A Fast Prediction Method for Airfoil Icing Shape Based on Empirical Wavelet Transform

Abstract

This invention provides a fast prediction method for airfoil icing shape based on empirical wavelet transform, comprising: acquiring icing meteorological parameters; inputting the icing meteorological parameters into a pre-trained target neural network to predict the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions and the first K order Fourier modes of the icing thickness curve signal, where K is a positive integer; constructing a bandpass filter based on the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions; obtaining empirical wavelet transform modes of each order based on the bandpass filter and the first K order Fourier modes of the icing thickness curve signal; superimposing the empirical wavelet transform modes of each order to obtain the icing thickness curve signal; and performing a target transform on the icing thickness curve signal to obtain the airfoil icing shape. By implementing this invention, high prediction accuracy can be maintained under different conditions, the prediction generalization ability is enhanced, and the prediction efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the field of wing icing prediction, specifically relating to a rapid prediction method for airfoil icing shape based on empirical wavelet transform. Background Technology

[0002] When aircraft fly in cloud, rain, snow, or fog conditions, supercooled water droplets in the air can impact the aircraft's surface and form ice. When the aircraft's wings, tail, and other lifting surfaces become icy, the aircraft's aerodynamic shape is damaged, leading to reduced lift and increased drag. Simultaneously, the stall angle of attack decreases, resulting in a deterioration in the aircraft's aerodynamic performance. Therefore, predicting aircraft icing under different weather conditions is crucial for ensuring flight safety.

[0003] Current methods for predicting aircraft icing primarily employ flight testing, wind tunnel testing, and numerical simulation. While numerical simulation is more time-efficient and less labor-intensive than flight testing and wind tunnel testing, it still consumes significant computational resources. Traditional numerical simulation of icing patterns involves iterative processes of flow field calculation, water droplet collection coefficient calculation, water-ice phase transition analysis, and mesh transformation, which is extremely time-consuming. By introducing intelligent prediction methods such as neural networks, computational efficiency can be significantly improved, enabling rapid and accurate prediction of icing patterns.

[0004] To accelerate ice shape prediction and reduce computational resource consumption, researchers have constructed a reduced-order model. Proper Orthogonal Decomposition (POD) is common in flow field analysis; this method can decompose a series of standard orthogonal modes from large amounts of data, making it a powerful data dimensionality reduction and decomposition method. In recent years, machine learning has expanded into multiple research and industrial fields. With the continuous development and maturation of neural networks, using numerical simulation methods combined with neural networks to predict wing icing has become a research hotspot. Researchers can first establish a detailed ice shape sample space through numerical simulation, and then train the neural network to learn the relationship between input meteorological condition parameters and icing shapes, thereby achieving rapid prediction of ice shapes under different icing conditions. Chang et al. proposed a new technique based on wavelet packet transform and artificial neural networks. Wavelet packet decomposition is used to reduce the number of input vectors to the neural network and improve training convergence, thereby predicting icing conditions on the wing surface. Massegur et al. proposed a framework for a low-dimensional airfoil icing model based on POD and a convolutional autoencoder (Conv-AE), which can well simulate extremely complex ice shapes.

[0005] The above methods can effectively improve prediction efficiency, but they lack consideration of the physical mechanism of icing, resulting in limited generalization ability of prediction, especially insufficient accuracy and reliability of prediction under different conditions. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a fast prediction method for airfoil icing shape based on empirical wavelet transform, so as to meet the need to improve the generalization ability of airfoil icing shape prediction.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] According to a first aspect, the present invention provides a method for rapid prediction of airfoil icing shape based on empirical wavelet transform, comprising: acquiring icing meteorological parameters; inputting the icing meteorological parameters into a pre-trained target neural network to predict the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions and the first K order Fourier modes of the icing thickness curve signal, wherein K is a positive integer; constructing a bandpass filter based on the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions; obtaining empirical wavelet transform modes of each order based on the bandpass filter and the first K order Fourier modes of the icing thickness curve signal; superimposing the empirical wavelet transform modes of each order to obtain the icing thickness curve signal; and performing a target transform on the icing thickness curve signal to obtain the airfoil icing shape.

[0009] Optionally, the target neural network includes a first neural network and a second neural network. The first neural network predicts the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions based on icing meteorological parameters. The second neural network predicts the first K-order Fourier modes of the icing thickness curve signal based on icing meteorological parameters. The samples for the training process of the first or second neural network are obtained as follows: the aerodynamic characteristics of the airfoil and icing shape samples under different icing conditions are constructed based on numerical simulations. Icing conditions include inflow velocity, temperature, liquid water content, and average droplet volume diameter. Icing shapes include fuzzy ice shape, clear ice shape, and supercooled large water droplet ice shape. Ice shape; determine the thickness of different ice shapes at the nodal positions on the airfoil surface under various icing conditions, and obtain the ice thickness curve signal under various icing conditions; perform Fourier transform on the ice thickness curve signal under various icing conditions to obtain the ice thickness curve signal spectrum under various icing conditions; based on the ice thickness curve signal spectrum under various icing conditions, obtain the first K order Fourier mode labels of the ice thickness curve signal under various icing conditions, and use them as the sample labels of the second neural network; take the minimum value of the ice thickness curve signal spectrum under various icing conditions as the empirical wavelet transform boundary value label under various icing conditions, and use it as the training sample label of the first neural network.

[0010] Optionally, both the first and second neural networks are backpropagation (BP) neural networks; the BP neural network adopts a single hidden layer structure, with the hidden layer containing 10 neurons; the activation function is Sigmoid, and the mean squared error is used as the model performance evaluation metric.

[0011] Optionally, based on the first K Fourier modes of the bandpass filter and the ice thickness curve signal, the empirical wavelet transform modes of each order are obtained, including: obtaining the predicted ice thickness curve signal based on the first K Fourier modes of the ice thickness curve signal; performing an inner product between the bandpass filter and the predicted ice thickness curve signal to obtain detail coefficients and approximation coefficients; determining the Nth-order empirical wavelet transform mode based on the empirical wavelet function and detail coefficients used to construct the bandpass filter, where N is a positive integer; and determining the 0th-order empirical wavelet transform mode based on the empirical wavelet scaling function and approximation coefficients used to construct the bandpass filter.

[0012] Optionally, the empirical wavelet transform modes of different orders are superimposed to obtain the icing thickness curve signal, including:

[0013]

[0014] Where f(t) is the ice thickness curve signal, For detail coefficients, The coefficients are approximation coefficients, where N represents the Nth mode, and Ψ n (ω) represents the empirical wavelet function, Φ n (ω) represents the scaling function of the empirical wavelet, Ψ n (t) and Φ n (t) represents Ψ n (ω) and Φ n Inverse Fourier transform of (ω), yes Fourier transform, yes Fourier transform.

[0015] Optionally, a fast prediction method for airfoil icing shape based on empirical wavelet transform further includes: calculating the leading-edge stagnation point ice thickness error h between the predicted airfoil icing shape and the original ice shape. sp ,include:

[0016]

[0017] Among them, h pre h represents the predicted ice thickness at the leading edge of the ice shape. sim This represents the ice thickness at the leading edge stagnation point of the ice shape obtained from numerical simulation.

[0018] Optionally, a rapid prediction method for airfoil icing profiles based on empirical wavelet transform further includes: calculating the lift-drag coefficients and stall angle of attack of the predicted icing airfoil and the original icing airfoil, respectively, and calculating their error e, including:

[0019]

[0020] Among them, (C)pre ) i This represents the predicted lift (or drag) coefficient of the icing airfoil at an angle of attack of i°, (C sim ) i This represents the lift (or drag) coefficient of the icing airfoil at an angle of attack of i°, obtained from numerical simulation.

[0021] According to a second aspect, embodiments of the present invention provide a rapid prediction device for airfoil icing shape based on empirical wavelet transform, comprising: a meteorological parameter acquisition module for acquiring icing meteorological parameters; a prediction module for inputting the icing meteorological parameters into a pre-trained target neural network to predict the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions and the first K Fourier modes of the icing thickness curve signal, wherein K is a positive integer; a bandpass filter construction module for constructing a bandpass filter based on the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions; a mode transformation module for obtaining empirical wavelet transform modes of each order based on the bandpass filter and the first K Fourier modes of the icing thickness curve signal; a curve signal determination module for superimposing the empirical wavelet transform modes of each order to obtain the icing thickness curve signal; and an ice shape determination module for performing a target transform on the icing thickness curve signal to obtain the airfoil icing shape.

[0022] According to a third aspect, an embodiment of the present invention provides an electronic device, the device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the steps of the method for rapid prediction of airfoil icing shape based on empirical wavelet transform as described in the first aspect or any embodiment of the first aspect.

[0023] According to a fourth aspect, embodiments of the present invention provide a computer storage medium storing computer instructions that, when executed by a processor, implement the steps of the rapid prediction method for airfoil icing shape based on empirical wavelet transform as described in the first aspect or any embodiment of the first aspect.

[0024] This invention provides a rapid prediction method for airfoil icing shape based on empirical wavelet transform. By exploring wavelet transform mode features under different icing types, the method predicts the airfoil icing shape using these features. Furthermore, the ice shape is reconstructed by superimposing empirical wavelet transform modes of various orders. This approach considers the icing physical mechanisms of different icing types, enabling the proposed prediction method to maintain good prediction accuracy under various conditions and improving its generalization ability. Moreover, the proposed method, using a neural network, can complete the prediction within one minute, while traditional numerical simulation methods require at least 10-20 minutes. This represents a significant reduction in prediction time and an improvement in prediction efficiency of at least 900%, providing a highly efficient and accurate solution for airfoil icing prediction.

[0025] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0026] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0027] Figure 1 This is a flowchart illustrating a specific example of a rapid prediction method for airfoil icing shape based on empirical wavelet transform in this invention.

[0028] Figure 2(a) shows the ice shape of supercooled large water droplets obtained by simulation in this invention;

[0029] Figure 2(b) shows the ice thickness curve signal corresponding to Figure 2(a);

[0030] Figure 3 This is a two-dimensional ice shape diagram of the airfoil surface predicted by the present invention;

[0031] Figure 4 This is the empirical wavelet transform mode diagram of the Mao Bingbing shape in this invention;

[0032] Figure 5(a) shows the ice shape of the raw ice obtained by simulation in this invention;

[0033] Figure 5(b) shows the ice thickness curve signal corresponding to Figure 5(a);

[0034] Figure 6 This is the empirical wavelet transform mode diagram of the Mingbing shape in this invention;

[0035] Figure 7(a) shows the ice shape of clear ice obtained through simulation in this invention;

[0036] Figure 7(b) shows the ice thickness curve signal corresponding to Figure 7(a);

[0037] Figure 8 This is the empirical wavelet transform mode diagram of the ice shape formed by the freezing of supercooled large water droplets in this invention;

[0038] Figure 9 This is a schematic diagram of the network structure of the first neural network in this invention;

[0039] Figure 10 This is a schematic diagram of the network structure of the second neural network in this invention;

[0040] Figure 11(a) shows the curve of lift coefficient as a function of angle of attack in this invention;

[0041] Figure 11(b) shows the curve of drag coefficient as a function of angle of attack in this invention;

[0042] Figure 12 This is a schematic block diagram of a specific example of an electronic device in an embodiment of the present invention. Detailed Implementation

[0043] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can also refer to the internal connection of two components; and they can refer to a wireless connection or a wired connection. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0045] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0046] Empirical Wavelet Transform (EWT): An adaptive signal analysis method. The core idea of ​​EWT is to decompose the signal into multiple local bandpass (local frequency band) sub-signals and achieve local time-frequency analysis by adaptively selecting the bandpass boundary and frequency band spacing.

[0047] This invention provides a fast prediction method for airfoil icing shape based on empirical wavelet transform, such as... Figure 1 As shown, it includes:

[0048] S101, obtain icing meteorological parameters;

[0049] S102, input the icing meteorological parameters into the pre-trained target neural network to predict the empirical wavelet transform boundary value of the icing thickness curve signal under airfoil icing conditions and the first K-order Fourier modes of the icing thickness curve signal, where K is a positive integer;

[0050] S103, construct a bandpass filter based on the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions;

[0051] S104. Based on the first K Fourier modes of the bandpass filter and the ice thickness curve signal, the empirical wavelet transform modes of each order are obtained.

[0052] S105, superimpose the empirical wavelet transform modes of each order to obtain the ice thickness curve signal;

[0053] S106, target transformation is performed on the icing thickness curve signal to obtain the airfoil icing shape.

[0054] For example, the icing meteorological parameters include inflow velocity, temperature, liquid water content (LWC), and median volume diameter (MVD). The target neural network may include two neural networks: a first neural network and a second neural network. The first neural network predicts the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions based on the icing meteorological parameters. The second neural network predicts the first K-order Fourier modes of the icing thickness curve signal based on the icing meteorological parameters. The first neural network and the second neural network may be convolutional neural networks or backpropagation neural networks. This embodiment does not limit the target neural network, and those skilled in the art can determine it as needed.

[0055] The ice thickness curve signal mentioned in this embodiment refers to the ice thickness curve of any one or more of the three ice formation conditions: rough ice, clear ice, and supercooled large water droplet ice. The horizontal axis of the curve represents the node position of the airfoil surface, and the vertical axis represents the ice thickness at that position along the normal direction of the airfoil surface. The empirical wavelet transform boundary values ​​refer to a series of dividing points in the Fourier spectrum of the signal, which divide the spectrum into multiple non-overlapping sub-bands. The first K Fourier modes of the ice thickness curve signal are obtained by performing a Fourier transform on the ice thickness curve signal, resulting in the first K amplitudes and frequencies of the signal spectrum. According to the Shannon criterion, the Fourier spectrum interval is normalized to the range [0, π]. Assuming that the signal consists of N empirical wavelet transform modes, the Fourier spectrum interval of the original signal is divided into N frequency bands.

[0056] Based on the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions, a bandpass filter is constructed to ensure a smooth transition of frequency amplitude at the boundary. Specifically, the empirical wavelet is defined as the frequency band Λ. n The bandpass filter is defined using the empirical wavelet function Ψ based on the Littlewood-Paley and Meyer wavelet method. n (ω) and the scaling function Φ of the empirical wavelet n (ω):

[0057]

[0058] In the formula, 0 < γ < 1, Λ n =[ω n-1 ,ω n ],ω n It is the frequency band boundary, Ψ n (ω) and Φ n (ω) represents Ψ n (t) and Φ n The Fourier transform of (t), β(x) = x 4 (35-84x+70x 2 -20x 3 ).

[0059] Based on the first K Fourier modes of the bandpass filter and the ice thickness curve signal, the empirical wavelet transform modes of each order are obtained, including: obtaining the predicted ice thickness curve signal f based on the first K Fourier modes of the ice thickness curve signal; performing an inner product between the bandpass filter and the predicted ice thickness curve signal to obtain detail coefficients and approximation coefficients; determining the Nth-order empirical wavelet transform mode based on the empirical wavelet function and detail coefficients used to construct the bandpass filter, where N is a positive integer; and determining the 0th-order empirical wavelet transform mode based on the empirical wavelet scaling function and approximation coefficients used to construct the bandpass filter.

[0060] Specifically, first, an inverse Fourier transform is performed on the first K Fourier modes, and the modes obtained from the inverse Fourier transform are summed to reconstruct the original signal f. Then, the empirical wavelet coefficients are obtained by the inner product of the signal and the bandpass filter, and the detail coefficients are... and approximation coefficients They are respectively:

[0061]

[0062] In the formula, F represents the complex conjugate. -1 This represents the inverse Fourier transform.

[0063] The zeroth-order empirical wavelet transform f0(t) and the Nth-order empirical wavelet transform mode f are obtained through empirical wavelet transform. n (t) is:

[0064]

[0065] In the formula, * denotes convolution, f n f(t) is the Nth-order empirical wavelet transform mode, and f0(t) is the 0th-order empirical wavelet transform mode.

[0066] By superimposing the empirical wavelet transform modes of different orders, the ice thickness curve signal is obtained:

[0067]

[0068] in, yes Fourier transform, yes Fourier transform.

[0069] Then, the above-mentioned icing thickness curve signal is transformed into a two-dimensional ice shape. See Figure 2(a) for an example of a two-dimensional ice shape formed by supercooled large water droplets, and Figure 2(b) for an example of a supercooled large water droplet icing thickness curve. These two can be converted to each other. Specifically, the process of transforming the icing thickness curve signal into a two-dimensional ice shape is as follows: The horizontal and vertical coordinates of the icing thickness curve signal are read, and the coordinates are matched. The node position on the airfoil surface is determined based on the horizontal coordinate, and the icing thickness along the normal direction of the airfoil surface at that position is determined based on the vertical coordinate, thus reconstructing the two-dimensional ice shape on the airfoil surface. Figure 3 As shown, the predicted ice shape will eventually be an ice shape of different thicknesses formed at different locations along the airfoil surface.

[0070] To facilitate understanding, this embodiment provides diagrams illustrating the process of reconstructing the airfoil icing shape from the empirical wavelet transform mode of the ice shape under different icing conditions. For example... Figure 4 As shown, the empirical wavelet transform modes of icing of raw ice include the 0th mode and the 1st mode. By superimposing the modes, the icing thickness curve signal of raw ice shown in Figure 5(b) can be obtained. By transforming the icing thickness curve signal of raw ice shown in Figure 5(b), the icing shape of raw ice shown in Figure 5(a) can be obtained.

[0071] like Figure 6 As shown, the empirical wavelet transform modes of open ice formation include the 0th, 1st, and 2nd modes. By superimposing the modes, the open ice thickness curve signal shown in Figure 7(b) can be obtained. By transforming the open ice thickness curve signal shown in Figure 7(b), the open ice shape shown in Figure 7(a) can be obtained.

[0072] Similarly, as Figure 8 As shown, the empirical wavelet transform modes for the freezing of supercooled large water droplets include the 0th, 1st, 2nd, 3rd, and 4th modes. By superimposing the modes, the supercooled large water droplet freezing thickness curve signal shown in Figure 2(b) can be obtained. By transforming the supercooled large water droplet freezing thickness curve signal shown in Figure 2(b), the supercooled large water droplet freezing shape shown in Figure 2(a) can be obtained.

[0073] This invention provides a rapid prediction method for airfoil icing shape based on empirical wavelet transform. By exploring wavelet transform mode features under different icing types, the method predicts the airfoil icing shape using these features. Furthermore, the ice shape is reconstructed by superimposing empirical wavelet transform modes of various orders. This approach considers the icing physical mechanisms of different icing types, enabling the proposed prediction method to maintain good prediction accuracy under various conditions and improving its generalization ability. Moreover, the proposed method, using a neural network, can complete the prediction within one minute, while traditional numerical simulation methods require at least 10-20 minutes. This represents a significant reduction in prediction time and an improvement in prediction efficiency of at least 900%, providing a highly efficient and accurate solution for airfoil icing prediction.

[0074] As an optional implementation, when the target neural network is a first neural network and a second neural network, the first neural network predicts the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions based on icing meteorological parameters, and the second neural network predicts the first K-order Fourier modes of the icing thickness curve signal based on icing meteorological parameters; the samples for the training process of the first neural network or the second neural network are obtained in the following way:

[0075] Based on numerical simulations, the aerodynamic characteristics of the airfoil and icing shape samples under different icing conditions were constructed. Icing conditions included inflow velocity, temperature, liquid water content, and average droplet volume diameter. Icing shapes included fuzzy ice, clear ice, and supercooled large droplet icing. The thickness of different ice shapes at nodal positions on the airfoil surface under each icing condition was determined, resulting in icing thickness curve signals for each icing condition. Fourier transforms were performed on the icing thickness curve signals under each icing condition to obtain the signal spectrum. Based on the signal spectrum of the icing thickness curve signals under each icing condition, the first K-order Fourier mode labels of the icing thickness curve signals under each icing condition were obtained and used as the sample labels for the second neural network. The minimum values ​​of the signal spectrum of the icing thickness curve signals under each icing condition were used as the boundary value labels of the empirical wavelet transform under each icing condition and used as the training sample labels for the first neural network.

[0076] Exemplarily, this embodiment provides a method for obtaining samples for training the first and second neural networks. Specifically, firstly, taking the NACA0012 and NACA23012 airfoils as examples, the aerodynamic characteristics of the airfoils and the ice shapes under different icing conditions are calculated using Ansys Fluent and FENSAP-ICE software. The results are compared with wind tunnel test data to verify the accuracy of the numerical simulation. It should be noted that different icing conditions include inflow velocity, temperature, liquid water content, and average droplet volume diameter. Then, the ice shapes of loose ice, clear ice, and supercooled large water droplets are calculated respectively, serving as samples for mode decomposition and neural network prediction. There are 40 examples for each icing type, totaling 120 examples. The thickness of the above two-dimensional ice shapes is calculated and transformed into an ice thickness curve signal, such as... Figure 2(a) and 2(b) As shown, the horizontal axis of the transformed curve represents the node position of the airfoil surface, and the vertical axis represents the icing thickness at that position along the normal direction of the airfoil surface.

[0077] Treating the ice thickness curve as a one-dimensional signal, we perform an empirical wavelet transform on it. Specifically, we first perform a Fourier transform on the signal to obtain its spectrum, including the real and imaginary parts. According to the Shannon criterion, the Fourier spectrum is normalized to the range [0, π]. Assuming the signal consists of N empirical wavelet transform modes, the Fourier spectrum of the original signal is divided into N frequency bands with a total of N+1 boundaries, and the boundary between each frequency band is ω. n , where ω0=0, ω N =π.

[0078] Each frequency band can be represented as:

[0079] Λ n =[ω n-1 ,ω n ];(8)

[0080] The transition region is:

[0081] T n =2τ n (9)

[0082] Where, τ n =γω n , 0 < γ < 1,

[0083] The entire Fourier spectrum range is represented as:

[0084]

[0085] Based on the signal spectrum of the ice thickness curve under various icing conditions, the first K order Fourier mode labels of the ice thickness curve signal under each icing condition are obtained. The minimum values ​​of the signal spectrum of the ice thickness curve under each icing condition are used as the boundary value labels of the empirical wavelet transform under each icing condition, and as the training sample labels of the first neural network.

[0086] This invention provides a method for rapid prediction of airfoil icing patterns based on empirical wavelet transform. By constructing aerodynamic characteristics of the airfoil and icing pattern samples under different icing conditions through numerical simulation, high-quality learning samples can be provided for neural network learning, thereby improving the prediction accuracy of the network. Furthermore, in this embodiment, the first neural network and the second neural network are trained respectively using the icing pattern samples constructed by numerical simulation and their corresponding labels, so that the two neural networks can make predictions separately. Compared with using a single neural network, the training difficulty is reduced and the training efficiency is improved.

[0087] As an optional implementation method, a fast prediction method for airfoil icing shape based on empirical wavelet transform is provided, wherein both the first and second neural networks are BP neural networks; the mean square error is used as the model performance evaluation index.

[0088] For example, this embodiment provides a fast prediction method for airfoil icing shape based on an empirical wavelet network with a single hidden layer structure containing 10 neurons; the activation function is sigmoid; the first neural network is a BP neural network that predicts the boundary of the airfoil icing shape (EWT); the input consists of four key icing meteorological parameters: inflow velocity, temperature, LWC, and MVD; the output consists of four boundary values ​​ω of the EWT. n ;BP neural network, such as Figure 9 As shown, a single hidden layer structure is adopted, with 10 neurons in the hidden layer; the activation function is Sigmoid; the dataset is divided into training set, validation set and test set according to the ratio of 70%, 15% and 15%; and the mean square error (MSE) is used as the model performance evaluation metric.

[0089] The second neural network is a backpropagation (BP) neural network that predicts the first 15 Fourier modes; the input consists of four key icing meteorological parameters: inflow velocity, temperature, LWC, and MVD, and the output is the first 15 Fourier modes of the signal f; the BP neural network, such as... Figure 10 As shown, a single hidden layer structure is adopted, with 10 neurons in the hidden layer, which outputs the real and imaginary parts of the Fourier mode; the activation function is Sigmoid; the dataset is divided into training, validation and test sets according to the ratio of 70%, 15% and 15%; and MSE is used as the model performance evaluation metric.

[0090] As an optional implementation, a fast prediction method for airfoil icing shape based on empirical wavelet transform further includes: calculating the leading-edge stagnation point ice thickness error h between the predicted airfoil icing shape and the original ice shape. sp ,include:

[0091]

[0092] Among them, h pre h represents the predicted ice thickness at the leading edge of the ice shape. sim This represents the ice thickness at the leading edge stagnation point of the ice shape obtained from numerical simulation.

[0093] For example, such as Figure 3 As shown, this includes an ice shape obtained from numerical simulation and a predicted ice shape, based on the above formula (11) for... Figure 3 The calculation is performed based on the situation, and the error h between the predicted ice shape and the ice thickness at the leading edge stagnation point of the original ice shape is calculated. sp The accuracy is 2.35%. This formula can effectively quantify the accuracy of the prediction.

[0094] As an optional implementation method, a fast prediction method for airfoil icing shape based on empirical wavelet transform further includes:

[0095] Calculate the lift-drag coefficients and stall angle of attack for both the predicted and original icing airfoils, and calculate their errors e, including:

[0096]

[0097] Among them, (C) pre ) i This represents the predicted lift (or drag) coefficient of the icing airfoil at an angle of attack of i°, (C sim ) i This represents the lift (or drag) coefficient of the icing airfoil at an angle of attack of i°, obtained from numerical simulation.

[0098] For example, to further evaluate the accuracy of the predicted icing shape, this embodiment generates a mesh around the predicted icing airfoil, and calculates the lift-drag coefficients of the predicted icing airfoil and the original icing airfoil using the following formulas:

[0099]

[0100] Among them, C l C represents the lift coefficient. d The vector represents the drag coefficient, L represents the lift acting on the airfoil, D represents the drag acting on the airfoil, ρ represents the air density, and V represents the air pressure coefficient. ∞ b represents the incoming flow velocity, and b represents the airfoil span.

[0101] Then, the airfoil aerodynamic characteristic curves are plotted, as shown in Figure 11(a) and Figure 11(b). Figure 11(a) shows the curve of lift coefficient as a function of angle of attack, and Figure 11(b) shows the curve of drag coefficient as a function of angle of attack. Then, the error e is calculated according to formula (12). The lift coefficient error is 0.64% and the drag coefficient error is 1.57% calculated by formula (12). The stall angle of attack is the same, which is 10°.

[0102] This embodiment proposes a rapid prediction method for airfoil icing shape based on empirical wavelet transform. It considers the overall aerodynamic performance of the icing airfoil to evaluate the accuracy of the prediction results, thus overcoming the shortcomings of existing evaluation methods that only evaluate the prediction results from the perspective of icing shape geometry, and improving the comprehensiveness of accuracy evaluation.

[0103] This invention provides a device for rapid prediction of airfoil icing shape based on empirical wavelet transform, comprising:

[0104] The meteorological parameter acquisition module is used to acquire icing meteorological parameters; please refer to the corresponding description in the above method embodiments for details, which will not be repeated here.

[0105] The prediction module is used to input icing meteorological parameters into a pre-trained target neural network to predict the empirical wavelet transform boundary value of the icing thickness curve signal under airfoil icing conditions and the first K-order Fourier modes of the icing thickness curve signal, where K is a positive integer; see the corresponding description in the above method embodiments for details, which will not be repeated here.

[0106] The bandpass filter construction module is used to construct a bandpass filter based on the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions; see the corresponding description in the above method embodiments for details, which will not be repeated here.

[0107] The mode transformation module is used to obtain the empirical wavelet transform modes of each order based on the first K Fourier modes of the bandpass filter and the ice thickness curve signal; see the corresponding description in the above method embodiment for details, which will not be repeated here.

[0108] The curve signal determination module is used to superimpose the empirical wavelet transform modes of various orders to obtain the icing thickness curve signal; the ice shape determination module is used to perform target transformation on the icing thickness curve signal to obtain the airfoil icing shape. For details, please refer to the corresponding descriptions in the above method embodiments, which will not be repeated here.

[0109] This application also provides an electronic device, such as... Figure 12 As shown, processor 501 and memory 502 are connected via a bus or other means.

[0110] Processor 501 can be a central processing unit (CPU). Processor 501 can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or combinations of the above types of chips.

[0111] The memory 502, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the airfoil icing shape fast prediction method based on empirical wavelet transform in this embodiment of the invention. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions, and modules stored in the memory.

[0112] Memory 502 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory 502 may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0113] The one or more modules are stored in the memory 502, and when executed by the processor 501, they perform actions such as... Figure 1 The embodiment shown illustrates a fast prediction method for airfoil icing shape based on empirical wavelet transform.

[0114] For specific details regarding the aforementioned electronic devices, please refer to the relevant documentation. Figure 1 The relevant descriptions and effects in the illustrated embodiments are for understanding purposes only and will not be repeated here.

[0115] This embodiment also provides a computer storage medium storing computer-executable instructions that can execute the airfoil icing shape fast prediction method based on empirical wavelet transform in any of the above method embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium may also include combinations of the above types of memory.

[0116] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A fast prediction method for airfoil icing shape based on empirical wavelet transform, characterized in that, include: Obtain icing meteorological parameters; The icing meteorological parameters are input into a pre-trained target neural network to predict the empirical wavelet transform boundary value of the icing thickness curve signal under airfoil icing conditions and the first K-order Fourier modes of the icing thickness curve signal, where K is a positive integer; Based on the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions, a bandpass filter is constructed. Based on the first K Fourier modes of the bandpass filter and the ice thickness curve signal, the empirical wavelet transform modes of each order are obtained. By superimposing the empirical wavelet transform modes of different orders, the ice thickness curve signal is obtained; The icing thickness curve signal is transformed to obtain the airfoil icing shape; Based on the first K Fourier modes of the bandpass filter and the icing thickness curve signal, the empirical wavelet transform modes of each order are obtained, including: The predicted ice thickness curve signal is obtained based on the first K Fourier modes of the ice thickness curve signal. The inner product of the bandpass filter and the predicted ice thickness curve signal is used to obtain the detail coefficients and approximation coefficients. Based on the empirical wavelet function and detail coefficients used to construct the bandpass filter, the Nth-order empirical wavelet transform mode is determined, where N is a positive integer; The zeroth-order empirical wavelet transform mode is determined based on the empirical wavelet scaling function and approximation coefficients used to construct the bandpass filter. By superimposing the empirical wavelet transform modes of different orders, the ice thickness curve signal is obtained, including: ； in, This is the ice thickness curve signal. For detail coefficients, The coefficients are approximation coefficients, and N represents the Nth order empirical wavelet transform mode. Represents the empirical wavelet function. The scaling function of the empirical wavelet is represented. and They are respectively and Inverse Fourier transform, yes Fourier transform, yes Fourier transform.

2. The method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to claim 1, characterized in that, The target neural network includes a first neural network and a second neural network. The first neural network predicts the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions based on icing meteorological parameters. The second neural network predicts the first K-order Fourier modes of the icing thickness curve signal based on icing meteorological parameters. The samples used in the training process of the first or second neural network are obtained in the following way: Based on numerical simulation, the aerodynamic characteristics of the airfoil and icing shape samples under different icing conditions were constructed. The icing conditions included incoming flow velocity, temperature, liquid water content, and average droplet volume diameter. The icing shapes included fuzzy ice shape, clear ice shape, and supercooled large water droplet icing shape. Determine the thickness of different ice shapes at nodal positions on the airfoil surface under various icing conditions, and obtain the icing thickness curve signal under various icing conditions; Fourier transform is performed on the ice thickness curve signals under various icing conditions to obtain the spectrum of the ice thickness curve signals under various icing conditions. Based on the signal spectrum of the ice thickness curve under various icing conditions, the first K order Fourier mode labels of the ice thickness curve signal under various icing conditions are obtained and used as the sample labels of the second neural network. The minimum values ​​of the signal spectrum of the ice thickness curve under various icing conditions are used as the boundary value labels of the empirical wavelet transform under various icing conditions, and as the training sample labels of the first neural network.

3. The method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to claim 2, characterized in that, Both the first and second neural networks are backpropagation (BP) neural networks. The BP neural network uses a single hidden layer structure, with the hidden layer containing 10 neurons; The activation function is Sigmoid, and the mean squared error is used as the model performance evaluation metric.

4. A method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to any one of claims 1-3, characterized in that, Also includes: The calculated and predicted icing shape of the airfoil and the ice thickness error at the leading edge stagnation point are compared. ,include: ； in, This indicates the ice thickness at the leading edge of the predicted ice shape. This represents the ice thickness at the leading edge stagnation point of the ice shape obtained from numerical simulation.

5. A method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to any one of claims 1-3, characterized in that, Also includes: Calculate the lift-drag coefficients and stall angle of attack for both the predicted and original icing airfoils, and calculate their errors. ,include: ； in, This indicates that the predicted icing airfoil at an angle of attack of... The lift coefficient or drag coefficient at that time This indicates that the icing airfoil obtained from numerical simulation has an angle of attack of... The lift coefficient or drag coefficient at that time.

6. A rapid prediction device for airfoil icing shape based on empirical wavelet transform, characterized in that, include: The meteorological parameter acquisition module is used to acquire icing meteorological parameters; The prediction module is used to input icing meteorological parameters into a pre-trained target neural network to predict the empirical wavelet transform boundary value of the icing thickness curve signal under airfoil icing conditions and the first K-order Fourier modes of the icing thickness curve signal, where K is a positive integer; The bandpass filter construction module is used to construct bandpass filters based on the empirical wavelet transform boundary values ​​of the icing thickness curve signal under airfoil icing conditions. The mode transformation module is used to obtain the empirical wavelet transform modes of each order based on the first K Fourier modes of the bandpass filter and the ice thickness curve signal. The curve signal determination module is used to superimpose the empirical wavelet transform modes of various orders to obtain the ice thickness curve signal; The ice shape determination module is used to perform target transformation on the icing thickness curve signal to obtain the airfoil icing shape. Based on the first K Fourier modes of the bandpass filter and the icing thickness curve signal, the empirical wavelet transform modes of each order are obtained, including: The predicted ice thickness curve signal is obtained based on the first K Fourier modes of the ice thickness curve signal. The inner product of the bandpass filter and the predicted ice thickness curve signal is used to obtain the detail coefficients and approximation coefficients. Based on the empirical wavelet function and detail coefficients used to construct the bandpass filter, the Nth-order empirical wavelet transform mode is determined, where N is a positive integer; The zeroth-order empirical wavelet transform mode is determined based on the empirical wavelet scaling function and approximation coefficients used to construct the bandpass filter. By superimposing the empirical wavelet transform modes of different orders, the ice thickness curve signal is obtained, including: ； in, This is the ice thickness curve signal. For detail coefficients, The coefficients are approximation coefficients, and N represents the Nth order empirical wavelet transform mode. Represents the empirical wavelet function. The scaling function of the empirical wavelet is represented. and They are respectively and Inverse Fourier transform, yes Fourier transform, yes Fourier transform.

7. An electronic device, the device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor performs the steps of the rapid prediction method for airfoil icing shape based on empirical wavelet transform as described in any one of claims 1-5.

8. A computer storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the steps of the fast prediction method for airfoil icing shape based on empirical wavelet transform as described in any one of claims 1-5.

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