A Method for Predicting the Cross-Flow Transition of a Supersonic Airliner Wing Based on a Multilayer Perceptron

Abstract

The present invention proposes a method for predicting the cross-flow transition of a supersonic airliner wing based on a multi-layer perceptron. First, for the wing of a supersonic airliner, a quasi-three-dimensional non-similar boundary layer is artificially constructed. Then, a training sample set is established, and each sample consists of the characteristic parameters and growth rate of each grid point, where the characteristic parameters serve as the input features of the multi-layer perceptron, and the growth rate serves as the output label. After that, the multi-layer perceptron is trained using the training sample set. Finally, the flow field of the supersonic airliner wing to be predicted is calculated under given working conditions, and the growth rate is obtained by inputting the characteristic parameters into the trained multi-layer perceptron. The disturbance growth factor N is calculated using the growth rate, and the cross-flow transition position of the supersonic airliner wing is determined. By artificially constructing a quasi-three-dimensional compressible non-similar boundary layer, the present invention saves the workload and computational cost of geometric modeling, grid generation, and aerodynamic calculation compared to the traditional real boundary layer sampling method.

Description

Technical Field

[0001] The present invention relates to the field of fluid mechanics simulation calculation, and particularly to a method for predicting cross-flow transition of a supersonic airliner wing based on a multi-layer perceptron. Background Art

[0002] For a supersonic airliner, effectively delaying the occurrence of transition can obtain considerable drag reduction benefits. Currently, in engineering practice, commercial CAE / CFD numerical simulation software is widely used for calculation, and the e N method based on LST is a typical method for predicting transition. However, this method involves solving eigenvalue problems and requires interactive operation, and users must monitor the results in real time, resulting in low efficiency. Summary of the Invention

[0003] Currently, research on transition prediction mainly samples two-dimensional similarity solutions or real boundary layers and uses subsonic and incompressible conditions. However, in the supersonic case, the boundary layer transition problem is affected by strong three-dimensional effects and high compressibility, and traditional solutions are not applicable. To accurately predict supersonic transition and solve the problem that traditional e N methods require interactive operation, the present invention proposes a method for predicting cross-flow transition of a supersonic airliner wing based on a multi-layer perceptron, focusing on the instability of cross-flow standing waves under strong three-dimensional effects.

[0004] The technical solution of the present invention is as follows:

[0005] A method for predicting cross-flow transition of a supersonic airliner wing based on a multi-layer perceptron, comprising the following steps:

[0006] Step 1: For the wing of a supersonic airliner, artificially construct a quasi-three-dimensional non-similar boundary layer; including the following steps:

[0007] Step 1.1: Let the sweep angle of the wing of the supersonic airliner be ; for the three-dimensional model of the wing, cut it to obtain the two-dimensional profile of the wing along the chord direction of the wing, determine the grid point range on the two-dimensional profile of the wing, and take several grid points within the grid point range;

[0008] Step 1.2: For the two-dimensional profile of the wing, given the pressure gradient distribution function , where is a function of the chordwise coordinate in the two-dimensional profile of the wing;

[0009] Step 1.3: Set the chordwise outer edge velocity at the initial position of the boundary layer in the two-dimensional profile of the wing as a function of the oncoming flow velocity and the spanwise outer edge velocity :

[0010]

[0011] Wherein and are set coefficients;

[0012] Step 1.4: Based on the pressure gradient distribution function given in Step 1.2 , with the chordwise outer edge velocity at the initial position of the boundary layer given in Step 1.3 as the initial condition, according to the freestream Mach number , freestream temperature , freestream unit Reynolds number , by solving the boundary layer equations, artificially construct a quasi-three-dimensional non-similar boundary layer;

[0013] Step 2: Establish a training sample set. Each sample in the training sample set consists of the characteristic parameters and growth rates of each grid point under a certain working condition, where the characteristic parameters are used as the input features of the multi-layer perceptron and the growth rate is used as the output label; the process of establishing the training sample set is as follows:

[0014] Step 2.1: For the given pressure gradient distribution function , sample the working conditions for the freestream Mach number , freestream temperature , freestream unit Reynolds number and the sweep angle ;

[0015] Step 2.2: Perform flow field calculations on the quasi-three-dimensional non-similar boundary layer obtained in Step 1 under each working condition sampled in Step 2.1 to obtain the flow field and the characteristic parameters of each grid point corresponding to the working condition;

[0016] Step 2.3: Perform linear stability analysis on the flow field under each working condition calculated in Step 2.2 to obtain the growth rate of each grid point. The specific process is as follows:

[0017] When performing linear stability analysis on the flow field under each working condition, set several groups of frequency and spanwise wave number combinations, and calculate the growth rate corresponding to each group of frequency and spanwise wave number combinations through linear stability analysis;

[0018] Then integrate the growth rate along the chordwise coordinate of the wing two-dimensional profile to obtain the variation curve of the disturbance growth factor with the chordwise coordinate; furthermore, obtain a set of variation curves of the disturbance growth factor with the chordwise coordinate;

[0019] Make a common tangent to two adjacent curves in the chordwise direction to obtain the common tangent line segment between the two adjacent curves, and then obtain several common tangent line segments;

[0020] Take the slope of each common tangent line segment as the growth rate of the grid points covered by the common tangent line segment in the chordwise direction;

[0021] Step 3: Establish a multi-layer perceptron and train the multi-layer perceptron using the training sample set obtained in Step 2;

[0022] Step 4: Perform a flow field calculation on the supersonic airliner wing to be predicted under given working conditions, obtain the characteristic parameters, normalize them, and then input them into the trained multi-layer perceptron to obtain the growth rate; calculate the disturbance growth factor using the growth rate , according to the disturbance growth factor Judge the crossflow transition position of the supersonic airliner wing.

[0023] Furthermore, in Step 1.1, on the two-dimensional section of the wing, along the chordwise direction of the wing, the first grid point is 0.0001 m away from the leading edge of the two-dimensional section of the wing, the last grid point is 0.1 m away from the leading edge, and the grid near the leading edge is locally refined, with a total of 120 grid points distributed.

[0024] Furthermore, in Step 1.2, when the wing is a sharp leading edge wing, the pressure gradient distribution function adopts

[0025] .

[0026] Furthermore, in Step 1.2, when the wing is a blunt leading edge wing, the pressure gradient distribution function adopts

[0027] .

[0028] Furthermore, in Step 1.3, for , Take it as 0.3, Take it as -0.15; for , Take it as 0.02, Take it as -0.01.

[0029] Furthermore, in Step 1.3, the outer edge velocity in the spanwise direction .

[0030] Furthermore, in Step 2.2, the characteristic parameters include the Mach number at the outer edge of the boundary layer , the Reynolds number of the crossflow thickness , the streamwise kinematic shape factor , the crossflow shape factor , the wall temperature and the temperature at the outer edge of the boundary layer The ratio and the maximum cross - flow velocity to the velocity at the outer edge of the boundary layer The ratio .

[0031] Furthermore, in step 2.2, the cross - flow thickness Reynolds number is defined as:

[0032]

[0033] where is the density at the outer edge of the boundary layer, is the viscosity coefficient at the outer edge of the boundary layer, is the cross - flow thickness, is the maximum cross - flow velocity.

[0034] Furthermore, in step 2.2, the streamwise kinematic shape factor is obtained through the streamwise velocity and the streamwise velocity at the outer edge as follows:

[0035]

[0036] where is the normal coordinate on the wing surface.

[0037] Furthermore, in step 2.2, the cross - flow shape factor is defined as the ratio of the wall height where the maximum cross - flow velocity is located to the cross - flow thickness The ratio:

[0038] .

[0039] Beneficial effects:

[0040] The supersonic airliner wing cross - flow transition prediction method based on a multi - layer perceptron proposed by the present invention takes into account the strong three - dimensional effects under supersonic conditions. By artificially constructing a quasi - three - dimensional compressible non - similarity boundary layer, compared with the traditional real - boundary - layer sampling method, it saves the workload and computational cost of geometric modeling, grid generation, and aerodynamic calculation.

[0041] In addition, for the problem that it is difficult to accurately identify the N - factor envelope for different frequencies and spanwise wave numbers of perturbations in the present invention, a piece - wise linear fitting method is used to approximate the envelope. At this time, the slope of the line segment in each interval can be used as an approximate value of the local growth rate of the envelope, so that the growth rate of each grid point can be obtained quickly.

[0042] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be learned by practice of the present invention. Brief Description of the Drawings

[0043] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0044] Figure 1 : Schematic diagram of artificial quasi-three-dimensional non-similar boundary layer;

[0045] Figure 2 : Schematic diagram of multi-layer perceptron model;

[0046] Figure 3 : Schematic diagram of boundary layer grid along inviscid streamline;

[0047] Figure 4 : Comparison diagram of multi-layer perceptron prediction results, standard stability analysis prediction results and actual flight infrared data in test condition 1;

[0048] Figure 5 : Comparison diagram of multi-layer perceptron prediction results, standard stability analysis prediction results and actual flight infrared data in test condition 2;

[0049] Figure 6 : Prediction results of disturbance growth factor in test condition 3;

[0050] Figure 7 : Test transition line in test condition 3;

[0051] Figure 8 : Predicted transition line in test condition 3. Detailed Embodiments

[0052] Embodiments of the present invention will be described in detail below. The embodiments are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

[0053] In view of the need for predicting crossflow transition of supersonic airliner wings, the present invention uses a multi-layer perceptron to model and predict crossflow transition, which specifically includes the following steps:

[0054] Step 1: For a supersonic airliner wing, artificially construct a quasi-three-dimensional non-similar boundary layer; including the following steps:

[0055] Step 1.1: Let the sweep angle of the supersonic airliner wing be ; For the three-dimensional model of the wing, cut to obtain two-dimensional wing profiles along the wing chord direction, determine the grid point range on the two-dimensional wing profile, and take several grid points within the grid point range;

[0056] In this embodiment, on the two-dimensional wing section, along the chord direction of the wing, the first grid point is 0.0001 m away from the leading edge of the two-dimensional wing section, and the last grid point is 0.1 m away from the leading edge. The grid near the leading edge is locally refined, and a total of 120 grid points are distributed.

[0057] Step 1.2: For the two-dimensional wing section, a pressure gradient distribution function is given , where is the chordwise coordinate in the two-dimensional wing section is a function of;

[0058] In this embodiment, two different pressure gradient distribution functions are designed for the sharp leading-edge wing and the blunt leading-edge wing respectively:

[0059]

[0060] is the pressure gradient distribution function obtained by fitting the pressure gradient distribution of the sharp leading-edge wing model;

[0061]

[0062] is the pressure gradient distribution function obtained by fitting the pressure gradient distribution of the blunt leading-edge wing model.

[0063] Step 1.3: Set the chordwise outer edge velocity at the initial boundary layer position in the two-dimensional wing section as a function of the oncoming flow velocity and the spanwise outer edge velocity :

[0064]

[0065] where and are set coefficients;

[0066] In this embodiment, for , is taken as 0.3, is taken as -0.15; for , is taken as 0.02, is taken as -0.01.

[0067] In this embodiment, the spanwise outer edge velocity .

[0068] Step 1.4: Based on the pressure gradient distribution function given in Step 1.2, with the chordwise outer edge velocity at the initial boundary layer position given in Step 1.3 is the initial condition. According to the incoming flow Mach number , incoming flow temperature , incoming flow unit Reynolds number , by solving the boundary layer equations, a quasi-three-dimensional non-similar boundary layer is artificially constructed;

[0069] For the artificially constructed quasi-three-dimensional non-similar boundary layer, the further explanation is as follows:

[0070] The so-called artificially constructed quasi-three-dimensional non-similar boundary layer means that by artificially giving the initial conditions and the pressure gradient distribution function, the laminar basic flow is obtained by using the conventional methods in the art to solve the boundary layer equations. Therefore, this is a hypothetical boundary layer flow model. However, compared with the traditional method that needs to first solve the inviscid flow field and extract the wall solution as an approximation of the flow parameters at the outer edge of the boundary layer, using the artificially constructed quasi-three-dimensional non-similar boundary layer can avoid the additional time consumption brought by dealing with geometry and grids.

[0071] The schematic diagram of the artificial quasi-three-dimensional non-similar boundary layer is as Figure 1 shown. Based on the incoming flow Mach number , incoming flow temperature and incoming flow unit Reynolds number on the influence of the initial conditions, different pressure gradient distribution functions are introduced on this basis to control the generation of different boundary conditions, and the non-similar boundary layer solutions under different flow conditions can be obtained by changing these parameters.

[0072] Step 2: Establish a training sample set. Each sample in the training sample set consists of the characteristic parameters and growth rates of each grid point under a certain working condition, where the characteristic parameters are used as the input features of the multi-layer perceptron, and the growth rate is used as the output label. The specific process of establishing the training sample set is as follows:

[0073] Step 2.1: For the given pressure gradient distribution function , perform working condition sampling on the incoming flow Mach number , incoming flow temperature , incoming flow unit Reynolds number and sweep angle ;

[0074] In this embodiment, the sampling points of the cross-flow standing wave compressible quasi-three-dimensional non-similar boundary layer are:

[0075]

[0076] Step 2.2: Perform flow field calculations on the quasi-three-dimensional non-similar boundary layer obtained in Step 1 under each operating condition sampled in Step 2.1 to obtain the flow field corresponding to the operating condition and the characteristic parameters of each grid point. The specific process of the flow field calculation can be achieved by using conventional means in the art;

[0077] In this embodiment, the selected characteristic parameters fully reflect the flow field information, specifically including the Mach number at the outer edge of the boundary layer , the Reynolds number of the cross-flow thickness , the kinematic shape factor in the flow direction , the cross-flow shape factor , the wall temperature and the ratio of the temperature at the outer edge of the boundary layer ; as well as the ratio of the maximum cross-flow velocity to the velocity at the outer edge of the boundary layer ; ;

[0078] To reflect the overall flow state, the characteristic parameters include the Mach number at the outer edge of the boundary layer and the Reynolds number of the cross-flow thickness ; is defined as:

[0079]

[0080] where is the density at the outer edge of the boundary layer, is the viscosity coefficient at the outer edge of the boundary layer, is the cross-flow thickness, is the maximum cross-flow velocity.

[0081] To reflect the temperature profile shape parameter, the characteristic parameters include the ratio of the wall temperature to the temperature at the outer edge of the boundary layer ; ;

[0082] To reflect the influence of the pressure gradient on the flow direction velocity profile of the boundary layer, the characteristic parameters include the kinematic shape factor in the flow direction , obtained from the flow direction velocity and the outer edge flow direction velocity as:

[0083]

[0084] where is the normal coordinate of the wing surface;

[0085] To reflect the distribution characteristics of the cross-flow velocity profile, the characteristic parameters include the cross-flow shape factor , defined as the maximum cross-flow velocity Height of the wall where it is located Ratio to the cross-flow thickness, which can also reflect the pressure gradient and the local sweep angle of the boundary layer Effect on the cross-flow velocity profile:

[0086]

[0087] Among them, the local sweep angle of the boundary layer is .

[0088] To further characterize the effect of the pressure gradient and the local sweep angle of the boundary layer on the cross-flow velocity profile, the characteristic parameters include the ratio of the maximum cross-flow velocity to the velocity at the outer edge of the boundary layer : .

[0089] Step 2.3: Perform linear stability analysis on the flow field under each working condition calculated in Step 2.2 to obtain the growth rate of each grid point. In the art, performing linear stability analysis itself is a conventional method; the process of directly obtaining the growth rate of each grid point in traditional linear stability analysis requires a huge amount of calculation. In actual calculations, due to the limitation of the amount of calculation, it is impossible to traverse all frequencies and spanwise wave numbers. Therefore, the present invention calculates the perturbation growth factor by means of piecewise linear fitting and uses the slope of the common tangent line segment between adjacent curves as the approximation value of the local growth rate of the perturbation growth factor

[0090] envelope curve. The specific process is as follows: When performing linear stability analysis on the flow field under each working condition, set several groups of frequency and spanwise wave number combinations, and calculate the growth rate corresponding to each group of frequency and spanwise wave number combinations through linear stability analysis; then integrate the growth rate along the chordwise coordinate of the two-dimensional wing section to obtain the variation curve of the perturbation growth factor with the chordwise coordinate; and each group of frequency and spanwise wave number combinations corresponds to a perturbation growth factor , and several groups of frequency and spanwise wave number combinations are set for each working condition, so as to obtain a set of variation curves of the perturbation growth factor with the chordwise coordinate; make a common tangent line to the two adjacent curves in the chordwise direction to obtain the common tangent line segment between the two adjacent curves, and then obtain several common tangent line segments; use the slope of each common tangent line segment as the growth rate of the grid points covered by the common tangent line segment along the chordwise direction.

[0091] Step 3: Establish a multi-layer perceptron and train the multi-layer perceptron using the training sample set obtained in Step 2.

[0092] In this embodiment, the multi-layer perceptron includes 5 hidden layers, with 40 neurons in each layer, and the activation function is uniformly taken as the Sigmoid function.

[0093] Before training, the maximum-minimum normalization method is used to normalize both the feature parameters and labels in the training samples to the range of 0 to 1. The training sample set is divided into a training set and a validation set according to a ratio of 9:1, and the loss is calculated on the training set and the validation set to observe the convergence trend. Finally, the trained multi-layer perceptron is obtained.

[0094] Step 4: When actually making predictions, the flow field of the supersonic airliner wing to be predicted is calculated under given working conditions to obtain the feature parameters. After normalization, they are input into the trained multi-layer perceptron to obtain the growth rate, and the disturbance growth factor is calculated using the growth rate. , according to the disturbance growth factor to judge the crossflow transition position of the supersonic airliner wing.

[0095] Data verification:

[0096] Next, the multi-layer perceptron is used to predict the N-factor envelope for the test conditions of the NASA standard model, and it is compared with the flight test results and the calculation results of the Lewis R. Owens standard stability analysis, so as to verify the prediction ability of the multi-layer perceptron proposed in the present invention, as well as the effectiveness and reliability of the training strategy based on the small-batch non-similar boundary layer stability analysis results and the fully data-driven transition modeling method in the real swept-wing flow.

[0097] To study the transition induced by crossflow instability in the supersonic boundary layer and its control mechanism, NASA designed a large-swept wing standard model and carried out a series of CFD calculations, flight and wind tunnel tests from 2014 to 2018. Among them, the flight test was completed on the F-15B carrier platform at the Armstrong Flight Research Center. It was observed that the leading edge of the transition on the wing surface was serrated, so it was considered to be caused by the instability of the crossflow standing wave.

[0098] The leading edge sweep angle of this standard model is 65°, the wingtip cut angle is 35°, the wing root chord length is 566.8 mm, the maximum thickness is 39.7 mm, the chord length perpendicular to the leading edge is 239.5 mm, the span is 266.7 mm, the sectional airfoil is a double circular arc airfoil, and the leading edge is connected by a parabola with a vertex radius of 0.254 mm. The extremely small head radius can effectively prevent the interference of the transition phenomenon caused by the instability of the leading edge attachment line. Three groups of flight test conditions at the NASA Langley Research Center are selected in this paper to verify the prediction ability of the multi-layer perceptron, as shown in Table 1:

[0099] Table 1 Test conditions

[0100]

[0101] The schematic diagram of the computational grid is shown in Figure 3 , and the calculation results and comparisons are as Figures 4 to 8 shown. It can be seen from the figure that compared with the existing methods for predicting the envelope of the disturbance growth factor in the similarity solution training, the present invention uses the results of the small-batch artificial non-similar boundary layer stability analysis, rather than the stability analysis data of the real boundary layer, to train the multi-layer perceptron. It can also be effectively applied to the prediction problem of the transition of the real boundary layer with strong three-dimensional flow effects such as a finite-span swept wing, and only needs to be trained once and can be used infinitely. The meaning of "artificial" here refers to that both the initial conditions and boundary conditions required for solving the non-similar boundary layer equations are artificially defined and expressed as functions of the oncoming flow parameters. This construction method eliminates the extra workload and computational cost of dealing with the real geometry, grid, and flow field, and uses the powerful learning ability of the multi-layer perceptron to obtain the relationship between the disturbance factor growth rate and the basic flow characteristic parameters. The test results of the real boundary layer show that the present invention can effectively predict the envelope of the disturbance growth factor.

[0102] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and purposes of the present invention.

Claims

1. A method for predicting the cross-flow transition of a supersonic airliner wing based on a multi-layer perceptron, characterized in that: Including the following steps: Step 1: For the wing of a supersonic airliner, artificially construct a quasi-three-dimensional non-similar boundary layer; including the following steps: Step 1.1: Set the sweep angle of the supersonic airliner wing to be ; For the three-dimensional model of the wing, obtain the two-dimensional wing profiles along the chord direction of the wing by slicing, determine the grid point range on the two-dimensional wing profile, and take several grid points within the grid point range; Step 1.2: For the two-dimensional wing section, a pressure gradient distribution function is given , where is the chordwise coordinate in the two-dimensional wing section is a function of; Step 1.3: Set the chordwise outer edge velocity at the initial boundary layer station in the two-dimensional wing section to be a function of the oncoming flow velocity and the spanwise outer edge velocity : wherein and are set coefficients; Step 1.4: Based on the pressure gradient distribution function given in Step 1.2 , using the chordwise outer edge velocity at the initial position of the boundary layer given in Step 1.3 as the initial condition, according to the incoming flow Mach number , incoming flow temperature , incoming flow unit Reynolds number , , by solving the boundary layer equations, artificially construct a quasi-three-dimensional non-similar boundary layer;​ Step 2: Establish a training sample set. Each sample in the training sample set consists of the characteristic parameters and growth rates of each grid point under a certain working condition, where the characteristic parameters are used as the input features of the multi-layer perceptron, and the growth rate is used as the output label; the process of establishing the training sample set is as follows: Step 2.1: For the given pressure gradient distribution function , sample the working conditions for the incoming flow Mach number , the incoming flow temperature , the incoming flow unit Reynolds number , and the sweep angle . Step 2.2: Perform flow field calculations on the quasi-three-dimensional non-similar boundary layer obtained in Step 1 under each working condition sampled in Step 2.1 to obtain the flow field and the characteristic parameters of each grid point corresponding to the working condition; Step 2.3: Conduct linear stability analysis on the flow field under each working condition calculated in Step 2.2 to obtain the growth rates of each grid point. The specific process is as follows: When conducting linear stability analysis on the flow field under each working condition, set several groups of frequency and spanwise wave number combinations, and calculate the growth rate corresponding to each group of frequency and spanwise wave number combinations through linear stability analysis; Integrate the growth rate along the chordwise coordinate of the two-dimensional wing section to obtain the disturbance growth factor as a function of the chordwise coordinate; and then obtain a set of disturbance growth factors as functions of the chordwise coordinate; Make a common tangent to two adjacent curves in the chordwise direction to obtain the common tangent line segment between the two adjacent curves, and then obtain several common tangent line segments; Use the slope of each common tangent line segment as the growth rate of the grid points covered by the common tangent line segment along the chordwise direction; Step 3: Establish a multi-layer perceptron and train the multi-layer perceptron using the training sample set obtained in Step 2; Step 4: Perform a flow field calculation on the supersonic airliner wing to be predicted under given working conditions. After obtaining the characteristic parameters and normalizing them, input them into the trained multi-layer perceptron to obtain the growth rate; calculate the disturbance growth factor using the growth rate , and based on the disturbance growth factor judge the cross-flow transition position of the supersonic airliner wing.

2. The method for predicting the crossflow transition of a supersonic airliner wing based on a multi-layer perceptron according to claim 1, wherein: In Step 1.1, on the two-dimensional section of the wing, along the chordwise direction of the wing, the first grid point is 0.0001 m away from the leading edge of the wing two-dimensional section, the last grid point is 0.1 m away from the leading edge, and the grid near the leading edge is locally refined, with a total of 120 grid points distributed.

3. The method for predicting the cross-flow transition of the wing of a supersonic airliner based on a multi-layer perceptron according to claim 1, wherein: In Step 1.2, when the wing is a sharp leading edge wing, the pressure gradient distribution function is used 。 4. The supersonic airliner wing crossflow transition prediction method based on a multi-layer perceptron according to claim 3, characterized in that: In Step 1.2, when the wing is a blunt leading edge wing, the pressure gradient distribution function is used 。 5. The supersonic airliner wing crossflow transition prediction method based on a multi-layer perceptron according to claim 4, characterized in that: In Step 1.3, for , is taken as 0.3, is taken as -0.15; for , is taken as 0.02, is taken as -0.

01.

6. The method for predicting the cross-flow transition of a supersonic airliner wing based on a multi-layer perceptron according to claim 1, characterized in that: In step 1.3, the outward edge velocity .

7. The method for predicting the cross-flow transition of the wing of a supersonic airliner based on a multi-layer perceptron according to claim 1, wherein: In step 2.2, the characteristic parameters include the Mach number at the outer edge of the boundary layer , the Reynolds number of the cross-flow thickness , the streamwise kinematic shape factor , the cross-flow shape factor , the wall temperature and the ratio of the temperature at the outer edge of the boundary layer as well as the ratio of the maximum cross-flow velocity to the velocity at the outer edge of the boundary layer .​​ 8. A method for predicting the crossflow transition of a supersonic airliner wing based on a multi-layer perceptron according to claim 7, characterized in that: In Step 2.2, the cross-flow thickness Reynolds number is defined as: wherein is the density at the outer edge of the boundary layer, is the viscosity coefficient at the outer edge of the boundary layer, is the cross-flow thickness, is the maximum cross-flow velocity.

9. The method for predicting the crossflow transition of a supersonic airliner wing based on a multi-layer perceptron according to claim 7, wherein: In step 2.2, the streamwise kinematic shape factor is obtained from the streamwise velocity and the streamwise velocity at the outer edge as follows: wherein is the normal coordinate of the wing surface.

10. The method for predicting the cross-flow transition of the wing of a supersonic airliner based on a multi-layer perceptron according to claim 7, wherein: In Step 2.2, the cross-flow shape factor is defined as the ratio of the height of the wall where the maximum cross-flow velocity is located to the cross-flow thickness : 。

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