A method for optimizing an aircraft climb trajectory

Abstract

The application is a kind of optimization method of aircraft climb trajectory, belonging to the field of aircraft / engine integrated design; the application takes the adjustable parameters of the engine and the flight height or flight speed as optimization variables at different flight energy heights (the flight height and flight speed at the same energy height correspond to each other), converts the optimization problem of the maximum installation thrust of the engine into the optimization problem of the maximum residual power of the aircraft, and simultaneously optimizes and solves the flight height, flight speed and adjustable parameters of the engine that make the residual power of the aircraft maximum. By sequentially increasing the flight energy height, the fastest climb trajectory of the aircraft can be gradually optimized, thereby avoiding the process of repeatedly optimizing the engine performance at different energy heights in the traditional graphical method. The application of the optimization method of the aircraft climb trajectory can avoid the waste of computing resources in the traditional graphical method, and effectively improve the optimization efficiency of the aircraft climb trajectory.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aircraft / engine integrated design, and particularly relates to a method for optimizing a climbing trajectory of an aircraft. BACKGROUND

[0002] An aircraft needs to quickly climb to a cruising state so as to efficiently perform a flight task. How to quickly optimize the fastest climbing trajectory of the aircraft is a great difficulty in the study of the climbing performance of the aircraft.

[0003] The fastest climbing trajectory of the aircraft is obtained by using a graphic method on page 74 of Aircraft Engine Design (2nd edition) written by Jack D. Mattingly, as shown in the figure. Figure 1 Since the aircraft climbs in the direction of the maximum residual power, the fastest climbing can be achieved, Figure 1 the curve connected by the tangent points of the medium residual power line and the equal energy height line is the fastest climbing trajectory of the aircraft. However, when the equal residual power line is obtained, the maximum installed thrust of the engine needs to be calculated multiple times in a wide flight envelope. For a high-performance aero-engine, the adjustable parameters are more, and multiple performance optimizations of the maximum installed thrust will consume a large amount of computing resources. In addition, it can be seen from Figure 1 that in the process of obtaining the fastest climbing trajectory by using the graphic method, only a small number of equal residual power lines around the fastest climbing trajectory are used, which causes a waste of a large amount of computing resources. Therefore, it is necessary to develop an efficient optimization method for the climbing trajectory of the aircraft. SUMMARY

[0004] The technical problem to be solved is:

[0005] In order to avoid the shortcomings of the prior art, the application provides a method for optimizing a climbing trajectory of an aircraft. The adjustable parameters of the engine and the flight height or flight speed are taken as optimization variables, the optimization problem of the maximum installed thrust of the engine is converted into the optimization problem of the maximum residual power of the aircraft, so that the flight height, flight speed and adjustable parameters of the engine which make the residual power of the aircraft maximum are simultaneously optimized, and the waste of computing resources by the traditional graphic method is solved.

[0006] The technical scheme of the application is: a method for optimizing a climbing trajectory of an aircraft, and the specific steps are as follows:

[0007] determining the minimum value, maximum value and step length of the flight energy height, the energy height being calculated from the flight height and flight speed;

[0008] selecting the adjustable parameters of the engine and the flight height or flight speed as optimization variables, wherein at a given energy height, only one of the flight height and flight speed is selected as an optimization variable;

[0009] Constraints of setting engine and airplane are set;

[0010] For each determined flight energy height, an optimization algorithm is used to solve the optimization variables, and the maximization of the residual power of the airplane is realized by minimizing the comprehensive objective function under the premise of meeting the constraints;

[0011] The flight height and flight speed that maximize the residual power under different flight energy heights are output, that is, the fastest climb trajectory of the airplane is generated.

[0012] A further technical solution of the present application is that the calculation formula of the energy height is as follows:

[0013]

[0014] In the formula, h represents the flight height, v represents the flight speed, and g represents the gravitational acceleration.

[0015] A further technical solution of the present application is that the adjustable parameters of the engine include the oil supply amount of the combustion chamber, the inlet guide vane angle of the compression component, the inlet guide vane angle of the turbine component, the mixing area ratio of the mixing chamber, and the throat area of the nozzle.

[0016] A further technical solution of the present application is that the constraints of the engine include that the surge margin of the compression component is not lower than a set value, the stable combustion margin of the combustion chamber is not lower than a set value, the outlet total temperature of the compression component is not higher than a set value, the outlet total pressure of the compression component is not higher than a set value, the rotor speed is not higher than a set value, and the outlet total temperature of the combustion chamber is not higher than a set value.

[0017] A further technical solution of the present application is that the constraints of the airplane include that the flight speed of the airplane at a specific height is not higher than a set value, and the flight speed of the airplane at a specific height is not lower than a set value.

[0018] A further technical solution of the present application is that the specific process of realizing the maximization of the residual power of the airplane by minimizing the comprehensive objective function is as follows:

[0019] Let the set optimization variables be X, and the dimensionless residual power f(X) of the airplane is calculated according to the following formula:

[0020]

[0021] In the formula, p(X) represents the residual power of the airplane; p Limit represents the upper limit value of the residual power of the airplane; it can be seen that f(X) decreases with the increase of p(X), so that the maximization problem of p(X) is converted into the minimization problem of f(X), and the order of magnitude of f(X) is in the order of 10 0 ;

[0022] The comprehensive constraint function g(X) is calculated according to the following formula:

[0023]

[0024] In the formula, the subscript i represents the serial number of the constraint parameter; I represents the total number of the constraint parameters; c i (X) and c i,Limit respectively represent the calculated value and the limited value of the i-th constraint parameter; S i is an identifier of the upper and lower limit constraint, S i = 1 for the upper limit constraint problem, and S i = -1 for the lower limit constraint problem;

[0025] The comprehensive objective function h(X) is calculated according to the following formula:

[0026] h(X) = f(X) + σ × g(X) (5)

[0027] In the formula, σ represents a penalty factor of the comprehensive constraint function;

[0028] An optimization algorithm is called to solve the optimization variable X so that h(X) is minimized.

[0029] A further technical solution of the present application is that the penalty factor σ is set to 10, so that the order of magnitude of σ × g(X) is in the order of 10 1 .

[0030] A further technical solution of the present application is that in the process of minimizing the comprehensive objective function h(X), g(X) is preferentially minimized, that is, the constraint condition of optimization is preferentially satisfied.

[0031] A further technical solution of the present application is that when the number of optimization variables is greater than 6, the optimization algorithm adopts a swarm intelligence optimization algorithm, including a genetic algorithm or a differential evolution algorithm; and when the number of optimization variables is less than 6, the optimization algorithm selects a sequential quadratic programming algorithm.

[0032] An electronic device comprises at least one processor, and a memory in communication connection with the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the optimization method of the aircraft climbing trajectory.

[0033] Advantages

[0034] The beneficial effects of the present invention are as follows: by applying the present invention's aircraft climb trajectory optimization method, the engine's adjustable parameters are incorporated into the flight altitude or flight speed as optimization variables, converting the optimization problem of maximizing the engine's installed thrust into the optimization problem of maximizing the aircraft's residual power. This allows the flight altitude, flight speed, and engine's adjustable parameters that maximize the aircraft's residual power to be simultaneously optimized and solved, thereby avoiding the traditional graphical method of repeatedly optimizing engine performance at different energy altitudes. This significantly reduces the time required to optimize the aircraft's climb trajectory. The specific advantages are analyzed as follows:

[0035] 1. Significantly reduces computational resource waste. This invention uses engine adjustable parameters (such as combustion chamber fuel supply and guide vane angle) along with flight altitude / speed as optimization variables, unifying the optimization objective (maximizing residual power) and avoiding repeated engine performance optimization processes.

[0036] 2. Improve optimization efficiency and flexibility. This invention converts the engine thrust maximization problem into a residual power maximization problem, more directly matching the climb performance requirements and simplifying the optimization logic. Algorithms are selected based on the number of optimization variables (e.g., genetic algorithms for multiple variables, sequential quadratic programming for fewer variables) to ensure algorithm convergence efficiency. For example, in this embodiment, a differential evolution algorithm is used to optimize more than six variables, avoiding the limitations of traditional gradient-based algorithms in multivariable scenarios.

[0037] 3. Technical versatility and scalability. This method is applicable to multiple engine types (such as the hybrid exhaust turbofan engine in the examples), and the optimization variables are scalable (such as the fan speed and guide vane angle in Table 1). By gradually generating trajectory points with increasing energy altitude steps (such as 2000m), the continuity and smoothness of the climb trajectory are ensured, avoiding the trajectory jump problem caused by insufficient discrete points in traditional methods.

[0038] 4. Engineering Practical Value. This invention reduces computing resource consumption, directly lowering the hardware and time costs of aircraft climb performance analysis. The rapid generation of optimization results provides efficient data support for flight control system design, fuel economy analysis, and other applications.

[0039] It has been verified that, when the number of flight speed calculation points at each energy altitude is N, the climb trajectory optimization method of the present invention can theoretically reduce the amount of calculation by approximately (N-1) / N*100% compared to the traditional graphical method. In an embodiment of the present invention, the aircraft climb trajectory optimization method of the present invention can reduce optimization time by 89.15% compared to the traditional graphical method. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a diagram of the traditional graphical method for finding the fastest climbing trajectory of an aircraft;

[0041] Figure 2 is a flow chart of an optional method for optimizing an aircraft climb trajectory according to an embodiment of the present application. DETAILED DESCRIPTION

[0042] The embodiments described below with reference to the drawings are exemplary and are intended to explain the present application, and should not be construed as limiting the present application.

[0043] Based on the existing conventional graphic method, engine performance (such as maximum installed thrust) needs to be repeatedly optimized at different energy altitudes, and a large number of equal residual power lines need to be generated within the flight envelope, resulting in problems such as redundant calculation. The present application provides a method for optimizing an aircraft climb trajectory, and the specific steps are as follows:

[0044] Step 1: determining the minimum value, maximum value and step length of the flight energy altitude, wherein the energy altitude is calculated from the flight altitude and the flight speed;

[0045] Step 2: selecting the adjustable parameters of the engine and the flight altitude or the flight speed as optimization variables, wherein at a given energy altitude, only one of the flight altitude and the flight speed is selected as an optimization variable;

[0046] Step 3: setting the constraint conditions of the engine and the aircraft;

[0047] Step 4: for each determined flight energy altitude, using an optimization algorithm to solve the optimization variables, and maximizing the residual power of the aircraft by minimizing the comprehensive objective function under the premise of meeting the constraint conditions;

[0048] Step 5: outputting the flight altitude and flight speed that maximize the residual power at different flight energy altitudes, i.e. generating the fastest climb trajectory of the aircraft.

[0049] The present application has significantly improved calculation efficiency and resource saving effect in theoretical derivation and example verification by integrating the collaborative optimization of engine and flight parameters, introducing intelligent algorithm adaptation mechanism, and strengthening the priority of constraint conditions, and has high engineering practical value and technical innovation.

[0050] The above technical solutions are further described below in conjunction with examples:

[0051] In one embodiment, taking an aircraft model using a hybrid exhaust turbofan engine as an example, the specific steps of the present embodiment are as follows:

[0052] Step 1: determining the minimum value, maximum value and step length of the flight energy altitude. The energy altitude z e is calculated as follows:

[0053]

[0054] where h denotes the flight altitude, v denotes the flight speed, and g denotes the gravitational acceleration.

[0055] where z e is usually given as 0 m; z e is calculated according to the cruising altitude and speed of the aircraft, for example, if the cruising altitude of the aircraft is 12000 m and the cruising speed is 236.144 m / s (0.8 Ma), then the maximum value of z e is 14845.1 m; and the step size of z e may be given as 2000 m, so that there are enough climb trajectory points to describe the climb trajectory of the aircraft.

[0056] Step 2: Select the adjustable parameters of the engine and the flight altitude or flight speed as the optimization variables. The adjustable parameters of the engine include, but are not limited to, the fuel supply amount of the combustion chamber, the inlet guide vane angle of the compression component, the inlet guide vane angle of the turbine component, the mixing area ratio of the mixing chamber, the throat area of the nozzle, etc. At a given energy altitude, only one of the flight altitude and the flight speed can be selected as the optimization variable, if the flight altitude is selected as the optimization variable, then the flight speed v is calculated according to the current energy altitude z e and the flight altitude h in the optimization process, as follows:

[0057]

[0058] The selected optimization variables and their upper and lower limits in this embodiment are shown in Table 1.

[0059] Table 1 Optimization variables and their upper and lower limits of the climb trajectory of the aircraft

[0060]

[0061]

[0062] Step 3: Set the constraints of the engine and the aircraft. The constraints of the engine include, but are not limited to, the surge margin of the compression component being not less than a certain value, the stable combustion margin of the combustion chamber being not less than a certain value, the outlet total temperature of the compression component being not higher than a certain value, the outlet total pressure of the compression component being not higher than a certain value, the rotor speed being not higher than a certain value, the outlet total temperature of the combustion chamber being not higher than a certain value, etc. The constraints of the aircraft include, but are not limited to, the flight speed of the aircraft at a certain altitude being not higher than a certain value, the flight speed of the aircraft at a certain altitude being not lower than a certain value, etc.

[0063] The selected constraint parameters and their upper and lower limits in this embodiment are shown in Table 2.

[0064] Table 2 Constraint parameters and their upper and lower limits of the optimization of the climb trajectory of the aircraft

[0065]

[0066] Step 4: For each energy altitude set in step 1, use the optimization algorithm to solve the optimization variables set in step 2 in turn, so that the aircraft's residual power is maximized while satisfying the constraints set in step 3. The specific steps are as follows:

[0067] Sub-step 1: Let the optimization variable set in step 2 be X, and calculate the aircraft's dimensionless residual power f(X) according to the following formula:

[0068]

[0069] Where p(X) represents the residual power of the aircraft; p Limit It is clear that f(X) decreases as p(X) increases, so the maximization problem of p(X) can be transformed into the minimization problem of f(X), and the order of magnitude of f(X) is 10 0 For this embodiment, p Limit 300m / s.

[0070] Sub-step 2: Calculate the comprehensive constraint function g(X) according to the following formula:

[0071]

[0072] Where, the subscript i represents the sequence number of the constraint parameter; I represents the total number of constraint parameters; c i (X) and c i,Limit Represent the calculated value and limit value of the i-th constraint parameter respectively; S i is the identifier of the upper and lower bound constraints. For the upper bound constraint problem S i =1, for the lower bound constraint problem S i =-1.

[0073] Sub-step 3: Calculate the comprehensive objective function h(X) according to the following formula:

[0074] h(X)=f(X)+σ×g(X) (5)

[0075] Where σ represents the penalty factor of the comprehensive constraint function.

[0076] Preferably, σ is set to 10, so that the order of σ×g(X) is 10 1 Level 1. Since the order of magnitude of f(X) is 10 0 Level 1, so in the process of minimizing h(X), g(X) will be minimized first, that is, the optimization constraints will be satisfied first.

[0077] Sub-step 4: Call the optimization algorithm to solve the optimization variable X so that h(X) is minimized.

[0078] For situations with a large number of optimization variables (approximately greater than 6), a swarm intelligence optimization algorithm such as a genetic algorithm or a differential evolution algorithm can be used as the optimization algorithm. For situations with a small number of optimization variables, a classic optimization algorithm such as a sequential quadratic programming algorithm can be used as the optimization algorithm. In this embodiment, the number of optimization variables is large, so a differential evolution algorithm is selected as the algorithm for solving the optimization variables.

[0079] Step 5: Output the flight speed and altitude that maximize the aircraft's remaining power at different energy altitudes, that is, the aircraft's fastest climbing trajectory.

[0080] For this embodiment, the energy height z in step 2 e The minimum, maximum and step length are 0m, 14845.1m and 2000m respectively. Therefore, in order to obtain the fastest climb trajectory, the optimization process in step 4 needs to be performed 9 times. If the traditional graphical method is used to solve the fastest climb trajectory, multiple engine performance optimizations need to be carried out at different flight speeds at each energy altitude to calculate similar attached Figure 1 The equal residual power line in [ 1 ]. If the number of flight speed calculation points at each energy altitude is N, the traditional graphical method requires 9*N engine performance optimizations. Therefore, compared to the traditional graphical method, the climb trajectory optimization method of the present invention can theoretically reduce the computational effort by approximately (N-1) / N*100%.

[0081] To further validate the effectiveness of the present invention, a climb trajectory optimization method was performed on an aircraft model using a hybrid exhaust turbofan engine. The table below shows the optimization times for the present invention's aircraft climb trajectory optimization method and a traditional graphical method, when N is set to 10. This shows that the present invention's aircraft climb trajectory optimization method can reduce optimization time by 89.15% compared to the traditional graphical method.

[0082] Table 3 Aircraft climb trajectory optimization time (s)

[0083]

[0084] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for optimizing an aircraft climbing trajectory, characterized in that The specific steps are as follows: Determining a minimum value, a maximum value, and a step size of a flight energy altitude, wherein the flight energy altitude is calculated from the flight altitude and the flight speed; Selecting an engine's adjustable parameters and a flight altitude or flight speed as optimization variables, wherein at a given flight energy altitude, only one of the flight altitude and flight speed is selected as the optimization variable; setting engine constraints and aircraft constraints; using an optimization algorithm to solve the optimization variables for each determined flight energy altitude, and maximizing the aircraft's residual power by minimizing a comprehensive objective function while satisfying the constraints; outputting the flight altitude and flight speed that maximize the residual power at different flight energy altitudes, thereby generating the aircraft's fastest climb trajectory; The specific process of maximizing the aircraft's remaining power by minimizing the comprehensive objective function is as follows: The optimization variables set are , calculate the aircraft's dimensionless residual power according to the following formula: : Where, Indicates the remaining power of the aircraft; Indicates the upper limit of the aircraft's remaining power; it can be seen that along with decreases with the increase of The maximization problem is transformed into minimization problem, and make The order of magnitude is 10 0 Level 1; The comprehensive constraint function is calculated as follows : (4) In the formula, the subscript Indicates the sequence number of the constraint parameter; Indicates the total number of constraint parameters; and Respectively represent The calculated and limited values ​​of the constraint parameters; is the identifier of the upper and lower bound constraints. For the upper bound constraint problem , for the lower bound constraint problem ; The comprehensive objective function is calculated as follows : (5) Where, represents the penalty factor of the comprehensive constraint function; Call the optimization algorithm to solve the optimization variable , making Minimum.

2. The method for optimizing an aircraft climbing trajectory according to claim 1, characterized in that: The calculation formula of the flight energy altitude is as follows: Where, Indicates the flight altitude, Indicates the flight speed, Represents the acceleration due to gravity.

3. The method for optimizing an aircraft climbing trajectory according to claim 1, characterized in that: The adjustable parameters of the engine include the fuel supply of the combustion chamber, the inlet guide vane angle of the compression component, the inlet guide vane angle of the turbine component, the mixing area ratio of the mixing chamber, and the nozzle throat area.

4. The method for optimizing an aircraft climbing trajectory according to claim 1, wherein: The constraints of the engine include that the surge margin of the compression component is not lower than the set value, the stable combustion margin of the combustion chamber is not lower than the set value, the total outlet temperature of the compression component is not higher than the set value, the total outlet pressure of the compression component is not higher than the set value, the rotor speed is not higher than the set value, and the total outlet temperature of the combustion chamber is not higher than the set value.

5. The method for optimizing an aircraft climbing trajectory according to claim 1, characterized in that: The constraints of the aircraft include that the flight speed of the aircraft at a specific altitude is not higher than a set value, and that the flight speed of the aircraft at a specific altitude is not lower than a set value.

6. The method for optimizing an aircraft climbing trajectory according to claim 1, characterized in that: The penalty factor Set to 10, so The order of magnitude is 10 1 Level 1.

7. The method for optimizing an aircraft climbing trajectory according to claim 1, characterized in that: The comprehensive objective function In the process of minimization, priority is given to minimization , that is, give priority to satisfying the optimization constraints.

8. The method for optimizing an aircraft climbing trajectory according to claim 1, characterized in that: When the number of optimization variables is greater than 6, the optimization algorithm adopts a swarm intelligence optimization algorithm, including a genetic algorithm or a differential evolution algorithm; when the number of optimization variables is less than 6, the optimization algorithm adopts a sequential quadratic programming algorithm.

9. An electronic device, characterized in that: The invention comprises at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to perform the method for optimizing the aircraft climb trajectory according to any one of claims 1 to 8.

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