A simulation analysis method for aircraft mission profile planning based on pseudo-spectral method

Abstract

The present invention discloses a simulation analysis method for aircraft mission profile planning based on pseudo-spectral method, which realizes the best overall performance of aircraft by coupling design of aircraft trajectory and wing variable curvature control strategy, mainly including building a multidisciplinary mathematical analysis model, establishing aircraft mission profile optimization problem, using multi-stage Radau pseudo-spectral method to discretize mission profile, converting continuous optimal control problem into nonlinear programming problem, using multidisciplinary coupling gradient calculation method to provide accurate gradient information, selecting solver suitable for large-scale sparse NLP problem to iteratively solve until convergence criterion is met, and post-processing and analyzing optimization results. The present invention can significantly improve the fuel efficiency of aircraft, increase range, optimize flight time, and provide optimal control strategy and trajectory planning scheme under different mission profiles and flight conditions, and has important theoretical value and engineering application prospects.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft design and trajectory optimization, and relates to trajectory optimization and multidisciplinary coupling design, and is specifically a simulation analysis method for aircraft mission profile planning based on a pseudo-spectral method. Background Art

[0002] Aircraft trajectory optimization is an important part of aircraft scheme design, overall design and mission planning. It runs through the entire aircraft design process and affects the design of multiple subsystems such as the overall aircraft, aerodynamic layout, guidance and control, power and structure. By optimizing the change law of control variables during flight, the flight performance boundary can be effectively explored on the premise of completing the flight mission, the flight quality can be significantly improved, and one or some performance indicators in the flight mission stage can be optimized.

[0003] The trajectory optimization problem is actually a nonlinear optimal control problem with state constraints and control constraints, that is, to find a control law that can meet various constraints to make a certain flight performance index optimal and give the optimized flight state. From its mathematical essence, the trajectory optimization of the aircraft can be abstracted as an open-loop optimal control problem that solves the functional extreme value under constraints such as differential equations, algebraic equations and inequalities. The numerical methods for trajectory optimization mainly include direct method and indirect method. Among them, the direct method based on pseudo-spectral method is widely used due to its high efficiency and good accuracy. The advantage of pseudo-spectral method is that it can achieve high discretization accuracy with a small number of points, and at the same time satisfy the co-state mapping theorem. The co-state variables can be derived from the optimal solution of the trajectory, and then the optimality of the trajectory optimization solution can be verified. The application of pseudo-spectral method improves the computational efficiency of trajectory optimization and is suitable for trajectory optimization of complex mission profiles.

[0004] With the continuous development of aviation technology, simply optimizing the flight path is no longer sufficient to meet the growing performance requirements. Comprehensive optimization of multiple goals such as improving flight efficiency and promoting continuous improvement of flight performance has become the core task of design. As an innovative aerodynamic design method, variable camber technology allows the wing curvature to be adjusted according to changes in flight conditions, and the airflow state on the wing surface is controlled, thereby optimizing the load distribution on the wing surface. However, the introduction of variable camber technology makes the performance optimization problem of the aircraft more complicated. The overall performance of the aircraft in performing the mission is closely related to the trajectory. The principle of variable camber technology determines that the trajectory will significantly affect the use strategy of variable camber and the comprehensive performance of the system. The flight trajectory determines the flight state of the aircraft at different times and directly affects the use strategy of variable camber. In turn, the implementation of variable camber control will change the aerodynamic characteristics of the aircraft, thereby affecting the flight performance and trajectory. This interaction makes it difficult for the traditional method of considering trajectory optimization and wing morphology control separately to obtain the global optimal solution. Therefore, coupling the trajectory optimization with the variable camber control strategy has become an important research direction. This coupled design method requires optimizing both control variables and state variables during trajectory planning to ensure that the vehicle can achieve optimal performance at each flight stage.

[0005] However, existing aircraft trajectory optimization methods still have certain limitations in terms of computational efficiency, optimization accuracy, and handling of complex constraints and multi-objective optimization. Therefore, how to improve the computational efficiency of trajectory optimization and solve multi-objective optimization problems under complex constraints while ensuring optimization accuracy has become a technical problem that needs to be solved urgently. Summary of the invention

[0006] 1. Purpose of the invention

[0007] In view of the fact that existing aircraft trajectory optimization methods fail to fully consider the coupling relationship between variable curvature technology and trajectory, as well as the defects and shortcomings in computational efficiency, optimization accuracy, and processing of complex constraints and multi-objective optimization, in order to solve at least one of the above and other technical problems in the prior art, the purpose of the present invention is to obtain the path flight parameters when one or some performance indicators of the aircraft in the flight mission phase reach the optimal level, and to construct a simulation and analysis method for aircraft mission profile planning based on the pseudo-spectral method. By establishing a mathematical model including aerodynamics, power, and mission profile analysis from a multidisciplinary perspective, the aircraft comprehensive performance index parameters are taken as the optimization target, the pseudo-spectral method is used to discretize the aircraft mission profile, and the coupled gradient is solved according to the unified formula of the mathematical model to realize the coupled design of the flight trajectory and the variable curvature control strategy, thereby improving the comprehensive performance of the aircraft.

[0008] (II) Technical solution

[0009] In order to achieve the purpose of the invention and solve the technical problems, the present invention adopts the following technical solutions:

[0010] A pseudo-spectral method-based simulation analysis method for aircraft mission profile planning is used to obtain the best overall performance of the aircraft by coupling the aircraft trajectory with the wing variable camber control strategy. Specifically, the method comprises at least the following steps when implemented:

[0011] SS1. Construct a multidisciplinary mathematical analysis model of the aircraft to describe the aircraft's motion characteristics, aerodynamic characteristics, propulsion characteristics and atmospheric environment under different flight conditions, including at least a flight dynamics sub-model, an aerodynamic sub-model including the effect of wing camber, a propulsion sub-model and an atmospheric model;

[0012] SS2. Based on the multidisciplinary mathematical analysis model of the aircraft constructed in step SS1, at least by defining the state variable set X, determining the track and curvature control variable set U, constructing the track optimization objective function J, and establishing the dynamic constraint equation set f (X,U, t ), set boundary conditions and path constraints g (X,U, t ), establish the aircraft mission profile optimization problem, where t time;

[0013] SS3. The mission profile is discretized using the pseudo-spectral method. First, the entire flight time interval is divided into several sub-intervals according to the complexity of the flight mission. Then, the pseudo-spectral method is applied in each sub-interval, and the appropriate distribution and number of points are selected to balance the accuracy and efficiency of the discretization process. Finally, the Lagrange interpolation polynomial is used to approximate the state variable X( t ) and the control variable U( t );

[0014] SS4. The continuous optimal control problem is transformed into a nonlinear programming problem. First, the integral term in the objective function J is discretized into the weighted sum of the function values ​​at the collocation points using the Gauss quadrature formula. Then, the dynamic constraint equations are transformed into f (X,U, t ) are discretized into algebraic constraints, and boundary conditions and path constraints are discretized at all collocation points g (X,U, t), then add sub-interval connection constraints to ensure the continuity of state variables at the junction of adjacent sub-intervals, and finally express the discretized optimal control problem as a standard nonlinear programming problem (NLP) for easy solution. At the same time, the multidisciplinary coupled gradient calculation method is used to provide the objective function gradient and constraint gradient of the nonlinear programming problem.

[0015] SS5. Select a solver suitable for large-scale sparse nonlinear programming problems, provide initial guess solutions for the state variables and control variable values ​​at all collocation points, set solver parameters and define convergence criteria, use multidisciplinary coupled gradient calculation methods in each iteration to provide accurate gradient information for the solver, iterate until the convergence criteria are met, and thus solve the nonlinear programming problem;

[0016] SS6. Post-process and analyze the optimization results, including trajectory reconstruction and performance evaluation, to verify the effectiveness and reliability of the optimization method and analyze the impact of the variable camber control strategy on flight performance.

[0017] (III) Technical Effect

[0018] Compared with the prior art, the aircraft mission profile planning simulation analysis method based on pseudospectral method of the present invention has the following beneficial and significant technical effects:

[0019] (1) The present invention provides a simulation analysis method for aircraft mission profile planning based on pseudo-spectral method. By coupling the aircraft trajectory with the wing variable curvature control strategy, the overall performance of the aircraft is significantly improved. This method not only takes into account the optimization of the flight trajectory, but also combines the wing variable curvature technology, so that the aircraft can flexibly adjust the wing shape under different flight conditions, thereby optimizing aerodynamic efficiency, reducing fuel consumption, and increasing range. Through the construction and application of multidisciplinary mathematical analysis models, the present invention effectively integrates multiple subsystems such as flight dynamics, aerodynamics, propulsion system and atmospheric environment to form a comprehensive optimization framework.

[0020] (2) The multi-stage Radau pseudo-spectral discretization technology of the present invention achieves efficient and accurate trajectory discretization. By dividing the continuous time interval into multiple sub-intervals, applying the Radau pseudo-spectral method in each sub-interval, and selecting the appropriate distribution and number of collocation points, the discretization process is both accurate and efficient. At the same time, the Lagrange interpolation polynomial is used to approximate the state variables and control variables in each sub-interval, and the continuous variables are discretized into node values, ensuring the accuracy and efficiency of the calculation.

[0021] (3) The present invention uses a multidisciplinary coupled gradient calculation method and a unified formula derivative equation to accurately calculate the gradient of the optimization objective function with respect to the design variables. This method significantly improves the efficiency and accuracy of solving nonlinear programming problems. In particular, for large-scale sparse systems, the adjoint method is used for gradient calculation, which not only improves the calculation efficiency but also reduces the calculation cost. By accurately providing gradient information, the optimization process is faster and more stable.

[0022] (4) The present invention significantly improves the comprehensive performance of the aircraft in the planning and simulation analysis of the aircraft mission profile, including key indicators such as fuel efficiency, range, and flight time. Through the coupled design of the track and variable curvature control strategy, the global optimization of the aircraft performance is achieved, which has important theoretical value and engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0024] Figure 1 A flowchart of a simulation analysis method for aircraft mission profile planning based on pseudo-spectral method;

[0025] Figure 2 The principle block diagram of the simulation analysis method for aircraft mission profile planning based on pseudo-spectral method;

[0026] Figure 3 The flowchart for the implementation of the discretization of mission profiles using the multi-stage Radau pseudospectral method;

[0027] Figure 4 Implementation flow chart for converting continuous optimal control problem into nonlinear programming problem;

[0028] Figure 5 A flowchart for calculating the gradient of the objective function with respect to the design variables using the unified formula derivative equation;

[0029] Figure 6 Implementation flow chart for selecting a solver and iteratively solving the optimal control problem;

[0030] Figure 7 It is a schematic diagram comparing the height changes of the reference configuration and the variable camber configuration profile during free cruising;

[0031] Figure 8 Schematic diagram of the comparison of free flight drag (a) and thrust (b) curves of the reference configuration and the variable camber configuration during free cruise;

[0032] Fig. 9 Schematic diagram of the comparison of the free flight lift coefficient (a), drag coefficient (b), and pitch moment coefficient (c) of the reference configuration and the variable camber configuration during free cruise;

[0033] Fig.10 Schematic diagram comparing the free flight lift-to-drag ratio change curves of the reference configuration and the variable camber configuration profile during free cruise. DETAILED DESCRIPTION

[0034] In order to better understand the present invention, the content of the present invention is further explained below in conjunction with embodiments. The described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limitations of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the art without making creative work are within the scope of protection of the present invention.

[0035] In view of the fact that existing aircraft trajectory optimization methods fail to fully consider the coupling relationship between variable curvature technology and trajectory, as well as the defects and shortcomings in computational efficiency, optimization accuracy, and processing of complex constraints and multi-objective optimization, in order to solve at least one of the above and other technical problems in the prior art, the purpose of the present invention is to obtain the path flight parameters when one or some performance indicators of the aircraft in the flight mission phase reach the optimal level, and to construct a simulation and analysis method for aircraft mission profile planning based on the pseudo-spectral method. By establishing a mathematical model including aerodynamics, power, and mission profile analysis from a multidisciplinary perspective, the aircraft comprehensive performance index parameters are taken as the optimization target, the pseudo-spectral method is used to discretize the aircraft mission profile, and the coupled gradient is solved according to the unified formula of the mathematical model to realize the coupled design of the flight trajectory and the variable curvature control strategy, thereby improving the comprehensive performance of the aircraft.

[0036] Example 1

[0037] Figure 1 , 2 The flowchart and principle block diagram of the aircraft mission profile planning simulation analysis method based on pseudo-spectral method of the present invention are shown. As a specific example, Figure 1 , 2 As shown, the aircraft mission profile planning simulation analysis method based on the pseudo-spectral method of the present invention is used to obtain the best overall performance of the aircraft by coupling the aircraft trajectory with the wing variable curvature control strategy, and mainly includes:

[0038] SS1. Construct a multidisciplinary mathematical analysis model for aircraft

[0039] A multidisciplinary mathematical analysis model of the aircraft is constructed to describe the motion characteristics, aerodynamic characteristics, propulsion characteristics and atmospheric environment of the aircraft under different flight conditions, including at least a flight dynamics sub-model, an aerodynamic sub-model including the influence of wing curvature, a power propulsion sub-model and an atmospheric model.

[0040] In some preferred examples, in the constructed multidisciplinary mathematical analysis model, the flight dynamics submodel can use the three-degree-of-freedom particle motion equation to describe the motion state of the aircraft, and at least include the time evolution of the position, velocity, and mass parameters of the aircraft. In addition, the flight dynamics submodel can, for example, use the particle hypothesis to establish the dynamic equation group of the longitudinal plane of the aircraft to fully describe the motion state and mass change of the aircraft, and its mathematical expression is:

[0041]

[0042] In the above expressions, r is the flight distance, h is the flight altitude, V is the flight speed, γ is the flight trajectory angle, m is the mass of the aircraft, T is the engine thrust, D For resistance, L For lift, α is the angle of attack, φ For engine mounting angle, g is the acceleration due to gravity, SFC is the fuel consumption rate.

[0043] In some preferred examples, in the constructed multidisciplinary mathematical analysis model, the aerodynamic sub-model including the influence of wing camber can be an aerodynamic proxy model constructed based on CFD simulation and combined with data sampling, which is used to describe the aerodynamic characteristics of the aircraft under different flight conditions under the wing camber control strategy. For example, a multi-fidelity Kriging proxy model can be used, which is trained by combining high-fidelity and low-fidelity sample data, where high-fidelity samples are used to provide accurate aerodynamic force evaluation, and low-fidelity samples are used to improve computational efficiency, and its expression is:

[0044]

[0045] in y high is the high-fidelity model output, y low is the low-fidelity model output, ρ ( x ) is the scaling / correlation factor, δ ( x ) is the difference function, and the input variables of the proxy model include the Mach number Ma, Angle of Attack α and a plurality of variable camber parameters, wherein the variable camber parameters at least include a tail wing twist angle Twist tailH 、Twist angle of the first aileron Aileron1 、Twist angle of the second aileron Aileron2 、First flap twist angle Twist Flap1 and the second flap twist angle Twist Flap2 , the output variable of the model is the aerodynamic coefficient, as shown in the following formula:

[0046]

[0047] in C L is the lift coefficient, C D is the drag coefficient, C M is the pitching moment coefficient.

[0048] In some preferred examples, in the constructed multidisciplinary mathematical analysis model, the power propulsion sub-model can be a propulsion proxy model constructed based on the engine characteristic parameter table, which is used to evaluate the thrust output and fuel consumption characteristics of the aircraft engine under different flight conditions. For example, a Kriging propulsion proxy model can be constructed based on the engine characteristic parameter table, and the thrust and fuel consumption characteristic curves of the engine at different flight altitudes and Mach numbers can be obtained through the proxy model, as shown in the following formula:

[0049]

[0050] The Mach number Ma , Flight altitude h and engine speed N is the input variable of the proxy model, engine thrust Trust and fuel consumption rate SFC is the output variable of the surrogate model.

[0051] In some preferred embodiments, in the constructed multidisciplinary mathematical analysis model, the atmospheric model is a standard atmospheric model or a numerical weather forecast model, which is used to describe the variation of atmospheric parameters with altitude and at least includes the vertical distribution of temperature, pressure, local sound speed and density parameters.

[0052] SS2. Establishing the spacecraft mission profile optimization problem

[0053] Based on the multidisciplinary mathematical analysis model of the aircraft constructed in step SS1, the aircraft mission profile optimization problem is established by at least defining the state variable set X, determining the trajectory and variable curvature control variable set U, constructing the trajectory optimization objective function J, establishing the dynamic constraint equation group f(X, U, t), setting boundary conditions and path constraints g(X, U, t), where is the time t.

[0054] In some preferred embodiments, the aircraft mission profile optimization problem can be established in the following manner: first, a state variable set X is defined, where the state variables are used to describe the flight state of the aircraft within the mission profile, including but not limited to the flight altitude. h , Flight speed V , flight distance r and aircraft mass m etc.; determine the track and curvature control variable set U, the track control variables are the parameters that need to be adjusted during the track optimization process, including but not limited to Mach number Ma, angle of attack α ,thrust T And variable curvature parameters δ Equal parameters, variable curvature parameters δ At least including the tail twist angle Twist tailH 、Twist angle of the first aileron Aileron1 、Twist angle of the second aileron Aileron2 、First flap twist angle Twist Flap1 and the second flap twist angle Twist Flap2 ; Construct the trajectory optimization objective function J, and select the goal of the optimization problem by minimizing fuel consumption, maximizing range, minimizing flight time or their weighted combination according to the mission requirements; establish the dynamic constraint equation group f (X,U, t ), describe the relationship between state variables and track control variables, constrain the changes of state variables and track control variables; set boundary conditions and path constraints g (X,U, t ), including at least initial state constraints, terminal state constraints and flight envelope constraints, to ensure that the aircraft remains within a safe and controllable range throughout the mission profile.

[0055] SS3. Discretization of mission profile using pseudo-spectral method

[0056] The pseudo-spectral method is used to discretize the mission profile. First, the entire flight time interval is divided into several sub-intervals according to the complexity of the flight mission. Then, the pseudo-spectral method is applied in each sub-interval, and the appropriate distribution and number of collocation points are selected to take into account the accuracy and efficiency of the discretization process. Finally, the Lagrange interpolation polynomial is used to approximate the state variable X(t) and control variable U(t) in each sub-interval.

[0057] In some preferred embodiments, Figure 3 As shown, the multi-stage Radau pseudo-spectral method is used to discretize the mission profile, and the implementation may specifically include the following sub-steps:

[0058] SS31. According to the complexity of the flight mission, the continuous entire flight time interval [ t 0 , t f ] is divided into N Subintervals[ t i , t i+1 ],in, t 0 , t f are the start time and end time of the flight mission respectively. t i , t i+1 are the start and end time of each sub-interval, N is the number of subintervals, i =0, 1,..., N -1;

[0059] SS32. For each subinterval [ t i , t i+1 ] performs time domain transformation and maps it to the standard interval [-1, 1];

[0060] SS33. Apply the Radau pseudospectral method in each subinterval and select K A Legendre-Gauss-Radau (LGR) distribution point;

[0061] SS34. Use K-1 order Lagrange interpolation polynomials to approximate the state variable X and control variable U in each subinterval and discretize the continuous variables into node values.

[0062] SS4. Convert continuous optimal control problems into nonlinear programming problems

[0063] The continuous optimal control problem is transformed into a nonlinear programming problem. First, the integral term in the objective function J is discretized into the weighted sum of the function values ​​at the collocation points using the Gauss quadrature formula. Then, the dynamic constraint equations f(X, U, t) are discretized into algebraic constraints using the differential matrix, and the boundary conditions and path constraints g(X, U, t) are discretized at all collocation points. Sub-interval connection constraints are then added to ensure the continuity of the state variables at the junction of adjacent sub-intervals. Finally, the discretized optimal control problem is expressed as a standard nonlinear programming problem (NLP) for easy solution. At the same time, the multidisciplinary coupled gradient calculation method is used to provide the objective function gradient and constraint gradient of the nonlinear programming problem.

[0064] In some preferred embodiments, Figure 4 As shown, the method of converting the continuous optimal control problem into a nonlinear programming problem may specifically include the following sub-steps when implemented:

[0065] SS41. Use Gauss quadrature formula to convert the objective function The integral term in is discretized into the weighted sum of the function values ​​at the collocation points, that is, ,in w i is the Gauss product weight, τ i Assign points to LGR;

[0066] SS42. Using the Radau pseudospectral method, the differential matrix D is transformed into the dynamic constraint equations. Discretization into algebraic constraints , where X and U are the vectors of state variables and control variables at all collocation points, respectively;

[0067] SS43. Apply boundary conditions and path constraints At each distribution point τ i The discretization is:

[0068] ;

[0069] SS44. For any two adjacent subintervals [ t i , t i+1 ]and[ t i+1 , t i+2 ], add a subinterval connection constraint X between its end and beginning end -X start = 0 to ensure the continuity of the state variable at the junction of adjacent subintervals, where X end For the subinterval [ ti , t i+1 ]’s terminal state variable, X start For the subinterval [ t i+1 , t i+2 ]’s initial state variable;

[0070] SS45. The discretized optimal control problem is expressed as a standard NLP problem, which is expressed as:

[0071]

[0072] The constraints include:

[0073] ;

[0074] SS46. Use multidisciplinary coupled gradient computation methods to provide objective function gradients and constraint gradients for nonlinear programming problems.

[0075] In a further preferred embodiment, Figure 5 As shown, the gradient of the optimization objective function J to the design variable x is calculated by using the derivative equation of the unified formula of the numerical model, which can specifically include the following sub-steps:

[0076] SS461. All input design variables, state variables, control variables and output variables are combined into a vector Z=(x,X,U,f) through the unified formula of the numerical model, where x represents the set of input design variables, X represents the set of state variables, U represents the set of control variables, and f represents the set of output variables;

[0077] SS462. Define the residual equation R(Z)=0 associated with the vector Z, where R=(R x ,R X ,R U ,R f ), R x , R X , R U , R f are the residual equations corresponding to the input design variable x, state variable X, control variable U and output variable f respectively;

[0078] SS463. Solve the unified derivative equation of the residual equation R with respect to the combination vector Z:

[0079]

[0080] Among them, the derivative of the combination vector Z with respect to the design variable x is contains the gradient of the output variable to be calculated with respect to the design variable , the gradient of the state variable with respect to the design variable and the gradient of the control variable with respect to the design variable ;

[0081] SS464. Choose to solve the forward system or the inverse system based on the relative size of the output variable set f and the input design variable set x:

[0082] when n f < n x When , solve the forward system ;

[0083] when n f ≥ n x When , solve the inverse system ;

[0084] in n f , n x are the dimensions of the output variable set f and the input design variable set x respectively;

[0085] SS465. Implement the adjoint method to calculate the derivative of the objective function J with respect to the design variable x. First, construct an adjoint vector λ that does not depend on the design variable and satisfies the adjoint equation , then calculate the derivative of the objective function J with respect to the design variable x ;

[0086] SS466. For the track control variables and the variable curvature control variables in the control variable set U, calculate their gradients to the objective function J:

[0087]

[0088] SS467. In each pseudo-spectral discretized subinterval, the gradients of the state variable X and the control variable U with respect to the design variable x are calculated using the Lagrange interpolation polynomial:

[0089]

[0090] Among them, L i is the Lagrange interpolation polynomial, X i and U i are the state variable and control variable values ​​at the i-th collocation point respectively;

[0091] SS468. For constraints at the junctions of subintervals, compute the gradients associated with the junction constraints:

[0092]

[0093] Where C is the connection constraint, X end , X start are the values ​​of the state variables at the end and beginning of adjacent subintervals.

[0094] SS5. Solving nonlinear programming problems based on pseudospectral discretization

[0095] Select a solver suitable for large-scale sparse nonlinear programming problems, provide initial guess solutions for the state variables and control variable values ​​at all matching points, set solver parameters and define convergence criteria, use multidisciplinary coupling gradient calculation methods in each iteration to provide accurate gradient information for the solver, iterate until the convergence criteria are met, and thus achieve the solution to the nonlinear programming problem.

[0096] In some preferred embodiments, Figure 6 As shown in FIG. 1 , a method for selecting a solver suitable for a large-scale sparse nonlinear programming problem and iteratively solving the problem to achieve the optimal control problem includes:

[0097] SS51. Select a nonlinear programming solver, including SNOPT, IPOPT or KNITRO solvers, to efficiently handle large-scale sparse nonlinear programming problems;

[0098] SS52. Provide initial guess solutions X0 and U0 for the state variables X and control variables U at all points. The initial guess solutions are generated based on experience or pre-calculation to improve the convergence speed and the quality of the solution results.

[0099] SS53. Set solver parameters, including the maximum number of iterations, allowable error and / or step size control parameters, and define convergence criteria, which are used to determine whether the iterative process achieves the expected accuracy;

[0100] SS54. In each iteration, a multidisciplinary coupled gradient calculation method is used to provide accurate gradient information to the solver, where the gradient expression of the objective function J with respect to the design variable x is: , where λ is the adjoint variable and R is the residual vector. The adjoint variable λ is obtained by solving the linear adjoint equation system , where Z is the combination vector Z=(x,X,U,f), x is the set of input design variables, X is the set of state variables, U is the set of control variables, and f is the set of output variables;

[0101] SS55. The solver optimizes the objective function and constraints based on the provided gradient information and set parameters, and updates the values ​​of state variables and control variables;

[0102] SS56. Iterate the solution until the convergence criterion is met, and check the terminal state constraints, path constraints, and dynamic constraints at the collocation points: If all constraints meet the allowable relative error conditions, solve the nonlinear programming problem transformed by the pseudo-spectral method; if the constraints are not met, increase the number of discrete points in each stage and iterate the solution again until all constraints are met.

[0103] SS6. Post-processing and analysis of optimization results

[0104] The optimization results are post-processed and analyzed, including trajectory reconstruction and performance evaluation, to verify the effectiveness and reliability of the optimization method and analyze the impact of the variable camber control strategy on flight performance.

[0105] In some preferred instances, the method for post-processing and analyzing the optimization results includes: reconstructing the discrete solution obtained by optimization into a continuous trajectory, and interpolating the discrete points into a continuous curve through Lagrange interpolation or spline interpolation method to obtain a smooth flight trajectory and a control variable change curve; calculating key performance indicators, including at least total fuel consumption, flight time, maximum speed and minimum altitude, and evaluating the pros and cons of the optimization scheme through these indicators; verifying whether the final solution satisfies all constraints, and ensuring that the optimization results achieve the optimization goals under the premise of satisfying boundary conditions, path constraints and connection constraints; comparing the optimal trajectories and performance indicators with and without variable curvature control, and quantifying the impact of variable curvature on flight performance.

[0106] In summary, this embodiment elaborates in detail the simulation analysis method for aircraft mission profile planning based on pseudo-spectral method proposed by the present invention. This method constructs a multidisciplinary mathematical model, establishes an optimization problem, discretizes using pseudo-spectral method, converts into a nonlinear programming problem and solves it, and finally realizes the coupled optimization of the aircraft track and the wing variable curvature control strategy. This method can not only effectively improve the overall performance of the aircraft, but also provide a solid foundation for subsequent research. However, this embodiment is only a specific implementation of this method, and there are other implementation methods that can be further explored and improved.

[0107] Example 2

[0108] Based on Example 1, this embodiment further studies the main implementation process of the above method proposed by the present invention in a specific application to the cruise mission profile of a certain type of wide-body passenger aircraft, and achieves improvement in aircraft performance by optimizing the track and wing variable curvature control strategy.

[0109] The optimization framework in this embodiment includes state variables and design variables. State variables include range, flight altitude, trajectory angle (gam), flight speed (Velocity) and weight (Mass), etc. Design variables are input control variables, including Mach number (Mach), angle of attack (Alpha), percentage physical speed (Rotate_V) and horizontal tail installation angle (Eta), etc. When the trailing edge variable curvature system is added, two sets of flaps (Airelon) and ailerons (Flap), etc. are also included. The constraints in the optimization process mainly include boundary constraints and path constraints. Among them, the flight process requires the pitch moment coefficient CM ≥ 0, and stipulates the fuel mass (mass fuel) of the starting and ending states. The specific variable definitions and constraints are shown in Table 1 below:

[0110] Table 1 Definition of variables for trajectory optimization of a wide-body aircraft

[0111]

[0112] This embodiment selects the longest range as the optimization target under fixed fuel consumption, and the upper and lower limits of the state variables and design variables are shown in Table 1. By comparing and analyzing the baseline configuration and the configuration after adding the variable camber technology, the improvement of the cruise performance by the variable camber technology is explored, and the optimization results are shown in Table 2 below:

[0113] Table 2 Comparison of cruise mission performance

[0114]

[0115] As can be seen from Table 2, in the step cruise mission profile, the range increases by 0.93% after adding the variable camber technology; in the free altitude cruise mission profile, the range increases by 1.13%. This shows that after adding the variable camber technology, the overall performance of the aircraft in executing the mission has been significantly improved.

[0116] Figures 7 to 10 The performance comparison between the baseline configuration and the variable camber configuration in free cruise is shown. Further analysis of the effect of variable camber technology on the flight path during each profile flight shows that in step cruise, the drag and thrust required are reduced after adding variable camber technology. In general, the lift-to-drag ratio of the variable camber technology configuration is higher. In free altitude cruise, such as Figures 7 to 10 As shown in Figure 2, there are obvious differences between the profile data of the reference configuration and the variable camber configuration: the lift coefficient of the variable camber configuration in the middle stage is significantly larger, close to about 0.5 ( Fig. 9 ); The resistance and required thrust of the variable camber configuration are smaller ( Figure 8 ); The variable camber configuration has a higher lift-to-drag ratio over the entire range ( Fig.10). These results show that the addition of the variable camber system allows the vehicle to fly at a higher lift coefficient, thus achieving a higher lift-to-drag ratio.

[0117] In summary, this embodiment combines the variable camber technology with the trajectory optimization, and studies the gain of the comprehensive performance of the aircraft after adding the variable camber system under different cruise profiles. The results show that compared with the traditional wing, the addition of the variable camber system can improve the lift-to-drag ratio over the entire range, thereby increasing the range by about 1%. This result verifies the effectiveness and practicality of the method of the present invention in improving the performance of the aircraft.

[0118] Through the above embodiments, the purpose of the present invention is fully and effectively achieved. Those skilled in the art can understand that the present invention includes but is not limited to the contents described in the drawings and the above specific embodiments. Although the present invention has been described with respect to the most practical and preferred embodiments currently considered, it should be understood that the present invention is not limited to the disclosed embodiments, and any modification that does not deviate from the functional and structural principles of the present invention will be included in the scope of the claims.

Claims

1. A simulation analysis method for aircraft mission profile planning based on pseudo-spectral method, characterized in that: The method comprises at least the following steps when implemented: SS1. Construct a multidisciplinary mathematical analysis model for aircraft, including a flight dynamics sub-model, an aerodynamic sub-model including the effect of wing camber, a propulsion sub-model, and an atmospheric model; SS2. Define the state variable set, determine the trajectory and curvature control variable set, construct the trajectory optimization objective function, establish the dynamic constraint equations, set boundary conditions and path constraints, and establish the aircraft mission profile optimization problem; SS3. The mission profile is discretized using the pseudo-spectral method. First, the entire flight time interval is divided into several sub-intervals. Then, the pseudo-spectral method is applied in each sub-interval, and the appropriate distribution and number of collocation points are selected. Finally, the state variables and control variables in each sub-interval are approximated using Lagrange interpolation polynomials. SS4. Convert the optimal control problem into a nonlinear programming problem. First, use the Gauss quadrature formula to discretize the integral term in the objective function into the weighted sum of the function values ​​at the collocation points. Then use the differential matrix to discretize the dynamic constraint equation into algebraic constraints. Discretize the boundary conditions and path constraints at all collocation points, add sub-interval connection constraints, and finally formulate the optimal control problem as a standard nonlinear programming problem. Use the multidisciplinary coupled gradient calculation method to provide the objective function gradient and constraint gradient. SS5. Select the solver, provide initial guess solutions for the state variables and control variable values ​​at all collocation points, set the solver parameters and define the convergence criteria, use the multidisciplinary coupled gradient calculation method to provide accurate gradient information for the solver in each iteration, and iterate until the convergence criteria are met; SS6. Post-process and analyze the optimization results.

2. The method for simulation analysis of aircraft mission profile planning based on pseudospectral method according to claim 1, characterized in that: In step SS1, in each sub-model of the multidisciplinary mathematical analysis model: The flight dynamics sub-model uses a three-degree-of-freedom particle motion equation to describe the motion state of the aircraft, and at least includes the time evolution of the aircraft position, velocity, and mass parameters; The aerodynamic sub-model including the influence of wing camber is an aerodynamic proxy model constructed based on CFD simulation and combined with data sampling, and is used to describe the aerodynamic characteristics of the aircraft under different flight conditions under the wing camber control strategy; The power propulsion sub-model is a propulsion proxy model constructed based on the engine characteristic parameter table, which is used to evaluate the thrust output and fuel consumption characteristics of the aircraft engine under different flight conditions; The atmospheric model is a standard atmospheric model or a numerical weather forecast model, which is used to describe the variation of atmospheric parameters with altitude, including at least the vertical distribution of temperature, pressure, local sound speed and density parameters.

3. The pseudo-spectral method-based simulation analysis method for aircraft mission profile planning according to claim 2, characterized in that: In the above step SS1, the flight dynamics sub-model uses the mass point hypothesis to establish the dynamic equations of the longitudinal plane of the aircraft, and its mathematical expression is: in, r is the flight distance, h is the flight altitude, V is the flight speed, γ is the flight trajectory angle, m is the mass of the aircraft, T is the engine thrust, D For resistance, L For lift, α is the angle of attack, φ For engine mounting angle, g is the acceleration due to gravity, SFC is the fuel consumption rate; The aerodynamic sub-model including the influence of wing camber adopts a multi-fidelity Kriging proxy model, which is trained by combining high-fidelity and low-fidelity sample data, and its expression is: in y high is the high-fidelity model output, y low is the low-fidelity model output, ρ ( x ) is the scaling / correlation factor, δ ( x ) is the difference function, and the input variables of the proxy model include the Mach number Ma , Angle of Attack α and a plurality of variable camber parameters, wherein the variable camber parameters at least include a tail wing twist angle Twist tailH 、Twist angle of the first aileron Aileron1 、Twist angle of the second aileron Aileron2 、First flap twist angle Twist Flap1 and the second flap twist angle Twist Flap2 , the output variable of the model is the aerodynamic coefficient; The power propulsion sub-model is a Kriging propulsion proxy model built based on the engine characteristic parameter table. The input variable of the model is the Mach number Ma , Flight altitude h and engine speed N , the output variable is the engine thrust T and fuel consumption rate SFC .

4. The pseudo-spectral method-based aircraft mission profile planning simulation analysis method according to claim 1, characterized in that: In step SS2, during the process of establishing the aircraft mission profile optimization problem: Define a state variable set X, which is used to describe the flight state of the aircraft within the mission profile and includes at least the flight altitude h , Flight speed V , flight distance r and aircraft mass m ; Determine the track and curvature control variable set U. The track control variables are the parameters that need to be adjusted during the track optimization process, including the Mach number Ma, the angle of attack α ,thrust T And variable curvature parameters δ , variable curvature parameter δ At least including the tail twist angle Twist tailH 、Twist angle of the first aileron Aileron1 、Twist angle of the second aileron Aileron2 、First flap twist angle Twist Flap1 and the second flap twist angle Twist Flap2 ; Construct the trajectory optimization objective function J, and select minimizing fuel consumption, maximizing range, minimizing flight time or their weighted combination to define the goal of the optimization problem according to the mission requirements; Establishing the dynamic constraint equations f (X, U, t ), describes the relationship between state variables and track control variables, and constrains the changes of state variables and track control variables; Setting boundary conditions and path constraints g (X, U, t ), including at least initial state constraints, terminal state constraints and flight envelope constraints, to ensure that the aircraft remains within a safe and controllable range throughout the mission profile.

5. The pseudo-spectral method-based aircraft mission profile planning simulation analysis method according to claim 1, characterized in that: In step SS3, the multi-stage Radau pseudo-spectral method is used to discretize the mission profile, including the following sub-steps: SS31. The entire flight time interval will be continuous. t 0, t f ] is divided into N Subintervals[ t i , t i+1 ],in t 0. t f are the start time and end time of the flight mission respectively. t i , t i+1 are the start and end time of each sub-interval, N is the number of subintervals, i =0, 1,..., N -1; SS32. For each subinterval [ t i , t i+1 ] is transformed into the time domain and mapped to the standard interval [-1, 1]; SS33. Apply the Radau pseudospectral method in each subinterval and select K LGR points; SS34. Use K -1st order Lagrange interpolation polynomial approximates the state variable X( t ) and the control variable U( t ), discretize continuous variables into node values.

6. The pseudo-spectral method-based aircraft mission profile planning simulation analysis method according to claim 5, characterized in that: Step SS4 includes at least the following sub-steps when implemented: SS41. Use Gauss quadrature formula to convert the objective function The integral term in is discretized into the weighted sum of the function values ​​at the collocation points ,in w i is the Gauss product weight, τ i Assign points to LGR; SS42. Using the Radau pseudospectral method, the differential matrix D is transformed into the dynamic constraint equations. Discretization into algebraic constraints , where X and U are the vectors of state variables and control variables at all collocation points, respectively; SS43. Apply boundary conditions and path constraints At each distribution point τ i The discretization is: SS44. For any two adjacent subintervals [ t i , t i+1 ]and[ t i+1 , t i+2 ], add a subinterval connection constraint X between its end and beginning end -X start = 0, where X end For the subinterval [ t i , t i+1 ]’s terminal state variable, X start For the subinterval [ t i+1 , t i+2 ]’s initial state variable; SS45. The discretized optimal control problem is expressed as a standard NLP problem, which is expressed as: The constraints include: SS46. Use multidisciplinary coupled gradient computation methods to provide objective function gradients and constraint gradients for nonlinear programming problems.

7. The pseudo-spectral method-based simulation analysis method for aircraft mission profile planning according to claim 6, characterized in that: In sub-step SS46, the multidisciplinary coupling gradient calculation method uses the numerical model unified formula derivative equation to calculate the gradient of the optimization objective function J to the design variable x, specifically including: SS461. All input design variables, state variables, control variables and output variables are combined into a vector Z=(x,X,U,f) through the unified formula of the numerical model, where x represents the set of input design variables, X represents the set of state variables, U represents the set of control variables, and f represents the set of output variables; SS462. Define the residual equation R(Z)=0 associated with the vector Z, where R=(R x ,R X ,R U ,R f ), R x , R X , R U , R f are the residual equations corresponding to the input design variable x, state variable X, control variable U and output variable f respectively; SS463. Solve the unified derivative equation of the residual equation R with respect to the combination vector Z: Among them, the derivative of the combination vector Z with respect to the design variable x is contains the gradient of the output variable to be calculated with respect to the design variable , the gradient of the state variable with respect to the design variable and the gradient of the control variable with respect to the design variable ; SS464. Choose to solve the forward system or the inverse system based on the relative size of the output variable set f and the input design variable set x: when n f < n x When , solve the forward system , when n f ≥ n x When , solve the inverse system , in n f , n x are the dimensions of the output variable set f and the input design variable set x respectively; SS465. Using the adjoint method to calculate the derivative of the objective function J with respect to the design variable x, we first construct an adjoint vector λ that does not depend on the design variable and satisfies the adjoint equation , then calculate the derivative of the objective function J with respect to the design variable x ; SS466. For the track control variables and the variable curvature control variables in the control variable set U, calculate their gradients to the objective function J: SS467. In each pseudo-spectral discretized subinterval, the gradients of the state variable X and the control variable U with respect to the design variable x are calculated using the Lagrange interpolation polynomial: Among them, L i is the Lagrange interpolation polynomial, X i and U i are the state variable and control variable values ​​at the i-th collocation point respectively; SS468. For constraints at the junctions of subintervals, compute the gradients associated with the junction constraints: Where C is the connection constraint, X end , X start are the values ​​of the state variables at the end and beginning of adjacent subintervals.

8. The pseudo-spectral method-based aircraft mission profile planning simulation analysis method according to claim 1, characterized in that: In step SS5, a method of selecting a solver suitable for a large-scale sparse nonlinear programming problem and iteratively solving the problem to achieve an optimal control problem includes: SS51. Select a nonlinear programming solver, including SNOPT, IPOPT or KNITRO; SS52. Provide an initial guess solution for the state variables X and the control variables U at all points, wherein the initial guess solution is generated based on experience or pre-calculation; SS53. Set solver parameters, including maximum number of iterations, tolerance and / or step size control parameters, and define convergence criteria; SS54. In each iteration, a multidisciplinary coupled gradient calculation method is used to provide gradient information to the solver, where the gradient expression of the objective function J with respect to the design variable x is: , λ is the adjoint variable, R is the residual vector, and λ is obtained by solving the linear adjoint equation system Obtain, where Z is the combination vector Z=(x,X,U,f), x is the set of input design variables, X is the set of state variables, U is the set of control variables, and f is the set of output variables; SS55. The solver optimizes the objective function and constraints based on the provided gradient information and set parameters, and updates the values ​​of state variables and control variables; SS56. Iterate the solution until the convergence criterion is met, and check the terminal state constraints, path constraints, and dynamic constraints at the collocation points: If all constraints meet the allowable relative error conditions, solve the nonlinear programming problem transformed by the pseudo-spectral method; if the constraints are not met, increase the number of discrete points in each stage and iterate the solution again until all constraints are met.

9. The pseudo-spectral method-based aircraft mission profile planning simulation analysis method according to claim 1, characterized in that: In step SS6, the method for post-processing and analyzing the optimization results includes: reconstructing the discrete solution obtained by optimization into a continuous trajectory, and interpolating the discrete points into a continuous curve by Lagrange interpolation or spline interpolation method; calculating key performance indicators, including total fuel consumption, flight time, maximum speed and / or minimum altitude; verifying whether the final solution meets all constraints; comparing the optimal trajectory and performance indicators with and without variable curvature control, and quantifying the impact of variable curvature on flight performance.

10. The pseudo-spectral method-based aircraft mission profile planning simulation analysis method according to claim 1, characterized in that: In step SS6, post-processing and analysis of the optimization results also include: Perturb key parameters and analyze their impact on the optimal solution to evaluate the sensitivity of the optimization results to parameter changes; consider uncertainty factors, including at least atmospheric disturbances and aerodynamic parameter errors, and ensure the robustness of the optimization scheme by analyzing the impact of uncertainty factors on the optimization results; use the Monte Carlo method for evaluation, use a large number of random samples to simulate the impact of uncertainty factors, and evaluate the stability and reliability of the optimization results under different disturbance conditions through statistical analysis.

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