A method for modeling unsteady aerodynamic forces based on neural network with embedded physical knowledge
By designing neural network architecture and training models through the non -regular pneumatic physical equation and first -order micro -division equation in deep neural networks, solve the complexity, parameter recognition difficulties and difficulty of parameter recognition in the existing non -furious power modeling method. The problem of not high accuracy has achieved high -precision and physical interpreting large -scale non -frequent non -regular power model.
Patent Information
- Application Number
- CN202411517736.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-29
- Publication Date
- 2025-01-28
- Estimated Expiration
- 2044-10-29
AI Technical Summary
The existing non-stable aerodynamic modeling methods have problems such as complex calculations, difficulty in identifying parameters, and low prediction accuracy, especially during large angle of attack maneuvering.
Using deep neural network methods based on embedded physics knowledge, a first -order micro -division equation is designed and trained by embedded non -ingrained pneumatic physical equation and non -firing normally dynamic power incremental incremental incremental increase in power. Pneumatic model.
This method can train non -regular power models with high predictive accuracy and physical interpretability under sparse data conditions, and overcomes the problems of complexity and parameter recognition difficulties.
Smart Images
Figure CN119026527B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of modeling, and in particular to an unsteady aerodynamic modeling method based on a neural network with embedded physical knowledge. Background Art
[0002] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
[0003] The high-angle-of-attack maneuvering process of an aircraft is often accompanied by rapid vortex separation in a large area of the wing and fuselage, and the flow undergoes phenomena such as attachment flow, separation flow, vortex breakup and reattachment flow, which generates unsteady aerodynamic forces with severe nonlinearity, coupling and hysteresis. The database consisting of static aerodynamic forces, rotating balance data and small perturbation dynamic derivatives obtained from wind tunnel tests cannot meet the needs of aircraft design and flight control. It is urgent to predict the unsteady aerodynamic forces during high-angle-of-attack maneuvers through unsteady aerodynamic modeling.
[0004] The existing unsteady aerodynamic modeling mainly includes mathematical modeling methods based on unsteady flow phenomena and physical mechanisms and artificial intelligence modeling methods based on the mapping relationship between flight state data and aerodynamic data. The more representative modeling methods based on physical mechanisms include aerodynamic derivative models, step response models, state space models, and differential equation models; the artificial intelligence modeling methods based on data features avoid the study of complex unsteady flow mechanisms, and the more representative ones include support vector machine models and neural network models.
[0005] However, in the actual modeling process, modeling methods based on physical mechanisms often have shortcomings such as high requirements for professional knowledge, too many model parameters, and difficulty in identification. Although artificial intelligence modeling methods based on data features have the advantages of low requirements for professional knowledge, simple operation, and fast prediction speed, due to the small number of unsteady aerodynamic training samples, the established unsteady neural network model has low prediction accuracy and lacks physical interpretability. Summary of the invention
[0006] The purpose of the present invention is to provide a method for modeling unsteady aerodynamic forces at high angles of attack based on a neural network with embedded physical knowledge to address the problems existing in the prior art. The physical knowledge of unsteady aerodynamic forces at high angles of attack is embedded in a deep neural network for modeling unsteady aerodynamic forces at high angles of attack, overcoming the complexity of calculations and the difficulty of parameter identification. The method can also use sparse unsteady aerodynamic data for training to obtain an unsteady aerodynamic force model at high angles of attack that is interpretable and has high prediction accuracy.
[0007] The technical solution of the present invention is as follows:
[0008] A method for modeling unsteady aerodynamic forces based on a neural network with embedded physical knowledge, comprising:
[0009] Step S1: determining the unsteady aerodynamic modeling problem, determining the unsteady aerodynamic physical equation of longitudinal motion and the structure of the unsteady aerodynamic physical equation according to the aircraft type and the unsteady aerodynamic modeling problem, and determining the unsteady aerodynamic increment first-order differential equation in the unsteady aerodynamic physical equation;
[0010] Step S2: According to the unsteady aerodynamic physical equation and the unsteady aerodynamic increment first-order differential equation, the function mapping relationship between various physical quantities and the influencing indicators of various physical quantities is determined;
[0011] Step S3: designing a neural network architecture according to the prediction items and the relationship between the prediction items in the unsteady aerodynamic physical equation structure and the static wind tunnel test data and the dynamic wind tunnel test data measured in the wind tunnel;
[0012] Step S4: Determine the number of layers, the number of nodes and the activation function of each network according to the function mapping relationship between each physical quantity and each physical quantity influencing index;
[0013] Step S5: designing a loss function according to the prediction items and the relationship between the prediction items in the unsteady aerodynamic physical equation structure;
[0014] Step S6: Select and divide samples according to the static and dynamic wind tunnel test data measured in the wind tunnel, and generate a training set using a K-fold cross validation method;
[0015] Step S7: Perform neural network training. When the number of iterations is less than N, re-iterate and calculate the loss function. When the number of iterations is equal to N, output the optimal parameters of the network and the large angle of attack unsteady aerodynamic model.
[0016] Furthermore, the step S1 comprises:
[0017] The unsteady aerodynamic physical equation for longitudinal motion consists of the static aerodynamic force, the quasi-steady aerodynamic force increment caused by the angular velocity, and the unsteady aerodynamic force increment caused by the unsteady separation, which can be expressed as:
[0018]
[0019] in:
[0020] is the unsteady aerodynamic force and unsteady aerodynamic force coefficient;
[0021] is the static aerodynamic force;
[0022] is the quasi-steady aerodynamic force increment;
[0023] is the unsteady aerodynamic force increment;
[0024] represents the angle of attack;
[0025] represents the angular rate;
[0026] Indicates exercise time.
[0027] Furthermore, the step S1 further includes:
[0028] The first-order differential equation of the unsteady aerodynamic force increment is expressed as follows:
[0029]
[0030] in:
[0031] is the change process of unsteady aerodynamic force increment;
[0032] is the unsteady incremental coefficient term;
[0033] is a non-stationary effect term.
[0034] Furthermore, the step S2 comprises:
[0035] It's about angle of attack Nonlinear function of
[0036] It's about angle of attack , angular velocity Function of
[0037] It's about angle of attack , angular velocity and exercise time Function of
[0038] It's about angle of attack Function of
[0039] It's about angle of attack , angular velocity function.
[0040] Furthermore, the step S3 comprises:
[0041] Step S31: According to the relationship between the unsteady aerodynamic physical equation and the unsteady aerodynamic increment first-order differential equation and the corresponding relationship between the static wind tunnel test data and the dynamic wind tunnel test data measured by the corresponding wind tunnel test, a quasi-steady term is designed to describe Neural Network , describing the unsteady increment term Neural Network , and the term describing the unsteady incremental coefficient Neural Network , describing the non-stationary effect term Neural Network ;
[0042] Step S32: Based on neural network , Neural Network , Neural Network , Neural Network , the neural network architecture is constructed through the loss function.
[0043] Furthermore, the step S31 includes:
[0044] According to the unsteady aerodynamic physics equation, a neural network is constructed , represents the angle of attack , angular velocity and quasi-steady aerodynamic force increment The function mapping relationship between them is used to learn the small disturbance motion parameters and the quasi-steady aerodynamic force increment The nonlinear relationship between the neural network The input is the angle of attack and angular rate , the output is the quasi-steady aerodynamic force increment ; Then the unsteady aerodynamic physical equation is updated as:
[0045]
[0046] in, The angle of attack established , angular velocity and quasi-steady aerodynamic force increment Neural network with function mapping relationship between ;
[0047] According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed. , represents the angle of attack , angular velocity and motion history and unsteady aerodynamics The function mapping relationship between them is used to learn the high angle of attack flight state and the unsteady aerodynamic force increment The nonlinear and unsteady relationship between the neural network The input is the angle of attack , angular velocity and exercise time , the output is the unsteady aerodynamic force increment :
[0048] According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed. , represents the angle of attack , angular velocity and non-stationary effects The function mapping relationship between them is used to learn the nonlinear unsteady relationship between the high angle of attack flight state and the unsteady aerodynamic force, the neural network The input is the angle of attack and angular rate , the output is the unsteady effect term ; Then the first-order differential equation of the unsteady aerodynamic force increment is updated as:
[0049]
[0050] in, The angle of attack established , angular velocity , exercise time and unsteady aerodynamic force increment Neural network with function mapping relationship between ; The angle of attack established , angular velocity and non-stationary effects Neural network with function mapping relationship between ;
[0051] According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed. , represents the angle of attack , angular velocity Unsteady aerodynamic force increment The function mapping relationship is used to learn the high angle of attack flight state and unsteady aerodynamic force increment Nonlinear and unsteady relationships between changing processes, neural networks The input is the angle of attack and angular rate , the output is the unsteady aerodynamic force increment .
[0052] Furthermore, the step S4 comprises:
[0053] Each neural network consists of an input layer, four hidden layers and an output layer. The number of nodes in the input layer is related to the input. The number of nodes in three of the four hidden layers is the same. Each hidden layer uses Sigmoid as the activation function, and the number of nodes in the output layer is 1. The physical quantities output by the four neural networks and the labeled physical quantities of the training samples are substituted into the corresponding functions and differential equations, and the loss function MSE and the loss function ODE are constructed through the difference between the two. Among them, MSE represents mean square error and ODE represents ordinary differential equation.
[0054] Furthermore, the loss function designed in step S5 is expressed as follows:
[0055]
[0056] in:
[0057]
[0058]
[0059] For neural networks The loss function MSE;
[0060] For neural networks , , The loss function ODE;
[0061] are the unsteady aerodynamic forces and unsteady aerodynamic coefficients calculated by the neural network prediction values;
[0062] To calculate the unsteady aerodynamic force and unsteady aerodynamic force coefficients through wind tunnel test measurements.
[0063] Furthermore, the step S6 comprises:
[0064] According to the database generated by the static wind tunnel test and the dynamic wind tunnel test, two reduced frequency data are selected as samples, and the training set is generated using the K-fold cross validation method. , , and set the learning rate and the maximum number of iterations N.
[0065] Furthermore, the step S7 comprises:
[0066] Step S71: Initialize the weight coefficients w10, w20, w30, w40 of the four neural networks;
[0067] Step S72: training the four neural networks and calculating the loss function;
[0068] Step S73: Use the optimization algorithm to update the weight coefficients w10, w20, w30, w40 and the loss function, train the four neural networks, minimize the loss function to obtain the optimal weight coefficients of the four neural networks, retrain and calculate the loss function when the number of iterations is less than N, and output the optimal network parameters when the number of iterations is equal to N.
[0069] Compared with the prior art, the present invention has the following beneficial effects:
[0070] 1. Compared with the existing modeling methods based on physical mechanisms, the present invention does not require in-depth research on physical mechanisms, but can directly select representative physical equations in the corresponding background to study the structure and physical meaning, which reduces the requirements for the professional knowledge of technicians and greatly shortens the modeling time.
[0071] 2. Compared with the existing modeling methods based on physical mechanisms, the present invention does not require parameter identification of physical equations or the specific analytical solution process of physical equations. Instead, it regards it as a numerical solution of a gridless method and outputs an approximate network model for solving partial differential equations through training. The output network solution can be well adapted to different time and space resolutions.
[0072] 3. Compared with the existing data-driven artificial intelligence modeling methods, the present invention does not require large-scale data samples. Through the constraints of physical equations, the complexity of the hypothesis space is greatly reduced, and such network output can well approximate the solution structure of the differential equation.
[0073] 4. Compared with the existing data-driven artificial intelligence modeling methods, the present invention uses a neural network with embedded specific physical prior information for modeling. Compared with the classical neural network, this modeling method has relatively better physical interpretability and generalization ability.
[0074] 5. The present invention can obtain an unsteady aerodynamic model with physical interpretability and relatively high accuracy under sparse sample conditions.
[0075] 6. With the powerful characterization ability of neural networks and their universal approximation theorems, the present invention can adaptively establish the mapping relationship between flight state parameters and aerodynamic forces, embed the physical knowledge of high angle of attack unsteady aerodynamic differential equations as loss functions into feedforward neural networks for training, and establish an unsteady aerodynamic prediction model driven by physical knowledge and data. This modeling method can learn a more generalized model with fewer data samples, and achieve accurate prediction of unsteady aerodynamic forces. BRIEF DESCRIPTION OF THE DRAWINGS
[0076] Figure 1 It is a flowchart of a method for modeling unsteady aerodynamic forces based on a neural network with embedded physical knowledge;
[0077] Figure 2 Schematic diagram of the neural network architecture constructed for the present invention. DETAILED DESCRIPTION
[0078] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.
[0079] The features and performance of the present invention are further described in detail below in conjunction with the embodiments.
[0080] Embodiment 1
[0081] See also Figure 1 , a method for modeling unsteady aerodynamic forces based on a neural network with embedded physical knowledge, specifically comprising the following steps:
[0082] Step S1: determining the unsteady aerodynamic modeling problem, determining the unsteady aerodynamic physical equation of longitudinal motion and the structure of the unsteady aerodynamic physical equation according to the aircraft type and the unsteady aerodynamic modeling problem, and determining the unsteady aerodynamic increment first-order differential equation in the unsteady aerodynamic physical equation;
[0083] Step S2: According to the unsteady aerodynamic physical equation and the unsteady aerodynamic increment first-order differential equation, the function mapping relationship between various physical quantities and the influencing indicators of various physical quantities is determined;
[0084] Step S3: designing a neural network architecture according to the prediction items and the relationship between the prediction items in the unsteady aerodynamic physical equation structure and the static wind tunnel test data and the dynamic wind tunnel test data measured in the wind tunnel;
[0085] Step S4: Determine the number of layers, the number of nodes and the activation function of each network according to the function mapping relationship between each physical quantity and each physical quantity influencing index;
[0086] Step S5: designing a loss function according to the prediction items and the relationship between the prediction items in the unsteady aerodynamic physical equation structure;
[0087] Step S6: Select and divide samples according to the static and dynamic wind tunnel test data measured in the wind tunnel, and generate a training set using a K-fold cross validation method;
[0088] Step S7: Perform neural network training. When the number of iterations is less than N, re-iterate and calculate the loss function. When the number of iterations is equal to N, output the optimal parameters of the network and the large angle of attack unsteady aerodynamic model.
[0089] In this embodiment, specifically, step S1 includes:
[0090] The unsteady aerodynamic physical equation for longitudinal motion consists of the static aerodynamic force, the quasi-steady aerodynamic force increment caused by the angular velocity, and the unsteady aerodynamic force increment caused by the unsteady separation, which can be expressed as:
[0091]
[0092] in:
[0093] is the unsteady aerodynamic force and unsteady aerodynamic force coefficient;
[0094] is the static aerodynamic force;
[0095] is the quasi-steady aerodynamic force increment;
[0096] is the unsteady aerodynamic force increment;
[0097] represents the angle of attack;
[0098] represents the angular rate;
[0099] Indicates exercise time.
[0100] In this embodiment, it should be noted that the first-order differential equation of the unsteady aerodynamic force increment is used to describe the additional aerodynamic force generated by the unsteady effect while ignoring the influence of the angular velocity and the rudder deflection angle history.
[0101] In this embodiment, specifically, the first-order differential equation of the unsteady aerodynamic force increment is expressed as follows:
[0102]
[0103] in:
[0104] is the change process of unsteady aerodynamic force increment;
[0105] is the unsteady incremental coefficient term;
[0106] is a non-stationary effect term.
[0107] In this embodiment, specifically, step S2 includes:
[0108] It's about angle of attack Nonlinear function of
[0109] It's about angle of attack , angular velocity Function of
[0110] It's about angle of attack , angular velocity and exercise time Function of
[0111] It's about angle of attack Function of
[0112] It's about angle of attack , angular velocity Function of
[0113] According to , and Determine the functional mapping relationship between various physical quantities and the influencing indicators of various physical quantities.
[0114] In this embodiment, specifically, step S3 includes:
[0115] Step S31: According to the relationship between the unsteady aerodynamic physical equation and the unsteady aerodynamic increment first-order differential equation and the corresponding relationship between the static wind tunnel test data and the dynamic wind tunnel test data measured by the corresponding wind tunnel test, a quasi-steady term is designed to describe Neural Network , describing the unsteady increment term Neural Network , and the term describing the unsteady incremental coefficient Neural Network , describing the non-stationary effect term Neural Network ;
[0116] Step S32: Based on neural network , Neural Network , Neural Network , Neural Network , the neural network architecture is constructed through the loss function, as follows Figure 2 As shown, where: Representing a neural network The output, Representing a neural network The output, Representing a neural network The output, Representing a neural network The output, represents the static aerodynamic force, represents the unsteady aerodynamic force and unsteady aerodynamic force coefficient calculated by the neural network prediction value;
[0117] In this embodiment, specifically, step S31 includes:
[0118] Neural Networks :According to the unsteady aerodynamic physics equation, a neural network is constructed , represents the angle of attack , angular velocity and quasi-steady aerodynamic force increment The function mapping relationship between them is used to learn the small disturbance motion parameters and the quasi-steady aerodynamic force increment The nonlinear relationship between the neural network The input is the angle of attack and angular rate , the output is the quasi-steady aerodynamic force increment ; Then the unsteady aerodynamic physical equation is updated as:
[0119]
[0120] in, The angle of attack established , angular velocity and quasi-steady aerodynamic force increment Neural network with function mapping relationship between ;
[0121] Neural Networks :According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed , represents the angle of attack , angular velocity and motion history and unsteady aerodynamics The function mapping relationship between them is used to learn the high angle of attack flight state and the unsteady aerodynamic force increment The nonlinear and unsteady relationship between the neural network The input is the angle of attack , angular velocity and exercise time , the output is the unsteady aerodynamic force increment :
[0122] Neural Networks :According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed , represents the angle of attack , angular velocity and non-stationary effects The function mapping relationship between them is used to learn the nonlinear unsteady relationship between the high angle of attack flight state and the unsteady aerodynamic force, the neural network The input is the angle of attack and angular rate , the output is the unsteady effect term ; Then the first-order differential equation of the unsteady aerodynamic force increment is updated as:
[0123]
[0124] in, The angle of attack established , angular velocity , exercise time and unsteady aerodynamic force increment Neural network with function mapping relationship between ; The angle of attack established , angular velocity and non-stationary effects Neural network with function mapping relationship between ;
[0125] Neural Networks :According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed , represents the angle of attack , angular velocity Unsteady aerodynamic force increment The function mapping relationship is used to learn the high angle of attack flight state and unsteady aerodynamic force increment Nonlinear and unsteady relationships between changing processes, neural networks The input is the angle of attack and angular rate , the output is the unsteady aerodynamic force increment .
[0126] In this embodiment, specifically, step S4 includes:
[0127] Each neural network consists of an input layer, four hidden layers and an output layer. The number of nodes in the input layer is related to the input. The number of nodes in three of the four hidden layers is the same. Each hidden layer uses Sigmoid as the activation function, and the number of nodes in the output layer is 1. The physical quantities output by the four neural networks and the labeled physical quantities of the training samples are substituted into the corresponding functions and differential equations, and the loss function MSE and the loss function ODE are constructed through the difference between the two. Among them, MSE represents mean square error and ODE represents ordinary differential equation.
[0128] In this embodiment, specifically, the loss function designed in step S5 is expressed as follows:
[0129]
[0130] in:
[0131] For neural networks The loss function MSE is Figure 2 In ;
[0132] For neural networks , , The loss function ODE;
[0133] are the unsteady aerodynamic forces and unsteady aerodynamic coefficients calculated by the neural network prediction values;
[0134] To calculate the unsteady aerodynamic force and unsteady aerodynamic force coefficients through wind tunnel test measurements.
[0135] In this embodiment, it should be noted that the neural network The loss function MSE is expressed as follows:
[0136]
[0137] Neural Networks Output , Neural Network Output Substitute the following equations to calculate the unsteady aerodynamic force and unsteady aerodynamic force coefficient predicted by the neural network: :
[0138]
[0139] The labeled physical quantity of the training sample , Substitute the following equations to calculate the unsteady aerodynamic force and unsteady aerodynamic force coefficient measured by wind tunnel test: :
[0140]
[0141] pass and The difference between the two constructs the loss function MSE:
[0142]
[0143] In this embodiment, it should be noted that the loss function ODE is expressed as follows:
[0144] Neural Networks Output , Neural Network Output Substitute the following equation to calculate the change process of the unsteady aerodynamic force increment predicted by the neural network: :
[0145]
[0146] The aerodynamic force increment calculated from wind tunnel test measurements Prediction with Neural Networks , Substitute the difference between the two to construct the loss function ODE:
[0147]
[0148] In this embodiment, specifically, step S6 includes:
[0149] According to the database generated by the static wind tunnel test and the dynamic wind tunnel test, two reduced frequency data are selected as samples, and the training set is generated using the K-fold cross validation method. , , and set the learning rate and the maximum number of iterations N.
[0150] In this embodiment, specifically, step S7 includes:
[0151] Step S71: Initialize the weight coefficients w10, w20, w30, w40 of the four neural networks;
[0152] Step S72: training the four neural networks and calculating the loss function;
[0153] Step S73: Use the optimization algorithm to update the weight coefficients w10, w20, w30, w40 and the loss function, train the four neural networks, minimize the loss function to obtain the optimal weight coefficients of the four neural networks, retrain and calculate the loss function when the number of iterations is less than N, and output the optimal network parameters when the number of iterations is equal to N.
[0154] The above-mentioned embodiments only express the specific implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the protection scope of the present application. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the technical solution concept of the present application, and these all belong to the protection scope of the present application.
[0155] This background section is provided to generally present the context of the invention, and the work of the presently named inventors, the work to the extent described in this background section, and aspects of this section that did not constitute prior art at the time of application are neither explicitly nor implicitly admitted to be prior art to the present invention.
Claims
1. A method for modeling unsteady aerodynamic forces based on a neural network with embedded physical knowledge, characterized in that: include: Step S1: determining the unsteady aerodynamic modeling problem, determining the unsteady aerodynamic physical equation of longitudinal motion and the structure of the unsteady aerodynamic physical equation according to the aircraft type and the unsteady aerodynamic modeling problem, and determining the unsteady aerodynamic increment first-order differential equation in the unsteady aerodynamic physical equation; Step S2: According to the unsteady aerodynamic physical equation and the unsteady aerodynamic increment first-order differential equation, the function mapping relationship between various physical quantities and the influencing indicators of various physical quantities is determined; Step S3: designing a neural network architecture according to the prediction items and the relationship between the prediction items in the unsteady aerodynamic physical equation structure and the static wind tunnel test data and the dynamic wind tunnel test data measured in the wind tunnel; Step S4: Determine the number of layers, the number of nodes and the activation function of each network according to the function mapping relationship between each physical quantity and each physical quantity influencing index; Step S5: designing a loss function according to the prediction items and the relationship between the prediction items in the unsteady aerodynamic physical equation structure; Step S6: Select and divide samples according to the static and dynamic wind tunnel test data measured in the wind tunnel, and generate a training set using a K-fold cross validation method; Step S7: Perform neural network training. When the number of iterations is less than N, re-iterate and calculate the loss function. When the number of iterations is equal to N, output the optimal parameters of the network and the large angle of attack unsteady aerodynamic model. The step S1 comprises: The unsteady aerodynamic physical equation for longitudinal motion consists of the static aerodynamic force, the quasi-steady aerodynamic force increment caused by the angular velocity, and the unsteady aerodynamic force increment caused by the unsteady separation, which can be expressed as: in: is the unsteady aerodynamic force and unsteady aerodynamic force coefficient; is the static aerodynamic force; is the quasi-steady aerodynamic force increment; is the unsteady aerodynamic force increment; represents the angle of attack; represents the angular rate; Indicates exercise time; The step S1 further includes: The first-order differential equation of the unsteady aerodynamic force increment is expressed as follows: in: is the change process of unsteady aerodynamic force increment; is the unsteady incremental coefficient term; is the non-steady effect term; The step S3 comprises: Step S31: According to the relationship between the unsteady aerodynamic physical equation and the unsteady aerodynamic increment first-order differential equation and the corresponding relationship between the static wind tunnel test data and the dynamic wind tunnel test data measured by the corresponding wind tunnel test, a quasi-steady term is designed to describe Neural Network , describing the unsteady increment term Neural Network , and the term describing the unsteady incremental coefficient Neural Network , describing the non-stationary effect term Neural Network ; Step S32: Based on neural network , Neural Network , Neural Network , Neural Network , the neural network architecture is constructed through the loss function; The step S31 comprises: According to the unsteady aerodynamic physics equation, a neural network is constructed , represents the angle of attack , angular velocity and quasi-steady aerodynamic force increment The function mapping relationship between them is used to learn the small disturbance motion parameters and the quasi-steady aerodynamic force increment The nonlinear relationship between the neural network The input is the angle of attack and angular rate , the output is the quasi-steady aerodynamic force increment ; Then the unsteady aerodynamic physical equation is updated as: in, The angle of attack established , angular velocity and quasi-steady aerodynamic force increment Neural network with function mapping relationship between ; According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed. , represents the angle of attack , angular velocity and motion history and unsteady aerodynamics The function mapping relationship between them is used to learn the high angle of attack flight state and the unsteady aerodynamic force increment The nonlinear and unsteady relationship between the neural network The input is the angle of attack , angular velocity and exercise time , the output is the unsteady aerodynamic force increment : According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed. , represents the angle of attack , angular velocity and non-stationary effects The function mapping relationship between them is used to learn the nonlinear unsteady relationship between the high angle of attack flight state and the unsteady aerodynamic force, the neural network The input is the angle of attack and angular rate , the output is the unsteady effect term ; Then the first-order differential equation of the unsteady aerodynamic force increment is updated as: in, The angle of attack established , angular velocity , exercise time and unsteady aerodynamic force increment Neural network with function mapping relationship between ; The angle of attack established , angular velocity and non-stationary effects Neural network with function mapping relationship between ; According to the first-order differential equation of unsteady aerodynamic force increment, a neural network is constructed. , represents the angle of attack , angular velocity Unsteady aerodynamic force increment The function mapping relationship is used to learn the high angle of attack flight state and unsteady aerodynamic force increment Nonlinear and unsteady relationships between changing processes, neural networks The input is the angle of attack and angular rate , the output is the unsteady aerodynamic force increment .
2. The unsteady aerodynamic modeling method based on a neural network with embedded physical knowledge according to claim 1 is characterized in that: The step S2 comprises: It's about angle of attack Nonlinear function of It's about angle of attack , angular velocity Function of It's about angle of attack , angular velocity and exercise time Function of It's about angle of attack Function of It's about angle of attack , angular velocity function.
3. The unsteady aerodynamic modeling method based on a neural network with embedded physical knowledge according to claim 2 is characterized in that: The step S4 comprises: Each neural network consists of an input layer, four hidden layers and an output layer. The number of nodes in the input layer is related to the input. The number of nodes in three of the four hidden layers is the same. Each hidden layer uses Sigmoid as the activation function, and the number of nodes in the output layer is 1. The physical quantities output by the four neural networks and the labeled physical quantities of the training samples are substituted into the corresponding functions and differential equations, and the loss function MSE and the loss function ODE are constructed through the difference between the two. Among them, MSE represents mean square error and ODE represents ordinary differential equation.
4. The unsteady aerodynamic modeling method based on a neural network with embedded physical knowledge according to claim 3 is characterized in that: The loss function designed in step S5 is expressed as follows: in: For neural networks The loss function MSE; For neural networks , , The loss function ODE; are the unsteady aerodynamic forces and unsteady aerodynamic coefficients calculated by the neural network prediction values; To calculate the unsteady aerodynamic force and unsteady aerodynamic force coefficients through wind tunnel test measurements.
5. The unsteady aerodynamic modeling method based on a neural network with embedded physical knowledge according to claim 4 is characterized in that: The step S6 comprises: According to the database generated by the static wind tunnel test and the dynamic wind tunnel test, two reduced frequency data are selected as samples, and the training set is generated using the K-fold cross validation method. , , and set the learning rate and the maximum number of iterations N.
6. The unsteady aerodynamic modeling method based on a neural network with embedded physical knowledge according to claim 5 is characterized in that: The step S7 comprises: Step S71: Initialize the weight coefficients w10, w20, w30, and w40 of the four neural networks; Step S72: training the four neural networks and calculating the loss function; Step S73: Use the optimization algorithm to update the weight coefficients w10, w20, w30, w40 and the loss function, train the four neural networks, minimize the loss function to obtain the optimal weight coefficients of the four neural networks, retrain and calculate the loss function when the number of iterations is less than N, and output the optimal network parameters when the number of iterations is equal to N.