An online space-ground data fusion method based on physical information neural network

Abstract

This invention discloses an online space-ground data fusion method based on a physical information neural network. The method comprises the following steps: constructing a fully connected neural network model; physically constraining the output values ​​of the fully connected neural network model to obtain the physical information neural network model; backpropagating the errors obtained by the physical constraints through a loss function; selecting wind tunnel test data and flight test data as feature inputs into the physical information neural network model, selecting the flight test data as labels, fusing the space-ground data, and continuously updating the input data in the time domain at a given step size to achieve online fusion. The method can obtain highly accurate fused data by combining a small amount of high-precision flight test data with a large amount of low-precision test data.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent fluid mechanics, and in particular relates to an online sky-ground data fusion method based on a physical information neural network. Background Art

[0002] In recent years, multi-source aerodynamic data fusion technology has garnered widespread attention in the field, addressing challenges such as the difficulty in acquiring ground-based aerodynamic data for spacecraft and poor ground-to-ground consistency. A number of aerodynamic data fusion methods have been developed, combining classical approaches such as weighted averaging, Kalman filtering, and the Kriging model. These methods utilize explicit algebraic formulas to effectively fuse aerodynamic data from different sources. While their principles are simple and clear, they struggle to meet the modeling requirements for high-dimensional, nonlinear, and complex data.

[0003] With the rapid development of artificial intelligence, intelligent algorithms such as fuzzy logic, support vector machines, extreme learning machines, and various neural network architectures are increasingly being applied to unsteady aerodynamic modeling. These intelligent algorithms, independent of prior physical knowledge, can be applied to the unsteady aerodynamic modeling of various aircraft configurations while ensuring sufficient nonlinear mapping accuracy. However, due to their "black box" nature, researchers cannot understand the underlying physical laws of the models, which to some extent limits their development.

[0004] Physics-Informed Neural Networks (PINNs) are a type of neural network that encodes the governing equations of a problem, such as partial differential equations (PDEs), as part of the neural network, alleviating to some extent the "black box" property of traditional neural networks.

[0005] The shortcomings of the prior art are summarized as follows:

[0006] 1. The existing aerodynamic prediction methods are seriously insufficient in simulating the unsteady aerodynamic forces during large-scale maneuvers, which directly affects the control accuracy.

[0007] 2. General flight data lacks active excitation and effective information, and is also affected by errors such as signal acquisition noise. It is difficult to meet the needs of high-precision aerodynamic parameter identification or correction of ground-to-ground data differences.

[0008] 3. Traditional neural networks have “black box” properties when used for unsteady aerodynamic modeling.

[0009] 4. Most existing modeling methods process existing data, and there is little research on online recognition of data being generated. Summary of the Invention

[0010] In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to provide an online ground-to-air data fusion method based on a physical information neural network to solve the problems in the prior art of mismatch between wind tunnel test data and flight test data and difficulty in online identification of flight test data.

[0011] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0012] The present invention provides an online space-ground data fusion method based on a physical information neural network, comprising the following steps:

[0013] 1) Build a fully connected neural network model;

[0014] 2) Physically constrain the output of the fully connected neural network model through the flight dynamics equation to obtain a physical information neural network model. The error obtained by the physical constraint is back-propagated through the loss function Smooth_L1;

[0015] 3) Select x1-dimensional wind tunnel test data and x2-dimensional flight test data as feature input physical information neural network model, 1≤x1 and x1∈N + , 1≤x2 and x2∈N + ; Select y dimensions of test flight data as labels, 1≤y≤6 and y∈N + ,To fuse the heaven and earth data, the data is continuously updated in the time domain with a given step size, achieving online fusion.

[0016] Furthermore, the step 1) specifically includes:

[0017] 11) Construct the input layer, hidden layer, and output layer of the fully connected neural network model; the number of neurons in the input layer is x1+x2, and the hidden layer has M layers, with the number of neurons being n1, n2, n3, ..., n respectively. M , M and n are adjustable hyperparameters, and the number of neurons in the output layer is y;

[0018] 12) Each neuron in the fully connected neural network model processes input through a weighted sum operation and a nonlinear activation function and generates output. Assuming that the current fully connected layer is the lth layer of the fully connected neural network model, the calculation formula of the neuron is expressed as:

[0019]

[0020] Where, is the weighted sum of the jth neuron in the lth layer, s l-1 is the number of neurons in the l-1 layer, is the weight from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, is the output of the i-th neuron in the l-1th layer, is the bias term of the j-th neuron in the l-th layer;

[0021] 13) The weighted sum is passed through a nonlinear activation function to produce the final output, which is expressed as follows:

[0022]

[0023] Where, is the output of the jth neuron in the lth layer, f is the activation function, and the activation function is the Sigmoid function, the hyperbolic tangent function, or the ReLU function.

[0024] Furthermore, the step 2) specifically includes:

[0025] 21) Physical constraints are imposed on the output values ​​of the fully connected neural network model through the six-degree-of-freedom flight dynamics equation, so that it converges to the label data under the constraints of boundary conditions, thereby obtaining a physical information neural network model. The physical constraint expression is:

[0026]

[0027]

[0028] c5=(I z -I x ) / I y

[0029] c6=I xz / I y

[0030] c7=1 / I y

[0031]

[0032] Where, f1, f2, f3, f4, f5, and f6 are the residuals of the six constraint equations; p, q, and r are the roll angular velocity, pitch angular velocity, and yaw angular velocity, respectively; V xb ,V yb ,V zb They are the X-axis speed, Y-axis speed, and Z-axis speed in the body coordinate system respectively; is the air dynamic pressure; S is the reference area; m is the mass of the aircraft; g is the gravity coefficient; θ is the pitch angle; φ is the roll angle; a x ,a y ,a z are the X-axis acceleration, Y-axis acceleration, and Z-axis acceleration in the body coordinate system; dp, dq, and dr are the roll angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; C X ,C Y ,CZ They are the X-axis prediction force coefficient, Y-axis prediction force coefficient, and Z-axis prediction force coefficient respectively; C l ,C m ,C n They are respectively the roll prediction moment coefficient, pitch prediction moment coefficient, and yaw prediction moment coefficient, I xz is the product of inertia between the X-axis and the Z-axis, I x ,I y ,I z They are the X-axis moment of inertia, Y-axis moment of inertia, and Z-axis moment of inertia;

[0033] 22) The error obtained by physical constraints is converged to 0 through the loss function Smooth_L1, which is expressed as follows:

[0034]

[0035] Where, L i is the sum of errors of the i-th loss function, N is the amount of data for each feature, Δ i is f in step 21) i ,i=1,2,…,6;

[0036] 23) The six loss functions of the physical information neural network model are integrated into a total loss function using the linear weighted superposition method, and the error is back-propagated. The expression is as follows:

[0037]

[0038] Where, Loss i is the total loss of the updated data for the i-th batch, β1, β2, β3, β4, β5, β6 are the loss weighted values ​​of the six dimensions respectively, Update the loss of data for batch i in six dimensions respectively.

[0039] Furthermore, the step 3) specifically includes:

[0040] 31) Use normal distribution to normalize the data values ​​of each dimension to eliminate the adverse effects caused by singular sample data. The expression is:

[0041]

[0042] Where x′ ij is the jth data point of the normalized i-th dimension feature, x ij is the jth data point of the i-th dimension feature before normalization, μ i is the mean of the i-th feature, σ i is the standard deviation of the i-th feature, and n is the number of data points for each feature;

[0043] 32) The normalized feature data is input into the physical information neural network model, and the stochastic gradient descent method is used to make the output value gradually approach the label data during continuous training. The label data is the aerodynamic parameters of the flight test data. That is, by correcting the wind tunnel test data in the feature, the output value of the physical information neural network model is made close to the aerodynamic parameters of the flight test data, thereby realizing the fusion of ground and space data; the expression is:

[0044]

[0045] Where θ is the parameter of the physical information neural network model, η is the learning rate, which is used to control the update step size. is the gradient of the loss function J(θ) with respect to the parameter θ, (x j ,y j ) is a sample randomly selected from all training samples;

[0046] 33) Online identification is realized in the entire time domain. The aerodynamic identification step value is set to s, so that each feature continuously updates s input data under the movement of the aerodynamic identification step. The expression is as follows:

[0047] Input i ={[R1 i ,R2 i ,...,R 16 i ],...,[R1 i+S R2 i+s ,...,R 16 i+s ]},i=0,1,2,..n

[0048] Where R1, R2,…, R 16 is the feature data of each dimension. When the data volume of each dimension is greater than or equal to s, online identification begins. i is the update batch of training data, and n is equal to the input data volume of each dimension minus the aerodynamic identification step value s.

[0049] Beneficial effects of the present invention:

[0050] 1. The method of the present invention can obtain high-precision fusion data through a small amount of high-precision test flight data and a large amount of low-precision test data.

[0051] 2. The present invention uses the six-degree-of-freedom dynamic equation of flight mechanics as a physical constraint, which reduces the "black box" property of the neural network to a certain extent and enhances the interpretability of the fused data.

[0052] 3. The present invention performs online identification and data fusion in the entire time domain. By giving an initial step size, points whose number is greater than the initial step size can be fitted individually, thereby improving the data fusion accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Schematic diagram of the method of the present invention. DETAILED DESCRIPTION

[0054] In order to facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and drawings. The contents mentioned in the embodiments are not intended to limit the present invention.

[0055] Reference Figure 1 As shown, the online space-ground data fusion method based on physical information neural network of the present invention comprises the following steps:

[0056] 1) Build a fully connected neural network model; specifically including:

[0057] 11) Construct the input layer, hidden layer, and output layer of the fully connected neural network model; the number of neurons in the input layer is x1+x2, and the hidden layer has M layers, with the number of neurons being n1, n2, n3, ..., n respectively. M , M and n are adjustable hyperparameters, and the number of neurons in the output layer is y;

[0058] 12) Each neuron in the fully connected neural network model processes input through a weighted sum operation and a nonlinear activation function and generates output. Assuming that the current fully connected layer is the lth layer of the fully connected neural network model, the calculation formula of the neuron is expressed as:

[0059]

[0060] Where, is the weighted sum of the jth neuron in the lth layer, s l-1 is the number of neurons in the l-1 layer, is the weight from the i-th neuron in the l-1th layer to the j-th neuron in the lth layer, is the output of the i-th neuron in the l-1th layer, is the bias term of the j-th neuron in the l-th layer;

[0061] 13) The weighted sum is passed through a nonlinear activation function to produce the final output, which is expressed as follows:

[0062]

[0063] Where, is the output of the jth neuron in the lth layer, f is the activation function, and the activation function is the Sigmoid function, the hyperbolic tangent function, or the ReLU function.

[0064] 2) Physically constrain the output of the fully connected neural network model through the flight dynamics equation to obtain a physical information neural network model. The error obtained by the physical constraint is back-propagated through the loss function Smooth_L1. Specifically,

[0065] 21) Physical constraints are imposed on the output values ​​of the fully connected neural network model through the six-degree-of-freedom flight dynamics equation, so that it converges to the label data under the constraints of boundary conditions, thereby obtaining a physical information neural network model. The physical constraint expression is:

[0066]

[0067]

[0068] c5=(I z -I x ) / I y

[0069] c6=I xz / I y

[0070] c7=1 / I y

[0071]

[0072] Where, f1, f2, f3, f4, f5, and f6 are the residuals of the six constraint equations; p, q, and r are the roll angular velocity, pitch angular velocity, and yaw angular velocity, respectively; V xb ,V yb ,V zb are the X-axis velocity, Y-axis velocity, and Z-axis velocity in the body coordinate system respectively; q is the air dynamic pressure; S is the reference area; m is the body mass; g is the gravity coefficient; θ is the pitch angle; φ is the roll angle; a x ,a y ,a z are the X-axis acceleration, Y-axis acceleration, and Z-axis acceleration in the body coordinate system; dp, dq, and dr are the roll angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; C X ,C Y ,C Z They are the X-axis prediction force coefficient, Y-axis prediction force coefficient, and Z-axis prediction force coefficient respectively; C l ,C m ,C n They are respectively the roll prediction moment coefficient, pitch prediction moment coefficient, and yaw prediction moment coefficient, I xz is the product of inertia between the X-axis and the Z-axis, I x ,I y ,I zThey are the X-axis moment of inertia, Y-axis moment of inertia, and Z-axis moment of inertia;

[0073] 22) The error obtained by physical constraints is converged to 0 through the loss function Smooth_L1, which is expressed as follows:

[0074]

[0075] Where, L i is the sum of errors of the i-th loss function, N is the amount of data for each feature, Δ i is f in step 21) i ,i=1,2,…,6;

[0076] 23) The six loss functions of the physical information neural network model are integrated into a total loss function using the linear weighted superposition method, and the error is back-propagated. The expression is as follows:

[0077]

[0078] Where, Loss i is the total loss of the updated data for the i-th batch, β1, β2, β3, β4, β5, β6 are the loss weighted values ​​of the six dimensions respectively, Update the loss of data for batch i in six dimensions respectively.

[0079] 3) Select the trajectory parameters of the wind tunnel test data with x1 dimensions and the flight test data with x2 dimensions as the feature input physical information neural network model, 1≤x1 and x1∈N + , 1≤x2 and x2∈N + , N + is a positive integer; the aerodynamic parameters of the flight test data in y dimensions are selected as labels, 1≤y≤6 and y∈N + , integrating the earth and sky data, the data is continuously updated in the time domain with a given step size to achieve online fusion; specifically including:

[0080] 31) Use normal distribution to normalize the data values ​​of each dimension to eliminate the adverse effects caused by singular sample data. The expression is:

[0081]

[0082] Where x′ ij is the jth data point of the normalized i-th dimension feature, x ij is the jth data point of the i-th dimension feature before normalization, μ i is the mean of the i-th feature, σ i is the standard deviation of the i-th feature, and n is the number of data points for each feature;

[0083] 32) The normalized feature data is input into the physical information neural network model, and the stochastic gradient descent method is used to make the output value gradually approach the label data during continuous training. The label data is the aerodynamic parameters of the test flight data. That is, by correcting the wind tunnel test data in the feature, the output value of the physical information neural network model is made close to the aerodynamic parameters of the test flight data, thereby realizing the fusion of ground and space data. The expression is:

[0084]

[0085] Where θ is the parameter of the physical information neural network model, η is the learning rate, which is used to control the update step size. is the gradient of the loss function J(θ) with respect to the parameter θ, (x j ,y j ) is a sample randomly selected from all training samples;

[0086] 33) Online identification is realized in the entire time domain. The aerodynamic identification step value is set to s, so that each feature continuously updates s input data under the movement of the aerodynamic identification step. The expression is as follows:

[0087] Input i ={[R1 i ,R2 i ,...,R 16 i ],...,[R1 i+S R2 i+s ,..,R 16 i+s ]}, i=0,1,2,..n

[0088] Where R1, R2,…, R 16 is the feature data of each dimension. When the data volume of each dimension is greater than or equal to s, online identification begins. i is the update batch of training data, and n is equal to the input data volume of each dimension minus the aerodynamic identification step value s.

[0089] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be considered as the scope of protection of the present invention.

Claims

1. An online space-ground data fusion method based on physical information neural network, characterized in that: Here are the steps: 1) Build a fully connected neural network model; 2) Physically constrain the output value of the fully connected neural network model to obtain a physical information neural network model, and backpropagate the error obtained by the physical constraint; 3) Select x1-dimensional wind tunnel test data and x2-dimensional flight test data as feature input physical information neural network model, 1≤x1 and x1∈N + , 1≤x2 and x2∈N + ; N + is a positive integer; select y dimensions of test flight data as labels, 1≤y≤6 and y∈N + ,Fusing the earth and sky data, the data is continuously updated in the time domain with a given step size to achieve online fusion; The step 2) specifically includes: 21) Physical constraints are imposed on the output values ​​of the fully connected neural network model through the six-degree-of-freedom flight dynamics equations, so that it converges to the label data under the constraints of boundary conditions, thereby obtaining a physical information neural network model. The physical constraint expression is: c5=(I z -I x ) / I y c6=I xz / I y c7=1 / I y Where f1, f2, f3, f4, f5, and f6 are the residuals of the six-degree-of-freedom flight dynamics equations; p, q, and r are the roll angular velocity, pitch angular velocity, and yaw angular velocity, respectively; V xb ,V yb ,V zb They are the X-axis speed, Y-axis speed, and Z-axis speed in the body coordinate system respectively; is the air dynamic pressure; S is the reference area; m is the mass of the aircraft; g is the gravity coefficient; θ is the pitch angle; φ is the roll angle; a x ,a y ,a z are the X-axis acceleration, Y-axis acceleration, and Z-axis acceleration in the body coordinate system; dp, dq, and dr are the roll angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; C X ,C Y ,C Z They are the X-axis prediction force coefficient, Y-axis prediction force coefficient, and Z-axis prediction force coefficient respectively; C l ,C m ,C n They are respectively the roll prediction moment coefficient, pitch prediction moment coefficient, and yaw prediction moment coefficient, I xz is the product of inertia between the X-axis and the Z-axis, I x ,I y ,I z They are the X-axis moment of inertia, Y-axis moment of inertia, and Z-axis moment of inertia; 22) The residual of the six-degree-of-freedom flight dynamics equation is converged to 0 through the loss function, which is expressed as follows: Where, L i is the sum of errors of the i-th loss function, N is the amount of data for each feature, Δ i is fi in step 21), i=1,2,…,6; 23) The six loss functions of the physical information neural network model are integrated into a total loss function using the linear weighted superposition method, and the error is back-propagated. The expression is as follows: Where, Loss j is the total loss function for the updated data of the jth batch, β1, β2, β3, β4, β5, β6 are the weighted values ​​of the six loss functions respectively, Update the loss function for the six j-th batches of data respectively.

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