Aerodynamic model construction method and aircraft surface pressure evaluation method

Abstract

Embodiments of the present application provide an aerodynamic model construction method and an aircraft surface pressure evaluation method. The aerodynamic model construction method includes: simplifying a blunt leading-edge waverider into a variable-sweep blunt plate; taking the pressure increment affecting the profile line of the symmetric plane of the variable-sweep blunt plate as the target variable of symbolic regression, and taking the physical parameters affecting the surface pressure of the variable-sweep blunt plate as the feature variables of symbolic regression to construct a formula; determining a candidate symbol set based on the semi-cylindrical surface pressure approximation formula, the spherical head cylinder surface pressure formula, and the spherical head blunt cone surface pressure approximation formula; constructing a training sample set of the surface pressure increment of the variable-sweep blunt plate based on CFD numerical simulation; and optimizing the constructed formula according to the candidate symbol set, the training sample set, and the physical parameters based on the symbolic regression algorithm to obtain an aerodynamic model. The aerodynamic model constructed in the present application can quickly and effectively evaluate the influence of the detached shock wave on the surface pressure distribution of a hypersonic aircraft under hypersonic conditions.

Description

Technical Field

[0001] Embodiments of the present application relate to the technical field of waverider configuration optimization, and in particular, to a method for constructing an aerodynamic model and a method for evaluating the surface pressure of an aircraft. Background Art

[0002] Currently, the theoretical models that can capture the influence of the detached shock wave at the blunt leading edge are all derived based on simple configurations, such as a blunt plate, a sphere-cylinder, a blunt cone, etc. There is still a lack of an efficient and high-fidelity aerodynamic model for the influence of the surface pressure distribution of complex configurations such as waveriders, and thus it is impossible to carry out efficient and high-fidelity waverider configuration optimization with the help of an aerodynamic model. Summary of the Invention

[0003] Embodiments of the present application provide a method for constructing an aerodynamic model and a method for evaluating the surface pressure of an aircraft, which can analyze the influence of the surface pressure distribution of complex configurations such as waveriders.

[0004] In the first aspect of the present application, a method for constructing an aerodynamic model is provided, including:

[0005] Simplify a blunt leading edge waverider into a variable-sweep blunt plate;

[0006] Take the pressure increment affecting the profile line of the symmetric plane of the variable-sweep blunt plate as the target variable of symbolic regression, and take the physical parameters affecting the surface pressure of the variable-sweep blunt plate as the characteristic variables of symbolic regression, and construct the following formula:

[0007] ΔP / P ∞ = f(x / R, Ma, α, Λ) (1);

[0009] Determine a set of candidate symbols based on the surface pressure approximation formula of a semi-cylinder, the surface pressure formula of a sphere-cylinder, and the surface pressure approximation formula of a sphere-cone;

[0010] Construct a training sample set of the surface pressure increment of the variable-sweep blunt plate based on CFD numerical simulation;

[0011] Based on the symbolic regression algorithm, optimize formula (1) according to the set of candidate symbols, the training sample set, and the physical parameters to obtain an aerodynamic model:

[0012]

[0013] where, ΔP is the pressure increment, P ∞ is the oncoming flow pressure, x is the distance of the surface along the flow direction from the head vertex, R is the blunt radius, Ma is the Mach number, α is the angle of attack, and Λ is the local leading edge sweep angle;

[0014] Among them, the physical parameters include the oncoming flow pressure, the distance of the surface along the flow direction from the head vertex, the blunt radius, the Mach number, the angle of attack, and the local leading edge sweep angle.

[0015] In a possible implementation manner, the simplifying the blunt leading edge waverider into a variable sweep blunt flat plate includes:

[0016] Simplify the streamline of the lower surface of the blunt leading edge waverider into a straight line, and transform the three-dimensional problem of the original surface of the blunt leading edge waverider into a two-dimensional aerodynamic modeling problem of the longitudinal section, so as to simplify the blunt leading edge waverider into the variable sweep blunt flat plate.

[0017] In a possible implementation manner, the determining the set of candidate symbols based on the semi-cylindrical surface pressure approximation formula, the spherical head cylindrical surface pressure formula, and the spherical head blunt cone surface pressure approximation formula includes:

[0018] The semi-cylindrical surface pressure approximation formula is expressed as follows:

[0019]

[0020] The spherical head cylindrical surface pressure formula is expressed as follows:

[0021]

[0022] Among them, P is the surface pressure, P ∞ is the free oncoming flow pressure, Ma ∞ is the free oncoming flow Mach number, C is the drag coefficient, χ is the distance of the surface along the flow direction from the head vertex, and d is the diameter of the blunt leading edge;

[0023] The spherical head blunt cone surface pressure approximation formula is expressed as follows

[0024] P = P C -P C -P 2 )e -η (5)

[0025] Among them,

[0026] Based on formula (3), formula (4), and formula (5), determine the operation symbols "+", "-", "×", "÷", "exp", "sin", and "cos" as the set of candidate symbols.

[0027] In a possible implementation manner, the constructing the training sample set of the surface pressure increment of the variable sweep blunt flat plate based on CFD numerical simulation includes:

[0028] Based on the variable sweep blunt flat plate, construct a sharp leading edge flat plate model and a blunt leading edge flat plate model;

[0029] Select a preset number of longitudinal interfaces on the pointed leading-edge flat plate model and the blunt leading-edge flat plate model respectively, where the positions of the longitudinal sections selected on the pointed leading-edge flat plate model and the blunt leading-edge flat plate model are the same;

[0030] For the preset working conditions, obtain the surface pressure of each section on the blunt leading-edge flat plate model and the surface pressure of each section on the pointed leading-edge flat plate model through CFD numerical simulation;

[0031] Use the surface pressure of the blunt leading-edge flat plate model minus the surface pressure of the pointed leading-edge flat plate model at the same position to obtain the pressure increment of different longitudinal sections as the training sample set.

[0032] In a possible implementation manner, the aerodynamic model obtained by optimizing formula (1) based on the symbolic regression algorithm according to the candidate symbol set, the training sample set, and the physical parameters includes:

[0033] Randomly select a first preset number of initial variable populations in the design space, limit the number of variables of each individual in each initial variable population to a second preset number, and select the independent variables of each individual from the physical parameters, the candidate symbol set, the power exponent, and the constant term;

[0034] For each individual, determine the corresponding formula according to the binary tree structure;

[0035] Based on the formula corresponding to each individual, obtain the pressure increment at each point of all longitudinal sections under the preset working conditions, and calculate the root mean square error between the calculated pressure increment and the pressure increment in the training sample set;

[0036] Perform a descending order sorting on the initial variable population based on the root mean square error, and determine the individual fitness according to the proportion of the sorting serial numbers;

[0037] Judge whether it is the last generation;

[0038] If so, the optimization ends and the aerodynamic model is obtained.

[0039] In a possible implementation manner, the aerodynamic model obtained by optimizing formula (1) based on the symbolic regression algorithm according to the candidate symbol set, the training sample set, and the physical parameters further includes:

[0040] If not, use the roulette wheel method to select the individuals after reproduction according to the fitness;

[0041] Determine the number of crossover individuals according to the preset crossover probability and randomly select the crossover individuals;

[0042] Cross the corresponding control variables of the selected individuals and complete gene mutation according to the preset gene mutation probability;

[0043] Generate a new population and optimize again.

[0044] In a possible implementation manner, the root mean square error of the calculated pressure increment and the pressure increment in the training sample set includes:

[0045] Calculate the root mean square error using the following formula:

[0046]

[0047] Where, RMSE i is the root mean square error, m is the number of all pressure increment sample points, y(x) is the pressure increment value at the x position corresponding to the training sample point, is the pressure increment result at the x position corresponding to each formula.

[0048] In a possible implementation manner, the determining of the individual fitness according to the proportion of the sorting serial numbers includes:

[0049] Determine the fitness using the following formula:

[0050]

[0051] Where, fitness i is the fitness, and rank is the sorting serial number.

[0052] In the second aspect of the present application, there is provided a method for evaluating the pressure on the surface of an aircraft, including using the aerodynamic model constructed by the aerodynamic model construction method described in any one of the first aspects to evaluate the pressure distribution on the surface of the aircraft.

[0053] In the aerodynamic model construction method and the method for evaluating the pressure on the surface of the aircraft provided in the embodiments of the present application, the constructed aerodynamic model can quickly and effectively evaluate the influence of the detached shock wave on the pressure distribution on the surface of the hypersonic aircraft under hypersonic conditions.

[0054] It should be understood that the content described in the summary of the invention section is not intended to limit the key or important features of the embodiments of the present application, nor is it used to limit the scope of the present application. Other features of the present application will become easily understood through the following description. Description of the Drawings

[0055] Combined with the drawings and referring to the following detailed description, the above and other features, advantages and aspects of the embodiments of the present application will become more obvious. In the drawings, the same or similar reference numerals represent the same or similar elements, where:

[0056] Figure 1 The flowchart of the aerodynamic model construction method according to an embodiment of the present application is shown.

[0057] Figure 2 The schematic diagram of the sharp leading-edge waverider passivation process according to an embodiment of the present application is shown.

[0058] Figure 3 The schematic diagram of the waverider symmetric plane profile according to an embodiment of the present application is shown.

[0059] Figure 4 The schematic diagram of the variable-sweep flat plate and its cross-section sweep angle distribution according to an embodiment of the present application is shown.

[0060] Figure 5 The schematic diagram of the cross-section position selection of the variable-sweep flat plate model according to an embodiment of the present application is shown.

[0061] Figure 6 The schematic diagram of the waverider verification model according to an embodiment of the present application is shown.

[0062] Figure 7 The schematic diagram of the comparison between the aerodynamic model formula and the VFD pressure increment according to an embodiment of the present application is shown. Detailed implementation manners

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application.

[0064] The level of the lift-to-drag ratio determines whether the range of a hypersonic vehicle can meet the mission requirements. Under hypersonic conditions, the vehicle will suffer from extremely high frictional drag and wave drag, and it is very difficult to improve the lift-to-drag ratio, facing an insurmountable "lift-to-drag ratio barrier".

[0065] Currently, the waverider is considered to be a new type of aerodynamic layout that is most promising to break through the hypersonic "lift-to-drag ratio barrier". With its high aerodynamic efficiency, the waverider configuration has broad application prospects in the design of hypersonic vehicles.

[0066] In practical engineering applications, in order to meet the thermal protection requirements, it is necessary to perform leading-edge passivation on the sharp leading-edge waverider. Under hypersonic conditions, a blunt leading edge will generate a detached shock wave, which will significantly change the surface pressure distribution of the waverider, thereby affecting the aerodynamic characteristics of the waverider.

[0067] Currently, all the theoretical models capable of capturing the influence of detached shock waves on blunt leading edges are derived based on simple configurations, such as blunt flat plates, spherical nose cylinders, blunt cones, etc. There is still a lack of an efficient and high-fidelity aerodynamic model for the influence of the surface pressure distribution of waverider configurations, and thus it is impossible to carry out efficient and high-fidelity waverider configuration optimization with the help of an aerodynamic model.

[0068] To solve the above problems, an embodiment of the present application provides a method for constructing an aerodynamic model. Figure 1 The flowchart of the method for constructing an aerodynamic model according to an embodiment of the present application is shown. Refer to Figure 1 This method includes the following steps:

[0069] Step 101, simplify the blunt leading edge waverider into a variable-sweep blunt flat plate.

[0070] To effectively evaluate the surface pressure distribution of the blunt waverider, factors such as variable sweep at the leading edge of the waverider, dihedral and anhedral on the interface, and non-straightness of the lower surface profile need to be considered in the theory. Considering the differences between different waveriders, it is too complex to directly study the blunt leading edge waverider. Therefore, the research object can be simplified.

[0071] By simplifying the blunt leading edge waverider into a variable-sweep blunt flat plate, the streamlines on the lower surface of the blunt leading edge waverider can be simplified into straight lines, and the three-dimensional problem of the original surface of the blunt leading edge waverider can be transformed into a two-dimensional aerodynamic modeling problem of the longitudinal section, so as to simplify the blunt leading edge waverider into a variable-sweep blunt flat plate.

[0072] Before simplifying the blunt leading edge waverider, the leading edge of the original sharp leading edge waverider needs to be blunt. Specifically, refer to Figure 2 The leading edge blunt can include the following steps: for any given original sharp leading edge waverider, assume the leading edge blunt radius is R; move the upper surface of the sharp leading edge waverider up by a distance of 2R; select a certain number of cross-sections along the flow direction, find the intersection points of each cross-section with the leading edge lines of the upper and lower surfaces, and make semi-circular arcs with a radius of R on the current cross-section according to the upper and lower intersection points; according to the leading edge lines of the upper and lower surfaces and the arcs of each cross-section, generate a blunt leading edge through grid surface generation; regenerate the bottom surface, and then a blunt waverider entity, that is, a blunt leading edge waverider, can be generated according to the upper surface, lower surface, blunt leading edge and bottom surface.

[0073] Step 102, take the pressure increment affecting the profile line of the symmetry plane of the variable-sweep blunt flat plate as the target variable of symbolic regression, and take the physical parameters affecting the surface pressure of the variable-sweep blunt flat plate as the characteristic variables of symbolic regression to construct a formula, and construct the following formula:

[0074] ΔP / P ∞ = f(x / R, Ma, α, Λ) (1)

[0076] where ΔP is the pressure increment, and P ∞ is the oncoming flow pressure, x is the distance of the body surface along the flow direction from the head vertex, R is the blunt radius, Ma is the Mach number, α is the angle of attack, and Λ is the local leading-edge sweep angle.

[0077] Figure 3 As shown in the waverider symmetric surface profile, the slight difference between it and the straight line leads to different pressure distributions. If the pressure distribution results on the straight line are directly applied to the waverider, the aerodynamic model cannot capture the influence of the slight changes in the waverider profile on the aerodynamic performance. When the difference between the waverider profile and the straight line is small, it can be considered that the pressure increment difference caused by bluntness is small. Therefore, the pressure increment caused by bluntness is selected as the target variable for symbolic regression. It should be noted that Figure 3 in the figure, the solid line is the original profile, and the dashed line is the straight line.

[0078] The physical parameters affecting the surface pressure of the variable-sweep blunt plate include the blunt radius, Mach number, flight altitude, angle of attack, and leading-edge line shape, etc. For any longitudinal section, the main factors affecting its pressure distribution include the distance χ of the body surface along the flow direction from the head vertex, the blunt radius R, the Mach number Ma, the angle of attack α, the local leading-edge sweep angle Λ, and the oncoming flow pressure P ∞ . Therefore, the distance χ of the body surface along the flow direction from the head vertex, the blunt radius R, the Mach number Ma, the angle of attack α, the local leading-edge sweep angle Λ, and the oncoming flow pressure P ∞ can be used as the characteristic variables for symbolic regression.

[0079] Step 103: Determine the candidate symbol set based on the semi-cylindrical surface pressure approximation formula, the spherical head cylinder surface pressure formula, and the spherical head blunt cone surface pressure approximation formula.

[0080] The semi-cylindrical surface pressure approximation formula is expressed as follows:

[0081]

[0082] The spherical head cylinder surface pressure formula is expressed as follows:

[0083]

[0084] where P is the surface pressure of the body, P∞ is the free oncoming flow pressure, Ma ∞ is the free oncoming flow Mach number, C is the drag coefficient, χ is the distance of the body surface along the flow direction from the head vertex, and d is the diameter of the blunt leading edge.

[0085] The spherical head blunt cone surface pressure approximation formula is expressed as follows

[0086] P = P C -(P C -P 2 )e -η(5)

[0087] Among them,

[0088] Based on formulas (3), (4), and (5), determine the operation symbols "+", "-", "×", "÷", "exp", "sin", and "cos" as the set of candidate symbols.

[0089] Step 104: Based on CFD numerical simulation, construct a training sample set of the surface pressure increment of the variable-sweep blunt plate.

[0090] First, based on the variable-sweep blunt plate, construct a sharp leading-edge plate model and a blunt leading-edge plate model. For example, the blunt radius of the blunt leading-edge plate model is 10 mm, and the leading-edge sweep angle distribution of the variable-sweep plate and its different cross-sections is as Figure 4 shown.

[0091] Then, select a preset number of longitudinal interfaces on the sharp leading-edge plate model and the blunt leading-edge plate model respectively. It should be noted that the positions of the longitudinal cross-sections selected on the sharp leading-edge plate model and the blunt leading-edge plate model are the same.

[0092] Then, for the preset working conditions, obtain the surface pressure of each cross-section on the blunt leading-edge plate model and the surface pressure of each cross-section on the sharp leading-edge plate model through CFD numerical simulation.

[0093] The working condition parameters of the preset working conditions are shown in Table 1:

[0094] Table 1 CFD simulation working condition parameters

[0095]

[0096] Finally, at the same position, subtract the surface pressure of the sharp leading-edge plate model from the surface pressure of the blunt leading-edge plate model to obtain the pressure increment of different longitudinal cross-sections as the training sample set. For example, the selection scheme of the longitudinal cross-sections is as Figure 5 shown, that is, the corresponding positions of the longitudinal cross-sections are z = 0 m, 0.1 m, 0.2 m, 0.3 m, 0.4 m, 0.5 m, 0.6 m respectively.

[0097] Step 105: Based on the symbolic regression algorithm, optimize formula (1) according to the set of candidate symbols, the training sample set, and the physical parameters to obtain the aerodynamic model:

[0098]

[0099] Among them, ΔP is the pressure increment, P ∞$p_{\infty}$ is the freestream pressure, $x$ is the distance along the flow direction from the leading edge vertex of the body surface, $R$ is the blunt radius, $Ma$ is the Mach number, $\alpha$ is the angle of attack, and $\Lambda$ is the local leading edge sweep angle.

[0100] Specifically, the optimization method may include the following steps:

[0101] Step 1501, randomly select a first preset number of initial variable populations within the design space, limit the number of variables of each individual in each of the initial variable populations to a second preset number, and select the independent variables of each individual from physical parameters, candidate symbol sets, power exponents, and constant terms. Exemplarily, the first preset number can be 20 - 30, and the second preset number can be 50.

[0102] Step 1502, for each individual, determine the corresponding formula according to the binary tree structure.

[0103] Step 1503, based on the formula corresponding to each individual, obtain the pressure increment at each point of all longitudinal sections under the preset working conditions, and calculate the root mean square error between the calculated pressure increment and the pressure increment in the training sample set.

[0104] The root mean square error is calculated using the following formula:

[0105]

[0106] where $RMSE$ i is the root mean square error, $m$ is the number of all pressure increment sample points, $y(x)$ is the pressure increment value at the $x$ position corresponding to the training sample point, is the pressure increment result at the $x$ position corresponding to each formula.

[0107] Step 1504, sort the initial variable populations in descending order based on the root mean square error, and determine the individual fitness according to the proportion of the sorting sequence numbers.

[0108] The fitness is determined using the following formula:

[0109]

[0110] where $fitness$ i is the fitness, and $rank$ is the sorting sequence number.

[0111] Step 1505, determine whether it is the last generation.

[0112] Step 1506, if so, the optimization ends and the aerodynamic model is obtained.

[0113] Step 1507, if not, use the roulette wheel method to select the individuals after reproduction according to the fitness.

[0114] Step 1508: Determine the number of crossover individuals according to a preset crossover probability and randomly select the crossover individuals.

[0115] Step 1509: Crossover the corresponding control variables of the individuals and complete gene mutation following a preset gene mutation probability.

[0116] Step 1510: Return to Step 1502.

[0117] The following further illustrates the embodiments of the present application with a specific example.

[0118] Take Figure 6 the shown waverider (total length 4m) as an example. Respectively obtain the pressure increments of different cross-sections on the lower surface of the waverider before and after passivation (passivation radius 10mm) under different flight conditions through CFD numerical simulation and the above formula (2). The comparison is as Figure 7 shown, where Approximation represents the result obtained by the formula.

[0119] As can be seen from Figure 7 it, the model is in good agreement with the CFD results, indicating that the aerodynamic force model constructed by using the aerodynamic force model construction method provided by the embodiments of the present application can effectively evaluate the influence of leading-edge passivation effect on the surface pressure distribution of hypersonic vehicles.

[0120] On the other hand, the present application also provides a method for evaluating the surface pressure of an aircraft, which uses the aerodynamic force model constructed by the above aerodynamic force model construction method to evaluate the surface pressure distribution of the aircraft.

[0121] The above are only some embodiments of the present application. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present application, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present application.

Claims

1. A method for constructing an aerodynamic model, characterized in that, it includes: simplifying the blunt leading-edge waverider into a variable-sweep blunt plate; taking the pressure increment affecting the profile line of the symmetric plane of the variable-sweep blunt plate as the target variable of symbolic regression, and taking the physical parameters affecting the surface pressure of the variable-sweep blunt plate as the characteristic variables of symbolic regression, and constructing the following formula: ΔP / P ∞ = f(x / R, Ma, α, Λ) (1); determining a set of candidate symbols based on the approximate formula for the surface pressure of a semi-cylinder, the formula for the surface pressure of a sphere-cylinder, and the approximate formula for the surface pressure of a sphere-cone; the approximate formula for the surface pressure of the semi-cylinder is expressed as follows: the formula for the surface pressure of the sphere-cylinder is expressed as follows: where P is the surface pressure, P ∞ is the free-stream pressure, Ma ∞ is the free-stream Mach number, C is the drag coefficient, x is the distance along the flow direction from the leading edge vertex of the surface, and d is the diameter of the blunt leading edge; the approximate formula for the surface pressure of the sphere-cone is expressed as follows P = P C -(P C -P 2 )e -η (5) Among them, based on formula (3), formula (4) and formula (5), determining the operation symbols "+", "-", "×", "÷", "exp", "sin" and "cos" as the set of candidate symbols; constructing a training sample set for the surface pressure increment of the variable-sweep blunt plate based on CFD numerical simulation; based on the symbolic regression algorithm, optimizing formula (1) according to the set of candidate symbols, the training sample set and the physical parameters to obtain an aerodynamic model: where ΔP is the pressure increment, P ∞ is the oncoming flow pressure, χ is the distance along the flow direction from the head vertex of the object surface, R is the blunt radius, Ma is the Mach number, α is the angle of attack, and Λ is the local leading-edge sweep angle; wherein, the physical parameters include the oncoming flow pressure, the distance along the flow direction from the head vertex of the object surface, the blunt radius, the Mach number, the angle of attack, and the local leading-edge sweep angle.

2. The method for constructing an aerodynamic model according to claim 1, characterized in that, the simplifying the blunt leading-edge waverider into a variable-sweep blunt plate includes: simplifying the streamline on the lower surface of the blunt leading-edge waverider into a straight line, and transforming the three-dimensional problem of the original object surface of the blunt leading-edge waverider into a two-dimensional aerodynamic modeling problem of the longitudinal section, so as to simplify the blunt leading-edge waverider into the variable-sweep blunt plate.

3. The method for constructing an aerodynamic model according to claim 2, characterized in that, the constructing a training sample set for the surface pressure increment of the variable-sweep blunt plate based on CFD numerical simulation includes: based on the variable-sweep blunt plate, constructing a sharp leading-edge plate model and a blunt leading-edge plate model; selecting a preset number of longitudinal interfaces on the sharp leading-edge plate model and the blunt leading-edge plate model respectively, wherein the positions of the longitudinal sections selected on the sharp leading-edge plate model and the blunt leading-edge plate model are the same; for the preset working conditions, obtaining the surface pressure of each section on the blunt leading-edge plate model and the surface pressure of each section on the sharp leading-edge plate model through CFD numerical simulation; using the surface pressure of the blunt leading-edge plate model minus the surface pressure of the sharp leading-edge plate model at the same position to obtain the pressure increment of different longitudinal sections as the training sample set.

4. The method for constructing an aerodynamic model according to claim 3, characterized in that, the optimizing formula (1) according to the set of candidate symbols, the training sample set and the physical parameters based on the symbolic regression algorithm to obtain an aerodynamic model includes: Randomly select an initial variable population of the first preset quantity within the design space, limit the number of variables of each individual in each of the initial variable populations to the second preset quantity, and select the independent variables of each individual from among the physical parameters, the candidate symbol set, the power exponent, and the constant term; For each individual, determine the corresponding formula according to the binary tree structure; Based on the formula corresponding to each individual, obtain the pressure increment at each point of all the longitudinal sections under the preset working conditions, and calculate the root mean square error between the calculated pressure increment and the pressure increment in the training sample set; Based on the root mean square error, perform a descending order sorting on the initial variable population, and determine the individual fitness according to the proportion of the sorting serial numbers; Judge whether it is the last generation; If so, the optimization ends, and the aerodynamic model is obtained.

5. The aerodynamic model construction method according to claim 4, wherein, the optimizing formula (1) based on the symbolic regression algorithm according to the candidate symbol set, the training sample set, and the physical parameters to obtain the aerodynamic model further includes: If not, use the roulette wheel method to select the individuals after reproduction according to the fitness; Determine the number of crossover individuals according to the preset crossover probability and randomly select the crossover individuals; Cross the corresponding control variables of the selected individuals and complete gene mutation following the preset gene mutation probability; Generate a new population and perform optimization again.

6. The aerodynamic model construction method according to claim 4, wherein, the calculating the root mean square error between the calculated pressure increment and the pressure increment in the training sample set includes: Calculate the root mean square error using the following formula: Among them, RMSE i is the root mean square error, m is the number of all pressure increment sample points, and y(x) is the pressure increment value at the x position corresponding to the training sample points. is the pressure increment result at the x position corresponding to each formula.

7. The aerodynamic model construction method according to claim 4, wherein, the determining the individual fitness according to the proportion of the sorting serial numbers includes: Determine the fitness using the following formula: Among them, fitness i is the fitness, and rank is the sorting serial number.

8. An aircraft surface pressure evaluation method, wherein, it includes using the aerodynamic model constructed by the aerodynamic model construction method according to any one of claims 1 to 7 to evaluate the pressure distribution on the aircraft surface.

Images