An aerodynamic parameter identification method based on an improved physical information neural network

Abstract

The application provides an aerodynamic parameter identification method based on an improved physical information neural network, comprising: obtaining a target flight state quantity in a flight process of an aircraft; inputting the target flight state quantity into the improved physical information neural network to obtain an aerodynamic parameter perturbation quantity, the aerodynamic parameter perturbation quantity being a difference quantitative value between a nominal aerodynamic parameter and an actual aerodynamic parameter in flight, a loss function of the improved physical information neural network being an integral loss function, the integral loss function establishing a connection between a dynamic model containing an estimated value and a real dynamic characteristic; and determining the actual aerodynamic parameter according to the aerodynamic parameter perturbation quantity and the corresponding nominal aerodynamic parameter. Through implementation of the application, the dynamic model containing the estimated value is connected with the real dynamic characteristic in an integral manner, correct dynamic information is ensured to be learned by the neural network in a training process, the accuracy of the aerodynamic parameter is improved, and the training difficulty is reduced.

Description

Technical Field

[0001] This invention belongs to the field of aircraft parameter identification technology, specifically relating to an aerodynamic parameter identification method based on an improved physical information neural network. Background Technology

[0002] Some guidance laws require aerodynamic parameters of the aircraft when calculating guidance commands, and accurate aerodynamic parameters play a crucial role in the performance of the guidance system. Since actual aerodynamic parameters generally cannot be directly measured during flight, nominal aerodynamic parameters obtained through wind tunnel testing or computational fluid dynamics are typically used to replace the actual aerodynamic parameters when calculating guidance commands. However, actual aerodynamic parameters are subject to perturbations relative to nominal parameters. These perturbations can lead to a decrease in guidance accuracy and, in some cases, affect the aircraft's performance and stability. To overcome this challenge, it is necessary to develop effective aerodynamic parameter identification methods to optimize aircraft performance and improve guidance system performance.

[0003] In the past, classical methods such as least squares (LS) and maximum likelihood estimation have been widely used in the field of aircraft parameter identification. In addition, Kalman filtering and its improved forms have also been extensively studied in aircraft parameter identification, with existing technologies utilizing different forms of Kalman filtering to identify time-varying aerodynamic parameters of aircraft. While these methods can provide good parameter identification tools for aircraft in most cases, they may suffer from increased computational complexity and decreased identification performance when dealing with aircraft systems exhibiting strong nonlinear dynamics and complex flight environments.

[0004] In recent years, with the continuous development of deep learning technology, intelligent learning methods represented by neural networks are considered a highly promising method for aircraft system identification due to their powerful nonlinear function mapping capabilities. One widely used method for aerodynamic parameter identification based on neural networks establishes a nonlinear mapping relationship between the aircraft's state variables—aerodynamic forces and aerodynamic torques—using neural networks, and then calculates the aircraft's aerodynamic parameters through methods such as aerodynamic formulas, partial differential equations, or further neural network mapping. Another method aims to directly establish a direct mapping relationship between the aircraft's state and aerodynamic parameters, which are closely related to these parameters, and then uses the finite difference method to further calculate aerodynamic derivatives to obtain more comprehensive aerodynamic parameter information. The idea of ​​calculating aerodynamic derivatives using neural network predictions based on the finite difference method has further promoted the development of neural partial differential equation methods. Using the direct differentiation of neural networks instead of the finite difference method allows for more convenient calculation of aerodynamic derivatives.

[0005] Although neural network technology has been extensively studied in the field of aerodynamic parameter identification, the lack of true values ​​during neural network training due to the inability to directly measure aerodynamic parameters in real-world scenarios significantly limits its practical application. From this perspective, it is crucial to fully utilize the physical relationships between measurable flight state variables and aerodynamic parameters to train neural networks capable of identifying these parameters. Physical Information Neural Networks (PINNs), developed by Raissi et al., are deep learning frameworks that embed physical knowledge. By adding loss function terms related to physical differential equations, they force the network to learn the intrinsic relationships between physical quantities. Therefore, PINNs can solve for unknown parameters in differential equations even without knowing the true values, thus gaining some traction in aerodynamic parameter identification. However, because the loss function in PINNs is related to the unknown parameters when solving for them, it leads to the problem of erroneous learning of physical laws. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a method and apparatus for identifying aerodynamic parameters based on an improved physical information neural network, so as to meet the need for obtaining accurate aerodynamic parameters.

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

[0008] According to a first aspect, the present invention provides an aerodynamic parameter identification method based on an improved physical information neural network, comprising: acquiring target flight state quantities during the flight of an aircraft; inputting the target flight state quantities into the improved physical information neural network to obtain aerodynamic parameter perturbation quantities, wherein the aerodynamic parameter perturbation quantities are quantified values ​​of the difference between nominal aerodynamic parameters and actual aerodynamic parameters during flight, and the loss function of the improved physical information neural network is an integral loss function, which establishes a connection between the dynamic model containing the estimated values ​​and the actual dynamic characteristics; and determining the actual aerodynamic parameters based on the aerodynamic parameter perturbation quantities and the corresponding nominal aerodynamic parameters.

[0009] Optionally, when the target flight state quantities include: flight time, angle of attack command, and Mach number during the flight of the aircraft, the target flight state quantities are input into the improved physical information neural network to obtain aerodynamic parameter perturbations, including: inputting the flight time, angle of attack command, and Mach number into the improved physical information neural network to obtain drag coefficient perturbations and lift coefficient perturbations; and determining the actual aerodynamic parameters based on the aerodynamic parameter perturbations and the corresponding nominal aerodynamic parameters, including: obtaining the actual drag coefficient based on the drag coefficient perturbation and the nominal drag coefficient; and obtaining the actual lift coefficient based on the lift coefficient perturbation and the nominal lift coefficient.

[0010] Optionally, the improved physical information neural network includes a first network and a second network. The first network is used to identify the drag coefficient perturbation, and the second network is used to identify the lift coefficient perturbation. Both the first network and the second network are RBF-BP hybrid network architectures. In the RBF-BP hybrid network architecture, the RBF layer is a single hidden layer, and the node center position and width are determined by the k-means clustering algorithm. The fully connected layer consists of 3 hidden layers, and the hyperbolic tangent function is used as the activation function of the fully connected layer.

[0011] Optionally, the integral loss function of the first network is:

[0012]

[0013] in, D represents the drag acting on the aircraft, m represents the aircraft mass, μ represents the Earth's gravitational constant, r represents the distance between the aircraft's center of mass and the Earth's center (also known as the geocentric distance), x represents the projected component of the relative distance between the aircraft and the target on the ground target frame, σ represents the ballistic deflection angle, θ represents the ballistic inclination angle, y represents the projected component of the relative distance between the aircraft and the target on the ground target frame, and R... e Represents the Earth's radius, N represents the total number of samples, and v k,i Indicates at t k The velocity at time i, where Δt represents the time interval, v k+1,i Indicates t k+1 The velocity at time i.

[0014] Optionally, the integral loss function of the second network is:

[0015]

[0016] in,

[0017] L represents the lift force acting on the aircraft, γ v Here, is the aerodynamic roll angle, also known as the tilt angle; m represents the aircraft mass; μ represents the Earth's gravitational constant; r represents the distance between the aircraft's center of mass and the Earth's center, also known as the geocentric distance; v represents the aircraft's velocity; σ represents the ballistic deflection angle; θ represents the ballistic tilt angle; y represents the projected component of the relative distance between the aircraft and the target on the ground target frame; x represents the projected component of the relative distance between the aircraft and the target on the ground target frame; z represents the projected component of the relative distance between the aircraft and the target on the ground target frame; R e Let N represent the Earth's radius, N represent the total number of samples, and θ represent the Earth's radius. k,i Indicates at t k The trajectory inclination angle at time i, where Δt represents the time interval, and θ k+1,iIndicates t k+1 The trajectory inclination angle at time i, σ k,i Indicates at t k The trajectory deflection angle at time i, σ k+1,i Indicates t k+1 The i-th trajectory deflection angle at time i.

[0018] Optionally, the improved physical information neural network training process includes: simulating the scenario of the reentry glider entering the terminal guidance phase and striking the target based on the three-degree-of-freedom dynamic model of the reentry glider, embedding a pre-set relationship between aerodynamic parameter perturbations and flight state data in the simulation; sampling the flight state data of the aircraft and the corresponding aerodynamic parameter perturbations during the simulation to obtain a training set and its labels, and a test set and its labels; inputting the training set and its labels into the improved physical information neural network to be trained until the target conditions are met, thus obtaining the improved physical information neural network; and verifying the improved physical information neural network based on the test set and its labels.

[0019] Optionally, the simulation scenario may embed a pre-defined relationship between aerodynamic parameter perturbations and flight state data, including:

[0020]

[0021] in, This represents the lift coefficient perturbation. The value represents the drag coefficient perturbation, t represents time, Ma represents the Mach number, and α represents the angle of attack.

[0022] According to the second aspect, this embodiment provides an aerodynamic parameter identification device based on an improved physical information neural network, comprising: a state quantity acquisition module for acquiring target flight state quantities during aircraft flight; an aerodynamic parameter perturbation determination module for inputting the target flight state quantities into the improved physical information neural network to obtain aerodynamic parameter perturbation quantities, wherein the aerodynamic parameter perturbation quantities are quantified values ​​of the difference between nominal aerodynamic parameters and actual aerodynamic parameters during flight, and the loss function of the improved physical information neural network is an integral loss function, which establishes a connection between the dynamic model containing the estimated values ​​and the actual dynamic characteristics; and an aerodynamic parameter determination module for determining actual aerodynamic parameters based on the aerodynamic parameter perturbation quantities and the corresponding nominal aerodynamic parameters.

[0023] According to a third aspect, an embodiment of the present invention provides an electronic device, the device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor performs the steps of the aerodynamic parameter identification method based on an improved physical information neural network as described in the first aspect or any embodiment of the first aspect.

[0024] According to a fourth aspect, embodiments of the present invention provide a computer storage medium storing computer instructions that, when executed by a processor, implement the steps of the aerodynamic parameter identification method based on an improved physical information neural network as described in the first aspect or any embodiment of the first aspect.

[0025] This embodiment provides an improved aerodynamic parameter identification method for physical information neural networks. It only requires the network to learn the relationship between the aircraft's flight state and aerodynamic parameter perturbations, without requiring the network to learn the differential characteristics between aircraft states or to possess flight state prediction capabilities. This embodiment replaces the loss function in the original PINNs framework with an integral-based loss function, avoiding the adversarial relationship between different loss functions during training and thus preventing training difficulties. Furthermore, by using integration, a connection is established between the dynamic model containing the estimated values ​​and the actual dynamic characteristics, ensuring that the neural network can learn correct dynamic information during training, thereby improving the accuracy of aerodynamic parameters.

[0026] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0027] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0028] Figure 1 A flowchart illustrating a specific example of an aerodynamic parameter identification method based on an improved physical information neural network provided by this invention;

[0029] Figure 2 This is a detailed structural diagram of the RBF-BP network in this invention;

[0030] Figure 3 This is a schematic diagram illustrating the entire process of identifying aerodynamic parameter perturbations using the improved PINNs in this invention.

[0031] Figure 4 This is a graph showing the decrease in the loss function during the training process of the neural network model for estimating the lift coefficient perturbation and the neural network model for estimating the drag coefficient perturbation in this invention;

[0032] Figure 5 The results of aerodynamic parameter identification by the trained model in this invention in simulated ballistics, as well as the aerodynamic parameter curves without aerodynamic deviations;

[0033] Figure 6 This is a diagram showing the relative estimation error of aerodynamic parameters in this invention;

[0034] Figure 7 Box plots showing the lift coefficient identification error and drag coefficient identification error under four different conditions in this invention;

[0035] Figure 8 This is a comparison diagram between FCN in this invention and the proposed method;

[0036] Figure 9 This is a schematic block diagram of a specific example of an electronic device in an embodiment of the present invention. Detailed Implementation

[0037] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can also refer to the internal connection of two components; and they can refer to a wireless connection or a wired connection. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0039] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0040] Aerodynamic parameters: These are a series of physical parameters related to the movement of an object in a fluid (such as air). These parameters describe the fluid dynamics and the interaction between the object and the fluid.

[0041] Physics-Information Neural Networks (PHNs) are a deep learning framework that combines physical laws with data-driven approaches to solve forward and inverse problems involving nonlinear partial differential equations. By incorporating physical information terms (such as physical laws, typically differential equations) into the loss function, the neural network learns not only the data distribution but also the physical laws described by the mathematical equations.

[0042] This embodiment proposes an aerodynamic parameter identification method based on an improved Physical Information Neural Network (PINNs). The method utilizes the neural network to predict the perturbations of the actual aerodynamic parameters of an aircraft relative to its nominal aerodynamic parameters, thereby achieving the identification of the actual aerodynamic parameters. This method aims to address the performance degradation problem inherent in general PINNs when the aerodynamic perturbations of an aircraft are complex functions of its flight state. Specifically, this embodiment provides an aerodynamic parameter identification method based on an improved Physical Information Neural Network, such as... Figure 1 As shown, it includes:

[0043] S101, acquire the target flight state variables during the flight of the aircraft;

[0044] S102, the target flight state quantity is input into the improved physical information neural network to obtain the aerodynamic parameter perturbation quantity. The aerodynamic parameter perturbation quantity is the quantified value of the difference between the nominal aerodynamic parameters and the aerodynamic parameters in actual flight. The loss function of the improved physical information neural network is the integral loss function, which establishes a connection between the dynamic model containing the estimated value and the real dynamic characteristics.

[0045] S103, determine the actual aerodynamic parameters based on the aerodynamic parameter perturbation amount and the corresponding nominal aerodynamic parameters.

[0046] For example, the improved physical information neural network proposed in this embodiment only needs to learn the relationship between the flight state of the aircraft and the aerodynamic parameter perturbation, without requiring the network to learn the differential characteristics between the flight states, nor requiring the network to have the ability to predict flight states. Therefore, this embodiment replaces the loss function in the original PINNs framework with an integral-based loss function to avoid the adversarial relationship between different loss functions during the training process, which would make network training difficult.

[0047] In this embodiment, the aerodynamic parameter perturbations solved are drag coefficient perturbation and lift coefficient perturbation, and the corresponding target flight state quantities include: flight time, angle of attack command, and Mach number during the aircraft's flight. The outputs are determined to be drag coefficient perturbation and lift coefficient perturbation, and the derivation process of the specific data types of the input target flight state quantities is as follows:

[0048] Physical models are a crucial foundation for constructing physical information neural networks. This embodiment uses the three-degree-of-freedom dynamic equations of a reentry glider, established in a ground coordinate system, as the theoretical model for aerodynamic parameter identification. The equations of motion for this model are as follows:

[0049]

[0050] In the formula, v, θ, and σ represent the velocity, trajectory inclination angle, and trajectory deflection angle of the aircraft, respectively; D and L represent the drag and lift acting on the aircraft, respectively; x, y, and z represent the three projected components of the relative distance between the aircraft and the target in the ground target system, respectively; γ v ρ is the aerodynamic roll angle, also known as the tilt angle; m is the mass of the aircraft; μ represents the Earth's gravitational constant, with μ = 3.985005 × 10⁻⁶. 14 ;R e Let R be the Earth's radius. e =6371000m. r represents the distance between the center of mass of the spacecraft and the center of the Earth, also known as the geocentric distance, and its expression is given by (2).

[0051]

[0052] The lift and drag acting on the aircraft can be calculated using (3).

[0053]

[0054] In the formula, q is the incoming flow pressure, which can be expressed as q = ρv 2 / 2 is calculated; ρ is the atmospheric density at the altitude of the aircraft; S is the characteristic area of ​​the aircraft; aerodynamic coefficient C L With C D The dimensionless drag coefficient and lift coefficient of the designed aircraft are respectively presented. In this embodiment, the aerodynamic coefficient data of CAV-H are used and fitted as a function related to the angle of attack and Mach number. The fitting formula is given by (4).

[0055]

[0056] In the formula, α is the angle of attack; Ma is the Mach number; and Zero drag coefficient and zero lift coefficient; The lift coefficient related to the angle of attack; and The lift coefficient is related to the Mach number; This is the induced drag coefficient; and The drag coefficient is related to the Mach number. According to the dynamic equation (1) and the definition of lift-drag coefficient (4), the control inputs of the three-degree-of-freedom aircraft dynamic equation are the angle of attack α and the roll angle γ. v The values ​​of each coefficient in (4) are shown in Table 1.

[0057] Table 1

[0058]

[0059] Generally, the aerodynamic parameters involved in flight are obtained from nominal expressions or interpolation tables obtained through offline acquisition and calculation, similar to equation (4). However, due to differences in environmental conditions and measurement errors during wind tunnel testing, the actual aerodynamic parameters of the aircraft are perturbed compared to those obtained from wind tunnel testing, causing the performance and effectiveness of flight control to deviate from the design specifications. The lift perturbation coefficient is defined. Drag perturbation coefficient The relationship between the actual aerodynamic coefficient and the nominal aerodynamic coefficient can be defined by (5).

[0060]

[0061] In the formula, C Lr and C Dr These represent the actual lift coefficient and drag coefficient of the aircraft during flight, respectively.

[0062] (1) and (5) indicate that flight state information such as v, θ, and σ implicitly contains information such as and The aerodynamic parameter uncertainty information shown can also be used to... and Once estimated, the actual aerodynamic coefficients during flight can be determined. Generally speaking, and During flight, it is a function of time, angle of attack, and Mach number, and can be defined by (6).

[0063]

[0064] Therefore, the drag coefficient perturbation and lift coefficient perturbation are related to flight time, angle of attack, and Mach number. Thus, the improved physical information neural network can learn the mapping relationship between flight time, angle of attack, Mach number, and the drag coefficient perturbation and lift coefficient perturbation. When the improved physical information neural network receives flight time, angle of attack, and Mach number, it can output the drag coefficient perturbation and lift coefficient perturbation based on the pre-learned mapping relationship. Then, as shown in formula (5), the actual drag coefficient is obtained based on the drag coefficient perturbation and the nominal drag coefficient; the actual lift coefficient is obtained based on the lift coefficient perturbation and the nominal lift coefficient.

[0065] In this embodiment, an integral loss function is used instead of the original loss function to construct an improved physical information neural network, specifically:

[0066] Physical Information Neural Networks (PINNs) combine neural networks with prior physical information, enabling the neural network to learn physical laws through a loss function that incorporates physical constraints. The core of PINNs consists of two parts: a deep neural network (DNN) structure and a physics-driven loss function. The powerful nonlinear fitting ability of DNNs is fundamental to PINNs' learning of physical information. The mapping relationship between the neural network input and output obtained using DNNs can be represented as N(·):

[0067]

[0068] In the formula, x in Indicates the input to the neural network; Let y represent the output of the neural network, then y represents the true value corresponding to the output of the neural network; w and b represent the weights and biases of the neural network, respectively.

[0069] The loss function of PINNs consists of a data-based loss function and a physical information-based loss function. The data-based loss function is defined as the mean squared error (MSE) loss function between the neural network output and the real training data.

[0070]

[0071] In the formula, ||·||2 represents the 2-norm of the vector.

[0072] Unlike (8), the loss function based on physical information is based on the constraints of physical equations and is also called the differential-based loss function in the general PINNs framework. Taking (1) as an example, the general form of the three-degree-of-freedom motion equations of an aircraft with unknown aerodynamic perturbation coefficients is defined as follows:

[0073]

[0074] In the formula, x represents the aircraft state; t represents time; and Θ represents the unknown parameter in the differential equation, such as the aerodynamic perturbation coefficient to be identified in this embodiment. and Similar to (8), a differential-based loss function can be defined according to (9):

[0075]

[0076] In the formula, f(·) represents the derivative value of the differential equation; This represents the partial derivative of the neural network output with respect to time t. (7) and (8) together constitute the loss function under the PINNs framework:

[0077] L total =ω L L Data +(1-ω L)L ODE (11)

[0078] In the formula, ω L The weights of the two loss functions in the total loss function are defined. Because L ODE The introduction of The resulting losses are also incorporated into the training process of the neural network. As the neural network is trained, It will approach the true Θ, thus completing the identification of unknown aerodynamic perturbation coefficients.

[0079] The PINNs based on (11) have proven their effectiveness in solving the forward problem of differential equations, but for solving the inverse problem of differential equations, i.e. parameter estimation, (11) still has some problems.

[0080] First, by observing the composition of (10), it can be found that its differential terms This does not represent the true dynamic characteristics of the system, because the neural network's estimate of the unknown parameter Θ... It is not entirely accurate, that is:

[0081]

[0082] In the formula, err ODE This indicates that the neural network estimate is included. The difference between the system dynamics characteristics and the actual system dynamics characteristics. Therefore, (10) is essentially forcing the neural network to learn an inaccurate system dynamic process. Even if the parameter Θ is incorrectly estimated, the total loss function is still small, and the neural network will enter the global optimum of the incorrect parameter.

[0083] Secondly, for parameter estimation problems such as solving unknown aerodynamic parameter deviations, aerodynamic parameters and their deviations are usually not directly measurable. Therefore, this embodiment does not use aerodynamic parameter data as the true values ​​for model training. Instead, it uses measurable physical quantities, such as velocity and angle, and the deviations between these physical quantities and the predicted values ​​of the physical equations as training errors to indirectly train the model to approximate the true unknown parameters. The lack of true values ​​limits the network's ability to evaluate the accuracy of prediction results, making it difficult for the network to learn effective patterns and information from the data, thus increasing the training difficulty of the physical information neural network.

[0084] To address the aforementioned issues and ensure that the neural network learns accurate system dynamics, this embodiment introduces an integral-based loss function, defined as follows:

[0085]

[0086] In the formula, and t k With t k+1 The i-th flight state quantity at time i. Equation (13) integrates the estimated value. The dynamic model is linked to the actual dynamic characteristics to ensure that the neural network can learn the correct dynamic information during training. Equation (13) can be solved using numerical integration. For simplicity, this embodiment uses the first-order Euler method to solve (13), so (13) can be rewritten as:

[0087]

[0088] Although solving integral equations using numerical integration methods introduces truncation errors, these errors also affect... The estimation accuracy is high, but the general numerical integration method usually has high accuracy for solving ordinary differential equations similar to equation (1), and the estimation error caused by the truncation error can generally be ignored.

[0089] This embodiment provides an improved aerodynamic parameter identification method for physical information neural networks. It only requires the network to learn the relationship between the aircraft's flight state and aerodynamic parameter perturbations, without requiring the network to learn the differential characteristics between aircraft states or to possess flight state prediction capabilities. This embodiment replaces the loss function in the original PINNs framework with an integral-based loss function, avoiding the adversarial relationship between different loss functions during training and thus preventing training difficulties. Furthermore, by using integration, a connection is established between the dynamic model containing the estimated values ​​and the actual dynamic characteristics, ensuring that the neural network can learn correct dynamic information during training, thereby improving the accuracy of aerodynamic parameters.

[0090] Furthermore, most PINNs frameworks employ fully connected neural network structures. Although existing technologies have demonstrated that Physical Information Neural Networks (PINNs) based on fully connected neural network structures can fit arbitrary nonlinear functions, in actual training, the training difficulty and complexity of PINNs based on fully connected network structures increase rapidly with the increasing complexity of nonlinear functions. Moreover, this network structure exhibits fitting difficulties when dealing with aerodynamic parameter identification problems involving unknown parameters without true values. To address these issues, this embodiment modifies the original PINNs structure to ensure that the neural network maintains good fitting accuracy even when aerodynamic deviations are complex nonlinear functions of flight state.

[0091] Specifically, in this embodiment, the physical information neural network adopts an RBF-BP hybrid network architecture. In the RBF-BP hybrid network architecture, the RBF layer is a single hidden layer, and the node center position and width are determined by the k-means clustering algorithm. The fully connected layer consists of 3 hidden layers, and the hyperbolic tangent function is used as the activation function of the fully connected layer.

[0092] When aerodynamic parameter deviations are complex functions of flight state variables, or when the functional relationship is not obvious, the training difficulty of PINNs with fully connected neural network structures increases significantly. To address this issue, this embodiment designs an RBF-BP hybrid network architecture, which, compared to fully connected neural networks, can significantly reduce network structure complexity and training difficulty while ensuring prediction accuracy.

[0093] The RBF network is a single-hidden-layer neural network that approximates the objective function through a linear weighted sum of multivariate basis functions. It maps the low-dimensional sample input to a high-dimensional space using radial basis functions, and then finds a hyperplane passing through all sample points in the high-dimensional space to achieve optimal approximation of the objective function. The output of the RBF network can be defined by (15):

[0094]

[0095] Where N is the number of hidden layer neurons in the RBF network; y is the network output vector; x is the network input vector; ω i The connection weights from the i-th neuron to the output node can be determined using the least squares method or updated during training; g i (x) is the response function of the i-th neuron to the input vector x, which is generally defined by the Gaussian radial basis function:

[0096]

[0097] In the formula, μ i and σ i Let μ represent the center point position and width of the i-th neuron, respectively. Generally, when initializing an RBF network, μ... i and σ i It can be initialized by the k-means clustering algorithm and then updated during training, which will achieve better performance than the random initialization method.

[0098] Equation (16) indicates that the response magnitude of each neuron in the RBF network to the input vector x is related to the distance between x and the neuron's center point. By weighting the response functions of different neurons, the RBF network can effectively approximate nonlinear functions. Furthermore, the RBF network utilizes the characteristic that the output response of radial basis functions depends only on the distance between the input vector and the center point. When the distance between the input vector and the neuron's center point is sufficiently far, the neuron's output approaches zero. Only neurons near the input vector have a significant impact on the output. This gives the RBF network a local approximation characteristic, enabling it to effectively extract features from datasets with strong nonlinearity and non-uniform distribution. Moreover, since the parameters and weights in the network are only locally effective, the RBF network has very high training efficiency.

[0099] As described above, the RBF network fits the objective function by determining a hyperplane in a high-dimensional space. The shape of the hyperplane is closely related to the connection weight vector ω. However, when the objective function is highly nonlinear and the dataset features are not clearly uniform, a single-layer network struggles to find an optimal set of weight vectors ω that ensures the determined hyperplane accurately passes through all sample points in the high-dimensional space. This leads to the limitations of the RBF network in approximating complex nonlinear functions. To address this, this embodiment designs an RBF-BP network structure. The output of the RBF hidden layer is connected to a fully connected network structure. During network training, the parameters of the fully connected network are updated simultaneously, utilizing the nonlinear fitting capability of the fully connected network to help optimize the hyperplane shape. Figure 2 A detailed structural diagram of the RBF-BP network is shown.

[0100] Since the aerodynamic parameter perturbation in this embodiment includes the lift coefficient perturbation and the drag coefficient perturbation, the improved physical information neural network in this embodiment includes a first network and a second network. The first network is used to identify the drag coefficient perturbation, and the second network is used to identify the lift coefficient perturbation. Both the first network and the second network are RBF-BP hybrid network architectures.

[0101] For example, by combining the three-degree-of-freedom dynamic equations of the aircraft (1) with the integral-based loss function (14), unlike general PINNs networks, this embodiment does not require the neural network to learn the differential dynamic characteristics of the system, but only requires the neural network to handle the aerodynamic parameter perturbations implicit in the dynamic equations through physical constraints. and Identification is performed. Therefore, in this embodiment, the flight state quantity related to the aerodynamic parameter deviation function is selected as the input of the neural network, and the state quantity is required to have actual measurability, as specifically defined in (17).

[0102] x in =[t,Ma,α] * ]T (17)

[0103] In the formula, α * The angle of attack command is selected because the angle of attack α cannot be directly measured. * Replace it.

[0104] When the neural network output is the target to be identified, due to aerodynamic parameter perturbations... and This will affect different variables in (1), and therefore the corresponding physical constraint loss functions will also be different. From the equations in (1), we can obtain the drag coefficient perturbation. By influencing drag D, the velocity v of the aircraft is affected, while the lift coefficient perturbation... The lift L affects the trajectory inclination angle θ and trajectory deflection angle σ of the aircraft. To avoid excessive complexity of a single network leading to poor identification of the perturbations of the two aerodynamic parameters, this embodiment uses two networks to identify the perturbations of the drag coefficient and the lift coefficient respectively. The specific neural network input-output relationship is shown in Table 2:

[0105] Table 2

[0106]

[0107] The auxiliary variables in Table 3 are used to close the dynamic equations of the aircraft, thereby calculating the loss function. The first three equations in (1) are defined as follows:

[0108]

[0109] Define the integral-based loss function for the three different variables respectively by (18):

[0110]

[0111] Based on the input-output relationship in Table 3, the loss functions of the two neural networks can be defined as follows:

[0112] L1 = L v (20)

[0113]

[0114] In summary, the entire process of identifying aerodynamic parameter perturbations using improved PINNs is as follows: Figure 3 As shown.

[0115] Scale differences between state variables can lead to network performance degradation. Therefore, this embodiment uses geophysical parameters to dimensionless the input variables. The dimensionless formula is as follows:

[0116]

[0117] In the formula, s is the original variable; Let x represent the dimensionless variable; k is the dimensionless coefficient. Input vector x in The dimensionless variables and dimensionless coefficients that need to be represented are shown in Table 3. The angle of attack command α... * The unit of measurement is radians.

[0118] Table 3

[0119]

[0120] All neural network training code in this embodiment is implemented using PyTorch. The RBF layer in the network structure is a single hidden layer with 1600 neurons. The center position and width of the neurons are determined by the k-means clustering algorithm. The fully connected layer consists of three hidden layers, each containing 96 neurons. The hyperbolic tangent function is used as the activation function for the fully connected layer, which is also a commonly used activation function in PINNs. To evaluate the performance of the proposed method, a fully connected neural network with 14 hidden layers, each containing 512 neurons, and with network input / output, loss function definition, and training method consistent with the proposed method, was constructed as the baseline model for this embodiment. This type of neural network is also widely used in parameter identification methods based on PINNs.

[0121] As an optional implementation, the improved physical information neural network training process includes: simulating a scenario where the reentry glider enters the terminal guidance phase and strikes a target based on a three-degree-of-freedom dynamic model of the reentry glider; embedding a pre-set relationship between aerodynamic parameter perturbations and flight state data in the simulation scenario; sampling the flight state data of the aircraft and the corresponding aerodynamic parameter perturbations during the simulation to obtain a training set and its labels, and a test set and its labels; inputting the training set and its labels into the improved physical information neural network to be trained until the target conditions are met, thus obtaining the improved physical information neural network; and verifying the improved physical information neural network based on the test set and its labels.

[0122] In this embodiment, the time-series dataset used for neural network training and validation is obtained from numerical simulation based on (1). To ensure the feasibility of the proposed method, this embodiment only uses aircraft state information that can be measured by the integrated navigation system. Considering that the actual angle of attack α during aircraft flight is difficult to measure directly, this embodiment uses the angle of attack command α. *The actual angle of attack is used instead of the actual angle of attack in the identification algorithm. The simulated scenario is that the reentry glider enters the terminal guidance phase to strike the target. The initial position coordinates of the glider and the target are (0,2000,0) and (42000,0,20000) respectively, and the values ​​of other initial parameters are shown in Table 4. In the simulation, and We selected time, angle of attack, and Mach number as functions to verify the neural network's ability to approximate complex nonlinear functions.

[0123]

[0124] in, This represents the lift coefficient perturbation. The value represents the drag coefficient perturbation, t represents time, Ma represents the Mach number, and α represents the angle of attack.

[0125] Table 4

[0126] Parameters Value Initial velocity (m / s) [2150,2200,2250,2300,2350] Initialflightpathangle(deg) [-34,-32,-30,-28,-26] Initialflightazimuthangle(deg) [-34,-32,-30,-28,-26]

[0127] The neural network optimizer uses the Adam optimizer. The training set accounts for 80% of the total data, and the test set accounts for 20% of the total data. The total number of training rounds is 20,000, and an early stopping strategy is adopted. The batch size of each training round is 128. A variable learning rate strategy is adopted, with an initial learning rate of 1e-4 and a learning rate of 1e-5 after 10,000 training rounds.

[0128] The following are the verification results of the method proposed in the above embodiments.

[0129] A trajectory with initial parameters not found in the neural network sample library is selected as a simulation example for neural network aerodynamic parameter deviation prediction. The initial parameters of the simulated trajectory used to verify the identification effect are as follows: the initial point parameters of the reentry glider entering the terminal guidance phase are: initial velocity 2225 m / s, initial trajectory inclination angle -30 degrees, initial trajectory deflection angle -27 degrees, initial vehicle position coordinates (0, 2000, 0), and target coordinates (42000, 0, 20000). The output of the neural network is the aerodynamic parameter perturbation. and The predicted lift coefficient and drag coefficient can be calculated based on (5).

[0130] Figure 4The paper demonstrates the decrease in loss function during the training of two neural networks ((a) a neural network model for estimating lift coefficient perturbation, and (b) a neural network model for estimating drag coefficient perturbation). The validation set loss function is used to assess whether the model is overfitting. Although there are slight fluctuations during the training, both models reach their peak performance around 17,000 epochs. The sudden drop at 10,000 epochs is due to a step change in the learning rate. The aerodynamic parameter identification results of the trained models in simulated ballistics and the aerodynamic parameter curves without aerodynamic deviations are shown below. Figure 5 As shown, (a) represents the lift coefficient, and (b) represents the drag coefficient. This demonstrates that a trained neural network can accurately identify aerodynamic parameters during flight. To more intuitively illustrate the model's identification accuracy, Figure 6 The relative estimation error of aerodynamic parameters is shown; the closer the error point is to the origin, the higher the prediction accuracy.

[0131] Table 5 provides more comprehensive statistical results, with the statistical indicators being mean squared error (MSE), root mean squared error (RMSE), and coefficient of determination (R²).

[0132] Table 5

[0133]

[0134] This embodiment treats the measurement noise as Gaussian white noise with a mean of 0 and a constant variance, and incorporates a data measurement process into the simulation. Specifically, the white noise parameters shown in Table 6 are used in the simulation. This embodiment will verify the insensitivity of the proposed method to measurement noise and data bias through the following cases:

[0135] Case 1: The identification results in the above identification effect verification are used as the benchmark for the effect verification of other cases.

[0136] Case 2: After adding measurement noise, the same training and test set creation method as in this embodiment is used to retrain the proposed network with the noisy dataset. The simulated ballistic parameters used for identification effect verification are the same as those used in the above identification effect verification. Measurement noise is also added during the simulation process to verify the learning ability of the proposed method on noisy data features.

[0137] Case 3: The neural network trained during the above identification effect verification is used to identify aerodynamic parameters of the simulated ballistic data containing noise. The initial ballistic parameters are the same as those during the above identification effect verification, in order to verify the insensitivity of the proposed method to noise data.

[0138] Case 4: Based on the noisy simulated ballistic data, a velocity bias term of 5 m / s is added to the flight velocity data to simulate the constant deviation that often exists in sensor measurements. This step aims to verify the insensitivity of the proposed method to data bias.

[0139] Figure 7 Figures (a) and (b) show box plots of the lift coefficient identification error and drag coefficient identification error for four different scenarios, respectively. (a) represents the lift coefficient estimation error, and (b) represents the drag coefficient estimation error. Table 7 provides the specific values ​​of the statistical indicators. As can be seen from the figures, the error distributions for scenarios 1 and 2 are similar, both within 5%. Furthermore, for drag coefficient identification, scenario 2 has a smaller overall identification error and a more concentrated distribution, indicating that the network has the ability to extract features from noisy data. The identification results for scenario 3 are also similar to those for scenario 1. Although the error distribution is more dispersed compared to scenarios 1 and 2, the maximum relative prediction error is still within 10%, indicating that the proposed method is insensitive to noisy data. In Case 4, despite the accuracy of the measurement results, the proposed method exhibits a certain degree of degradation in its ability to identify aerodynamic parameters when faced with noisy data containing numerical bias. This may be because, despite the presence of measurement noise, the noise itself does not alter the flight state, such as the physical relationships between physical quantities like speed and angle of attack commands. By utilizing a loss function based on physical information, the network can still extract the physical constraints between these physical quantities. This also explains why the network is somewhat insensitive to noisy data in Case 3, while the data bias term somewhat obscures these physical connections, leading to a decrease in network performance.

[0140] Table 6

[0141]

[0142] Table 7

[0143]

[0144] This section uses a fully connected neural network as the benchmark model and compares it with the method proposed in this embodiment. Except for the network structure, both methods use the same hyperparameters, training methods, training set data and loss function.

[0145] Figure 8 Table 8 describes the aerodynamic parameter identification results of FCN and the proposed method. Figure 8The figure shows a comparison between FCN and the proposed method: (a) lift coefficient, (b) drag coefficient. Although the vast majority of errors are within 10%, FCN with 14 hidden layers still performs poorly in predicting aerodynamic parameters. Simple fully connected networks struggle to fit complex functions without real-value information, while the RBF-BP network proposed in this embodiment achieves accurate estimation of aerodynamic parameters.

[0146] Table 8

[0147]

[0148] This application also provides an electronic device, such as... Figure 9 As shown, processor 501 and memory 502 are connected via a bus or other means.

[0149] Processor 501 can be a central processing unit (CPU). Processor 501 can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or combinations of the above types of chips.

[0150] The memory 502, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the aerodynamic parameter identification method based on the improved physical information neural network in this embodiment of the invention. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions, and modules stored in the memory.

[0151] Memory 502 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory 502 may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0152] The one or more modules are stored in the memory 502, and when executed by the processor 501, they perform actions such as... Figure 1 The aerodynamic parameter identification method based on an improved physical information neural network in the illustrated embodiment.

[0153] For specific details regarding the aforementioned electronic devices, please refer to the relevant documentation. Figure 1 The relevant descriptions and effects in the illustrated embodiments are for understanding purposes only and will not be repeated here.

[0154] This embodiment also provides a computer storage medium storing computer-executable instructions that can execute the aerodynamic parameter identification method based on an improved physical information neural network in any of the above method embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium may also include combinations of the above types of memory.

[0155] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A method for identifying aerodynamic parameters based on an improved physical information neural network, characterized in that, include: Acquire the target flight state variables during the flight process of the aircraft; The target flight state variables are input into the improved physical information neural network to obtain aerodynamic parameter perturbation variables. The aerodynamic parameter perturbation variables are the quantified values ​​of the difference between the nominal aerodynamic parameters and the aerodynamic parameters in actual flight. The loss function of the improved physical information neural network is an integral loss function, which establishes a connection between the dynamic model containing the estimated values ​​and the actual dynamic characteristics. Determine the actual aerodynamic parameters based on the aerodynamic parameter perturbation and the corresponding nominal aerodynamic parameters; The improved physical information neural network includes a first network and a second network. The first network is used to identify the drag coefficient perturbation, and the second network is used to identify the lift coefficient perturbation. Both the first network and the second network are RBF-BP hybrid network architectures. The integral loss function of the first network is: ； in, , This represents the drag acting on the aircraft. Indicates the mass of the aircraft. Represents the Earth's gravitational constant. The distance between the center of mass of the aircraft and the center of the Earth is called the geocentric distance, and x represents the projected component of the x-coordinate of the relative distance between the aircraft and the target in the ground target frame. Indicates the trajectory deflection angle. The inclination angle represents the trajectory angle, and y represents the projected component of the y-coordinate of the relative distance between the aircraft and the target in the ground target system. Let N represent the Earth's radius and the total number of samples. Indicates in The velocity at time i, Indicates time interval, express The first moment One speed; The integral loss function of the second network is: ； in, , , This represents the lift force acting on the aircraft. This is the aerodynamic roll angle, also known as the tilt angle. Indicates the mass of the aircraft. Represents the Earth's gravitational constant. It represents the distance between the center of mass of the spacecraft and the center of the Earth, also known as the geocentric distance. Indicates the speed of the aircraft. Indicates the trajectory deflection angle. The plane represents the trajectory inclination angle; y represents the projected component of the relative distance between the aircraft and the target in the y-coordinate of the ground target frame; x represents the projected component of the relative distance between the aircraft and the target in the x-coordinate of the ground target frame; and z represents the projected component of the relative distance between the aircraft and the target in the z-coordinate of the ground target frame. Let N represent the Earth's radius and the total number of samples. Indicates in The trajectory inclination angle at time i, Indicates time interval, express The first moment A ballistic tilt angle Indicates in The trajectory deflection angle at time i, express The first moment One ballistic deviation angle.

2. The aerodynamic parameter identification method based on an improved physical information neural network according to claim 1, characterized in that, When the target flight state quantities include: flight time, angle of attack command, and Mach number during the aircraft's flight process, the target flight state quantities are input into the improved physical information neural network to obtain aerodynamic parameter perturbations, including: By inputting flight time, angle of attack command, and Mach number into an improved physical information neural network, the drag coefficient perturbation and lift coefficient perturbation are obtained. Based on the aerodynamic parameter perturbation and the corresponding nominal aerodynamic parameters, determine the actual aerodynamic parameters, including: The actual drag coefficient is obtained from the drag coefficient perturbation and the nominal drag coefficient. The actual lift coefficient is obtained from the lift coefficient perturbation and the nominal lift coefficient.

3. The aerodynamic parameter identification method based on an improved physical information neural network according to claim 2, characterized in that, In the RBF-BP hybrid network architecture, the RBF layer is a single hidden layer, and the node center position and width are determined by the k-means clustering algorithm. The fully connected layer consists of 3 hidden layers, and the hyperbolic tangent function is used as the activation function of the fully connected layer.

4. The aerodynamic parameter identification method based on an improved physical information neural network according to claim 1, characterized in that, The improved training process for physical information neural networks includes: Based on the three-degree-of-freedom dynamic model of the reentry glider, a simulation of the scenario in which the reentry glider enters the terminal guidance phase to strike the target is carried out. The simulation incorporates the pre-set relationship between the aerodynamic parameter perturbation and the flight state data. During the sampling simulation process, the flight state data of the aircraft and the corresponding aerodynamic parameter perturbations are used to obtain the training set and its labels, and the test set and its labels. The training set and its labels are input into the improved physical information neural network to be trained until the target conditions are met, thus obtaining the improved physical information neural network. The improved physical information neural network is validated based on the test set and its labels.

5. The aerodynamic parameter identification method based on an improved physical information neural network according to claim 4, characterized in that, The simulation scenario embeds pre-defined relationships between aerodynamic parameter perturbations and flight state data, including: ； in, This represents the lift coefficient perturbation. The variable represents the drag coefficient perturbation, t represents time, and Ma represents the Mach number. Indicates the angle of attack during flight.

6. A device for identifying aerodynamic parameters based on an improved physical information neural network, characterized in that, include: The state quantity acquisition module is used to acquire the target flight state quantities during the flight process of the aircraft; The aerodynamic parameter perturbation determination module is used to input the target flight state quantity into the improved physical information neural network to obtain the aerodynamic parameter perturbation quantity. The aerodynamic parameter perturbation quantity is the quantified value of the difference between the nominal aerodynamic parameters and the aerodynamic parameters in actual flight. The loss function of the improved physical information neural network is an integral loss function, which establishes a connection between the dynamic model containing the estimated value and the real dynamic characteristics. The aerodynamic parameter determination module is used to determine the actual aerodynamic parameters based on the aerodynamic parameter perturbation and the corresponding nominal aerodynamic parameters. The improved physical information neural network includes a first network and a second network. The first network is used to identify the drag coefficient perturbation, and the second network is used to identify the lift coefficient perturbation. Both the first network and the second network are RBF-BP hybrid network architectures. The integral loss function of the first network is: ； in, , This represents the drag acting on the aircraft. Indicates the mass of the aircraft. Represents the Earth's gravitational constant. The distance between the center of mass of the aircraft and the center of the Earth is called the geocentric distance, and x represents the projected component of the x-coordinate of the relative distance between the aircraft and the target in the ground target frame. Indicates the trajectory deflection angle. The inclination angle represents the trajectory angle, and y represents the projected component of the y-coordinate of the relative distance between the aircraft and the target in the ground target system. Let N represent the Earth's radius and the total number of samples. Indicates in The velocity at time i, Indicates time interval, express The first moment One speed; The integral loss function of the second network is: ； in, , , This represents the lift force acting on the aircraft. This is the aerodynamic roll angle, also known as the tilt angle. Indicates the mass of the aircraft. Represents the Earth's gravitational constant. It represents the distance between the center of mass of the spacecraft and the center of the Earth, also known as the geocentric distance. Indicates the speed of the aircraft. Indicates the trajectory deflection angle. The plane represents the trajectory inclination angle; y represents the projected component of the relative distance between the aircraft and the target in the y-coordinate of the ground target frame; x represents the projected component of the relative distance between the aircraft and the target in the x-coordinate of the ground target frame; and z represents the projected component of the relative distance between the aircraft and the target in the z-coordinate of the ground target frame. Let N represent the Earth's radius and the total number of samples. Indicates in The trajectory inclination angle at time i, Indicates time interval, express The first moment A ballistic tilt angle Indicates in The trajectory deflection angle at time i, express The first moment One ballistic deviation angle.

7. An electronic device, the device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor performs the steps of the aerodynamic parameter identification method based on an improved physical information neural network as described in any one of claims 1-5.

8. A computer storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the steps of the aerodynamic parameter identification method based on the improved physical information neural network as described in any one of claims 1-5.

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