algebraic equation constraint that the state variable should satisfy at the collocation points can be obtained: where D ki represents the constraint of the state variable; The optimal control problem at this time is transformed into: making the state variable X after discretization i , the control variable U k , and the terminal time t f , under the premise of satisfying the constraints of the dynamic equation, solve for the minimum of the J function; For the initial altitude H0, initial velocity V0, initial ballistic angle θ0, and end altitude H f , end velocity V f , end ballistic angle θ f , allowable minimum non-start margin ξ min Perform a deviation to form a sample trajectory; the trajectory optimization model predicts the optimal angle of attack and fuel equivalent ratio based on the input flight state, trajectory target, and constraints.

Images