A flying wing unmanned aerial vehicle model correction method based on PIKAN

Abstract

The present application belongs to the technical field of model correction, and relates to a model correction method based on a Kolmogorov-Arnold network of physical information. The method first establishes a database based on aerodynamic coefficients and constructs an aerodynamic data set; secondly, the Kolmogorov-Arnold network is used to fit the reference aerodynamic model, so as to accurately capture the mapping relationship between the flight state and the aerodynamic coefficients; finally, the model correction is carried out in combination with the flight data, and the physical information constraint is introduced, so as to effectively inhibit the interference of noise. Compared with the deep learning network, the aerodynamic fitting method based on the Kolmogorov-Arnold network has higher accuracy in aerodynamic coefficient fitting and parameter estimation; at the same time, the Kolmogorov-Arnold network with the introduction of physical information can significantly improve the model correction accuracy in the noise-containing scene.

Description

Technical Field

[0001] This invention belongs to the field of model correction technology and relates to a method for correcting flying-wing UAV models based on PIKAN. Background Technology

[0002] Flying-wing UAVs are a typical example of unconventional aerodynamic layout aircraft. They eliminate the tail fin and lack a clear boundary between the fuselage and wings, exhibiting a blended wing-body characteristic. This layout offers unique aerodynamic advantages, significantly enhancing the UAV's stealth performance, providing a good lift-to-drag ratio, and facilitating high-altitude, long-range missions. However, flying-wing UAVs face model uncertainties during actual flight, especially given the multiple combined control surfaces. The resulting changes in overall aerodynamic characteristics due to these combined controls are difficult to accurately determine, further complicating the model's uncertainty. Therefore, improving the accuracy of aerodynamic models is crucial.

[0003] Model corrections mostly employ aerodynamic identification methods for aerodynamic models. Taking the flight dynamics system as the object, based on identification theory and state data acquired from sensors, aerodynamic model information is calculated, improving the accuracy of online aerodynamic models. Aerodynamic identification technology mainly includes traditional aerodynamic identification methods and intelligent identification methods. Traditional aerodynamic identification methods assume the aerodynamic model has a certain form and structure and use traditional mathematical methods for parameter estimation to solve for the aerodynamic parameters to be identified in the model based on flight test data. However, traditional identification methods require pre-determining the nonlinear system structure, while intelligent identification methods can utilize the learning and approximation capabilities of methods such as deep learning to extract the dynamic characteristics of the system based on input and output data, without needing prior knowledge of the system's structure and parameters, thus overcoming the limitations of traditional methods. However, the fully connected structure of deep learning networks (DNNs) essentially achieves the training process by passing multiple linear functions through a nonlinear activation function. This results in low efficiency when dealing with complex nonlinear problems. Furthermore, deep learning algorithms have always been considered a "black box" with poor interpretability.

[0004] In recent years, the Kolmogorov-Arnold Network (KAN) has been proposed as a novel neural network architecture. Based on the Kolmogorov-Arnold representation theorem, it introduces a separate function into each connection between two nodes in a continuous layer, providing a promising alternative to traditional deep learning. However, regardless of the type of neural network, they all suffer from data dependence. In unsuitable situations such as high data noise, the fitting noise can be amplified, making it difficult to meet the physical laws of real-world problems. To address this issue, a Physics-Informed Neural Network (PINN) has been proposed. PINN introduces physical equations into the loss function to ensure that the model's predictions conform to actual physical laws, thereby avoiding unreasonable results that may occur with data-driven models, enhancing interpretability, and making it suitable for aerodynamic identification and fitting research. In summary, KAN improves training efficiency and interpretability compared to traditional deep learning; while PINN enhances noise resistance by incorporating physical information compared to traditional deep learning. Therefore, combining the two to form a new Physics-Informed Kolmogorov-Arnold Network (PIKAN) can take into account the above advantages.

[0005] In published studies, some scholars have begun PIKAN research, but it has not been applied to the field of aerodynamic identification. In current identification research, Kimathi et al. (Robust Aerodynamic Parameter Estimation of Unmanned Aircraft Based on Two-step Identification[J]. Periodicapolytechnica. Electrical engineering and computer science, 2023, 67(3): 217-224.) proposed a robust estimation method for UAV aerodynamic parameters based on two-step identification, aiming to solve the heteroscedasticity problem, and used the least squares method to estimate aerodynamic parameters. Statistical analysis was performed through the Cramer-Lau boundary, and the identification model was verified by dynamic simulation. Fyfe (Low-Speed ​​Flight Testing and System Identification of a Small-Scale Supersonic Uncrewed Aerial Vehicle[D]. Calgary, Canada: University of Calgary, 2025.) used the maximum likelihood method, combined with maneuver-specific autonomous data and orthogonal functions, to identify 25 local aerodynamic coefficients. Nayeem (UAV States Estimation and Wind Field Reconstruction [D]. Stillwater, USA: Oklahoma State University, 2025.) successfully estimated the state and environmental wind field of UAVs using a traditional extended Kalman filter in the absence of an accurate aerodynamic model. Karali et al. (Design of a Deep Learning Based Nonlinear Aerodynamic Surrogate Model for UAVs [C]. Orlando, FL: AIAA Scitech 2020 Forum, 2020: 1288.) designed a deep learning-based nonlinear aerodynamic surrogate model that can quickly determine the nonlinear aerodynamic characteristics of UAVs without any special input data or preprocessing stage, and can rapidly predict aerodynamic performance using only geometric configuration parameters.George et al. (Recurrentneural networks for aerodynamic parameter estimation with Lyapunov stability analysis[J]. Systems Science & Control Engineering, 2024, 12(1): 2363387.) proposed an aerodynamic parameter estimation method based on recurrent neural networks and Lyapunov stability analysis. This method utilizes recurrent neural networks to process time-series data, enabling accurate identification of parameters such as aerodynamic coefficients and engine thrust. Zan et al. (High-dimensional aerodynamic data modeling using a machine learning method based on a convolutional neural network[J]. Advances in Aerodynamics, 2022, 4(1):39.) proposed a machine learning method based on convolutional neural networks for high-dimensional aerodynamic data modeling to address the high-dimensional challenges in aerodynamic load prediction, aerodynamic shape optimization, and flight control. Experiments by Liu et al. (KAN: Kolmogorov-ArnoldNetworks[R]. arXiv preprint arXiv:2404.19756, 2024.) demonstrate that smaller-scale KANs can achieve or even surpass the accuracy of large multilayer perceptrons in tasks such as data fitting and partial differential equation solving, and exhibit better interpretability. Summary of the Invention

[0006] To address the challenge of ground-based numerical model simulations failing to fully reproduce realistic aerodynamic characteristics, this invention proposes a PIKAN-based model correction method for flying-wing unmanned aerial vehicles (UAVs). This method first establishes a database based on aerodynamic coefficients and constructs an aerodynamic dataset. Second, it employs a Kolmogorov-Arnold Network (KAN) to fit a baseline aerodynamic model, accurately capturing the mapping relationship between flight states and aerodynamic coefficients. Finally, it combines flight data to perform model correction and introduces physical information into the KAN, forming a Physics-Informed Kolmogorov-Arnold Network (PIKAN) to effectively suppress noise interference. Compared to deep learning networks, the Kolmogorov-Arnold network-based aerodynamic fitting method achieves higher accuracy in aerodynamic coefficient fitting and parameter estimation. Furthermore, the PIKAN network, incorporating physical information, significantly improves model correction accuracy in noisy scenarios.

[0007] The technical solution of the present invention: A PIKAN-based method for correcting flying-wing UAV models includes flying-wing UAV dynamics modeling, baseline KAN model construction, and PIKAN corrected model construction. The specific steps are as follows: Step (1) Dynamic modeling of flying-wing UAV The longitudinal force and moment coefficients of the established flying-wing UAV dynamic model are shown below: In the formula: It is the body coordinate system x Directional force coefficient and z Directional coefficient; It is the pitch moment coefficient. For the angle of attack, For speed, The pitch angular velocity, For control surface configuration, For thrust, For the inner front edge flap, For the outer front edge flap, All-moving wingtips, For elevons, To bend and straighten one's wings, As a drag rudder, The pitch thrust vector, This is the yaw thrust vector.

[0008] Based on the above expressions for force and moment coefficients, the expressions for body force and pitch moment of the flying wing UAV can be further obtained.

[0009] In the formula: , for x and z Directional force, For pitching moment, Atmospheric density; Wing area; For the average aerodynamic chord length, It is the thrust vector arm; The longitudinal dynamics model of the flying-wing UAV is shown below: In the formula: For speed, For thrust, For the angle of attack, Due to the resistance encountered, For quality, It is the acceleration due to gravity. For the track angle, For lift, For rotational inertia, The pitch angular velocity, For pitching moment, This represents the forward displacement distance. For flight altitude, The pitch angle.

[0010] Step (2) Construction of the baseline KAN model To establish a nonlinear mapping relationship between the flight state parameters of a flying-wing UAV and the target aerodynamic parameters, this invention uses KAN to construct a baseline aerodynamic model. KAN introduces a learnable one-dimensional function into the network connection to characterize the nonlinear influence of input variables on output variables, making it suitable for modeling scenarios with multivariate coupling and strong nonlinearity in flying-wing UAV aerodynamic models.

[0011] In the longitudinal dynamics modeling in step (1), the angle of attack, elevator aileron deflection, pitch flap deflection and pitch angular velocity are selected as network inputs, and the pitch moment coefficient is selected as network output.

[0012] The network input vector is: in, The input vector for the KAN network, d For the input dimension; the first The input vector of each sample Represented as: in, for Angle of attack input for each sample, for The elevator input for each sample, for pitch flap input for each sample, for The pitch angular velocity input for each sample.

[0013] The corresponding network output is represented as: in, for Predicted pitch moment coefficient values ​​for each sample This is a KAN mapping relationship. These are the parameters to be trained for the KAN.

[0014] have d Dimensional input and c The KAN with 3D output can be defined as a matrix of a one-dimensional function. As shown in the following formula.

[0015] in, For the first The input to the first A one-dimensional mapping function between the outputs. This one-dimensional mapping function can be expressed as: in, One-dimensional mapping function The single-variable independent variable represents a single input quantity in a certain component of the input vector or in a certain layer of transmission process; For parameters; It is a spline function; These are basis functions.

[0016] The overall mapping relationship of KAN is represented as follows: in, For network input vectors, For the network output vector, For composite operators, This refers to the number of KAN layers. In this invention, since the network output is the pitch moment coefficient, therefore... Corresponding to the pitch moment coefficient output; for the first For each sample, the network output is... .

[0017] The network is trained using an offline database, and the loss function is constructed as follows: in, The number of training samples, For offline databases Reference values ​​for pitch moment coefficients for each sample.

[0018] The baseline KAN model is obtained by updating the network parameters by minimizing the loss function: in, For the number of iterations, The learning rate for KAN. It is the first The parameters for the next iteration.

[0019] After training, a baseline KAN model is obtained, which includes flight state parameters and control inputs to pitch moment coefficients, providing an initial model basis for subsequent online corrections.

[0020] Step (3) Based on the KAN model, construct the PIKAN modified model. The PIKAN correction model is based on the baseline KAN model obtained in step (2), introduces physical information, takes online flight data as input, takes the corrected pitch moment coefficient as output, and trains the network parameters by combining data loss and physical loss, so that the model output can approximate the online data while satisfying the longitudinal dynamic relationship of the flying wing UAV.

[0021] (3.1) Data loss construction Construct the data loss between the network output and the online reference value. : in, For the number of online samples, For the first Reference values ​​for pitch moment coefficients corresponding to each online sample.

[0022] (3.2) Physical loss construction Constructing the physical loss function for: in, The number of physical information samples. The physical prediction value of pitch angular velocity. For online The pitch rate reference value was obtained from the sample flight measurement. The physical loss establishes the dynamic physical relationship between the network output pitch moment coefficient and the actual flight pitch rate.

[0023] Physical prediction of pitch angular velocity The specific calculation method is as follows: First, calculate the predicted pitch acceleration value based on the longitudinal dynamic equation in step (1). : in, This represents the longitudinal dynamic mapping relationship. Other known state parameters and flight condition parameters are used in the dynamic calculations.

[0024] Next, the pitch acceleration is discretely integrated to obtain the predicted pitch angular velocity value. : in, For online angular acceleration of the sample This represents the sampling time interval.

[0025] (3.3) Input / output definition Using the baseline KAN model as the correction target, the angle of attack, elevator deflection, pitch flap deflection, and pitch rate from the online flight data are used as network inputs. One online sample Represented as: in, for Angle of attack input for an online sample, for The elevator input for an online sample, for The pitch flap input for an online sample. for The pitch angular velocity input for each online sample.

[0026] Based on the baseline KAN model, physical information is introduced to form the PIKAN modified model, as shown below: in, for The predicted PIKAN pitch moment coefficient for each online sample. For the PIKAN modified model, These are the parameters to be trained for PIKAN.

[0027] (3.4) Joint Loss and Parameter Update Construct the PIKAN total loss function for: in, To reduce data loss weights, This represents the weight of physical loss.

[0028] Update network parameters by minimizing the total loss function: in, For network parameters, These are the optimal network parameters.

[0029] The parameter iterative update formula is: in, For the number of iterations, The learning rate for PIKAN. It is the first The parameters for the next iteration.

[0030] After training, a PIKAN correction model is obtained. This correction model utilizes offline databases, online flight data, and longitudinal physical information, which can improve the model's accuracy and robustness under actual flight conditions.

[0031] (3.5) Correction process The model correction process of this invention includes: training a KAN model based on an offline database to obtain a baseline KAN model; acquiring online flight data and performing Butterworth filtering preprocessing; constructing a data loss term using online samples and a physical loss term using the longitudinal dynamics equations; and iteratively optimizing the joint loss function to obtain the PIKAN corrected model. Through the above process, a closed-loop model optimization of the longitudinal dynamics of a flying-wing UAV is achieved, from offline fitting to online correction.

[0032] The beneficial effects of this invention are: This invention addresses the core issue of discrepancies between ground numerical simulation data and the actual characteristics of flying-wing UAVs, proposing a model correction method based on the physically-informed Kolmogorov-Arnold network. It deeply integrates the high training efficiency and strong interpretability of KAN with the physically-informed characteristics of PINN. Compared to traditional deep learning networks, KAN captures the mapping relationship between flight state and aerodynamic coefficients more accurately, and its training process is more efficient and interpretable. By introducing physical information, it suppresses noise error amplification at the loss function design level, overcoming the one-way shortcomings of single models in terms of accuracy or noise resistance. Simulation and verification results show that the model correction accuracy of this method is significantly better than traditional deep learning methods under noisy conditions, providing more reliable model support for controlled flying-wing UAVs. Attached Figure Description

[0033] Figure 1 This is a flowchart of a model correction method based on PIKAN; Figure 2 This is the control surface configuration for the ICE flying wing UAV; Figure 3 This is a deep learning network diagram; Figure 4 This is the KAN fitting block diagram; Figure 5 This is a comparison chart of the accuracy of the pitch moment coefficients of KAN and DNN; Figure 6 This is a comparison chart of the losses of KAN and DNN; Figure 7 This is a comparison chart of the static stability coefficient accuracy of KAN and DNN; Figure 8 This is a comparison chart of the evacuation rudder effectiveness accuracy of KAN and DNN. Figure 9 It is a Butterworth angle-of-attack filter curve; Figure 10 It is the Butterworth elevator filter curve; Figure 11 This is a comparison chart of the accuracy of the pitch moment coefficients of PIKAN and PINN; Figure 12 This is a comparison chart of PIKAN and PINN losses; Figure 13 This is a comparison chart of the static stability coefficient accuracy of PIKAN and PINN; Figure 14 This is a comparison chart of the PIKAN and PINN elevator rudder effectiveness accuracy. Detailed Implementation

[0034] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0035] The overall flowchart of the PIKAN-based model correction method is as follows: Figure 1 As shown, first according to Figure 2 Dynamic modeling was performed on the control surface configuration of the flying wing UAV shown, and then... Figure 3 Deep neural networks and Figure 4 Offline KAN model accuracy comparison. Figure 5-8 The image shows a comparison of the accuracy of KAN and DNN. Next, Butterworth filtering is applied to the flight data. Figure 9-10 The filtering curves are shown, and finally, PIKAN and PINN are compared and analyzed through simulation. Figure 11-14 This is a comparison chart of the accuracy of PIKAN and PINN. The specific steps are as follows: (1) Obtain offline model data When acquiring offline model fitting data, a dynamic model is first established. To model the flying-wing UAV, it is necessary to analyze its forces and moments. This invention focuses on the longitudinal direction, and the specific force and moment coefficients are shown below: In the formula: It is the body coordinate system x Directional force coefficient and z Directional coefficient; It is the pitch moment coefficient. For the angle of attack, For speed, The pitch angular velocity, For control surface configuration, For thrust, For the inner front edge flap, For the outer front edge flap, All-moving wingtips, For elevons, To bend and straighten one's wings, As a drag rudder, The pitch thrust vector, This is the yaw thrust vector. Using these equations, the body forces and moments can be derived.

[0036] In the formula: , for x and z Directional force, For pitching moment, Atmospheric density; Wing area; For the average aerodynamic chord length, It is the thrust vector lever arm, and its dynamic model is shown below: In the formula: For speed, For thrust, For the angle of attack, Due to the resistance encountered, For quality, It is the acceleration due to gravity. For the track angle, For lift, For rotational inertia, The pitch angular velocity, For pitching moment, This represents the forward displacement distance. For flight altitude, The pitch angle.

[0037] The offline modeling data is generated randomly from sample points, as shown below. The inputs are angle of attack, elevons, pitch flaps, and pitch rate, and the output is the pitch moment coefficient. The sample value range is shown in the following formula, resulting in a total of 8019 sample points: The range of values ​​for the longitudinal samples is shown below, resulting in a total of 8019 sample points.

[0038] (2) Simulation comparison of KAN and DNN model fitting The KAN and DNN parameter settings are shown in Table 1. Model fitting is performed and accuracy is compared. Table 1 Optimizing Network Parameter Settings

[0039] Table 2 Comparison of KAN and DNN Accuracy

[0040] To assess the fitting accuracy of model parameters, a comparison was made between Deep Neural Networks (DNNs) and Kolmogorov-Arnold Networks (KANs). The table above shows that KAN significantly outperforms DNNs in fitting accuracy across all core parameters. While DNNs struggle to reach ideal accuracy even after 6000 training iterations, KANs achieve ideal accuracy in just 1749 iterations. Furthermore, the Mean Absolute Error (MAE) of the coefficient terms is significantly lower than that of DNNs. Down to The errors in static stability coefficient, elevator aileron effect, pitch flap effect, and angular velocity term were also greatly reduced, confirming that KAN has a better ability to fit the parameters.

[0041] (3) Design of longitudinal flight control law for flying wing UAV First, the offline model is skewed, and a traditional control law is used to generate a set of pitch angle attitude control data with noise (introducing sensor noise). The control law is as follows: in, For pitch angle command, For speed commands, For throttle, , , , , These are control parameters.

[0042] In real-time aerodynamic modeling, it is essential to efficiently acquire motion data for all rigid body degrees of freedom. Research indicates that under various flight conditions, applying automatically orthogonally optimized multi-sine perturbation signals to the control surfaces can effectively stimulate the aerodynamic response characteristics of the aircraft. This perturbation input, by superimposing the optimized excitation signal onto the actuator commands of the control instructions, forms a composite control surface command, thereby achieving active excitation of the flight system.

[0043] Setting the application in The excitation input for each control surface is Its expression is shown in the following formula: In the formula: To be applied to the first Excitation inputs for each control surface; This indicates a sinusoidal harmonic component containing a single phase shift; This represents the total number of available harmonic frequency combinations; The period of the excitation signal; These are the amplitude parameters of each sinusoidal wave component; It is a time variable.

[0044] To achieve uniform power distribution, The expression is as follows: In the formula: This indicates the number of sinusoidal components included in the equation; It is the input stimulus amplitude.

[0045] To address the high-frequency noise environment caused by the sensor, this invention employs a Butterworth filter to filter the acquired data. The specific filter transfer function is shown in the following equation: in, It is the order of the filter; It is the input signal frequency; Cutoff frequency. This is the square of the filter's amplitude-frequency response. In this invention, the filter order is set to 4, and the cutoff frequency is 2.5 Hz.

[0046] (4) Construction of physical loss function and joint training The pitch angular velocity, which has a physical meaning, can be obtained by integrating the pitch angular acceleration, and the physical loss function is defined as follows: The data loss function is shown in the following formula: Combining data loss and physical loss, the final error loss function is expressed as follows: in, and These are the data loss weights and physical loss weights, respectively.

[0047] (5) Model correction and comparison simulation based on PIKAN The static stability coefficient, elevon rudder effect, and pitch flap rudder effect were adjusted by +10%, -20%, and -10% respectively. A step simulation of the pitch angle from 3 degrees to 5 degrees was performed. The flight data was introduced into noise processing (±0.5° and 1° of white noise were introduced into the angle of attack and elevon rudder respectively), and filtered using a Butterworth filter. The data was then introduced into the KAN fitting network model for PIKAN model correction.

[0048] The network structures of PIKAN and PINN (Physics-Informed Neural Network) are consistent with those of KAN / DNN, and both are trained 2000 times.

[0049] Table 3. Accuracy Comparison of PIKAN and PINN

[0050] As can be seen from the filtering curve, the smoothness of the signal after Butterworth filtering is significantly improved compared with the original noisy signal. The fluctuation noise of angle of attack and elevator aileron is effectively suppressed, which not only preserves the core change characteristics of the signal, but also avoids the interference of noise on model training.

[0051] For the model correction task of flying-wing UAVs, the accuracy performance of deep neural networks (DNN) and Kolmogorov-Arnold networks (KAN) in the physical information embedding scenario was compared. As shown in the table above, PIKAN's errors in all key parameters are significantly lower than PINN's, and the MAE of the pitch moment coefficient is significantly lower than that of DNN. Down to The static stability coefficient error converged from 0.0163 to 0.0138, and the errors of each rudder effect term and angular velocity term were also reduced by more than 50%. The results show that, compared with the traditional fully connected structure, PIKAN has higher model correction accuracy and faster convergence speed under the same number of training epochs.

Claims

1. A method for correcting a flying-wing unmanned aerial vehicle (UAV) model based on PIKAN, characterized in that, The specific steps are as follows: Step (1) Dynamic modeling of flying-wing UAV Step (2) Construction of the baseline KAN model In the longitudinal dynamics modeling of step (1), the angle of attack, elevator aileron deflection, pitch flap deflection and pitch angular velocity are selected as network inputs, and the pitch moment coefficient is selected as network output. After training, a baseline KAN model is obtained, which includes flight state parameters and control inputs to pitch moment coefficients, providing an initial model basis for subsequent online corrections. Step (3) Based on the KAN model, construct the PIKAN modified model. The PIKAN correction model is based on the baseline KAN model obtained in step (2), introduces physical information, takes online flight data as input, takes the corrected pitch moment coefficient as output, and trains the network parameters by combining data loss and physical loss, so that the model output can approximate the online data while satisfying the longitudinal dynamic relationship of the flying wing UAV.

2. The method for correcting a flying-wing UAV model based on PIKAN according to claim 1, characterized in that, Step (1) is as follows: The longitudinal force and moment coefficients of the flying-wing UAV dynamics model are shown below: In the formula: It is the body coordinate system x Directional force coefficient and z Directional coefficient; It is the pitch moment coefficient. For the angle of attack, For speed, The pitch angular velocity, For control surface configuration, For thrust, For the inner front edge flap, For the outer front edge flap, All-moving wingtips, For elevons, To bend and straighten one's wings, As a drag rudder, The pitch thrust vector, This is the yaw thrust vector; Based on the above expressions for force and moment coefficients, we can further obtain the expressions for the body force and pitch moment of the flying wing UAV. In the formula: , for x and z Directional force, For pitching moment, Atmospheric density; Wing area; For the average aerodynamic chord length, It is the thrust vector arm; The longitudinal dynamics model of the flying-wing UAV is shown below: In the formula: For speed, For thrust, For the angle of attack, Due to the resistance encountered, For quality, It is the acceleration due to gravity. For the track angle, For lift, For rotational inertia, The pitch angular velocity, For pitching moment, This represents the forward displacement distance. For flight altitude, The pitch angle.

3. The method for correcting a flying-wing UAV model based on PIKAN according to claim 1, characterized in that, Step (2) is as follows: The network input vector is: in, The input vector for the KAN network, d For the input dimension; the first The input vector of each sample Represented as: in, for Angle of attack input for each sample, for The elevator input for each sample, for pitch flap input for each sample, for Input the pitch angular velocity of each sample; The corresponding network output is represented as: in, for Predicted pitch moment coefficient values ​​for each sample This is a KAN mapping relationship. These are the parameters to be trained for the KAN class. have d Dimensional input and c The KAN of the one-dimensional output is defined as a matrix of a one-dimensional function. As shown in the following formula; in, For the first The input to the first A one-dimensional mapping function between the outputs; the one-dimensional mapping function is expressed as: in, One-dimensional mapping function The single-variable independent variable represents a single input quantity in a certain component of the input vector or in a certain layer of transmission process; For parameters; It is a spline function; are basis functions; The overall mapping relationship of KAN is represented as follows: in, For network input vectors, For the network output vector, For composite operators, The number of KAN layers; in this invention, since the network output is the pitch moment coefficient, therefore Corresponding to the pitch moment coefficient output; for the first For each sample, the network output is... ; The network is trained using an offline database, and the loss function is constructed as follows: in, The number of training samples, For offline databases Reference values ​​for pitch moment coefficients for each sample; The baseline KAN model is obtained by updating the network parameters by minimizing the loss function: in, For the number of iterations, The learning rate for KAN. It is the first The parameters for the next iteration.

4. The method for correcting a flying-wing UAV model based on PIKAN according to claim 1, characterized in that, Step (3) is as follows: (3.1) Data loss construction Construct the data loss between the network output and the online reference value. : in, For the number of online samples, For the first Reference values ​​of pitch moment coefficients for each online sample; (3.2) Physical loss construction Constructing the physical loss function for: in, The number of physical information samples. The physical prediction value of pitch angular velocity. For online Reference value of pitch angular velocity obtained from sample flight measurements; (3.3) Input / output definition Using the baseline KAN model as the correction target, the angle of attack, elevator deflection, pitch flap deflection, and pitch rate from the online flight data are used as network inputs. One online sample Represented as: in, for Angle of attack input for an online sample, for The elevator input for an online sample, for The pitch flap input for an online sample. for The pitch angular velocity input for each online sample; Based on the baseline KAN model, physical information is introduced to form the PIKAN modified model, as shown below: in, for The predicted PIKAN pitch moment coefficient for each online sample. For the PIKAN modified model, These are the parameters to be trained for PIKAN; (3.4) Joint Loss and Parameter Update Construct the PIKAN total loss function for: in, To reduce data loss weights, For physical loss weights; Update network parameters by minimizing the total loss function: in, For network parameters, The optimal network parameters; The parameter iterative update formula is: in, For the number of iterations, The learning rate for PIKAN. It is the first Parameters at the next iteration; (3.5) Correction process A baseline KAN model is obtained by training a KAN based on an offline database; online flight data is acquired and preprocessed using Butterworth filtering; a data loss term is constructed using online samples, and a physical loss term is constructed using the longitudinal dynamics equation; the joint loss function is iteratively optimized to obtain the PIKAN modified model; through the above process, a closed-loop model optimization of the longitudinal dynamics of the flying-wing UAV from offline fitting to online correction is achieved.

5. The method for correcting a flying-wing UAV model based on PIKAN according to claim 4, characterized in that, In step (3.2), the physical prediction value of the pitch angular velocity The specific calculation method is as follows: First, calculate the predicted pitch acceleration value based on the longitudinal dynamic equation in step (1). : in, This represents the longitudinal dynamic mapping relationship. Other known state parameters and flight condition parameters are included in the dynamic calculations; Next, the pitch acceleration is discretely integrated to obtain the predicted pitch angular velocity value. : in, For online angular acceleration of the sample This represents the sampling time interval.

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