Aerodynamic parameter identification method based on improved physical information neural network

Abstract

The invention provides an aerodynamic parameter identification method based on an improved physical information neural network. The aerodynamic parameter identification method comprises the steps of obtaining a target flight state quantity in a flight process of an aircraft; the target flight state quantity is input into the improved physical information neural network, aerodynamic parameter perturbation is obtained, the aerodynamic parameter perturbation is a difference quantized value between a nominal aerodynamic parameter and an aerodynamic parameter in actual flight, and a loss function of the improved physical information neural network is an integral loss function; the integral loss function establishes a relation between a dynamic model containing an estimated value and real dynamic characteristics; and according to the aerodynamic parameter perturbation amount and the corresponding nominal aerodynamic parameter, determining an actual aerodynamic parameter. According to the method, the dynamic model containing the estimated value is associated with the real dynamic characteristics in an integral manner, so that the neural network can learn correct dynamic information in the training process, the accuracy of aerodynamic parameters is improved, and the training difficulty is reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft parameter identification, and in particular relates to an aerodynamic parameter identification method based on an improved physical information neural network. Background Art

[0002] Some guidance laws require the aerodynamic parameter information of the aircraft when calculating the guidance instructions. The real and accurate aerodynamic parameter information plays a vital role in the performance of its guidance system. Since the actual aerodynamic parameters cannot be directly measured during flight, the nominal aerodynamic parameters obtained by wind tunnel tests or computational fluid dynamics are usually used to replace the real aerodynamic parameters when calculating the guidance instructions. However, the actual aerodynamic parameters will have certain perturbations relative to the nominal aerodynamic parameters. This perturbation will lead to a decrease in guidance accuracy and, in some cases, will affect the performance and stability of the aircraft. In order to overcome this challenge, it is necessary to develop an effective aerodynamic parameter identification method to optimize the performance of the aircraft and improve the performance of the guidance system.

[0003] In the past, classical methods such as the least squares method (LS) and the maximum likelihood estimation method have been widely used in the field of aircraft parameter identification. In addition, Kalman filtering and its improved forms have also been deeply studied in the field of aircraft parameter identification. In the prior art, different forms of Kalman filtering technology are used to identify the time-varying aerodynamic parameters of aircraft. In most cases, the above methods can provide good parameter identification means for aircraft, but when these methods face aircraft systems with strong nonlinear dynamics and complex flight environments, there may be problems of increased computational complexity and decreased identification performance.

[0004] In recent years, with the continuous development of deep learning technology, intelligent learning methods represented by neural networks are considered to be a very 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 uses neural networks to establish a nonlinear mapping relationship between the aircraft state quantities aerodynamic force and aerodynamic torque, and then obtains the aerodynamic parameters of the aircraft through calculations such as aerodynamic formulas, partial differential methods, or further neural network mapping. Another method hopes to directly establish a direct mapping relationship between the aircraft state and aerodynamic parameters that are closely related to the aerodynamic parameters, and then use the finite difference method to further calculate the aerodynamic derivatives to obtain more comprehensive aerodynamic parameter information. The idea of ​​using neural network prediction values ​​to calculate aerodynamic derivatives based on the finite difference method has further promoted the development of neural partial differential methods. Using direct differentiation of neural networks instead of finite difference methods can more conveniently calculate aerodynamic derivatives.

[0005] Although neural network technology has been widely studied in the field of aerodynamic parameter identification, the aerodynamic parameters of aircraft cannot be directly measured in actual situations, and the problem of missing true values ​​will be faced when training neural networks, which greatly limits the practical application of neural network methods. From this perspective, the physical connection between measurable flight state quantities and aerodynamic parameters should be fully utilized to train neural networks so that they can identify aircraft aerodynamic parameters. Physical information neural networks (PINNs) are a deep learning framework embedded with physical knowledge developed by Raissi et al., which forces the network to learn the intrinsic connection between physical quantities by adding loss function terms related to physical differential equations. Therefore, PINNs can solve unknown parameters in differential equations without knowing the true value, and thus have been studied in the field of aerodynamic parameter identification. However, since the loss function is related to the unknown parameters when PINNs solves the unknown parameters in differential equations, this leads to the problem of PINNs learning physical laws incorrectly. Summary of the invention

[0006] In view of this, the object of the present invention is to provide a method and device for aerodynamic parameter identification based on an improved physical information neural network to meet the demand for obtaining accurate aerodynamic parameters.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] According to a first aspect, the present invention provides an aerodynamic parameter identification method based on an improved physical information neural network, comprising: obtaining a target flight state quantity during the flight 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 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 being an integral loss function, which establishes a connection between a dynamic model containing estimated values ​​and actual dynamic characteristics; determining the actual aerodynamic parameters based on the aerodynamic parameter perturbation quantity and the corresponding nominal aerodynamic parameters.

[0009] Optionally, when the target flight state quantity includes: the flight time, angle of attack command and Mach number during the flight of the aircraft, the target flight state quantity is 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; determining 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; 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 perturbation of the drag coefficient, and the second network is used to identify the perturbation of the lift coefficient, and the first network and the second network are both RBF-BP hybrid network architectures; in the RBF-BP hybrid network architecture, the RBF layer is a single hidden layer, the node center position and width are determined by the k-means clustering algorithm, the fully connected layer is composed 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 mass of the aircraft, μ represents the gravitational constant of the earth, r represents the distance between the center of mass of the aircraft and the center of the earth, also known as the distance from the center of the earth, x represents the projection component of the x-coordinate of the relative distance between the aircraft and the target on the ground target system, σ represents the ballistic deviation angle, θ represents the ballistic inclination angle, y represents the projection component of the y-coordinate of the relative distance between the aircraft and the target on the ground target system, and R e represents the radius of the earth, N represents the total number of samples, v k,i Indicates that at t k The i-th speed at time, Δt represents the time interval, v k+1,i Indicates t k+1 The i-th speed at time.

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

[0015]

[0016] in,

[0017] L represents the lift acting on the aircraft, γ v is the aerodynamic roll angle, also known as the roll angle, m represents the mass of the aircraft, μ represents the gravitational constant of the earth, r represents the distance between the center of mass of the aircraft and the center of the earth, also known as the distance from the center of the earth, v represents the speed of the aircraft, σ represents the ballistic deviation angle, θ represents the ballistic inclination angle, y represents the projection component of the y coordinate of the relative distance between the aircraft and the target on the ground target system, x represents the projection component of the x coordinate of the relative distance between the aircraft and the target on the ground target system, z represents the projection component of the z coordinate of the relative distance between the aircraft and the target on the ground target system, R e represents the radius of the earth, N represents the total number of samples, θ k,i Indicates that at t k The i-th ballistic inclination at time, Δt represents the time interval, θ k+1,iIndicates t k+1 The i-th ballistic inclination angle at time, σ k,i Indicates that at t k The i-th ballistic deflection angle at time, σ k+1,i Indicates t k+1 The i-th ballistic deviation angle at time.

[0018] Optionally, the improved physical information neural network training process includes: simulating a scenario in which the re-entry glide vehicle enters the terminal guidance phase and strikes a target based on a three-degree-of-freedom dynamics model of the re-entry glide vehicle, wherein a relationship between a pre-set aerodynamic parameter perturbation and flight status data is embedded in the simulation; sampling the flight status data of the aircraft and the corresponding aerodynamic parameter perturbations during the simulation process 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 for training until the target conditions are met, thereby obtaining an improved physical information neural network; and verifying the improved physical information neural network based on the test set and its labels.

[0019] Optionally, a relationship between a pre-set aerodynamic parameter perturbation and flight status data is embedded in the simulation scenario, including:

[0020]

[0021] in, represents the lift coefficient perturbation, represents the perturbation of the drag coefficient, t represents time, Ma represents the Mach number, and α represents the flight 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, including: a state quantity acquisition module, used to obtain the target flight state quantity during the flight of the aircraft; an aerodynamic parameter perturbation quantity determination module, 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 a 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 actual dynamic characteristics; an aerodynamic parameter determination module, used to determine the actual aerodynamic parameters based on the aerodynamic parameter perturbation quantity and the corresponding nominal aerodynamic parameters.

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

[0024] According to the fourth aspect, an embodiment of the present invention provides a computer storage medium having computer instructions stored thereon, which, 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 physical information neural network aerodynamic parameter identification method, which only requires the network to learn the relationship between the flight state of the aircraft and the aerodynamic parameter perturbation, but does not require the network to learn the differential characteristics between the aircraft states, nor does it require the network to have the ability to predict the flight state. This embodiment replaces the loss function in the original PINNs framework with an integral-based loss function to avoid the confrontation of different loss functions during the training process, which leads to difficulties in network training. In addition, the dynamic model containing the estimated value is connected with the real dynamic characteristics by means of integration, ensuring that the neural network can learn the correct dynamic information during the training process, thereby improving the accuracy of the aerodynamic parameters.

[0026] Other advantages, objectives and features of the present invention will be described in the following description and will be apparent to those skilled in the art to some extent, or those skilled in the art may be taught from the practice of the present invention. The objectives and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0028] Figure 1 A specific example flow chart of a method for identifying aerodynamic parameters based on an improved physical information neural network provided by the present invention;

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

[0030] Figure 3 It is a schematic diagram of the whole process of aerodynamic parameter perturbation identification by the improved PINNs in the present invention;

[0031] Figure 4 A graph showing the decrease of the loss function during the training of the lift coefficient perturbation estimation neural network model and the drag coefficient perturbation estimation neural network model in the present invention;

[0032] Figure 5 The aerodynamic parameter identification results of the trained model in the present invention in the simulated trajectory and the aerodynamic parameter curve diagram without aerodynamic deviation;

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

[0034] Figure 7 It is a box plot of lift coefficient identification error and drag coefficient identification error in four cases in the present invention;

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

[0036] Fig. 9 It is a principle block diagram of a specific example of an electronic device in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, it can also be the internal connection of two components, it can be a wireless connection, or it can be a wired connection. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0039] In addition, 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: refers to a series of physical parameters related to the movement of an object in a fluid (such as air). These parameters describe the fluid dynamics characteristics and the interaction between the object and the fluid.

[0041] Physically-informed neural networks: A deep learning framework that combines physical laws and data-driven methods to solve forward and inverse problems involving nonlinear partial differential equations. By adding physical information terms (such as physical laws, usually differential equations) to 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 improved physical information neural networks (PINNs), which uses neural networks to predict the perturbations of the actual aerodynamic parameters of the aircraft relative to the nominal aerodynamic parameters, thereby realizing the identification of the actual aerodynamic parameters. This method aims to solve the performance degradation problem of general PINNs when the aerodynamic perturbations of the aircraft are complex functions of the flight state. Specifically, an embodiment of the present invention provides an aerodynamic parameter identification method based on improved physical information neural networks, such as Figure 1 As shown, including:

[0043] S101, obtaining a target flight state quantity during the flight of the aircraft;

[0044] S102, inputting the target flight state quantity into the improved physical information neural network to obtain the aerodynamic parameter perturbation quantity, where the aerodynamic parameter perturbation quantity is a quantified value of the difference between the nominal aerodynamic parameters and the aerodynamic parameters in the actual 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 value and the real dynamic characteristics;

[0045] S103, determining actual aerodynamic parameters according to the aerodynamic parameter perturbation and the corresponding nominal aerodynamic parameters.

[0046] Exemplarily, 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 perturbation of the aerodynamic parameters, and does not require the network to learn the differential characteristics between the aircraft states, nor does it require the network to have the ability to predict the flight state. Therefore, this embodiment replaces the loss function in the original PINNs framework with an integral-based loss function to avoid the confrontation of different loss functions during the training process, which leads to difficulties in network training.

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

[0048] The physical model is an important foundation for the physical information neural network. This embodiment uses the three-degree-of-freedom dynamics equation of the reentry glider aircraft established in the ground coordinate system as the theoretical model for aerodynamic parameter identification. The motion equation of this model is as follows:

[0049]

[0050] In the formula, v, θ, σ are the velocity, ballistic inclination and ballistic deviation of the aircraft respectively; D and L represent the drag and lift acting on the aircraft respectively; x, y, z represent the three projection components of the relative distance between the aircraft and the target on the ground target system respectively; γ v 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, μ=3.985005×10 14 ; R e is the radius of the earth, and R e =6371000m. r represents the distance between the center of mass of the aircraft and the center of the earth, also known as the distance from the center of the earth, 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 obtained by q = ρv 2 / 2 is calculated; ρ is the atmospheric density at the height of the aircraft; S is the characteristic area of ​​the aircraft; the aerodynamic coefficient C L With C D The dimensionless drag coefficient and lift coefficient of the designed aircraft are shown respectively. This embodiment adopts the aerodynamic coefficient data of CAV-H and fits it to a function related to the angle of attack and the Mach number. The fitting formula is given by (4).

[0055]

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

[0057] Table 1

[0058]

[0059] Generally speaking, the aerodynamic parameter data involved in the flight process are generally obtained from the nominal expression or interpolation table similar to equation (4) collected and solved offline. However, due to differences in environmental conditions and measurement errors in wind tunnel tests, the actual aerodynamic parameters of the aircraft are perturbed compared with the aerodynamic parameters obtained from wind tunnel tests, resulting in the performance and effect of flight control deviating from the design indicators. Definition of lift perturbation coefficient 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 They respectively represent the actual lift coefficient and drag coefficient of the aircraft during flight.

[0062] (1) and (5) show that the flight state information such as v, θ, σ implies and The uncertainty information of aerodynamic parameters shown in the figure can be used to calculate the uncertainty of aerodynamic parameters. and By estimating it, the actual aerodynamic coefficient during flight can be determined. and During the flight, it is a function of time, angle of attack and Mach number, and can be defined by (6).

[0063]

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

[0065] In this embodiment, an integral loss function is used to replace the original loss function to form an improved physical information neural network. Specifically:

[0066] Physical information neural networks (PINNs) combine neural networks with prior physical information, and enable neural networks to learn physical laws through loss functions that include physical constraints. The core of PINNs includes two parts: deep neural network (DNNs) structure and physical driven loss function. Among them, the powerful nonlinear fitting ability of DNNs is the basis for PINNs to learn physical information. The mapping relationship between the input and output of the neural network obtained by DNNs can be expressed as N(·):

[0067]

[0068] In the formula, x in represents the neural network input; represents the output of the neural network, and y represents the true value corresponding to the output of the neural network; w and b represent the weight and bias 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 square error (MSE) loss function between the neural network output and the real data of the training sample:

[0070]

[0071] Where ||·||2 represents the 2-norm of the vector.

[0072] Different from (8), the loss function based on physical information is based on the physical equation constraints 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 equation of the aircraft with unknown aerodynamic perturbation coefficients is defined as:

[0073]

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

[0075]

[0076] In the formula, f(·) represents the derivative value of the differential equation; 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 Defines the weights of the two loss functions in the total loss function. ODE The introduction of The loss is also incorporated into the training process of the neural network. As the neural network is trained, It will approach the real Θ and complete the identification of the unknown aerodynamic perturbation coefficient.

[0079] PINNs based on (11) have proven their effectiveness in solving the direct problem of differential equations, but for solving the inverse problem of differential equations, that is, the parameter estimation problem, (11) still has certain problems.

[0080] First, observing the composition of (10), we can find that its differential term does not represent the true system dynamics, because the neural network's estimate of the unknown parameter Θ It is not entirely accurate, namely:

[0081]

[0082] In the formula, err ODE Indicates that it contains the neural network estimate The difference between the system dynamics characteristics and the real system dynamics characteristics. Therefore, (10) essentially forces the neural network to learn an inaccurate system dynamics process. Even if the parameter Θ is misestimated, the total loss function is still small, and the neural network will enter the global optimal point of the wrong parameter.

[0083] Secondly, for solving parameter estimation problems such as unknown aerodynamic parameter deviations, aerodynamic parameters and aerodynamic parameter deviation data are usually not directly measurable. Therefore, this embodiment does not use aerodynamic parameter data as the true value for model training, but uses measurable physical quantities such as speed, angle, etc., and the deviation 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 ability of the network to evaluate the accuracy of the prediction results, making it difficult for the network to learn effective patterns and information from the data, thereby increasing the difficulty of training the physical information neural network.

[0084] In order to solve the above problems and ensure that the neural network learns the real system dynamics information, this embodiment introduces an integral-based loss function, which is defined as follows:

[0085]

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

[0087]

[0088] Although the use of numerical integration methods to solve integral equations will introduce truncation errors, this error will also affect However, general numerical integration methods usually have high accuracy for solving ordinary differential equations similar to equation (1), and the estimation error caused by truncation error can generally be ignored.

[0089] This embodiment provides an improved physical information neural network aerodynamic parameter identification method, which only requires the network to learn the relationship between the flight state of the aircraft and the aerodynamic parameter perturbation, but does not require the network to learn the differential characteristics between the aircraft states, nor does it require the network to have the ability to predict the flight state. This embodiment replaces the loss function in the original PINNs framework with an integral-based loss function to avoid the confrontation of different loss functions during the training process, which leads to difficulties in network training. In addition, the dynamic model containing the estimated value is connected with the real dynamic characteristics by means of integration, ensuring that the neural network can learn the correct dynamic information during the training process, thereby improving the accuracy of the aerodynamic parameters.

[0090] Furthermore, a fully connected neural network structure is often used in a general PINNs framework, although the prior art has shown that a physical information neural network (PINNs) based on a fully connected neural network structure can fit any nonlinear function. However, in actual training, as the complexity of nonlinear functions increases, the training difficulty and complexity of PINNs based on a fully connected network structure will increase rapidly, and this network structure has difficulty fitting when facing aerodynamic parameter identification, a type of problem in solving unknown parameters without true values. In response to the above problems, this embodiment modifies the original PINNs structure to ensure that the neural network can maintain good fitting accuracy even when the aerodynamic deviation is a complex nonlinear function of the flight state.

[0091] Specifically, the physical information neural network in this embodiment adopts an RBF-BP hybrid network architecture, in which the RBF layer is a single hidden layer, 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 the aerodynamic parameter deviation is a complex function of the flight state quantity, or the functional relationship is not obvious, the difficulty of training PINNs using a fully connected neural network structure increases significantly. To address this problem, this embodiment designs an RBF-BP hybrid network architecture, which can significantly reduce the complexity of the network structure and the difficulty of training while ensuring the prediction accuracy compared to a fully connected neural network.

[0093] The RBF network is a single hidden layer neural network that approximates the target function through the linear weighted sum of multivariate basis functions. It maps the sample input in the low-dimensional space to a high-dimensional space through the radial basis function, and then finds a hyperplane passing through all sample points in the high-dimensional space to achieve the optimal approximation of the target 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 is the connection weight from the ith neuron to the output node, which can be determined by the least squares method or updated during the training process; g i (x) is the response function of the ith neuron to the input vector x, which is generally defined by a Gaussian radial basis function:

[0096]

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

[0098] Formula (16) indicates that the response size of each neuron in the RBF network to the input vector x is related to the distance between x and the center point of the neuron. Through the weighted combination of different neuron response functions, the RBF network can effectively approximate nonlinear functions. At the same time, the RBF network utilizes the characteristic of the radial basis function that the output response only depends on the distance between the input vector and the center point. When the input vector is far enough from the center of the neuron node, the output of the neuron node is close to zero, and only the neurons near the input vector will have a significant impact on the output. This makes the RBF network have a local approximation characteristic and can effectively extract the features of data sets with strong nonlinear and non-uniform distribution characteristics. At the same time, since the parameters and weights in the network are only valid locally, the RBF network has a very high training efficiency.

[0099] As mentioned above, the RBF network achieves the fitting of the objective function by determining the hyperplane in the high-dimensional space, and the shape of the hyperplane is closely related to the connection weight vector ω. However, when the objective function is highly nonlinear and the characteristics of the data set are uneven and not obvious, it is difficult for a single-layer network to find an optimal set of weight vectors ω so that the determined hyperplane passes through all sample points in the high-dimensional space accurately, which leads to the limitations of the RBF network in the problem of complex nonlinear function approximation. For this reason, the present embodiment designs an RBF-BP network structure, and the RBF hidden layer output will be connected to a fully connected network structure. During the network training process, the parameters of the fully connected network are simultaneously updated, and the nonlinear fitting ability of the fully connected network is used to help optimize the shape of the hyperplane. Figure 2 The detailed structure diagram of the RBF-BP network is shown.

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

[0101] For example, by combining the three-degree-of-freedom dynamics equations of the aircraft (1) with the integral-based loss function (14), unlike the general PINNs network, this embodiment does not require the neural network to learn the differential dynamics characteristics of the system, but only requires the neural network to perturb the aerodynamic parameters implicit in the dynamics equations through physical constraints. and Therefore, this embodiment selects the flight state quantity related to the aerodynamic parameter deviation function as the input of the neural network, and requires the state quantity to be actually measurable, and the specific definition is shown in (17).

[0102] x in =[t,Ma,α * ]T (17)

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

[0104] When the output of the neural network is the one to be identified, due to the perturbation of the aerodynamic parameters and It will affect different variables in (1), so the corresponding physical constraint loss function will also be different. From the equations in (1), it can be obtained that the drag coefficient perturbation The drag D affects the speed v of the aircraft, and the lift coefficient perturbation The lift L affects the trajectory inclination angle θ and trajectory deviation angle σ of the aircraft. In order to avoid the poor identification effect of the two aerodynamic parameter perturbations caused by the high complexity of a single network, this embodiment uses two networks to identify the drag coefficient perturbation and the lift coefficient perturbation 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 and thus calculate the loss function. The first three equations in (1) are defined as:

[0108]

[0109] The integral-based loss functions for three different variables are defined by (18):

[0110]

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

[0112] L1=L v (20)

[0113]

[0114] In summary, the whole process of aerodynamic parameter perturbation identification using improved PINNs is as follows: Figure 3 shown.

[0115] The scale difference between state variables will lead to the degradation of network performance. Therefore, this embodiment uses geophysical parameters to non-dimensionalize the input variables. The dimensionless formula is as follows:

[0116]

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

[0118] Table 3

[0119]

[0120] All neural network training codes in this embodiment are implemented using Pytorch. In the network structure, the RBF layer is a single hidden layer, providing 1600 neuron nodes. The node center position and width are determined by the k-means clustering algorithm. The fully connected layer consists of 3 hidden layers, each hidden layer includes 96 neurons, and the hyperbolic tangent function is used as the activation function of the fully connected layer, which is also the commonly used activation function in PINNs. In order to evaluate the performance of the proposed method, a fully connected neural network with 14 hidden layers and 512 neuron nodes in each layer is constructed as the benchmark model of 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 in which the re-entry glide vehicle enters the terminal guidance phase and strikes a target based on a three-degree-of-freedom dynamics model of the re-entry glide vehicle, wherein a relationship between a pre-set aerodynamic parameter perturbation and flight status data is embedded in the simulation scenario; sampling the flight status data of the aircraft and the corresponding aerodynamic parameter perturbation during the simulation process 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, thereby obtaining an 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 data set used for neural network training and verification is obtained by numerical simulation based on (1). In order to ensure the feasibility of the proposed method, this embodiment only uses the aircraft state information that can be measured by the integrated navigation system. Considering that the actual angle of attack α of the aircraft during flight is difficult to measure directly, this embodiment uses the angle of attack command α *Instead of the actual angle of attack, it is used for the identification algorithm. The simulation scenario is that the reentry glider enters the terminal guidance phase to attack the target. The initial position coordinates of the aircraft and the target are (0, 2000, 0) and (42000, 0, 20000) respectively. The values ​​of other initial parameters are shown in Table 4. In the simulation, and The functions of time, angle of attack and Mach number are selected to verify the approximation ability of neural networks to complex nonlinear functions.

[0123]

[0124] in, represents the lift coefficient perturbation, represents the perturbation of the drag coefficient, t represents time, Ma represents the Mach number, and α represents the flight 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, the test set accounts for 20% of the total data, the total number of training rounds is 20,000, and the early stopping strategy is adopted. The training batch size of each round is selected as 128, and a variable learning rate strategy is adopted. The initial learning rate is 1e-4, and the learning rate is reduced to 1e-5 after 10,000 rounds of training.

[0128] The verification results of the method proposed in the above embodiment are given below.

[0129] A trajectory whose initial parameters are not in the neural network sample library is selected as a simulation example of the neural network aerodynamic parameter deviation prediction. The initial parameters of the simulated trajectory used for identification effect verification are as follows: the initial point parameters of the reentry glider entering the terminal guidance phase are: initial speed 2225m / s, initial trajectory inclination -30deg, initial trajectory deviation -27deg, the initial position coordinates of the aircraft are (0,2000,0), and the target coordinates are (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 according to (5).

[0130] Figure 4The figure shows the decrease of the loss function during the training of two neural networks ((a) lift coefficient perturbation estimation neural network model, (b) drag coefficient perturbation estimation neural network model). The validation set loss function is used to evaluate whether the model is overfitting. Although there are slight fluctuations during the process, the two models reach the performance peak around 17,000 rounds. The sudden drop at 10,000 rounds is caused by the step change of the learning rate. The aerodynamic parameter identification results of the trained model in the simulated trajectory and the aerodynamic parameter curve without aerodynamic deviation are shown in Figure 2. Figure 5 As shown in the figure, (a) represents the lift coefficient and (b) represents the drag coefficient. This shows that the neural network can accurately identify the aerodynamic parameters during flight after training. In order to more intuitively demonstrate the model 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] At the same time, Table 5 gives more abundant statistical results, and the statistical indicators are mean square error (MSE), root mean square error (RMSE) and determination coefficient (R2).

[0132] Table 5

[0133]

[0134] In this embodiment, the measurement noise is regarded as Gaussian white noise with a mean of 0 and a constant variance, and a data measurement process is added during the simulation process. Specifically, in the simulation process, the white noise parameters shown in Table 6 are used. This embodiment verifies the insensitivity of the proposed method to measurement noise and data deviation through the following cases:

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

[0136] Case 2: After adding measurement noise, the same training set and test set preparation method as in the present embodiment is used to retrain the proposed network with the noisy data set. The simulation trajectory parameters used for recognition effect verification are the same as the parameters used in the above recognition effect verification. Measurement noise is also added in the simulation process to verify the learning ability of the proposed method for the noisy data features.

[0137] Case 3: The aerodynamic parameters of the simulated trajectory data containing noise are identified using the neural network trained during the above identification effect verification. The initial trajectory parameters are the same as those during the above identification effect verification to verify the insensitivity of the proposed method to noise data.

[0138] Case 4: Based on the simulated trajectory data containing noise, 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 measurement. This step aims to verify the insensitivity of the proposed method to data bias.

[0139] Figure 7 (a) and (b) respectively give the box plots of the lift coefficient identification error and the drag coefficient identification error in four cases. (a) represents the lift coefficient estimation error, and (b) represents the drag coefficient estimation coefficient. Table 7 gives the specific values ​​of the statistical indicators. As can be seen from the figure, the error distribution of Case 1 and Case 2 is similar, both within 5%, and for the drag coefficient identification, the identification error of Case 2 is smaller overall and the distribution is more concentrated, which shows that the network has the ability to extract features from noisy data. The identification result of Case 3 is also similar to that of Case 1. Although the error distribution is more dispersed than that of Case 1 and Case 2, the maximum prediction relative error is still within 10%, indicating that the proposed method is insensitive to noisy data. In case 4, in the face of noisy data with numerical deviations, although the measurement results are still very accurate, the identification performance of the proposed method for aerodynamic parameters has a certain degradation phenomenon. Combined with the results of case 3, this may be because despite the existence of measurement noise, the noise itself does not change the flight state, such as the physical relationship between physical quantities such as speed and angle of attack instructions. Using the loss function based on physical information, the network can still extract the physical constraint relationship between physical quantities. This also explains why the network is insensitive to noisy data in case 3, and the data bias term blurs this physical connection to a certain extent, resulting in a decline in network performance.

[0140] Table 6

[0141]

[0142] Table 7

[0143]

[0144] This section uses a fully connected neural network as a benchmark model and compares it with the method proposed in this embodiment. Except for the network structure, the two 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 the comparison between FCN and the proposed method: (a) lift coefficient, (b) drag coefficient. Although most of the errors are within the range of 10%, the prediction results of FCN with 14 hidden layers for aerodynamic parameters are still poor. It is difficult for a simple fully connected network 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] The present application also provides an electronic device, such as Fig. 9 As shown, a processor 501 and a memory 502, wherein the processor 501 and the memory 502 may be connected via a bus or other means.

[0149] The processor 501 may be a central processing unit (CPU). The processor 501 may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or a combination of the above chips.

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

[0151] The memory 502 may include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function; the data storage area may store data created by the processor, etc. In addition, the memory may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory 502 may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0152] The one or more modules are stored in the memory 502, and when executed by the processor 501, the following is performed: Figure 1 The aerodynamic parameter identification method based on the improved physical information neural network in the illustrated embodiment.

[0153] For details of the above electronic equipment, please refer to Figure 1 The corresponding related descriptions and effects in the illustrated embodiments can be understood and will not be repeated here.

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

[0155] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention rather than 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 in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A method for aerodynamic parameter identification based on improved physical information neural network, characterized in that: include: Obtain the target flight state quantity during the flight of the aircraft; The target flight state quantity is input into the improved physical information neural network to obtain the aerodynamic parameter perturbation quantity, which is the quantitative 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 actual aerodynamic parameters are determined according to the aerodynamic parameter perturbations and the corresponding nominal aerodynamic parameters.

2. The aerodynamic parameter identification method based on improved physical information neural network according to claim 1 is characterized in that: When the target flight state quantity includes: the flight time, angle of attack instruction and Mach number during the flight of the aircraft, the target flight state quantity is input into the improved physical information neural network to obtain the aerodynamic parameter perturbation quantity, including: The flight time, angle of attack command and Mach number are input into the improved physical information neural network to obtain the perturbation of the drag coefficient and the perturbation of the lift coefficient; According to the aerodynamic parameter perturbation and the corresponding nominal aerodynamic parameters, the actual aerodynamic parameters are determined, including: According to the drag coefficient perturbation and the nominal drag coefficient, the actual drag coefficient is obtained; The actual lift coefficient is obtained according to the lift coefficient perturbation and the nominal lift coefficient.

3. The aerodynamic parameter identification method based on improved physical information neural network according to claim 2 is characterized in that: 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, and the first network and the second network are both RBF-BP hybrid network architectures; In the RBF-BP hybrid network architecture, the RBF layer is a single hidden layer, the node center position and width are determined by the k-means clustering algorithm, the fully connected layer consists of three 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 improved physical information neural network according to claim 3 is characterized in that: The integral loss function of the first network is: in, D represents the drag acting on the aircraft, m represents the mass of the aircraft, μ represents the gravitational constant of the earth, r represents the distance between the center of mass of the aircraft and the center of the earth, also known as the distance from the center of the earth, x represents the projection component of the x-coordinate of the relative distance between the aircraft and the target on the ground target system, σ represents the ballistic deviation angle, θ represents the ballistic inclination angle, y represents the projection component of the y-coordinate of the relative distance between the aircraft and the target on the ground target system, and R e represents the radius of the earth, N represents the total number of samples, v k,i Indicates that at t k The i-th speed at time, Δt represents the time interval, v k+1,i Indicates t k+1 The i-th speed at time.

5. The aerodynamic parameter identification method based on improved physical information neural network according to claim 3 or 4, characterized in that: The integral loss function of the second network is: in, L represents the lift acting on the aircraft, γ v is the aerodynamic roll angle, also known as the roll angle, m represents the mass of the aircraft, μ represents the gravitational constant of the earth, r represents the distance between the center of mass of the aircraft and the center of the earth, also known as the distance from the center of the earth, v represents the speed of the aircraft, σ represents the ballistic deviation angle, θ represents the ballistic inclination angle, y represents the projection component of the y coordinate of the relative distance between the aircraft and the target on the ground target system, x represents the projection component of the x coordinate of the relative distance between the aircraft and the target on the ground target system, z represents the projection component of the z coordinate of the relative distance between the aircraft and the target on the ground target system, R e represents the radius of the earth, N represents the total number of samples, θ k,i Indicates that at t k The i-th ballistic inclination at time, Δt represents the time interval, θ k+1,i Indicates t k+1 The i-th ballistic inclination angle at time, σ k,i Indicates that at t k The i-th ballistic deflection angle at time, σ k+1,i Indicates t k+1 The i-th ballistic deviation angle at time.

6. The aerodynamic parameter identification method based on improved physical information neural network according to claim 1 is characterized in that: The improved physics-informed neural network training process includes: According to the three-degree-of-freedom dynamics model of the re-entry glide vehicle, a simulation is conducted on the scenario of the re-entry glide vehicle entering the terminal guidance phase and striking the target, in which the relationship between the pre-set aerodynamic parameter perturbation and the flight status data is embedded; The flight state data of the aircraft and the corresponding aerodynamic parameter perturbations during the sampling simulation process are obtained 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 condition is met, thereby obtaining the improved physical information neural network; Validate the improved physically-informed neural network on the test set and its labels.

7. The aerodynamic parameter identification method based on improved physical information neural network according to claim 6 is characterized in that: The relationship between the pre-set aerodynamic parameter perturbation and flight status data is embedded in the simulation scenario, including: in, represents the lift coefficient perturbation, represents the perturbation of the drag coefficient, t represents time, Ma represents the Mach number, and α represents the flight angle of attack.

8. An aerodynamic parameter identification device based on an improved physical information neural network, characterized in that: include: A state quantity acquisition module is used to obtain the target flight state quantity during the flight of the aircraft; an aerodynamic parameter perturbation determination module, which is used to input the target flight state quantity into the improved physical information neural network to obtain the aerodynamic parameter perturbation, where the aerodynamic parameter perturbation is a quantitative value of the difference between the nominal aerodynamic parameters and the aerodynamic parameters in actual 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 value and the real dynamic characteristics; The aerodynamic parameter determination module is used to determine the actual aerodynamic parameters according to the aerodynamic parameter perturbation and the corresponding nominal aerodynamic parameters.

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

10. A computer storage medium having computer instructions stored thereon, characterized in that: When the instruction is executed by the processor, the steps of the aerodynamic parameter identification method based on the improved physical information neural network described in any one of claims 1-7 are implemented.

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