A Trajectory Optimization Method for Variable Camber of a Blended Wing Body Aircraft

Abstract

The present invention provides a trajectory optimization method for variable camber of a blended wing body aircraft. Based on the blended wing body aircraft, the variable camber design is combined with the flight path planning, covering the non-linear optimal control problem of state constraints and control constraints. The parameterization method is selected to transform the optimal control problem in the continuous space into a non-linear programming, and the pseudo-spectral method, which can obtain a higher solution accuracy at a smaller computational cost in the direct method, is used to solve the trajectory optimization problem. The present invention incorporates the trajectory optimization into the multidisciplinary optimization of the aircraft, thereby dynamically combining and matching each subsystem, considering the influence of the time history of each system, exploring the best deformation trend / schedule during the entire cruise mission, and quantifying the potential benefits of the variable camber blended wing body aircraft throughout the flight mission.

Description

Technical Field

[0001] The present invention discloses a trajectory optimization method for variable camber of a blended wing body aircraft, which relates to the fields of aircraft aerodynamic design, aircraft trajectory optimization, and neural network modeling, and is mainly applied to the design field of variable camber of a blended wing body aircraft. Background Art

[0002] After years of development, the current conventional layout form of a cylindrical fuselage plus wings has difficulty in further improving the aerodynamic efficiency. The aggressive goals of green aviation, namely "energy conservation, emission reduction, and noise reduction", have promoted the overall innovation of civil aviation technology. A series of unconventional layouts have become the common research direction of various countries. Among them, the blended wing body (BWB) layout has attracted wide attention due to its high cruise efficiency, light structural weight, high fuel efficiency, low noise, etc., and has become the mainstream solution for the next generation of subsonic civil aircraft.

[0003] Aircraft design is usually a compromise choice considering various flight conditions. For many years, people have been exploring the possibility of changing the wing shape during flight so that the aircraft can always maintain good performance. Among them, the technology of continuously variable camber trailing edge has been widely studied. On the one hand, compared with other wing camber change methods, the trailing edge deformation has less impact on the internal structural components of the wing and is easy to implement. On the other hand, through the optimization and comparison research on the fully deformed wing and the wing with only the trailing edge deformed, it is found that most of the improvement in aerodynamic performance can be obtained by only deforming the wing trailing edge.

[0004] The design of variable camber of the wing trailing edge enhances the ability of the aircraft to adapt to various flight conditions. Combining it with a BWB layout aircraft, it is expected that the aircraft can maintain the best flight performance throughout the whole flight range to fully exert the advantage of high aerodynamic efficiency of the BWB layout. However, since the BWB layout aircraft cancels the traditional horizontal tail and vertical tail, its control surfaces are mainly arranged at the trailing edge part of the fuselage, and the longitudinal force arm is shorter than that of the conventional layout aircraft. When the same pitching moment needs to be trimmed, the BWB layout will pay a greater trim drag penalty.

[0005] Furthermore, considering that the trailing edge control surface can only deflect continuously during dynamic flight, the BWB layout may not always maintain the best aerodynamic shape to continuously obtain the optimal aerodynamic benefit. Therefore, how much actual benefit the variable camber wing can bring still needs further research.

[0006] Traditional aircraft design adopts a serial design concept. Designers first select different key disciplines to design and optimize the aircraft according to the mission profile, and then optimize its flight trajectory. This approach essentially artificially separates the static and dynamic design variables that should be coupled together, ignoring the influence of the time history of each system state on the overall performance of the aircraft, and thus is very likely to lose the overall optimal solution. Summary of the Invention

[0007] In view of the above problems, considering that the overall performance of the aircraft during mission execution is related to the mission profile and flight trajectory, an accurate connection is established between the trailing-edge bending angle of the aircraft and its aerodynamic characteristics. At the same time, trajectory optimization is incorporated into the multidisciplinary optimization of the aircraft, thereby dynamically combining and matching each subsystem, effectively improving the overall performance of the aircraft during mission execution, which is of great significance and practical engineering value for the design of the aircraft.

[0008] Therefore, the present invention proposes a trajectory optimization method for a variable-camber aircraft. By combining deformation simulation with trajectory optimization, the influence of the time history of each system is considered, the optimal deformation trend / timetable during the entire cruise mission is explored, and the potential benefits of the variable-camber BWB layout aircraft throughout the flight mission are quantified.

[0009] To quantify the mission benefits that can be obtained by improving the BWB layout aircraft with variable-camber technology, the present invention provides a variable-camber trajectory optimization method for a wing-body blended layout aircraft, in order to provide certain technical support for the design of the wing-body blended layout aircraft.

[0010] The core content of the present invention is as follows: An optimization method that combines variable-camber design with trajectory planning is proposed.

[0011] Regarding the trajectory optimization as a non-linear optimal control problem covering state constraints and control constraints, a direct method is selected to transform the optimal control problem in the continuous space into a non-linear programming problem through a parameterization method and obtain the optimal solution by combining with a non-linear programming algorithm.

[0012] Specifically, the pseudo-spectral method, which can obtain a higher solution accuracy with a smaller computational cost in the direct method, is used to solve the trajectory optimization problem.

[0013] To achieve the above object, the technical solution adopted by the present invention is:

[0014] A variable-camber trajectory optimization method for a wing-body blended layout aircraft, comprising the following steps:

[0015] Step 1: Using the Kriging surrogate model method, based on neural networks, establish a Kriging variable-camber aerodynamic surrogate model to establish a relatively accurate connection between the trailing-edge bending angle of the aircraft wing and the aerodynamic characteristics of the wing-body blended layout aircraft, including:

[0016] Step 1.1: Construct an aerodynamic database for the trailing-edge camber of the aircraft wing, obtain the initial sample points, and the relationship between the input and output of the initial sample points;

[0017] Step 1.2: Allocate the training set, test set, and validation set based on the relationship between the input and output of the initial sample points;

[0018] Step 1.3: Train the Kriging variable camber aerodynamic surrogate model based on the neural network using the training set, test set, and validation set to quickly evaluate the aerodynamic performance of the wing-body blended layout aircraft under given flight conditions and the wing trailing edge camber angle of the aircraft during trajectory optimization;

[0019] Step 1.4: Examine the accuracy of the Kriging variable camber aerodynamic surrogate model through cross-validation. If the accuracy does not meet the requirements, return to Step 1.1;

[0020] Step 2: Establish a multidisciplinary analysis model for the coupled loop in trajectory optimization using a parameterization method to incorporate trajectory optimization into the multidisciplinary optimization of the aircraft, and dynamically combine and match each sub-model. The sub-models of the multidisciplinary analysis model include the flight dynamics model, aircraft weight model, fuel weight model, and propulsion surrogate model;

[0021] Step 3: Solve the cruise constant altitude flight trajectory optimization using the Radau pseudospectral method based on the Kriging variable camber aerodynamic surrogate model and the multidisciplinary analysis model, including: converting the continuous flight time interval of the wing-body blended layout aircraft into a grid interval, solving the Radau pseudospectral differential matrix of the grid interval, converting the dynamic differential equation constraints of the continuous flight time optimal control problem of the wing-body blended layout aircraft into algebraic constraints, and converting the continuous flight time optimal control problem of the wing-body blended layout aircraft into a nonlinear programming problem;

[0022] Step 4: Solve using an optimization algorithm.

[0023] In the said Step 1, the method for obtaining the initial sample points and the relationship between the input and output of the initial sample points is as follows:

[0024] Step 1.1.1: Sample within the design parameter space through experimental design and obtain the initial sample points;

[0025] Step 1.1.2: Adopt the fixed-axis deflection method and use the parameterization method to achieve the variable camber of the wing trailing edge of the aircraft, obtain the wing trailing edge camber angle of the aircraft for the initial sample points as the input of the initial sample points;

[0026] Step 1.1.3: Generate the grid after the variable camber of the trailing edge of the aircraft through the inverse distance weighted dynamic grid technology;

[0027] Step 1.1.4: Calculate the grid after the trailing edge camber change of the aircraft through the aerodynamic solver, and obtain the aerodynamic coefficients of the initial sample points as the outputs of the initial sample points.

[0028] In the said Step 1, the expression of the Kriging camber change aerodynamic surrogate model is:

[0029] ,

[0030] where the symbol represents the surrogate model, CL is the lift coefficient, CD is the drag coefficient, CM is the moment coefficient, mach is the Mach number, alt is the flight altitude, alpha is the angle of attack, and flapi is the trailing edge camber angle.

[0031] In the said Step 2, the flight dynamics model, the aircraft weight model, the fuel weight model, and the propulsion surrogate model are successively expressed as:

[0032]

[0033] where range is the range, alt is the flight altitude, V is the flight speed, is the track angle, and α is the angle of attack; L, D, T, m are respectively the lift, drag, thrust, and weight, g is the acceleration due to gravity, and the symbol represents the derivative of this term with respect to time, is the total design weight of the aircraft, is the crew weight, is the payload weight, is the fuel weight, is the empty weight of the aircraft, is the fuel consumption rate per second, SFC is the specific fuel consumption rate, T max is the maximum thrust, mach is the Mach number.

[0034] In the said Step 3, the calculation method for solving the cruise constant altitude flight trajectory optimization using the Radau pseudospectral method is:

[0035] Step 3.1: Convert the continuous flight time interval into the grid interval:

[0036] Step 3.1.1: Divide the continuous flight time interval into K grid intervals,

[0037] where is the start time of the continuous flight time interval, is the end time of the continuous flight time interval;

[0038] Step 3.1.2: Within each grid interval of the K grid intervals the time range can be transformed by the transformation formula into The transformation formula is:

[0039] ,

[0040] where k is the k-th grid interval of the K grid intervals, , , is the collocation point within the grid interval;

[0041] Step 3.2: Using the Radau pseudospectral method, within the k-th grid interval select N LGR collocation points. The N LGR collocation points , , ,

[0042] where the N LGR collocation points are the roots of the polynomial, is the N-th order orthogonal polynomial:

[0043] ;

[0044] Step 3.3: Using the N LGR collocation points as nodes to construct the global interpolation polynomial of the state variable, compensating the terminal collocation point during the interpolation of the global interpolation polynomial of the state variable The state variable is constructed by using N + 1 Lagrange interpolation polynomials as:

[0045] ,

[0046] where, is the state variable, is the Lagrange interpolation basis function;

[0047] Step 3.4: Using the N LGR collocation points as nodes to construct the global interpolation polynomial of the control variable. The control variable is constructed by using N of the Lagrange interpolation polynomials as:

[0048] ,

[0049] where, is the control variable;

[0050] Step 3.5: Differentiate the global interpolation polynomial of the state variable to obtain the derivative of the state variable:

[0051] ,

[0052] where is the Radau pseudospectral differentiation matrix at the k-th grid interval, and discretize the derivative of the state variable at the N LGR collocation points to obtain the discretized form of the state variable:

[0053] ;

[0054] Step 3.6: Use Lagrangian integration to replace the integral term of the objective function to obtain the discretized form of the objective function:

[0055] ,

[0056] where J is the objective function, are the Lagrangian polynomial coefficients;

[0057] Step 3.7: Discretize the path constraint function C[S(t), U(t), t] at the N LGR collocation points in the k-th grid interval to obtain the discretized form of the path constraint function:

[0058] .

[0059] In step 4, the optimization algorithm is the sequential quadratic programming (SQP) algorithm. Description of the Drawings

[0060] Figure 1 is the flow chart of the present invention.

[0061] Figure 2 is the geometric diagram of the blended wing-body aircraft in the present invention.

[0062] Figure 3 is the surface pressure distribution and streamline diagram at the design point of the baseline configuration in the present invention.

[0063] Figure 4 is the rudder surface division diagram of the baseline configuration in the present invention.

[0064] Figure 5 is the FFD control volume of the trailing edge deflection and the variable camber deflection effect diagram of the baseline configuration in the present invention.

[0065] Figure 6 is the relationship diagram between the pseudospectral method and the original trajectory optimization problem in the present invention.

[0066] Figure 7It is a schematic diagram of the characteristic curve of the thrust and fuel consumption rate of the turbofan engine in the present invention.

[0067] Figure 8 It is the comparison of the trajectories before and after the variable camber of the reference configuration during constant-altitude flight in the present invention. Detailed implementation manners

[0068] Now, the present invention will be further described in detail in combination with the method embodiments. The following will further describe the present invention in detail with reference to the drawings and specific embodiments. The following embodiments are only descriptive and not restrictive, and the protection scope of the present invention cannot be limited thereby.

[0069] As Figure 1 shown in the process schematic diagram, the trajectory optimization of the blended wing-body layout aircraft using the variable camber technology consists of the following steps.

[0070] Step 1: Construct an aerodynamic surrogate model for the variable camber of the trailing edge of the aircraft wing.

[0071] The aircraft with variable camber at the trailing edge of the wing will adaptively change its aerodynamic shape according to different flight conditions. The flight conditions are the state information of the aircraft, including flight altitude, flight speed, Mach number, trajectory angle, aircraft weight, etc. Therefore, in order to update and match the aerodynamic characteristics of the aircraft with different shapes in a timely manner during trajectory analysis, the present invention uses the Kriging surrogate model method to establish a Kriging variable camber aerodynamic surrogate model.

[0072] As Figure 2 shown, for the blended wing-body layout aircraft, the span of the reference configuration is 65.5 m, the fuselage length is 41 m, and the reference area is 849.51 square meters. Its designed cruise state is: Mach number (Ma) Ma = 0.84, lift coefficient C L = 0.19, Reynolds number (Re) Re = 12.94 million. The moment is self-trimmed at its design point, the cruise angle of attack is 3.12°, the drag coefficient C D = 90.4 counts, and the lift-to-drag ratio is 21.02. Figure 3 shows the pressure contour and streamline distribution on the upper surface of the wing at the design point. As can be seen from Figure 3 it, the pressure distribution in the central body and the wing-body transition region is basically shock-free, there is a weak shock wave in the outer wing section, and there is no separation in the entire surface streamline.

[0073] Step 1.1: Construct an aerodynamic database for the variable camber of the trailing edge of the aircraft wing.

[0074] As Figure 1Aerodynamic database sampling process for the trailing edge camber change of the wing shown in the left half. Samples are taken within the design parameter space through design of experiments to obtain the initial samples of the design parameters. Then, the trailing edge camber of the BWB configuration is achieved through parametric methods in a fixed-axis deflection manner, and the mesh of the wing trailing edge with camber change of the aircraft is automatically generated by the dynamic mesh technology and provided to the aerodynamic solver for calculation to obtain the aerodynamic coefficients of the initial sample points.

[0075] The rudder surface division used when the trailing edge of the wing of the aircraft with the baseline shape has camber change is as Figure 4 shown. Six control rudders are arranged along the span direction, including one rudder at the trailing edge of the central body and five rudders at the trailing edge of the wing. In the present invention, the deflection angle (rudder deflection angle) range of each rudder is [-4°, +4°], and it is specified that downward deflection is positive and upward deflection is negative.

[0076] The trailing edge camber change of the aircraft wing is achieved in a fixed-axis deflection manner, and the parameterization of the trailing edge camber is realized through the Free-Form Deformation (FFD) method. The FFD method realizes the geometric parameterization process based on the idea of the deformation of an elastic body under force. The FFD control volume is constructed through the FFD method, and the constructed FFD control volume and the effects before and after deflection are as Figure 5 shown. It can be seen that the wing surface after camber change still maintains the characteristics of continuity and smoothness.

[0077] Among them, the basic idea of the FFD parameterization method is to parameterize the deformation amount of the object to be deformed to achieve the purpose of controlling the deformation. It avoids parameterizing the geometric shape itself, greatly reduces the dependence on the data format and layout form of the initial configuration, and can smoothly describe the shapes of curves, surfaces and three-dimensional geometric bodies, and is conveniently applied to the overall and local shape design.

[0078] And the mesh of the aircraft trailing edge with camber change is automatically generated by the Inverse Distance Weighted (IDW) dynamic mesh technology and provided to the aerodynamic solver for calculation to obtain the aerodynamic coefficients of the initial sample points.

[0079] Among them, the aerodynamic solver uses the computational fluid dynamics (CFD) flow field simulation method based on the Reynolds-Averaged Navier-Stokes (RANS) equation, adopts the implicit time marching method, the Jameson-Schmidt-Turkel second-order central space discretization format, and the Shear Stress Transport turbulence model.

[0080] Step 1.2: For the problem of high non - linearity between the shape and aerodynamic characteristics during the process of variable camber at the trailing edge of the aircraft wing due to the influence of shock waves, select to establish a relatively accurate relationship between the variable camber angle at the trailing edge of the aircraft wing and the aerodynamic characteristics of the wing - body blended layout aircraft based on the Kriging surrogate model method.

[0081] Based on the relationship between the input and output of the initial sample points, allocate the training set, test set, and validation set. Those skilled in the art can select the allocation ratio of the training set, the test set, and the validation set according to experience. For example, the allocation ratio of the training set, the test set, and the validation set is 0.9:0.07:0.03. Among them, the input of the initial sample points is the variable camber angle at the trailing edge of the aircraft wing , and the output is the aerodynamic force coefficient.

[0082] And based on the training set, the test set, and the validation set, train the Kriging variable - camber aerodynamic surrogate model based on the neural network. Realize the rapid evaluation of the aerodynamic performance under given flight conditions and configurations during trajectory optimization. The expression of the Kriging variable - camber aerodynamic surrogate model is:

[0083] (1), the symbol represents the surrogate model, .

[0084] Among them, C L is the lift coefficient, C D is the drag coefficient, C M is the moment coefficient, mach is the Mach number, alt is the flight altitude, alpha is the angle of attack, flap i is the trailing - edge variable camber angle.

[0085] Considering that during the analysis process, it is necessary to update and match the performance of each subsystem in a timely manner, construct models of each subsystem through empirical formulas or surrogate model methods to improve the optimization efficiency.

[0086] Since the pseudo - spectral method requires the derivative information of the output with respect to the input provided by each system when solving the trajectory. Use the surrogate modeling toolbox (SMT) to construct the Kriging variable - camber aerodynamic surrogate model, so as to obtain the corresponding aerodynamic performance according to the input rudder deflection combination, and at the same time, obtain the derivatives of each aerodynamic performance with respect to each control surface. Use the SMT toolbox to construct the Kriging variable - camber aerodynamic surrogate model to quickly obtain the maximum thrust, specific fuel consumption rate at a given altitude and Mach number, and their derivatives with respect to altitude and Mach number.

[0087] Step 1.3: Examine the accuracy of the Kriging variable camber aerodynamic surrogate model through cross-validation. If the accuracy does not meet the requirements shown in Table 1, repeat Steps 1.1 to 1.2, add the initial sample points, and retrain the Kriging variable camber aerodynamic surrogate model until the accuracy meets the requirements. Finally, obtain the variable camber deflection angle and aerodynamic coefficient of the optimal configuration.

[0088] In the present invention, the requirements that the Kriging variable camber aerodynamic surrogate model needs to meet are shown in Table 1. According to the method of the present invention, the accuracy of the performance of the Kriging variable camber aerodynamic surrogate model meets the requirements in Table 1, and a relatively accurate relationship between the variable camber angle of the trailing edge of the aircraft wing and the aerodynamic characteristics of the wing-body fusion configuration can be obtained.

[0089] Table 1 Accuracy requirements that the Kriging variable camber aerodynamic surrogate model needs to meet

[0090] Mean Absolute Error (MAE) Mean Relative Error (MRE) <![CDATA C L > < 5e-3 <5% <![CDATA C D > < 2e-4 <5% <![CDATA C M > < 1e-3 <5%

[0091] The performance evaluation results of the Kriging variable camber surrogate model in the present invention are shown in Table 2, and the accuracy meets the requirements.

[0092] Table 2 Evaluation results of the performance of the Kriging variable camber surrogate model.

[0093] Mean Absolute Error (MAE) Mean Relative Error (MRE) <![CDATA C L > 2e-3 < 5e-3 3.44% <![CDATA C D > 1.5e-4 < 2e-4 2.91% <![CDATA C M > 9.6e-4 < 1e-3 2.56%

[0094] Step 2: Establish other multidisciplinary analysis models for the coupling loop in trajectory optimization. The specific steps are as follows:

[0095] Step 2.1: Establish a flight dynamics model.

[0096] The present invention only considers the case where the aircraft flies in the vertical plane and assumes that the engine installation angle is 0 and the thrust is in the same direction as the flight trajectory. range is the range, alt is the flight altitude, velocity is the flight speed (abbreviated as V ), gam is the trajectory angle (abbreviated as ); alpha is the angle of attack (abbreviated as α), L, D, T, m are the lift, drag, thrust, and weight respectively, g is the acceleration due to gravity, and the symbol "" represents the derivative of this term with respect to time. The present invention does not consider the case of the existence of a wind field. The mathematical expression of the unsteady motion equation of the aircraft flying in the vertical plane is, that is, the equation of the flight dynamics model is:

[0097] (2)

[0098] Step 2.2: Establish a weight model.

[0099] The total design weight of the aircraft, including the crew weight, payload weight, fuel weight, and empty aircraft weight, is expressed by the following equation:

[0100] (3)

[0101] Where, is the total design weight of the aircraft, is the crew weight, is the payload weight, is the fuel weight, is the empty aircraft weight.

[0102] Where, the total design weight of the aircraft , and g is the acceleration due to gravity.

[0103] Step 2.3: Establish a fuel weight model.

[0104] Since the fuel weight decreases with time during flight, the fuel consumption rate per second can be obtained by multiplying the thrust by the specific fuel consumption per unit thrust:

[0105] (4)

[0106] Where, SFC is the specific fuel consumption rate.

[0107] Where, the relationship between the weight model and the fuel weight model is that the fuel weight .

[0108] Step 2.4: Establish a propulsion surrogate model.

[0109] Two large bypass ratio turbofan engines actually used in engineering are adopted, and the engines are simplified, ignoring the fuel consumption differences at different speeds and the influence of the throttle coefficient. It is assumed that the engines always operate at 95% speed during the cruise mission trajectory optimization process of the present invention. At this time, the maximum thrust T max , the specific fuel consumption rate SFC are only related to the altitude alt , Mach number mach . Based on the engine speed-altitude characteristic parameter table, the propulsion surrogate model is constructed in this paper:

[0110] (5)

[0111] Where, ，h is in hours as the time unit.

[0112] The characteristic curves of the thrust and fuel consumption rate of a single engine obtained based on the propulsion agent model are as Figure 7 shown.

[0113] In this step, the equations of the flight dynamics model give the relationships satisfied among parameters such as the range, flight altitude, flight speed, and weight of the aircraft. The fuel weight in the aircraft weight model is constrained by the fuel weight model. The propulsion agent model gives the constraint relationships among thrust, Mach number, and flight altitude, as well as the constraint relationships between fuel consumption rate and Mach number and flight altitude.

[0114] In addition, those skilled in the art can know that the flight altitude, flight speed, and Mach number of the aircraft satisfy certain constraint relationships. At the same speed of the aircraft, its Mach number will vary due to the different speed of sound in the air at the altitude. The higher the altitude, the lower the speed of sound, and the higher the Mach number, so the flight speed at high altitude will decrease to avoid shock.

[0115] Therefore, there is a parameter constraint relationship between the Kriging variable camber aerodynamic agent model in step 1 and the multidisciplinary analysis model in step 2.

[0116] The present invention incorporates trajectory optimization into the multidisciplinary optimization of the aircraft by establishing a multidisciplinary analysis model and selects to transform the optimal control problem in the continuous space into a nonlinear programming through a parameterization method.

[0117] Step 3: Solve the cruise constant altitude flight trajectory optimization by the pseudospectral method.

[0118] In the present invention, referring to Figure 1 , after establishing the Kriging variable camber aerodynamic agent model and the multidisciplinary analysis model in step 1 and step 2, based on the dynamically generated Kriging variable camber aerodynamic agent model and the multidisciplinary analysis model, the method of step 3 is used to solve the objective function value of the aircraft performance, and the dynamic differential equation constraint of the continuous-time optimal control problem is transformed into an algebraic constraint. The influence of the time history of each system of the aircraft is considered, and the potential benefits of the entire flight mission of the variable camber BWB layout aircraft are quantified.

[0119] In the present invention, there is no requirement for the order of establishing the Kriging variable camber aerodynamic agent model and the multidisciplinary analysis model in step 1 and step 2. Step 3 performs trajectory optimization based on the models in step 1 and step 2. At the same time, according to the flight state of the aircraft, the parameter values of the models in step 1 and step 2 are dynamically changed, and step 3 performs dynamic trajectory optimization based on the changed Kriging variable camber aerodynamic agent model and the multidisciplinary analysis model.

[0120] In the present invention, the cruise mission of the aircraft is set to fly at a constant altitude of 11.5 km for 15,000 km. This case is used to study the performance of the aircraft during level flight at the designed altitude. The initial Mach number is set to Ma = 0.84, and the Mach number constraint range is Ma = 0.8 - 0.86. The optimization problem is shown in Table 3. Among them, for the baseline configuration, only the trailing edge bending angle of the central body flap 0 is used for trimming, while for the variable camber configuration, all the trailing edge control surfaces are involved in trimming.

[0121] Table 3 Trajectory optimization problem of variable camber during constant altitude flight

[0122]

[0123] The specific steps are as follows:

[0124] Step 3.1: Time interval conversion.

[0125] The continuous flight time interval of the wing-body blended layout aircraft is divided into K grid intervals.

[0126] Among them, is the start time of the continuous flight time interval, is the end time of the continuous flight time interval.

[0127] Within the k-th grid interval , the time range can be transformed by the transformation formula into , where, , k is the k-th grid interval among the K grid intervals, is the collocation point within the grid interval.

[0128] The transformation formula is: (6)

[0129] Step 3.2: Discretization of state variables and control variables.

[0130] Using the Radau pseudospectral method, within the k-th grid interval , the state variables and control variables are discretized at the Legendre Gauss-Radau (LGR) points. Select N LGR collocation points , where, , is the N-th order orthogonal polynomial:

[0131] (7)

[0132] Construct a global interpolation polynomial of the state variable and the control variable with these discrete collocation points as nodes. Since the LGR collocation points include the starting point but not the ending point, in order to ensure the complete mapping of the physical continuous time interval and the time interval in the pseudospectral method, compensate for the terminal collocation points when constructing the global interpolation polynomial of the state variable , so that the terminal state integral constraint does not need to be considered. Therefore, the state variable is constructed by using N + 1 Lagrange interpolation polynomials as:

[0133] (8)

[0134] where is the state variable, is the Lagrange interpolation basis function.

[0135] The dynamic equation holds only at the LGR collocation points, so the interpolation nodes of the control variable only include the N LGR collocation points, and the control variable is constructed by using N Lagrange interpolation polynomials as:

[0136] (9)

[0137] where is the control variable, is the Lagrange interpolation basis function.

[0138] Step 3.3: Discretize the state variable. In the pseudospectral method, since the state variable is approximated by the N + 1 Lagrange interpolation polynomials, the derivative of the state variable can be obtained by taking the derivative of the N LGR collocation points:

[0139] (10)

[0140] where is the Radau pseudospectral differential matrix at the k-th grid interval. Discretize the above formula at the N LGR collocation points to get:

[0141] (11)

[0142] Step 3.4: Discretize the objective function and the path constraint function. By using Lagrange integration to replace the integral term of the objective function for the dynamic differential equation of the continuous-time optimal control problem, the objective function can be discretized as:

[0143] (12)

[0144] where J is the objective function, is the Lagrange polynomial coefficient.

[0145] The path constraint function C[S(t), U(t), t] is discretized at the N LGR collocation points in the k-th grid interval to obtain:

[0146] (13)

[0147] The present invention uses a differential matrix to transform the dynamic differential equation constraints of the continuous flight time optimal control problem of the wing-body blended layout aircraft into algebraic constraints, and transforms the continuous-time optimal control problem of the BWB aircraft into a nonlinear programming problem.

[0148] Step 4: Finally, an optimization algorithm is used for solution.

[0149] The present invention can be programmed in the MATLAB environment and solved in combination with the SNOPT toolkit, or it can also be solved based on other compilers using the SNOPT toolkit through the Python software package. The SNOPT is a toolkit for quickly solving large-scale nonlinear optimization problems, and its main core algorithm is the sequential quadratic programming (SQP) algorithm. The optimization algorithm in the present invention is not limited to the sequential quadratic programming (SQP) algorithm, and those skilled in the art can select an algorithm for solving the nonlinear programming problem according to needs, such as the interior point method.

[0150] The comparison of the constant altitude flight results is shown in Figure 8 , compared with the 79.49 kg of fuel consumed during the flight of the baseline configuration, the variable camber configuration only consumes 77.45 kg of fuel, saving 2.6% of fuel consumption. After adding the variable camber technology, the thrust required throughout the process is reduced, and the changes in altitude and speed become smoother, improving the flight stability. Generally, the lift-to-drag ratio of the variable camber technology configuration is higher throughout the whole flight. After adding the variable camber technology, the overall performance of the aircraft performing the mission is improved significantly, and it can be considered that this improvement only includes the improvement of the aerodynamic performance by the trailing edge variable camber technology.

[0151] In summary, in the variable camber trajectory optimization method of the wing-body blended layout aircraft proposed by the present invention, the optimization results of the embodiments show that the method of the present invention achieves the design intention, combines the variable camber design of the wing-body blended layout aircraft with the trajectory planning, and intuitively and clearly quantifies the potential benefits that can be brought by using the variable camber technology on the wing-body blended layout aircraft.

Claims

1. A method for optimizing the trajectory of a wing-body fusion layout aircraft with variable curvature, characterized in that: The steps are as follows: Step 1: Using the Kriging proxy model method, based on the neural network, a Kriging variable camber aerodynamic proxy model is established to establish a more accurate relationship between the wing trailing edge camber angle of the aircraft and the aerodynamic characteristics of the wing-body blended layout aircraft, including: Step 1.1: constructing an aerodynamic database of the variable curvature of the wing trailing edge of the aircraft, obtaining initial sample points, and the relationship between the input and output of the initial sample points; Step 1.2: Based on the relationship between the input and output of the initial sample point, a training set, a test set, and a validation set are allocated; Step 1.3: Based on the training set, the test set and the validation set, the neural network-based Kriging variable camber aerodynamic proxy model is trained to quickly evaluate the aerodynamic performance of the wing-body blended layout aircraft under given flight conditions and the wing trailing edge camber angle of the aircraft during trajectory optimization; Step 1.4: Check the accuracy of the Kriging variable curvature aerodynamic proxy model by cross-validation. If the accuracy does not meet the requirements, return to step 1.1; Step 2: A multidisciplinary analysis model for coupling loops in trajectory optimization is established using a parameterized method to incorporate trajectory optimization into aircraft multidisciplinary optimization, and to dynamically combine and match sub-models. The sub-models of the multidisciplinary analysis model include a flight dynamics model, an aircraft weight model, a fuel weight model, and a propulsion proxy model. Step 3: Based on the Kriging variable camber aerodynamic proxy model and the multidisciplinary analysis model, the Radau pseudo-spectral method is used to solve the cruise altitude control flight trajectory optimization, including: converting the continuous flight time interval of the wing-body fusion layout aircraft into a grid interval, solving the Radau pseudo-spectral differential matrix of the grid interval, converting the dynamic differential equation constraints of the continuous flight time optimal control problem of the wing-body fusion layout aircraft into algebraic constraints, and converting the continuous flight time optimal control problem of the wing-body fusion layout aircraft into a nonlinear programming problem; Step 4: Use optimization algorithm to solve.

2. The trajectory optimization method for variable curvature of a wing-body blended layout aircraft according to claim 1, characterized in that: The method for obtaining the initial sample point and the relationship between the input and output of the initial sample point is: Step 1.1.1: Sampling in the design parameter space through experimental design and obtaining the initial sample points; Step 1.1.2: adopting a fixed-axis deflection method, realizing the curvature of the wing trailing edge of the aircraft through a parameterized method, and obtaining the curvature angle of the wing trailing edge of the aircraft at the initial sample point as the input of the initial sample point; Step 1.1.3: Generate a mesh after the curvature of the trailing edge of the aircraft is changed by using an inverse distance weighted moving mesh technique; Step 1.1.4: Calculate the grid of the aircraft trailing edge after the curvature changes by an aerodynamic solver to obtain the aerodynamic coefficient of the initial sample point as the output of the initial sample point.

3. The trajectory optimization method for variable curvature of a wing-body blended layout aircraft according to claim 1, characterized in that: The expression of the Kriging variable camber aerodynamic proxy model is: Among them, the symbol Represents the proxy model, , C L is the lift coefficient, C D is the drag coefficient, C M is the torque coefficient, mach is the Mach number, alt is the flight altitude, alpha is the angle of attack, is the bending angle of the trailing edge of the wing of the aircraft.

4. The method for optimizing the trajectory of a wing-body blended aircraft with variable curvature according to claim 1, characterized in that: The flight dynamics model, the aircraft weight model, the fuel weight model, and the propulsion proxy model are expressed in sequence as follows: ， in, range For the voyage, alt is the flight altitude, V is the flight speed, is the trajectory angle, α is the angle of attack; L, D, T, m are lift, drag, thrust and weight, respectively. g is the acceleration due to gravity, symbol represents the time derivative of this term, is the total design weight of the aircraft, The weight of the occupant, is the effective load weight, is the fuel weight, is the empty weight of the aircraft, is the fuel consumption rate per second, SFC is the unit fuel consumption rate, T max is the maximum thrust, mach is the Mach number.

5. The method for optimizing the trajectory of a wing-body blended aircraft with variable curvature according to claim 1, characterized in that: The calculation method for solving the optimization of the cruise altitude control flight trajectory using the Radau pseudo-spectral method is: Step 3.1: Convert the continuous flight time interval into the grid interval: Step 3.1.1: Divide the continuous flight time interval into K grid intervals, in, is the starting time of the continuous flight time interval, is the end time of the continuous flight time interval; Step 3.1.2: In each grid interval of the K grid intervals The time range can be converted into , the conversion formula is: ， Wherein, k is the kth grid interval in the K grid intervals, , , is the distribution point within the grid interval; Step 3.2: Using the Radau pseudospectral method, the kth grid interval In the example, N LGR points are selected, and the N LGR points are , Among them, the N LGR points is a polynomial The root, is an N-order orthogonal polynomial: ； Step 3.3: Use the N LGR points as nodes to construct a global interpolation polynomial of the state variable, and compensate the terminal points when interpolating the global interpolation polynomial of the state variable , the state variable is constructed using N+1 Lagrange interpolation polynomials: ， in, is the state variable, is the Lagrange interpolation basis function; Step 3.4: Use the N LGR collocation points as nodes to construct a global interpolation polynomial of the control variable. The control variable is constructed using the N Lagrange interpolation polynomials as follows: ， in, is the control variable; Step 3.5: Derivative the global interpolation polynomial of the state variable to obtain the derivative of the state variable: ， in, is the Radau pseudospectral differential matrix at the kth grid interval, and the derivative of the state variable is discretized on the N LGR collocation points to obtain the discretized form of the state variable: ； Step 3.6: Use Lagrange integral to replace the integral term of the objective function to obtain the discretized form of the objective function: ， in, J is the objective function, are the Lagrange polynomial coefficients; Step 3.7: Discretize the path constraint function C[S(t),U(t),t] on the N LGR points in the kth grid interval to obtain the discretized form of the path constraint function: 。 6. The method for optimizing the trajectory of a wing-body blended aircraft with variable curvature according to claim 1, characterized in that: The optimization algorithm is a sequential quadratic programming algorithm.

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