Aircraft climbing trajectory optimization method

Abstract

The invention discloses an optimization method of an aircraft climbing trajectory, and belongs to the field of aircraft / engine integrated design. According to the method, on different flight energy heights (the flight heights and the flight speeds under the equal-energy height are in one-to-one correspondence), the adjustable parameters of the engine and the flight heights or the flight speeds are jointly taken as optimization variables, and the optimization problem of the maximum installation thrust of the engine is converted into the optimization problem of the maximum residual power of the aircraft; therefore, the flight height, the flight speed and the adjustable parameters of the engine which enable the residual power of the aircraft to be maximum are optimized and solved at the same time. The fastest climbing trajectory of the aircraft can be obtained through step-by-step optimization by sequentially increasing the flight energy height, so that the process of repeatedly optimizing the engine performance at different energy heights in a traditional graphic method is avoided. By applying the method for optimizing the climbing trajectory of the aircraft, the problem of waste of computing resources in a traditional graphical method can be avoided, and the optimization efficiency of the climbing trajectory of the aircraft can be effectively improved.

Description

Technical Field

[0001] The invention belongs to the field of aircraft / engine integrated design, and in particular relates to a method for optimizing an aircraft climbing trajectory. Background Art

[0002] Aircraft need to quickly climb to the cruising state to perform flight missions efficiently. How to quickly optimize the fastest climbing trajectory of the aircraft is a major difficulty in the study of aircraft climbing performance.

[0003] Jack D. Mattingly's "Aircraft Engine Design" (2nd edition) uses a graphical method to find the fastest climbing trajectory of an aircraft, as shown in page 74. Figure 1 As shown in Figure 2, the fastest climb can be achieved by climbing in the direction with the largest remaining power. Figure 1 The curve formed by the tangent points of the medium residual power line and the equal energy altitude line is the fastest climbing trajectory of the aircraft. However, to obtain the equal residual power line, it is necessary to calculate the maximum installed thrust of the engine multiple times within a wider flight envelope. For high-performance aircraft engines, there are many adjustable parameters, and multiple performance optimizations of the maximum installed thrust will consume a lot of computing resources. In addition, Figure 1 It can be seen that in the process of using the graphical method to obtain the fastest climb trajectory, only a small number of equal residual power lines around the fastest climb trajectory are used, which results in a large waste of computing resources. Therefore, it is necessary to develop an efficient aircraft climb trajectory optimization method. Summary of the invention

[0004] Technical issues to be solved:

[0005] In order to avoid the shortcomings of the prior art, the present invention provides a method for optimizing the climb trajectory of an aircraft. The method incorporates the adjustable parameters of the engine and the flight altitude or the flight speed as optimization variables, and converts the optimization problem of maximizing the installed thrust of the engine into the optimization problem of maximizing the residual power of the aircraft, thereby simultaneously optimizing and solving the flight altitude, flight speed and adjustable parameters of the engine that maximize the residual power of the aircraft, and solving the problem of waste of computing resources in traditional graphical methods.

[0006] The technical solution of the present invention is: a method for optimizing an aircraft climbing trajectory, the specific steps are as follows:

[0007] Determine 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;

[0008] 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 the optimization variable;

[0009] Set engine and aircraft constraints;

[0010] For each determined flight energy altitude, the optimization variable is solved using an optimization algorithm, and the aircraft residual power is maximized by minimizing the comprehensive objective function under the premise of satisfying the constraint conditions;

[0011] Output the flight altitude and flight speed that maximize the remaining power at different flight energy altitudes, that is, generate the fastest climbing trajectory of the aircraft.

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

[0013]

[0014] Where h represents the flight altitude, v represents the flight speed, and g represents the acceleration due to gravity.

[0015] A further technical solution of the present invention is: 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.

[0016] A further technical solution of the present invention is: 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.

[0017] A further technical solution of the present invention is: the constraint conditions of the aircraft include that the flight speed of the aircraft at a specific altitude is not higher than a set value, and the flight speed of the aircraft at a specific altitude is not lower than a set value.

[0018] A further technical solution of the present invention is: the specific process of maximizing the aircraft residual power by minimizing the comprehensive objective function is as follows:

[0019] Let the set optimization variable be X, and calculate the dimensionless residual power f(X) of the aircraft according to the following formula:

[0020]

[0021] Where p(X) represents the residual power of the aircraft; p Limit represents the upper limit of the aircraft's remaining power; it can be seen that f(X) decreases as p(X) increases, thus converting the p(X) maximization problem into the f(X) minimization problem, and making the order of magnitude of f(X) around 10 0 Level 1;

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

[0023]

[0024] In the formula, 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 Respectively represent the calculated value and limit value of the i-th constraint parameter; S i is the identifier of the upper and lower constraints. For the upper limit constraint problem S i =1, for the lower bound constraint problem S i = -1;

[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 the penalty factor of the comprehensive constraint function;

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

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

[0030] A further technical solution of the present invention is: in the process of minimizing the comprehensive objective function h(X), g(X) is minimized first, that is, the optimization constraints are satisfied first.

[0031] A further technical solution of the present invention is: 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 selects a sequential quadratic programming algorithm.

[0032] An electronic device 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 so that the at least one processor can execute the method for optimizing the aircraft climbing trajectory.

[0033] Beneficial Effects

[0034] The beneficial effect of the present invention is that: by applying the optimization method of the aircraft climbing trajectory of the present invention, the adjustable parameters of the engine and the flight altitude or flight speed are taken together as optimization variables, and the optimization problem of maximizing the installed thrust of the engine is converted into the optimization problem of maximizing the residual power of the aircraft, thereby simultaneously optimizing and solving the flight altitude, flight speed and adjustable parameters of the engine that maximize the residual power of the aircraft, thereby avoiding the process of repeatedly optimizing the engine performance at different energy altitudes by the traditional graphical method, and thus significantly reducing the optimization time of the aircraft climbing trajectory. The specific advantages are analyzed as follows:

[0035] 1. Significantly reduce the waste of computing resources. The present invention uses the engine adjustable parameters (such as the fuel supply of the combustion chamber, the guide vane angle, etc.) and the flight altitude / flight speed as optimization variables, unifies the optimization goal (maximizing the remaining power), and avoids repeated engine performance optimization processes.

[0036] 2. Improve optimization efficiency and flexibility. The present invention converts the engine thrust maximization problem into the residual power maximization problem, which more directly matches the climbing performance requirements and simplifies the optimization logic. Select an algorithm according to the number of optimization variables (such as genetic algorithm for multiple variables and sequential quadratic programming for fewer variables) to ensure the convergence efficiency of the algorithm. For example, the differential evolution algorithm is used in the embodiment to optimize more than 6 variables, avoiding the limitations of traditional gradient algorithms in multi-variable scenarios.

[0037] 3. Technical versatility and extensibility. This method is applicable to multiple types of engines (such as the mixed exhaust turbofan engine in the embodiment), and the optimization variables are extensible (such as the fan speed, guide vane angle, etc. in Table 1). By gradually generating trajectory points by increasing the energy altitude step (such as 2000m), the continuity and smoothness of the climbing trajectory are ensured, avoiding the trajectory jump problem caused by insufficient discrete points in the traditional method.

[0038] 4. Engineering practical value. The present invention reduces the consumption of computing resources and can directly reduce the hardware and time costs of aircraft climbing performance analysis. The rapid generation of its optimization results can provide efficient data support for flight control system design, fuel economy analysis, etc.

[0039] It has been verified that when the number of calculation points of the flight speed at each energy altitude is taken as N, the climb trajectory optimization method of the present invention can theoretically reduce the amount of calculation by about (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 the optimization time by 89.15% compared to the traditional graphical method. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0041] Figure 2 The present invention is a flowchart of an optional method for optimizing an aircraft climbing trajectory according to an embodiment of the present invention. DETAILED DESCRIPTION

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

[0043] Based on the fact that the existing traditional graphical method needs to repeatedly optimize the engine performance (such as the maximum installed thrust) at different energy altitudes and generate a large number of equal residual power lines within the flight envelope, resulting in problems such as calculation redundancy, the present invention provides an optimization method for the aircraft climbing trajectory, and the specific steps are as follows:

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

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

[0046] Step 3: Set engine and aircraft constraints;

[0047] Step 4: For each determined flight energy altitude, the optimization variable is solved using an optimization algorithm, and the aircraft residual power is maximized by minimizing the comprehensive objective function under the premise of satisfying the constraint conditions;

[0048] Step 5: Output the flight altitude and flight speed that maximize the remaining power at different flight energy altitudes, that is, generate the fastest climbing trajectory of the aircraft.

[0049] The present invention integrates the coordinated optimization of engine and flight parameters, introduces an intelligent algorithm adaptation mechanism, and strengthens the priority of constraint conditions. It demonstrates significant improvement in computing efficiency and resource conservation in both theoretical derivation and implementation example verification, and has high engineering practical value and technological innovation.

[0050] The above technical solution is further explained below with reference to examples:

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

[0052] Step 1: Determine the minimum, maximum and step length of the flight energy altitude. Energy altitude z e The calculation method is as follows:

[0053]

[0054] Where h represents the flight altitude, v represents the flight speed, and g represents the acceleration due to gravity.

[0055] Among them, z e The minimum value of z is usually given as 0m; e The maximum value of z is calculated based on the aircraft's cruising altitude and speed. For example, if the aircraft's cruising altitude is 12,000 m and its cruising speed is 236.144 m / s (0.8 Ma), then z e The maximum value of is 14845.1m; according to experience, z e The step size can be given as 2000m, so that there are enough climb trajectory points to describe the aircraft's climb trajectory.

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

[0057]

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

[0059] Table 1 Optimization variables and upper and lower limits of aircraft climbing trajectory

[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 is not less than a certain value, the stable combustion margin of the combustion chamber is not less than a certain value, the total temperature at the outlet of the compression component is not higher than a certain value, the total pressure at the outlet of the compression component is not higher than a certain value, the rotor speed is not higher than a certain value, the total temperature at the outlet of the combustion chamber is 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 specific altitude is not higher than a certain value, the flight speed of the aircraft at a specific altitude is not lower than a certain value, etc.

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

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

[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 remaining power is maximized under the premise of 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 dimensionless residual power f(X) of the aircraft 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 It is 300m / s.

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

[0071]

[0072] In the formula, 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 Respectively represent the calculated value and limit value of the i-th constraint parameter; S i is the identifier of the upper and lower constraints. For the upper limit 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 magnitude of σ×g(X) is 10 1 First level. Since the order of magnitude of f(X) is 10 0 Therefore, 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 the case where the number of optimization variables is large (the number of optimization variables is approximately greater than 6), the optimization algorithm can select a swarm intelligence optimization algorithm such as a genetic algorithm and a differential evolution algorithm; for the case where the number of optimization variables is small, the optimization algorithm can select a classic optimization algorithm such as a sequential quadratic programming algorithm. In this embodiment, the number of optimization variables is large, so the 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 of are 0m, 14845.1m and 2000m respectively. Therefore, in order to obtain the fastest climbing trajectory, the optimization process in step 4 needs to be performed 9 times. If the traditional graphical method is used to solve the fastest climbing trajectory, multiple engine performance optimizations need to be performed at different flight speeds at each energy altitude to calculate similar attached Figure 1 If the number of calculation points of the flight speed at each energy altitude is taken as N, the traditional graphical method needs to carry out 9*N times of engine performance optimization. It can be seen that compared with the traditional graphical method, the climb trajectory optimization method of the present invention can theoretically reduce the amount of calculation by about (N-1) / N*100%.

[0081] In order to further verify the effectiveness of the present invention, the optimization of the climbing trajectory is carried out based on an aircraft model using a hybrid exhaust turbofan engine. When N is 10, the optimization time of the aircraft climbing trajectory optimization method of the present invention and the traditional graphical method is shown in the table below. It can be seen that compared with the traditional graphical method, the aircraft climbing trajectory optimization method of the present invention can reduce the optimization time by 89.15%.

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

[0083]

[0084] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary 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 intent of the present invention.

Claims

1. A method for optimizing an aircraft climbing trajectory, characterized in that The specific steps are as follows: Determine 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; 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 the optimization variable; Set engine and aircraft constraints; For each determined flight energy altitude, the optimization variable is solved using an optimization algorithm, and the aircraft residual power is maximized by minimizing the comprehensive objective function under the premise of satisfying the constraint conditions; Output the flight altitude and flight speed that maximize the remaining power at different flight energy altitudes, that is, generate the fastest climbing trajectory of the aircraft.

2. The method for optimizing an aircraft climbing trajectory according to claim 1, characterized in that: The energy height is calculated as follows: Where h represents the flight altitude, v represents the flight speed, and g 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 throat area of ​​the nozzle.

4. The method for optimizing an aircraft climbing trajectory according to claim 1, characterized in that: 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 constraint conditions of the aircraft include that the flight speed of the aircraft at a specific altitude is not higher than a set value, and 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 specific process of maximizing the aircraft's remaining power by minimizing the comprehensive objective function is as follows: Let the set optimization variable be X, and calculate the dimensionless residual power f(X) of the aircraft according to the following formula: Where p(X) represents the residual power of the aircraft; p Limit represents the upper limit of the aircraft's remaining power; it can be seen that f(X) decreases as p(X) increases, thus converting the p(X) maximization problem into the f(X) minimization problem, and making the order of magnitude of f(X) around 10 0 Level 1; The comprehensive constraint function g(X) is calculated according to the following formula: In the formula, 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 Respectively represent the calculated value and limit value of the i-th constraint parameter; S i is the identifier of the upper and lower constraints. For the upper limit constraint problem S i =1, for the lower bound constraint problem S i = -1; The comprehensive objective function h(X) is calculated according to the following formula: h(X)=f(X)+σ×g(X) (5) In the formula, σ represents the penalty factor of the comprehensive constraint function; Call the optimization algorithm to solve the optimization variable X so that h(X) is minimized.

7. The method for optimizing an aircraft climbing trajectory according to claim 6, characterized in that: The penalty factor σ is set to 10, so that the order of magnitude of σ×g(X) is 10 1 Level 1.

8. The method for optimizing an aircraft climbing trajectory according to claim 6, characterized in that: In the process of minimizing the comprehensive objective function h(X), g(X) is minimized first, that is, the optimization constraints are satisfied first.

9. The method for optimizing an aircraft climbing trajectory according to claim 6, 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 selects a sequential quadratic programming algorithm.

10. 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 so that the at least one processor can execute the method for optimizing the aircraft climbing trajectory according to any one of claims 1 to 9.

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