Airfoil icing ice shape rapid prediction method based on empirical wavelet transform

Abstract

The invention provides an airfoil icing ice shape rapid prediction method based on empirical wavelet transform. The airfoil icing ice shape rapid prediction method comprises the steps of obtaining icing meteorological parameters; the icing meteorological parameters are input into a pre-trained target neural network, the empirical wavelet transform boundary value of the icing thickness curve signal and the first K-order Fourier modals of the icing thickness curve signal under the airfoil icing condition are predicted, and K is a positive integer; constructing a band-pass filter according to the empirical wavelet transform boundary value of the icing thickness curve signal under the airfoil icing condition; according to the band-pass filter and the front K-order Fourier mode of the icing thickness curve signal, obtaining each-order empirical wavelet transform mode; the empirical wavelet transformation modes of all orders are superposed, and an icing thickness curve signal is obtained; and performing target transformation on the icing thickness curve signal to obtain an airfoil icing ice shape. By implementing the method and the device, relatively high prediction accuracy can be kept under different conditions, the generalization ability of prediction is enhanced, and meanwhile, the prediction efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the field of wing icing prediction, and particularly relates to a method for quickly predicting the ice shape of an airfoil based on empirical wavelet transform. Background Art

[0002] When an aircraft flies in meteorological environments such as clouds, rain, snow, and fog, supercooled water droplets in the air will impact the aircraft surface and form ice layers. When the lifting surfaces such as the wings and tail fins of the aircraft are iced, the aerodynamic shape of the aircraft is damaged, resulting in a decrease in lift and an increase in drag. At the same time, the stall angle of attack decreases, deteriorating the aerodynamic performance of the aircraft. Therefore, predicting the icing conditions of an aircraft under different meteorological conditions is crucial for ensuring flight safety.

[0003] Currently, the existing aircraft icing predictions mainly adopt the following methods: flight tests, wind tunnel tests, and numerical simulations. Although the numerical simulation method is more time-saving and labor-saving than flight tests and wind tunnel tests, it still consumes a large amount of computing resources. Traditional numerical simulations of ice shapes need to go through cyclic iterations of flow field calculation, water droplet collection coefficient calculation, water-ice phase change analysis, and grid transformation, which is very time-consuming. By introducing intelligent prediction methods such as neural networks, the computing efficiency can be significantly improved, enabling fast and accurate prediction of ice shapes.

[0004] To accelerate the speed of ice shape prediction and reduce the consumption of computing resources, researchers have constructed reduced-order models. Proper Orthogonal Decomposition (POD) is very common in flow field analysis. This method can decompose a series of standard orthogonal modes from a large amount of data and is a very powerful data dimensionality reduction and decomposition method. In recent years, machine learning has been extended to multiple research and industrial fields. With the continuous development and maturity 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 methods, and then train neural networks to learn the relationship between the input meteorological condition parameters and the ice shape, thereby realizing the fast prediction of ice shapes under different icing conditions. Chang et al. proposed a new technology combining wavelet packet transform and artificial neural network. Wavelet packet decomposition is used to reduce the number of input vectors of the neural network and improve training convergence, thereby predicting the icing conditions on the wing surface. Massegur et al. proposed a framework for a low-dimensional model of airfoil icing based on POD and convolutional autoencoder (Conv-AE), which can well simulate extremely complex ice shapes.

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

[0006] In view of this, the purpose of the present invention is to provide a fast prediction method for airfoil icing shapes based on empirical wavelet transform to meet the requirement of improving the generalization ability of airfoil icing shape prediction.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] According to a first aspect, the present invention provides a fast prediction method for airfoil icing shapes based on empirical wavelet transform, including: obtaining 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 and the first K Fourier modes of the icing thickness curve signal under the condition of airfoil icing, where K is a positive integer; constructing a band-pass filter according to the empirical wavelet transform boundary values of the icing thickness curve signal under the condition of airfoil icing; obtaining each order of empirical wavelet transform modes according to the band-pass filter and the first K Fourier modes of the icing thickness curve signal; superimposing each order of empirical wavelet transform modes to obtain the icing thickness curve signal; 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 the condition of airfoil icing according to the icing meteorological parameters, and the second neural network predicts the first K Fourier modes of the icing thickness curve signal according to the icing meteorological parameters; the samples in the training process of the first neural network or the second neural network are obtained in the following manner: constructing the aerodynamic characteristics of the airfoil and the icing shape samples under different icing conditions according to numerical simulation, and the icing conditions include the incoming flow velocity, temperature, liquid water content, and average volume diameter of water droplets; the icing shapes include rime ice shapes, glaze ice shapes, and supercooled large droplet icing shapes; determining the thickness of different ice shapes at the node positions on the airfoil surface under each icing condition to obtain the icing thickness curve signals under each icing condition; performing Fourier transform on the icing thickness curve signals under each icing condition to obtain the icing thickness curve signal spectra under each icing condition; obtaining the first K Fourier mode labels of the icing thickness curve signals under each icing condition according to the icing thickness curve signal spectra under each icing condition as the sample labels of the second neural network; taking the minimum values of the icing thickness curve signal spectra under each icing condition as the empirical wavelet transform boundary value labels under each icing condition as the training sample labels of the first neural network.

[0010] Optionally, both the first neural network and the second neural network are BP neural networks; the BP neural network adopts a single hidden layer structure, and the hidden layer contains 10 neurons; the activation function is Sigmoid, and the mean square error is used as the model performance evaluation index.

[0011] Optionally, according to the first K Fourier modes of the band-pass filter and the icing thickness curve signal, each order of empirical wavelet transform modes are obtained, including: obtaining a predicted icing thickness curve signal according to the first K Fourier modes of the icing thickness curve signal; taking the inner product of the band-pass filter and the predicted icing thickness curve signal to obtain detail coefficients and approximation coefficients; determining the Nth-order empirical wavelet transform mode according to the empirical wavelet function for constructing the band-pass filter and the detail coefficients, where N is a positive integer; determining the 0th-order empirical wavelet transform mode according to the empirical wavelet scaling function for constructing the band-pass filter and the approximation coefficients.

[0012] Optionally, the icing thickness curve signals are obtained by superimposing each order of empirical wavelet transform modes, including:

[0013]

[0014] where f(t) is the icing thickness curve signal, are the detail coefficients, are the approximation coefficients, N represents the Nth order mode, Ψ n (ω) represents the empirical wavelet function, Φ n (ω) represents the empirical wavelet scaling function, Ψ n (t) and Φ n (t) are the inverse Fourier transforms of Ψ n (ω) and Φ n (ω) respectively, is 's Fourier transform, is 's Fourier transform.

[0015] Optionally, a method for rapidly predicting the ice shape of an airfoil based on empirical wavelet transform further includes: calculating the leading edge stagnation point ice thickness error h sp between the predicted ice shape of the airfoil and the original ice shape, including:

[0016]

[0017] where h pre represents the leading edge stagnation point ice thickness of the predicted ice shape, and h sim represents the leading edge stagnation point ice thickness of the ice shape obtained by numerical simulation.

[0018] Optionally, a method for rapidly predicting the ice shape of an airfoil based on empirical wavelet transform further includes: respectively calculating the lift and drag coefficients and stall angles of attack of the predicted ice airfoil and the original ice airfoil, and calculating their error e, including:

[0019]

[0020] where, (Cpre ) i represents the lift (or drag) coefficient of the predicted ice-airfoil at an angle of attack of i°, (C sim ) i represents the lift (or drag) coefficient of the ice-airfoil obtained by numerical simulation at an angle of attack of i°.

[0021] According to a second aspect, an embodiment of the present invention provides a rapid prediction device for ice-airfoil ice shape based on empirical wavelet transform, including: 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 value of the ice thickness curve signal and the first K Fourier modes of the ice thickness curve signal in the case of airfoil icing, where K is a positive integer; a band-pass filter construction module for constructing a band-pass filter according to the empirical wavelet transform boundary value of the ice thickness curve signal in the case of airfoil icing; a modal transformation module for obtaining each order of empirical wavelet transform modes according to the band-pass filter and the first K Fourier modes of the ice thickness curve signal; a curve signal determination module for superimposing each order of empirical wavelet transform modes to obtain the ice thickness curve signal; and an ice shape determination module for performing a target transformation on the ice thickness curve signal to obtain the ice-airfoil ice shape.

[0022] According to a third aspect, an embodiment of the present invention provides an electronic device, the device including: a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the steps of the rapid prediction method for ice-airfoil ice shape based on empirical wavelet transform according to the first aspect or any one of the embodiments of the first aspect.

[0023] According to a fourth aspect, an embodiment of the present invention provides a computer storage medium, on which computer instructions are stored, and when the instructions are executed by a processor, the steps of the rapid prediction method for ice-airfoil ice shape based on empirical wavelet transform according to the first aspect or any one of the embodiments of the first aspect are implemented.

[0024] The present invention provides a rapid prediction method for ice-airfoil ice shape based on empirical wavelet transform. By exploring the wavelet transform modal characteristics under different icing types, using the wavelet transform modal characteristics under different icing types to predict the ice-airfoil ice shape, and restoring the ice shape by superimposing each order of empirical wavelet transform modes, the icing physical mechanism of different icing types is considered, so that the prediction method proposed in this embodiment can have good prediction accuracy under different conditions and improve the generalization ability of the prediction. And the method proposed in this embodiment can complete the prediction within 1 minute through a neural network, while the traditional numerical simulation method requires at least 10 - 20 minutes. In contrast, the prediction time is greatly shortened, and the prediction efficiency is increased by at least 900%, providing an efficient and accurate solution for airfoil icing prediction.

[0025] Other advantages, objectives and features of the present invention will be described in the subsequent specification, and to some extent will be obvious to those skilled in the art, or those skilled in the art can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to make the objectives, technical solutions and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0027] Figure 1 It is a flowchart of a specific example of a method for quickly predicting the ice shape of an airfoil based on empirical wavelet transform in the present invention;

[0028] Figure 2(a) is an ice shape diagram of supercooled large droplets obtained by simulation in the present invention;

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

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

[0031] Figure 4 It is the empirical wavelet transform modal diagram of the rime ice shape in the present invention;

[0032] Figure 5(a) is a rime ice shape diagram obtained by simulation in the present invention;

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

[0034] Figure 6 It is the empirical wavelet transform modal diagram of the clear ice shape in the present invention;

[0035] Figure 7(a) is the clear ice shape obtained by simulation in the present invention;

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

[0037] Figure 8 It is the empirical wavelet transform modal diagram of the ice shape of supercooled large droplets in the present invention;

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

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

[0040] Figure 11(a) is a curve of the lift coefficient changing with the angle of attack in the present invention;

[0041] Figure 11(b) shows the curve of the drag coefficient varying with the angle of attack in the present invention;

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

[0043] Next, the technical solutions of the present invention will be clearly and completely described in conjunction with the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0044] In the description of the present invention, it should be noted that, unless otherwise clearly defined and limited, the terms "mounted", "connected" and "connected" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be a direct connection or an indirect connection through an intermediate medium, and it may also be the communication inside two components. It can be a wireless connection or a wired connection. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0045] In addition, the technical features involved in 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 a signal into multiple sub-signals with local band-pass (local frequency bands), and to achieve local time-frequency analysis by adaptively selecting the band-pass boundaries and frequency band intervals.

[0047] An embodiment of the present invention provides a method for quickly predicting the ice shape of an airfoil based on empirical wavelet transform, as Figure 1 shown, including:

[0048] S101, obtaining icing meteorological parameters;

[0049] S102, 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 and the first K Fourier modes of the icing thickness curve signal under the condition of airfoil icing, where K is a positive integer;

[0050] S103, constructing a band-pass filter according to the empirical wavelet transform boundary values of the icing thickness curve signal under the condition of airfoil icing;

[0051] S104. Obtain the empirical wavelet transform modes of each order according to the first K Fourier modes of the band - pass filter and the icing thickness curve signal.

[0052] S105. Superimpose the empirical wavelet transform modes of each order to obtain the icing thickness curve signal.

[0053] S106. Perform a target transformation on the icing thickness curve signal to obtain the ice shape of the airfoil.

[0054] Exemplarily, the icing meteorological parameters include the incoming flow velocity, temperature, liquid water content (LWC), and median volume diameter (MVD) of water droplets. 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 in the case of airfoil icing according to the icing meteorological parameters, and the second neural network predicts the first K Fourier modes of the icing thickness curve signal according to the icing meteorological parameters. The first neural network and the second neural network can be convolutional neural networks or BP neural networks. This embodiment does not limit the target neural network, and those skilled in the art can determine it according to needs.

[0055] In this embodiment, the icing thickness curve signal mentioned is the total icing thickness curve of any one or several of the three icing cases of rime ice, clear ice, and supercooled large - droplet icing. The abscissa of this curve is the node position on the airfoil surface, and the ordinate is the icing thickness in the normal direction of the airfoil surface at this position. The empirical wavelet transform boundary values refer to a series of segmentation points determined in the Fourier spectrum of the signal, and these segmentation points divide the spectrum into multiple non - overlapping sub - frequency bands. The first K Fourier modes of the icing thickness curve signal are the first K amplitudes and frequencies selected from the spectrum obtained by performing a Fourier transform on the icing thickness curve signal. According to the Shannon criterion, the Fourier spectrum interval is normalized within the range of [0, π]. Assuming that the signal is composed of N empirical wavelet transform modes, the Fourier spectrum interval of the original signal is divided into N frequency bands.

[0056] Construct a band - pass filter according to the empirical wavelet transform boundary values of the icing thickness curve signal in the case of airfoil icing, so that the amplitude of the frequency smoothly transitions at the boundary. Specifically, the empirical wavelet is defined as a band - pass filter on the frequency band Λ n Define the empirical wavelet function Ψ n (ω) and the scaling function Φ n (ω) of the empirical wavelet according to the methods of Littlewood - Paley and Meyer wavelets:

[0057]

[0058] where \(0\lt\gamma\lt1\), \(\Lambda\) n \(=[\omega\) n-1 ,\(\omega\) n , \(\omega\) n is the frequency band boundary, \(\Psi\) n \((\omega)\) and \(\Phi\) n \((\omega)\) are the Fourier transforms of \(\Psi\) n \((t)\) and \(\Phi\) n \((t)\) respectively, and \(\beta(x)=x\) 4 (35 - 84x + 70x 2 - 20x 3 ).

[0059] Based on the first \(K\) Fourier modes of the band - pass filter and the icing thickness curve signal, the empirical wavelet transform modes of each order are obtained, including: based on the first \(K\) Fourier modes of the icing thickness curve signal, the predicted icing thickness curve signal \(f\) is obtained; the inner product of the band - pass filter and the predicted icing thickness curve signal is taken to obtain the detail coefficients and the approximation coefficients; based on the empirical wavelet function for constructing the band - pass filter and the detail coefficients, the \(N\) - th order empirical wavelet transform mode is determined, where \(N\) is a positive integer; based on the empirical wavelet scaling function for constructing the band - pass filter and the approximation coefficients, the 0 - th order empirical wavelet transform mode is determined.

[0060] Specifically, first, the inverse Fourier transform is performed on the first \(K\) Fourier modes, and the modes obtained by the inverse Fourier transform are added together to reconstruct the original signal \(f\). Then, the empirical wavelet coefficients are obtained from the inner product of the signal and the band - pass filter, and the detail coefficients and the approximation coefficients are respectively:

[0061]

[0062] where denotes the complex conjugate, and \(F\) -1 denotes the inverse Fourier transform.

[0063] The 0 - th order empirical wavelet transform \(f\) 0 (t) and the \(N\) - th order empirical wavelet transform mode \(f\) n (t) are:

[0064]

[0065] where \(*\) represents convolution, \(f\) n (t) is the \(N\) - th order empirical wavelet transform mode, and \(f\) 0 (t) is the 0 - th order empirical wavelet transform mode.

[0066] The icing thickness curve signal is obtained by superimposing the empirical wavelet transform modes of each order:

[0067]

[0068] Among them, is the Fourier transform of is the Fourier transform of

[0069] Then, the above icing thickness curve signal is transformed into a two-dimensional ice shape. It can be seen that Fig. 2(a) shows the two-dimensional ice shape of supercooled large droplet icing, and Fig. 2(b) shows the icing thickness curve of supercooled large droplet icing. The two can be converted into each other. Specifically, the process of transforming the icing thickness curve signal into a two-dimensional ice shape is as follows: read the horizontal and vertical coordinates of the icing thickness curve signal, correspond the horizontal and vertical coordinates, determine the node positions on the airfoil surface according to the horizontal coordinate, and determine the icing thickness in the normal direction of the airfoil surface at this position according to the vertical coordinate, so as to restore the two-dimensional ice shape on the airfoil surface. As Figure 3 shown, it is predicted that the ice shape will finally be ice shapes with different thicknesses formed at different positions along the airfoil surface.

[0070] For easy understanding, this embodiment gives the process diagrams of restoring the airfoil icing shape from the empirical wavelet transform modes under different icing conditions. As Figure 4 shown, it is the empirical wavelet transform mode of rime icing, including the 0th order mode and the 1st order mode. By superimposing each order mode, the rime icing thickness curve signal shown in Fig. 5(b) can be obtained. By transforming the rime icing thickness curve signal shown in Fig. 5(b), the rime ice shape shown in Fig. 5(a) can be obtained.

[0071] As Figure 6 shown, it is the empirical wavelet transform mode of clear ice icing, including the 0th order mode, the 1st order mode and the 2nd order mode. By superimposing each order mode, the clear ice icing thickness curve signal shown in Fig. 7(b) can be obtained. By transforming the clear ice icing thickness curve signal shown in Fig. 7(b), the clear ice shape shown in Fig. 7(a) can be obtained.

[0072] Similarly, as Figure 8 shown, it is the empirical wavelet transform mode of supercooled large droplet icing, including the 0th order mode, the 1st order mode, the 2nd order mode, the 3rd order mode and the 4th order mode. By superimposing each order mode, the supercooled large droplet icing thickness curve signal shown in Fig. 2(b) can be obtained. By transforming the supercooled large droplet icing thickness curve signal shown in Fig. 2(b), the supercooled large droplet ice shape shown in Fig. 2(a) can be obtained.

[0073] An embodiment of the present invention provides a fast prediction method for airfoil icing shapes based on empirical wavelet transform. By exploring the wavelet transform modal characteristics under different icing types, the airfoil icing shapes are predicted using the wavelet transform modal characteristics under different icing types, and the ice shapes are restored by superimposing each order of empirical wavelet transform modes. Considering the icing physical mechanisms of different icing types, the prediction method proposed in this embodiment can have good prediction accuracy under different conditions, improving the generalization ability of the prediction. Moreover, the method proposed in this embodiment can complete the prediction within 1 minute through a neural network, while the traditional numerical simulation method takes at least 10 - 20 minutes. In comparison, the prediction time is significantly shortened, and the prediction efficiency is increased by at least 900%, providing an efficient and accurate solution for airfoil icing prediction.

[0074] As an alternative embodiment, when the target neural network is the first neural network and the second neural network, the first neural network predicts the empirical wavelet transform boundary value of the icing thickness curve signal in the case of airfoil icing according to the icing meteorological parameters, and the second neural network predicts the first K-order Fourier modes of the icing thickness curve signal according to the icing meteorological parameters; the samples in the training process of the first neural network or the second neural network are obtained according to the following method:

[0075] Construct the aerodynamic characteristics of the airfoil and the icing shape samples under different icing conditions according to numerical simulation. The icing conditions include the incoming flow velocity, temperature, liquid water content, and average volume diameter of water droplets; the icing shapes include rime ice shapes, glaze ice shapes, and supercooled large droplet icing shapes; determine the thickness of different ice shapes at the node positions on the airfoil surface under each icing condition to obtain the icing thickness curve signal under each icing condition; perform Fourier transform on the icing thickness curve signal under each icing condition to obtain the spectrum of the icing thickness curve signal under each icing condition; according to the spectrum of the icing thickness curve signal under each icing condition, obtain the first K-order Fourier mode labels of the icing thickness curve signal under each icing condition as the sample labels of the second neural network; take the minimum value of the spectrum of the icing thickness curve signal under each icing condition as the empirical wavelet transform boundary value label under each icing condition as the training sample label of the first neural network.

[0076] Exemplarily, this embodiment provides a method for obtaining samples for training the first neural network and the second neural network. Specifically, first, taking the NACA0012 and NACA23012 airfoils as examples, the Ansys Fluent and FENSAP-ICE software are used to calculate the aerodynamic characteristics of the airfoils and the ice shapes under different icing conditions, and compare them with the wind tunnel test data to verify the accuracy of the numerical simulation. It should be noted that different icing conditions include the incoming flow velocity, temperature, liquid water content, and average volume diameter of water droplets. Then, the ice shapes of rime ice, glaze ice, and supercooled large droplet icing are calculated respectively as samples for modal decomposition and neural network prediction. There are 40 cases for each icing type, with a total of 120 cases. Calculate the thickness of the above two-dimensional ice shapes and transform them into icing thickness curve signals, as Figure 2(a) and 2(b) shown. The abscissa of the transformed curve is the node position on the airfoil surface, and the ordinate is the icing thickness in the normal direction of the airfoil surface at this position.

[0077] Regarding the icing thickness curve as a one-dimensional signal, perform empirical wavelet transform on it. Specifically, first perform Fourier transform on the signal to obtain the spectrum of the signal, including the real part and the imaginary part. According to the Shannon criterion, normalize the Fourier spectrum interval within the range of [0, π]. Assuming that the signal is composed of N empirical wavelet transform modes, the Fourier spectrum interval of the original signal is divided into N frequency bands, with a total of N + 1 boundaries. The boundary between each frequency band is ω n , where ω 0 = 0, ω N = π.

[0078] Each frequency band can be expressed 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 interval is expressed as:

[0084]

[0085] According to the signal spectra of the icing thickness curves under various icing conditions, the first K-order Fourier mode labels of the icing thickness curve signals under various icing conditions are obtained. The minimum values of the signal spectra of the icing thickness curves under various icing conditions are used as the empirical wavelet transform boundary value labels under various icing conditions, serving as the first neural network training sample labels.

[0086] An embodiment of the present invention provides a method for quickly predicting the ice shape of an airfoil based on empirical wavelet transform. By numerically simulating the aerodynamic characteristics of the airfoil and the ice shape samples under different icing conditions, high-quality learning samples can be provided for the neural network to learn, improving the network prediction accuracy. Moreover, the first neural network and the second neural network in this embodiment are respectively trained through the ice shape samples constructed by numerical simulation and their corresponding labels, so that the two neural networks can make predictions respectively. Compared with using a single neural network, the training difficulty is reduced and the training efficiency is improved.

[0087] As an optional implementation, for a method for quickly predicting the ice shape of an airfoil based on empirical wavelet transform, both the first neural network and the second neural network are BP neural networks; and the BP neural network uses the mean square error as the model performance evaluation index.

[0088] Exemplarily, the empirical wavelet network provided in this embodiment adopts a single hidden layer structure, and the hidden layer contains 10 neurons; the activation function is Sigmoid. For the method for quickly predicting the ice shape of an airfoil based on empirical wavelet transform, the first neural network is a BP neural network for predicting the boundary of EWT; the input is 4 key icing meteorological parameters: free stream velocity, temperature, LWC, MVD, and the output is 4 boundary values ω of EWT. n ; The BP neural network is as Figure 9 shown, adopting a single hidden layer structure, the hidden layer contains 10 neurons; the activation function is Sigmoid, and the data set is divided into a training set, a validation set, and a test set according to the ratio of 70%, 15%, and 15%, and the mean square error (MSE) is used as the model performance evaluation index.

[0089] The second neural network is a BP neural network for predicting the first 15 Fourier modes; the input is 4 key icing meteorological parameters: free stream velocity, temperature, LWC, MVD, and the output is the first 15 Fourier modes of the signal f; the BP neural network, as Figure 10 shown, adopts a single hidden layer structure, the hidden layer contains 10 neurons, and the real part and the imaginary part of the output Fourier modes are output; the activation function is Sigmoid, and the data set is divided into a training set, a validation set, and a test set according to the ratio of 70%, 15%, and 15%, and the MSE is used as the model performance evaluation index.

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

[0091]

[0092] where h pre represents the leading-edge stagnation ice thickness of the predicted ice shape, and h sim represents the leading-edge stagnation ice thickness of the ice shape obtained by numerical simulation.

[0093] Exemplarily, as shown in Figure 3 , including an ice shape obtained by numerical simulation and a predicted ice shape, calculate for the situation of Figure 3 using the above formula (11), and the leading-edge stagnation ice thickness error h between the predicted ice shape and the original ice shape sp is 2.35%. The accuracy of the prediction can be effectively quantified by this formula.

[0094] As an alternative implementation, a rapid prediction method for airfoil icing shapes based on empirical wavelet transform further includes:

[0095] Respectively calculate the lift and drag coefficients and stall angles of attack of the predicted icing airfoil and the original icing airfoil, and calculate their error e, including:

[0096]

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

[0098] Exemplarily, to further evaluate the accuracy of the predicted ice shape, in this embodiment, a grid is generated around the predicted icing airfoil, and the lift and drag coefficients of the predicted icing airfoil and the original icing airfoil are calculated respectively by the following formula:

[0099]

[0100] where C l represents the lift coefficient, C d 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, V ∞ represents the oncoming flow velocity, and b represents the airfoil span.

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

[0102] The present embodiment proposes a method for rapid prediction of airfoil icing ice shape based on empirical wavelet transform, which considers the overall aerodynamic performance of the iced wing to judge the accuracy of the prediction result, thereby making up for the defect of the existing evaluation method that the prediction result is only evaluated from the aspect of the geometric characteristics of the ice shape, and improving the comprehensiveness of the accuracy evaluation.

[0103] The embodiment of the present invention provides an airfoil icing ice shape rapid prediction device based on empirical wavelet transform, comprising:

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

[0105] The prediction module is used to input the 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 the condition of airfoil icing and the first K-order Fourier modes of the icing thickness curve signal, where K is a positive integer; please refer to the corresponding description of the above method embodiment for details, which will not be repeated here.

[0106] The bandpass filter construction module is used to construct a bandpass filter according to the empirical wavelet transform boundary value of the ice thickness curve signal under the condition of airfoil icing; please refer to the corresponding description of the above method embodiment for details, which will not be repeated here.

[0107] The modal conversion module is used to obtain the empirical wavelet transform modes of each order according to the bandpass filter and the first K-order Fourier modes of the ice thickness curve signal; please refer to the corresponding description of the above method embodiment for details, which will not be repeated here.

[0108] The curve signal determination module is used to superimpose the modes of each order of empirical wavelet transformation to obtain the ice thickness curve signal; the ice shape determination module is used to perform target transformation on the ice thickness curve signal to obtain the airfoil ice shape. For details, please refer to the corresponding description of the above method embodiment, which will not be repeated here.

[0109] The present application also provides an electronic device, such as Figure 12 As shown, a processor 501 and a memory 502, wherein the processor 501 and the memory 502 may be connected via a bus or other means.

[0110] The processor 501 may be a Central Processing Unit (CPU). The processor 501 may 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, etc., such as chips, 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 rapid prediction method based on empirical wavelet transform in the embodiments of the present invention. The processor executes various functional applications and data processing of the processor by running the non-transitory software programs, instructions, and modules stored in the memory.

[0112] The memory 502 may include a program storage area and a data storage area. Among them, the program storage area can store an operating system and application programs required for at least one function; the data storage area can store data created by the processor, etc. In addition, the memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, a flash memory device, or other non-transitory solid-state storage devices. In some embodiments, the memory 502 may optionally include a memory remotely set relative to the processor, and these remote memories can be connected to the processor through a network. Examples of the above networks include, but are not limited to, the Internet, an enterprise intranet, a local area network, a mobile communication network, and combinations thereof.

[0113] The one or more modules are stored in the memory 502 and, when executed by the processor 501, execute the airfoil icing shape rapid prediction method based on empirical wavelet transform in the embodiments as Figure 1 shown.

[0114] The specific details of the above electronic device can be understood by referring to the corresponding relevant descriptions and effects in the embodiments Figure 1 shown, and will not be elaborated here.

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

[0116] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. 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 in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A method for rapid prediction of airfoil icing shape based on empirical wavelet transform, characterized in that: include: Obtain icing meteorological parameters; The icing meteorological parameters are input 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; According to the empirical wavelet transform boundary value of ice thickness curve signal under airfoil icing condition, a bandpass filter is constructed. According to the bandpass filter and the first K-order Fourier modes of the ice thickness curve signal, the empirical wavelet transform modes of each order are obtained; The empirical wavelet transform modes of each order are superimposed to obtain the ice thickness curve signal; The ice thickness curve signal is transformed to obtain the airfoil ice shape.

2. The method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to claim 1 is 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 value of the ice thickness curve signal under the condition of airfoil icing according to the icing meteorological parameters. The second neural network predicts the first K-order Fourier modes of the ice thickness curve signal according to the icing meteorological parameters. The samples of the first neural network or the second neural network training process are obtained according to the following method: According to numerical simulation, the aerodynamic characteristics of the airfoil and the ice shape samples under different icing conditions are constructed. The icing conditions include the incoming flow velocity, temperature, liquid water content, and average volume diameter of water droplets. The ice shapes include hairy ice shape, bright ice shape, and supercooled large water droplet ice shape. Determine the thickness of different ice shapes at the node positions on the airfoil surface under various icing conditions, and obtain ice thickness curve signals under various icing conditions; Performing Fourier transform on the ice thickness curve signal under each icing condition to obtain the spectrum of the ice thickness curve signal under each icing condition; According to the spectrum of the ice thickness curve signal under each icing condition, the first K-order Fourier modal labels of the ice thickness curve signal under each icing condition are obtained as the second neural network sample labels; The minimum value of the spectrum of the ice thickness curve signal under each icing condition is used as the boundary value label of the empirical wavelet transform under each icing condition and as the label of the first neural network training sample.

3. The method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to claim 2 is characterized in that: The first neural network and the second neural network are both BP neural networks; The BP neural network adopts a single hidden layer structure, and the hidden layer contains 10 neurons; The activation function is Sigmoid, and the mean square error is used as the model performance evaluation indicator.

4. The method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to claim 1, characterized in that: According to the bandpass filter and the first K-order Fourier modes of the ice thickness curve signal, the empirical wavelet transform modes of each order are obtained, including: According to the first K-order Fourier modes of the ice thickness curve signal, the predicted ice thickness curve signal is obtained; The band-pass filter and the predicted ice thickness curve signal are inner-producted to obtain detail coefficients and approximate coefficients; According to the empirical wavelet function and detail coefficients of the bandpass filter, the N-order empirical wavelet transform mode is determined, where N is a positive integer; According to the empirical wavelet scaling function and approximate coefficients of the bandpass filter, the 0th order empirical wavelet transform mode is determined.

5. The method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to claim 4 is characterized in that: The empirical wavelet transform modes of each order are superimposed to obtain the ice thickness curve signal, including: Where, f(t) is the ice thickness curve signal, is the detail coefficient, is the approximate coefficient, N represents the Nth-order empirical wavelet transform mode, 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) are Ψ n (ω) and Φ n The inverse Fourier transform of (ω) is yes The Fourier transform of yes The Fourier transform of .

6. A method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to any one of claims 1 to 5, characterized in that: Also includes: The error h between the leading edge stagnation point ice thickness of the airfoil ice shape predicted by calculation and the original ice shape sp ,include: Among them, h pre represents the ice thickness at the leading edge of the predicted ice shape, h sim Represents the ice thickness at the leading edge stagnation point of the ice shape obtained by numerical simulation.

7. A method for rapid prediction of airfoil icing shape based on empirical wavelet transform according to any one of claims 1 to 5, characterized in that: Also includes: Calculate the lift and drag coefficients and stall angle of attack of the predicted icing airfoil and the original icing airfoil respectively, and calculate their errors e, including: Where, (Cpre)i represents the predicted lift coefficient or drag coefficient of the icing airfoil at an angle of attack of i°, (C sim ) i It represents the lift coefficient or drag coefficient of the icing airfoil obtained by numerical simulation at an angle of attack of i°.

8. A device for rapid prediction of airfoil icing shape based on empirical wavelet transform, characterized in that: include: A meteorological parameter acquisition module, used to obtain icing meteorological parameters; A 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; A bandpass filter building module is used to build a bandpass filter according to the empirical wavelet transform boundary value of the ice thickness curve signal under the condition of airfoil icing; A mode conversion module is used to obtain empirical wavelet transform modes of each order according to the bandpass filter and the first K-order Fourier modes of the ice thickness curve signal; The curve signal determination module is used to superimpose the empirical wavelet transform modes of each order 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.

9. An electronic 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 any one of claims 1 to 7.

10. A computer storage medium having computer instructions stored thereon, characterized in that: When the instruction is executed by the processor, the steps of the method for rapid prediction of airfoil icing shape based on empirical wavelet transform described in any one of claims 1-7 are implemented.

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