A wind speed operator network construction method suitable for motion-induced unsteady aerodynamic force

Abstract

The application discloses a wind speed operator network construction method suitable for motion-induced unsteady aerodynamic force, and belongs to the field of aircraft aeroelasticity. Specifically, for a target airfoil or wing, a sweep frequency sweep amplitude value training signal of motion is given, CFD simulation or wind tunnel test is performed, and unsteady aerodynamic forces corresponding to each motion signal are obtained. Then, a driving model of unsteady aerodynamic force data is built according to a VONet architecture. Two neural network modules are respectively inputted with motion information and wind speed information, and the output is corresponding aerodynamic force coefficients. After the driving model is trained, a two-dimensional aerodynamic work matrix is constructed by using aerodynamic work coefficients of different incoming flow wind speeds and motion amplitudes, an energy graph of the incoming flow wind speed-motion amplitude is drawn, and the energy graph is output in combination with the aerodynamic work coefficients to predict a flutter instability boundary. The application greatly reduces the calculation time and cost, and can rapidly and accurately predict at any wind speed and frequency within a training domain.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aeroelasticity, and particularly relates to a wind speed operator network construction method suitable for motion-induced unsteady aerodynamic force. BACKGROUND

[0002] Motion-induced unsteady aerodynamic force is an important research branch in fluid mechanics.

[0003] Motion-induced unsteady aerodynamic force not only depends on the current flow state and boundary conditions, but also depends on the flow history in the previous period of time. In addition to static nonlinear factors such as spatial discontinuity and flow separation, motion-induced unsteady aerodynamic force often accompanies dynamic nonlinear effects over time and is coupled with a structural system to form complex aeroelastic phenomena. Due to its complexity and importance, this problem has received extensive attention in the engineering applications of helicopters, turbomachinery, flapping wing dynamics and wind turbines.

[0004] Because motion-induced unsteady aerodynamic force often produces strong nonlinearity and time delay effects, it is difficult for traditional engineering algorithms to meet the accuracy requirements, and high-precision numerical simulation methods require a large amount of computing power and cost, so the industry urgently needs a high-precision fast prediction method.

[0005] In recent years, the reduced-order model based on neural networks has provided a new idea for this problem. After training with wind tunnel experiment and numerical simulation data, the neural network model can perform high-precision fast prediction. However, due to the lack of prior knowledge and the integration of physical mechanisms, the generalization of the traditional neural network architecture is weak, and the physical laws hidden in the flow cannot be revealed.

[0006] Integrating prior knowledge to enhance model generalization and further exploring hidden physical laws is a feasible solution. SUMMARY

[0007] The application proposes a wind speed operator network construction method (VONet, Velocity Operation Net) suitable for motion-induced unsteady aerodynamic force to solve the existing problems of motion-induced unsteady aerodynamic force. By introducing the concept of wind speed operator, the traditional single network structure is changed to a combination network structure of motion net and velocity net using point multiplication, fully considering the physical effects of incoming wind speed and reduced wind speed in flow phenomena, which is equivalent to mapping wind speed as a function operator. Compared with the traditional network architecture, the application has the advantages of strong interpretability, strong nonlinearity capturing ability and high generalization precision.

[0008] The wind speed operator network construction method suitable for motion-induced unsteady aerodynamic force has the following specific steps:

[0009] Step one, for the target airfoil or wing, given the motion training signal at different reduced wind speeds, CFD simulation or wind tunnel test is performed to obtain the unsteady aerodynamic force corresponding to each motion signal.

[0010] Step two, according to the VONet architecture, a driving model of unsteady aerodynamic force data is built.

[0011] The VONet architecture is composed of two neural networks: motion net and velocity net.

[0012] The input of the motion net neural network is the motion time series vector [α t-n+1 ,α t-n+2 ,…,α t ] of length n, and the output is the vector D of length n: D(α t-n+1 ,α t-n+2 ,…,α t )=[d1,d2,…,d n ];

[0013] The input of the velocity net neural network is the incoming wind speed U ∞ and the reduced wind speed U * , and the output is the vector F of length n: F(U ∞ ,U * )=[f1,f2,…,f n ] T ;

[0014] The inner product of the output vectors of the two neural networks is obtained: the unsteady aerodynamic moment coefficient C m (t) at the corresponding motion and wind speed: C m (t)=D·F=f1d1+f2d2+…+f n d n ;

[0015] Step three, use each motion signal and the corresponding unsteady aerodynamic force to train the driving model, and when the relative error is stable and less than 5%, the optimal parameters of the driving model are obtained.

[0016] Step four, using the driving model with optimal parameters, the periodic aerodynamic work coefficient E f of the dynamic stall process under different working conditions is solved by the complex Simpson integration method:

[0017]

[0018] Where, is the pitch rate in the motion process, T is a motion period, and t is the motion time.

[0019] Step five, using different inflow wind speed and motion amplitude aerodynamic work coefficient, construct two-dimensional aerodynamic work matrix, draw the energy graph of the inflow wind speed-motion amplitude, and combine the energy graph of the aerodynamic damping coefficient to predict the flutter instability boundary.

[0020] Written as a two-dimensional aerodynamic work matrix E:

[0021]

[0022] The two-dimensional matrix is drawn as an energy graph with the horizontal coordinate as the inflow wind speed and the vertical coordinate as the motion amplitude, so that the wind speed boundary of the aerodynamic work coefficient of 0 can be obtained directly from the graph, and the flutter instability boundary under different structural damping conditions can be judged by combining the damping coefficient of the structure.

[0023] Compared with the prior art, the present application has the following advantages:

[0024] (1) The present application is suitable for the wind speed operator network construction method of motion-induced unsteady aerodynamic force, which greatly shortens the calculation time of motion-induced unsteady aerodynamic force prediction and improves the prediction accuracy; the network architecture only needs to perform CFD calculation at several wind speeds to complete the training, greatly reducing the calculation time and cost, and can perform fast and accurate prediction at any wind speed and frequency within the training domain.

[0025] (2) The wind speed operator network construction method of motion-induced unsteady aerodynamic force of the present application has clear physical meaning compared with the traditional neural network architecture, and can reveal the physical mechanism contained in the wind speed. Since the inflow wind speed and the reduced wind speed are introduced as operators, the network architecture proposed by the present application has stronger variable wind speed generalization ability and can capture the change of dynamic stall mechanism at the key reduced wind speed.

[0026] (3) The wind speed operator network construction method of motion-induced unsteady aerodynamic force of the present application, thanks to the good generalization and precision of the wind speed operator network architecture, can predict the boundary of stall flutter occurrence in combination with the aerodynamic damping coefficient and the energy graph, further expanding the application scenarios of the network architecture. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a flowchart of the wind speed operator network construction method for motion-induced unsteady aerodynamic force in the present application.

[0028] Figure 2 is a specific structure diagram of the VONet neural network used in the present application. DETAILED DESCRIPTION

[0029] In order to make the technical scheme of the present application clearer and easier to understand, the present application will be further described in detail below with reference to the drawings.

[0030] For the problem of motion-induced unsteady aerodynamic force, the application proposes a wind speed operator network construction method suitable for motion-induced unsteady aerodynamic force, as shown in Figure 1 , the specific steps are as follows:

[0031] Step one, for the target airfoil or wing, the forced motion training signal with clear physical information under different reduced wind speeds is given, CFD simulation or wind tunnel test is carried out, and the unsteady aerodynamic lift or moment corresponding to each motion signal is obtained.

[0032] Step two, build an unsteady aerodynamic force data-driven model according to the VONet architecture;

[0033] The VONet architecture is composed of two neural network units: motion net and velocity net.

[0034] The motion net model selects long short-term memory (LSTM) or gated recurrent unit (GRU) neural network, takes the motion time series vector [α t-n+1 ,α t-n+2 ,…,α t ] of length n of the given motion under any wind speed as input, which represents the motion information from t-n+1 to t time, and takes the vector D of length n as output: D(α t-n+1 ,α t-n+2 ,…,α t )=[d1,d2,…,d n ];

[0035] The velocity net model selects a fully connected neural network (FCNN), takes the incoming flow wind speed U ∞ and the reduced wind speed U * as input, and takes the vector F of length n as output: F(U ∞ ,U * )=[f1,f2,…,f n ] T ;

[0036] The same length vectors output by the two networks are inner products, and the final output variable of the VONet architecture is obtained: the unsteady aerodynamic moment coefficient C m (t) under the corresponding motion and wind speed: C m (t)=D·F=f1d1+f2d2+…+f n d n ;

[0037] Under the incoming flow wind speed U ∞ and the reduced wind speed U * , the motion time series vector [αt-n+1 ,α t-n+2 ,…,α t ] to the dynamic stalling moment coefficient C m (t) is: G(a)(U):<D(a t-n+1 ,α t-n+2 ,…,α t ), F(U ∞ , U * )>→C m (t);

[0038] The VONet model is trained using Adam optimization algorithm. The input signal of any sinusoidal pitch motion within the training range and its corresponding aerodynamic force data are used to test the trained model, and the relative error of aerodynamic force prediction is used to measure the accuracy and generalization of the model. To prevent overfitting, the model parameters with the best generalization under different working conditions are selected and retained.

[0039] Step three, use each motion signal and the corresponding unsteady aerodynamic force to train the driving model, and after the relative error of the training data is less than 5%, get multiple sets of driving model parameters.

[0040] The input signal of any given motion within the training wind speed and oscillation frequency range and its corresponding aerodynamic force data are used to test the generalization of the trained driving model, and the relative error of aerodynamic force prediction is used to measure the accuracy of the driving model. The model parameters with the best generalization under different working conditions are selected and retained for subsequent prediction.

[0041] Step four, use the driving model with optimal parameters to solve the periodic aerodynamic work coefficient E f of the dynamic stalling process under different working conditions by the complex Simpson integration method.

[0042] First, the driving model is used to obtain high-precision prediction results of the dynamic stalling aerodynamic force under variable wind speed and amplitude, and the complex Simpson integration method is used to solve the periodic aerodynamic work coefficient E f of the dynamic stalling process under different working conditions.

[0043] The formula is as follows:

[0044]

[0045] Where, is the pitch angle velocity in the motion process, T is a motion period, and t is the motion time.

[0046] Step five, use the aerodynamic work coefficients under different incoming flow wind speeds and motion amplitudes to construct a two-dimensional aerodynamic work matrix, draw an energy graph of incoming flow wind speed-motion amplitude, and combine the aerodynamic damping coefficient output energy graph to predict the wind speed of the flutter instability boundary.

[0047] The variation of the aerodynamic work coefficient with the reduced wind speed is analyzed to explore the changes in the physical mechanism of aerodynamic work at certain key reduced wind speeds, such as the transition from linear to nonlinear aerodynamic work characteristics, the transition from damping to excitation, and the like.

[0048] The aerodynamic work coefficients of different incoming wind speeds (U1-U p ) and motion amplitudes (A1-A q ) are calculated by the VONet model to reveal the physical mechanisms of dynamic stall at different wind speeds, and a two-dimensional aerodynamic work matrix E is written as:

[0049]

[0050] The two-dimensional matrix is plotted as an energy graph with the incoming wind speed as the horizontal coordinate and the motion amplitude as the vertical coordinate, so that the wind speed boundary with an aerodynamic work coefficient of 0 can be directly obtained from the graph. In combination with the damping coefficient of the structure, the flutter instability boundary under different structural damping conditions can be determined.

[0051] Embodiment:

[0052] In this embodiment, step (1) designs training signals for the VONet model and solves the corresponding unsteady aerodynamic forces.

[0053] The training signals input into the VONet model are composed of sweep frequency sweep amplitude motion signals of airfoils or wings at different reduced wind speeds, and the output is the unsteady aerodynamic lift or moment coefficient corresponding to the motion.

[0054] The input training signals should cover a wide range of motion frequencies and amplitudes, and different incoming wind speeds should also be considered, so as to ensure that accurate information of unsteady aerodynamic forces under different wind speeds can be obtained, and the model has a certain generalization for different reduced wind speeds, incoming wind speeds and motion amplitudes. The corresponding input training signals should be in the form of sweep frequency signals or signals with known input rules. The designed training input signals are used as given motions to perform CFD (Computational Fluid Dynamics) simulation or wind tunnel test of the target airfoil or wing to obtain the unsteady aerodynamic forces corresponding to the training signals.

[0055] This combination of "incoming wind speed-unsteady motion-unsteady aerodynamic force" data will serve as the training data for the data-driven model.

[0056] Step (2) builds an unsteady aerodynamic force data-driven model according to the VONet architecture, and trains and tests the generalization of the model.

[0057] For the generalization goal of variable frequency and variable amplitude unsteady aerodynamic forces, two training strategies are proposed: sweep frequency with constant oscillation amplitude pitch motion signals and sweep oscillation amplitude with constant frequency pitch motion signals.

[0058] First, the training strategy of constant amplitude frequency sweep is given: determine the frequency range [f0, f1] of the training signal. Take the result of the stall flutter wind tunnel test as an example, the oscillation frequency of the stall flutter limit cycle of this object is between 2 Hz and 3 Hz, therefore, the designed training signal is a linear sweep form of 2 Hz-3 Hz, with a time length of 20 seconds. Select a large amplitude A (take 40°) that has occurred deep dynamic stall:

[0059] α(t) = Asin(2π(2+0.025t)t)

[0060] Where, α is the angle of attack, t is the time. Under different incoming flow velocities U = [6, 8, 10, 12] (m / s), the training signal with the above sweep motion is used for CFD calculation or wind tunnel test to obtain the corresponding unsteady aerodynamic lift or moment coefficients.

[0061] The training strategy of constant frequency sweep amplitude gives a fixed pitch oscillation frequency, and learns the aerodynamic characteristics of dynamic stall at different amplitudes through the way of sinusoidal change of oscillation amplitude:

[0062] α(t) = 40sin(0.05πt)sin(5πt)

[0063] Where, the given signal time length is 10s, and in this time range, the oscillation amplitude increases from 0° to 40° sinusoidally, and the pitch oscillation frequency remains constant at 2.5 Hz.

[0064] Take the training of unsteady aerodynamic force of a single degree of freedom airfoil pitch oscillation as an example:

[0065] What VONet learns is the mapping relationship from the angle of attack time series α ∞ ,α * ,…,α t-n+1 to the unsteady aerodynamic moment coefficient C t-n+2 (t) under a certain incoming flow velocity U t : m

[0066] G(α)(U):<d(α t-n+1 ,α t-n+2 ,…,α t ),f(U ∞ ,U * )>→C m (t)

[0067] For example Figure 2 ​As shown, the VONet architecture consists of two neural network units, motion net and velocity net. For the problem of modeling motion-induced unsteady aerodynamic forces, a long short-term memory (LSTM) or gated recurrent unit (GRU) neural network is chosen as the model of motion net, taking a time series of angle of attack vectors a t-n+1 , a t-n+2 , …, a t of length n as input, representing the motion information from time t-n+1 to t, and outputting a vector d of length n;

[0068] A fully connected neural network (FCNN) is chosen as the model of velocity net, taking the free-stream wind speed U ∞ and the reduced wind speed U * as input, and outputting a vector f of length n;

[0069] The inner product of the output vectors d and f of the two networks gives the final output variable of VONet, which is the unsteady aerodynamic moment coefficient C m (t) at the corresponding motion and wind speed.

[0070] The VONet model is trained using optimization algorithms such as Adam. An appropriate learning rate is set, and when the training error stabilizes, it is considered that the training has converged. The generalization ability of the reduced-order model is tested using a sinusoidal test signal, and if the requirements are met, it is considered that the training of the VONet unsteady aerodynamic data-driven model is complete.

[0071] In essence, this network decouples the information of unsteady aerodynamic motion changes and wind speed changes. The motion net unit encodes the general characteristics of unsteady aerodynamic forces from a given motion time series input, and the velocity net unit encodes the influence of wind speed on the phase and amplitude of unsteady aerodynamic forces from wind speed input. The output vectors d and f of the two network units are encoded by inner product to obtain the dynamic stall moment coefficient C m (t) at the corresponding time point.

[0072] The trained model is tested using input signals of any sinusoidal pitch motion within the training wind speed and frequency range and their corresponding aerodynamic force data. The relative error of aerodynamic force prediction is used to measure the accuracy and generalization of the model. To prevent overfitting, the model parameters with the best generalization under different working conditions are selected and retained.

[0073] Step (3) uses the VONet unsteady aerodynamic force model to output dynamic stall aerodynamic moments with continuous variable frequency and variable amplitude, explores the changes in aerodynamic characteristics under different reduction frequencies, reveals the physical mechanisms of dynamic stall under different wind speeds, and introduces the aerodynamic work coefficient to predict the stall flutter boundary based on the energy diagram.

[0074] First, VONet is used to obtain high-precision prediction results of dynamic stall aerodynamic forces under variable wind speed and amplitude, and the aerodynamic work coefficient E f is calculated by the complex Simpson integral method under different working conditions. The aerodynamic damping coefficient represents the periodic work of the unsteady aerodynamic moment under sinusoidal motion, and the formula is as follows:

[0075]

[0076] Further analysis of the change process of the aerodynamic work coefficient with the reduction frequency is carried out to explore the changes in the physical mechanisms of dynamic stall under certain key reduction wind speeds, such as the transition of the aerodynamic work coefficient from linear to nonlinear, and the transition from damping to excitation. Using the above calculation results, the energy diagram is used to further predict the instability boundary corresponding to the incoming flow wind speed. When the aerodynamic work coefficient changes from negative to positive, it indicates that the aerodynamic moment changes from damping to excitation, thereby inducing stall flutter.

[0077] The wind speed operator network (VONet) architecture proposed in the application is divided into motion net and velocity net two parts, and the two networks are connected through output point multiplication. The framework uses LSTM or GRU neural network as the motion net, and gives the motion time sequence as the input of the motion net. The fully connected neural network is used as the velocity net, and the constant incoming flow wind speed and the reduction wind speed measuring unsteady effect are used as the input of the velocity net. The unsteady aerodynamic lift or moment coefficient corresponding to the motion and wind speed is used as the output after point multiplication. The network structure of the wind speed operator network architecture proposed in the application is light and compact, has good interpretability, strong nonlinear capture ability and high generalization precision, uses the wind speed operator learning method to predict the motion-induced unsteady aerodynamic force, can explore the physical mechanisms contained in the wind speed change, has stronger variable wind speed generalization ability, and can be further combined with the energy diagram to be applied to the prediction of the instability boundary of fluid-solid coupling.

Claims

1. A wind speed operator network construction method suitable for motion-induced unsteady aerodynamic forces, characterized by, The specific steps are as follows: Step one, for the target airfoil or wing, given the motion training signal at different reduced wind speeds, CFD simulation or wind tunnel test is carried out to obtain the unsteady aerodynamic force corresponding to each motion signal; Step two, a driving model of unsteady aerodynamic force data is built according to the VONet architecture; The VONet architecture is composed of two neural networks, motion net and velocity net: The motion net neural network selects a long short-term memory or a threshold cyclic unit neural network, an input is a motion time sequence vector [a t-n+1 , a t-n+2 , …, a t ] with a length of n, and an output is a vector D with a length of n: D(a t-n+1 , a t-n+2 , …, a t ) = [d1, d2, …, d n ]; The velocity net neural network selects a fully connected neural network, the input is the incoming flow wind speed U ∞ and the reduced wind speed U * , the output is a vector F of length n: F(U ∞ ,U * ) = [f1, f2, …, fn] n ] T ; The output vectors of the two neural networks are inner multiplied to obtain the final output variable of the driving model: the unsteady aerodynamic moment coefficient C m (t) : C m (t) = D - F = f1d1+ f2d2+... + f n d n ; Step three, the driving model is trained using each motion signal and the corresponding unsteady aerodynamic force, and the optimal parameters of the driving model are obtained when the relative error is less than 5%; Step four, using the driving model under the optimal parameters, the periodic aerodynamic work coefficient of the dynamic stall process under different working conditions is solved by the complex Simpson integral method; Step five, using the aerodynamic work coefficient of different incoming flow wind speeds and motion amplitudes, a two-dimensional aerodynamic work matrix is constructed, an energy graph of incoming flow wind speed-motion amplitude is drawn, and the energy graph is combined with the aerodynamic damping coefficient to output the energy graph to predict the flutter instability boundary.

2. The wind speed operator network construction method for motion-induced unsteady aerodynamic forces according to claim 1, wherein, The step four cycle gas dynamic work coefficient E f : wherein is the pitch angular velocity during the motion, T is a motion period, and t is a motion time.

3. The wind speed operator network construction method for motion-induced unsteady aerodynamic forces of claim 1, wherein, The two-dimensional aerodynamic work matrix E in step five: U1-U p A1-A q is the corresponding amplitude of motion; plot this two-dimensional matrix as an energy diagram with the horizontal axis as the incoming flow wind speed and the vertical axis as the amplitude of motion, so that the wind speed boundary of the aerodynamic work coefficient being 0 can be directly obtained from the diagram, and the flutter instability boundary under different structural damping conditions can be determined in combination with the damping coefficient of the structure.

4. The wind speed operator network construction method for motion-induced unsteady aerodynamic forces of claim 1, wherein, In the step 2, the incoming wind speed U ∞ and reduced wind speed U * Next, the motion time vector [α t-n+1 ,α t-n+2 ,…,α t ] to the dynamic stall torque coefficient C m The mapping relationship of (t) is: G(a)(u): <D(a t-n+1 , a t-n+2 ,…, a t ), F(u ∞ , u * ) -> C m (t).

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