Aircraft external flow field inversion method based on Fourier neural operator

Abstract

The invention discloses an aircraft external flow field inversion method based on a Fourier neural operator, and belongs to the technical field of fluid mechanics. The aircraft external flow field inversion method comprises the following steps: obtaining training data; constructing a neural network agent model by adopting a Fourier neural operator to obtain a Fourier neural operator model; randomly initializing a Fourier neural operator model, and training the Fourier neural operator model by using the training data to fit a mapping relationship between the aircraft surface pressure measuring point and the aircraft external flow field; and inputting the external flow field data of the aircraft into the trained Fourier neural operator model, and inverting a real external flow field of the aircraft. According to the method, the neural network agent model is constructed by introducing the Fourier neural operator, the velocity field and the pressure field outside the aircraft are inversed through the surface pressure intensity of the aircraft, the calculation efficiency higher than that of a convolutional neural network can be achieved, meanwhile, when the resolution of input and output data is changed, retraining is not needed, and the calculation efficiency is improved. And relatively high inversion accuracy can be maintained.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid mechanics, and in particular to an aircraft external flow field inversion method based on Fourier neural operator. Background Art

[0002] During the operation of the aircraft, it is necessary to monitor the external flow field of the aircraft and sense the flight status of the aircraft. Generally speaking, the external flow field environment of the aircraft can be sensed by placing sensors on the outside of the aircraft. However, since the surface velocity field is not easy to obtain, and the pressure field on the aircraft surface is relatively easy to measure, the pressure field on the aircraft surface is used to invert the external flow field of the aircraft. Therefore, inverting the global flow field through the pressure field data on the aircraft surface has become an important part of flow field perception. However, only a limited number of measurement point data can be obtained through sensors on the surface of the aircraft, and the external flow field (velocity field, pressure field) of the aircraft is high-dimensional data, and CFD simulation in fluid mechanics usually requires a lot of computing time and computing resources, which is not suitable for flow field inversion tasks.

[0003] The existing use of proxy models for inversion is a typical method to improve this situation. Compared with the CFD method, the proxy model has accurate calculation results and less calculation. After the proxy model is trained, the proxy model can be used for rapid inversion. Among the commonly used proxy model methods, support vector machine (SVM), Gaussian process regression (GP), convolutional neural network (CNN), etc. are commonly used methods, but SVM and GP cannot handle high-dimensional regression problems. Although CNN has achieved great success in various visual tasks, it can learn hidden features in the data through end-to-end training under the premise of meeting sufficient samples. However, when using the CNN structure to learn complex data, it is accompanied by a deeper and more complex network structure, which cannot meet the real-time requirements of aircraft flow field inversion. Moreover, the above-mentioned method is used to construct a proxy model, which can often only learn data with fixed input and output resolutions. When facing flow field data with different resolutions, it needs to be retrained, which is inefficient. Summary of the invention

[0004] In order to solve some or all of the technical problems existing in the above-mentioned prior art, the present invention provides a method for inverting the external flow field of an aircraft based on a Fourier neural operator. By introducing the Fourier neural operator to construct a neural network proxy model, the velocity field and pressure field outside the aircraft are inverted using the aircraft surface pressure. This can achieve higher computing efficiency than a convolutional neural network. At the same time, when the resolution of the input and output data is changed, no retraining is required, and a high inversion accuracy can be maintained.

[0005] The technical solution of the present invention is as follows:

[0006] The present invention provides an aircraft external flow field inversion method based on Fourier neural operator, the method comprising:

[0007] Get training data;

[0008] A neural network proxy model is constructed using a Fourier neural operator to obtain a Fourier neural operator model;

[0009] The Fourier neural operator model is randomly initialized, and the Fourier neural operator model is trained using training data to fit the mapping relationship between the pressure measurement points on the aircraft surface and the external flow field of the aircraft;

[0010] The external flow field data of the aircraft is input into the trained Fourier neural operator model to invert the actual external flow field of the aircraft.

[0011] Furthermore, in the above-mentioned aircraft external flow field inversion method based on Fourier neural operator, the acquired training data includes point position data detected by sensors set on the aircraft during the flight of the aircraft.

[0012] Furthermore, in the above-mentioned aircraft external flow field inversion method based on Fourier neural operator, the point data includes pressure point data.

[0013] Furthermore, in the above-mentioned aircraft external flow field inversion method based on Fourier neural operator, the neural network proxy model constructed by using Fourier neural operator includes:

[0014] Among them, the Fourier neural operator is expressed as v0→v1...→v t →v t+1 Iterative architecture;

[0015] Among them, v t →v t+1 Updated by the following formula;

[0016] v t+1 (x) = σ(Wv t (x)+(K(θ)v t )(x))

[0017] Among them, v t+1 represents the function at time t+1, x represents the input signal, σ represents the nonlinear activation function, W represents the linear transformation, and v t represents the function at time t, θ represents the network parameters, K represents a bounded linear operator and is described by the network parameters θ, and K(θ) represents the neural network agent model described by the network parameters θ;

[0018] Among them, when the Fourier neural operator is used to construct the neural network proxy model, the bounded linear operator K is used as the integral operator for kernel transformation, and the neural network is used to parameterize it, and the convolution operator defined in the Fourier space is used to replace the integral operator. The neural network proxy model constructed by the Fourier neural operator includes:

[0019] (K(θ)v t )(x)=F -1 (R θ ·(Fv t ))(x)

[0020] Among them, F -1 Represents the inverse Fourier transform operation, R θ Represents a transformation matrix.

[0021] Furthermore, in the above-mentioned aircraft external flow field inversion method based on Fourier neural operator, training the Fourier neural operator model using training data includes:

[0022] The pressure measurement point data on the aircraft surface is taken as input, and the aircraft surface flow field corresponding to the pressure measurement point data is taken as output. The collected measurement point data on the aircraft surface is used to construct and train the Fourier neural operator using the fft module in the Pytorch deep learning framework. During the training process, the pressure measurement point data is output to the stacked Fourier layer through one or more channels. Each Fourier layer updates the function's features through a bounded linear operator K, a linear transformation W, and a nonlinear activation function σ. A multi-channel one-dimensional feature vector is obtained through a one-dimensional Fourier operator, and then the multi-channel one-dimensional feature vector is merged into a two-dimensional feature map, which is then inverted through a two-dimensional Fourier operator to obtain the aircraft surface flow field image.

[0023] Furthermore, in the above-mentioned aircraft external flow field inversion method based on Fourier neural operator, the channel includes: a measurement point data input coordinate channel and a pressure value channel.

[0024] Furthermore, in the above-mentioned vehicle external flow field inversion method based on Fourier neural operator, the vehicle surface flow field image including the flow velocity and pressure of the vehicle surface flow field image is inverted by two-dimensional Fourier operator.

[0025] Furthermore, in the above-mentioned vehicle external flow field inversion method based on Fourier neural operator, it also includes inputting the vehicle external flow field data into the trained Fourier neural operator model, inverting the real aircraft external flow field and displaying it through a rectangular flow field, and cutting the external flow field along the body-fitting structure grid of the wing in CFD to describe the aircraft external flow field.

[0026] Furthermore, in the above-mentioned aircraft external flow field inversion method based on Fourier neural operator, the aircraft external flow field data is input into the trained Fourier neural operator model, and the real aircraft external flow field is inverted, including:

[0027] The physical field matrix of the aircraft's external flow field is learned through the Fourier neural operator model to obtain the coordinate matrix of the aircraft's external flow field;

[0028] Restore the real external flow field of the aircraft through the coordinate matrix;

[0029] The image of the actual external flow field of the aircraft is drawn through the coordinate matrix and the physical field matrix.

[0030] The main advantages of the technical solution of the present invention are as follows:

[0031] The aircraft external flow field inversion method based on Fourier neural operator of the present invention introduces Fourier neural operator to construct a neural network proxy model, inputs the pressure measurement point values ​​on the aircraft surface, and the neural operator model outputs the velocity field and pressure field outside the aircraft. It can achieve higher computing efficiency than convolutional neural network. At the same time, when the resolution of input and output data is changed, no retraining is required, and a high inversion accuracy can be maintained. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings described herein are used to provide a further understanding of the embodiments of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0033] Figure 1 A schematic diagram of a flow chart of an aircraft external flow field inversion method based on Fourier neural operator according to an embodiment of the present invention;

[0034] Figure 2 A schematic diagram of the structure of a Fourier neural operator in a method for inverting an aircraft's external flow field based on a Fourier neural operator provided in one embodiment of the present invention;

[0035] Figure 3 It is a schematic diagram of the architecture of the inversion model in the aircraft external flow field inversion method based on Fourier neural operator according to one embodiment of the present invention;

[0036] Figure 4 A schematic diagram of constructing a Fourier neural operator in an aircraft external flow field inversion method based on a Fourier neural operator according to an embodiment of the present invention;

[0037] Figure 5 A schematic diagram of a wing flow field grid in an aircraft external flow field inversion method based on a Fourier neural operator according to an embodiment of the present invention;

[0038] Figure 6This is a sample example diagram of a method for inverting the external flow field of an aircraft based on a Fourier neural operator according to an embodiment of the present invention;

[0039] Figure 7 This is a schematic diagram of a rectangular flow field inverted by a Fourier neural operator model in a method for inverting an external flow field of an aircraft based on a Fourier neural operator according to an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0041] The technical solution provided by the embodiments of the present invention is described in detail below with reference to the accompanying drawings.

[0042] As attached Figure 1-7 As shown, an embodiment of the present invention provides an aircraft external flow field inversion method based on Fourier neural operator, the method comprising the following steps S1-S4:

[0043] Step S1: Obtain training data.

[0044] In one embodiment of the present invention, the acquired training data includes point data detected by sensors disposed on the aircraft during the flight of the aircraft.

[0045] Specifically, the above-mentioned point data includes pressure point data.

[0046] Step S2: Use the Fourier neural operator to construct a neural network proxy model to obtain a Fourier neural operator model.

[0047] Specifically, the neural network agent model constructed using Fourier neural operator includes:

[0048] like Figure 2 As shown, the Fourier neural operator is represented as v0→v1...→v t →v t+1 Iterative architecture, where v0(x) = P(a(x)) projects the input value from the real space into an infinite-dimensional space for parameterization, and the output u(x) = Q(v t (x)) transforms v by local transformation Q t (x) is projected into the real space. In each iteration, v is updated t →v t+1 is defined as a combination of a bounded linear operator and a nonlinear activation function.

[0049] Define v in the following way t →v t+1 Update method:

[0050] v t+1 (x) = σ(Wv t (x)+(K(θ)v t )(x))

[0051] Among them, v t+1 represents the function at time t+1, x represents the input signal, σ represents the nonlinear activation function, W represents the linear transformation, and v t represents the function at time t, θ represents the network parameters, K represents a bounded linear operator and is described by the network parameters θ, and K(θ) represents the neural network agent model described by the network parameters θ;

[0052] Among them, when the Fourier neural operator is used to construct the neural network proxy model, the bounded linear operator K is used as the integral operator for kernel transformation, and the neural network is used to parameterize it, and the convolution operator defined in the Fourier space replaces the integral operator:

[0053] Among them, the kernel integral operator K is defined as:

[0054] (K(θ)v t )(x)=∫ D k(x,y,θ)v t (y)dy

[0055] Among them, k(θ) plays the role of kernel function and can be learned from data. The above two formulas realize the generalization of neural networks to infinite dimensions.

[0056] Next, we will use Fourier transform to parameterize k(θ) for efficient calculation.

[0057] Define the convolution operator in Fourier space to replace the kernel integral operator, assuming that f represents the Fourier transform and F -1 represents the inverse Fourier transform, then:

[0058] (Ff) j (k) = ∫ D f j (x)e -2iπ＜x,k＞ dx

[0059] (F -1 f) j (k) = ∫ D f j (k)e 2iπ<x,k> dk

[0060] By ordering kθ (x,y)=k θ (xy) Then applying the convolution theorem, we can find that:

[0061] (K(θ)v t )(x)=F -1 (R θ ·(Fv t ))(x)

[0062] Where D is the integration domain, R θ Represents the Fourier transform of a periodic function.

[0063] Therefore, the neural network agent model constructed using Fourier neural operator includes:

[0064] (K(θ)v t )(x)=F -1 (R θ ·(Fv t ))(x)

[0065] like Figure 2 As shown, (a) represents the complete architecture of the neural operator: starting from input a; lifting to a higher dimensional channel space through the neural network P; applying four layers of integral operators and activation functions; passing back to the target dimension through the neural network Q; output u. (b) represents the Fourier layer: starting from input v. At the top: applying the Fourier transform F; linearly transforming the low-frequency signal to filter out the higher-frequency signal; then applying the inverse Fourier transform F -1 . At the bottom: a local linear transformation W is applied.

[0066] Specifically, the Fourier neural operator model is randomly initialized, and the Fourier neural operator model is trained using training data to fit the mapping relationship between the pressure measurement points on the aircraft surface and the external flow field of the aircraft;

[0067] Furthermore, in one embodiment of the present invention, training the Fourier neural operator model using training data includes:

[0068] The pressure measurement point data on the aircraft surface is taken as input, and the flow field on the aircraft surface corresponding to the pressure measurement point data is taken as output. The fft module in the Pytorch deep learning framework is used to construct and train the Fourier neural operator based on the collected measurement point data on the aircraft surface.

[0069] Specifically, Figure 3-4As shown in the figure, the measured point data is output to the stacked Fourier layers through one or more channels. Each Fourier layer updates the features of the Fourier neural operator model through a bounded linear operator K, a linear transformation W and a nonlinear activation function σ. After the one-dimensional Fourier operator, a multi-channel one-dimensional feature vector is obtained, and then the multi-channel one-dimensional feature vector is merged into a two-dimensional feature map. The merged two-dimensional feature map is then inverted through a 2-d Fourier neural operator with a temporal RNN structure to obtain the flow field image of the aircraft surface.

[0070] Specifically, the above-mentioned channels include: a measurement point data input space coordinate channel and a pressure value channel.

[0071] Specifically, the aircraft surface flow field image including the flow velocity and pressure of the aircraft surface flow field image is inverted by a two-dimensional Fourier operator.

[0072] Step S4: Input the aircraft external flow field data into the trained Fourier neural operator model to invert the actual aircraft external flow field.

[0073] The physical field matrix of the aircraft's external flow field is learned through the Fourier neural operator model to obtain the coordinate matrix of the aircraft's external flow field; the real external flow field of the aircraft is restored through the coordinate matrix; and the image of the aircraft's actual external flow field is drawn through the coordinate matrix and the physical field matrix.

[0074] As an example, after learning the physical field matrix of the aircraft's external flow field through the Fourier neural operator model, the coordinate matrix X, Y of the aircraft's external flow field is obtained; the actual external flow field of the aircraft is restored through the coordinate matrix X, Y, and the flow field image of the coordinate matrix X, Y corresponds to the coordinates x, y input by the measurement point data. The image of the actual flow field can be drawn through the coordinate matrix and the physical field matrix.

[0075] Furthermore, in one embodiment of the present invention, the method further includes inputting the aircraft external flow field data into a trained Fourier neural operator model, inverting the actual aircraft external flow field and then displaying it through a rectangular flow field.

[0076] Specifically, in order to avoid the disadvantages of rectangular coordinate discretization and to avoid the difficulty in describing the wing edge and the serration of the wing shape caused by the slender shape of the wing, if the flow field is discretized using Cartesian rectangular coordinates, the external flow field can be cut along the body-fitting structure grid of the wing in CFD, thereby achieving an accurate description of the external flow field, such as Figure 5 As shown, Figure 5 The middle arrow i indicates the direction of the cutting line, and the arrow j indicates the direction of the wing.

[0077] Specifically, the flow field is expanded to obtain a rectangular flow field, the upper part of which represents the body-contacting wall, and the lower part represents the outside of the flow field. The left and right columns are the same, and the shear line is located at the tail of the wing. Figure 6-7 As shown, Figure 6 This is a sample example diagram of a method for inverting the external flow field of an aircraft based on a Fourier neural operator according to an embodiment of the present invention; Figure 7 This is a schematic diagram of a rectangular flow field inverted by a Fourier neural operator model in a method for inverting an external flow field of an aircraft based on a Fourier neural operator according to an embodiment of the present invention.

[0078] In summary, the aircraft external flow field inversion method based on Fourier neural operator of the present invention introduces Fourier neural operator to construct a neural network proxy model, and uses the aircraft surface pressure to invert the velocity field and pressure field outside the aircraft, which can achieve higher computing efficiency than convolutional neural network. At the same time, when the resolution of input and output data is changed, no retraining is required, and a high inversion accuracy can be maintained.

[0079] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In addition, "front", "back", "left", "right", "upper" and "lower" in this article are all referenced to the placement state shown in the accompanying drawings.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for inverting the external flow field of an aircraft based on Fourier neural operator, characterized in that: include: Get training data; A neural network proxy model is constructed using a Fourier neural operator to obtain a Fourier neural operator model; The Fourier neural operator model is randomly initialized, and the Fourier neural operator model is trained using training data to fit the mapping relationship between the pressure measurement points on the aircraft surface and the external flow field of the aircraft; The external flow field data of the aircraft is input into the trained Fourier neural operator model to invert the actual external flow field of the aircraft.

2. The method for inverting the external flow field of an aircraft based on Fourier neural operator according to claim 1 is characterized in that: The acquired training data includes point position data detected by sensors installed on the aircraft during the flight of the aircraft.

3. The method for inverting the external flow field of an aircraft based on Fourier neural operator according to claim 2 is characterized in that: The point data includes pressure point data.

4. The method for inverting the external flow field of an aircraft based on Fourier neural operator according to claim 1, characterized in that: The neural network agent model constructed using Fourier neural operators includes: The Fourier neural operator is represented as v0→v1...→v t →v t+1 Iterative architecture; Among them, v t →v t+1 Updated by the following formula; v t+1 (x)=σ(Wv t (x)+(K(θ)v t )(x)) Among them, v t+1 represents the function at time t+1, x represents the input signal, σ represents the nonlinear activation function, W represents the linear transformation, and v t represents the function at time t, θ represents the network parameters, K represents a bounded linear operator and is described by the network parameters θ, and K(θ) represents the neural network agent model described by the network parameters θ; Among them, when the Fourier neural operator is used to construct the neural network proxy model, the bounded linear operator K is used as the integral operator for kernel transformation, and the neural network proxy model is used for parameterization, and the convolution operator defined in the Fourier space replaces the integral operator. The neural network proxy model constructed by the Fourier neural operator includes: (K(θ)v t )(x)=F -1 (R θ ·(Fv t ))(x) Among them, F -1 Represents the inverse Fourier transform operation, R θ Represents a transformation matrix.

5. The method for inverting the external flow field of an aircraft based on Fourier neural operator according to claim 4 is characterized in that: Training the Fourier neural operator model using training data includes: The pressure measurement point data on the aircraft surface is taken as input, and the aircraft surface flow field corresponding to the pressure measurement point data is taken as output. The collected measurement point data on the aircraft surface is used to construct and train the Fourier neural operator using the fft module in the Pytorch deep learning framework. During the training process, the pressure measurement point data is output to the stacked Fourier layers through one or more channels. Each Fourier layer updates the features of the Fourier neural operator model through a bounded linear operator K, a linear transformation W and a nonlinear activation function σ. A multi-channel one-dimensional feature vector is obtained through a one-dimensional Fourier operator, and then the multi-channel one-dimensional feature vector is merged into a two-dimensional feature map, which is then inverted through a two-dimensional Fourier operator to obtain the aircraft surface flow field image.

6. The method for inverting the external flow field of an aircraft based on Fourier neural operator according to claim 5 is characterized in that: The channels include: a measuring point data input coordinate channel and a pressure value channel.

7. The method for inverting the external flow field of an aircraft based on Fourier neural operator according to claim 5, characterized in that: The aircraft surface flow field image including the flow velocity and pressure of the aircraft surface flow field image is inverted by two-dimensional Fourier operator.

8. The method for inverting the external flow field of an aircraft based on Fourier neural operator according to claim 1, characterized in that: It also includes inputting the aircraft's external flow field data into a trained Fourier neural operator model, inverting the real aircraft's external flow field and then displaying it through a rectangular flow field, and cutting the inverted real aircraft flow field along the body-fitting structural grid of the wing in CFD to describe the aircraft's external flow field.

9. The method for inverting the external flow field of an aircraft based on Fourier neural operator according to claim 4, characterized in that: The external flow field data of the aircraft is input into the trained Fourier neural operator model to invert the real external flow field of the aircraft, including: The physical field matrix of the aircraft's external flow field is learned through the Fourier neural operator model to obtain the coordinate matrix of the aircraft's external flow field; Restore the real external flow field of the aircraft through the coordinate matrix; The image of the actual external flow field of the aircraft is drawn through the coordinate matrix and the physical field matrix.

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