CN112597700B - Aircraft trajectory simulation method based on neural network - Google Patents
Aircraft trajectory simulation method based on neural network Download PDFInfo
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- CN112597700B CN112597700B CN202011477057.2A CN202011477057A CN112597700B CN 112597700 B CN112597700 B CN 112597700B CN 202011477057 A CN202011477057 A CN 202011477057A CN 112597700 B CN112597700 B CN 112597700B
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Abstract
The invention provides an aircraft trajectory simulation method based on a neural network, which can improve the speed of trajectory simulation calculation on the premise of ensuring the simulation precision. The aircraft trajectory simulation method based on the neural network realizes solving precision similar to that of the traditional numerical solving method based on the neural network algorithm method and by means of the universal approximation property of the neural network. Meanwhile, due to reusability of the neural network method, the trained optimization model can continuously reuse the ballistic equation solving neural network of the existing aircraft, purposeful initialization of the ballistic equation solving neural network is realized, the neural network model for solving the original ballistic equation is used as an initialization model, training time of the neural network for solving a new aircraft ballistic motion equation is greatly shortened, and solving speed of the ballistic equation is improved.
Description
Technical Field
The invention relates to the technical field of trajectory simulation, in particular to an aircraft trajectory simulation method based on a neural network.
Background
In the overall design of the aircraft, the ballistic design and the ballistic simulation have important significance, and the ballistic design of the aircraft is an important component in the overall design process of the aircraft. The speed and accuracy of the ballistic simulation calculations determine the cycle time of the aircraft ballistic design and the performance of the product. In order to achieve such capability, a core problem to be solved is how to achieve rapid calculation of a trajectory equation based on a neural network, and at present, the most widely used aircraft trajectory calculation method is a fourth-order lungkat tower method, which can be regarded as an improved method of an eulerian method, and compared with the eulerian method, precision is improved. However, discretization processing still needs to be performed on the solving process, the calculation precision and speed are determined by the selection of the algorithm step size, too large calculation error is easily caused if the step size is too long, too long training time is caused if the step size is too small, and the simulation speed and precision are difficult to consider.
Therefore, in view of the above situation, a new solution is needed to improve the speed of aircraft trajectory simulation and achieve a fast and accurate optimization design of aircraft trajectory while ensuring the accuracy of aircraft trajectory simulation.
Disclosure of Invention
In view of this, the invention provides an aircraft trajectory simulation method based on a neural network, which can improve the speed of trajectory simulation calculation on the premise of ensuring the simulation accuracy.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the invention discloses an aircraft trajectory simulation method based on a neural network, which comprises the following steps:
step 1, solving offline pre-training of a neural network of a ballistic equation: the method comprises the steps of constructing a neural network and fusing an aircraft trajectory motion differential equation into the neural network;
the method comprises the following steps that an aircraft trajectory motion differential equation is fused into a neural network, wherein the goal of fusing the aircraft trajectory motion differential equation into the neural network is to express the aircraft trajectory equation into a regularization term of a neural network loss function, the regularization term is connected with a neural network structure, and training errors generated due to the fact that the input-output relation does not meet the trajectory motion equation are gradually reduced in the training process of the neural network;
step 2, on-line training of a neural network fused into a ballistic equation: and carrying out secondary training aiming at the ballistic equation of the aircraft of a specific model on the basis of the neural network model obtained by off-line training.
Wherein, the step 1 specifically comprises the following substeps:
step 1.1, constructing a neural network;
the neural network structure comprises an input layer, an output layer and 4 hidden layers, wherein the number of nodes of the input layer is 1, the number of nodes of the output layer is 4, the number of nodes of the hidden layers are all 10, a ReLu function is used as an activation function, and AdamaOptizer is used as an optimizer of the neural network;
the input parameter of the neural network is the motion time t of the aircraft, and the output parameter is the aircraft speed v (t), the aircraft trajectory inclination angle theta (t), the aircraft x-axis displacement x (t) and the aircraft y-axis displacement y (t) which are obtained by network calculation;
step 1.2, constructing a loss function;
the loss function is used for calculating the difference between the forward calculation result of each iteration of the neural network and the true value to generate gradient information;
the loss function comprises a data term and a regularization term; the regularization part is obtained according to deformation of each differential equation in the ballistic motion differential equation set by adopting the mean square error MSE which is the same as that of the traditional neural network;
and 1.3, training a neural network to enable the neural network to gradually approximate to a special solution of an aircraft trajectory motion equation, so as to obtain an optimal solution of the parameters enabling the value of the loss function to be as small as possible.
In step 1.3, optimization is carried out on the neural network by using a tena optimizer of the tenaerflow self-carrying.
Wherein, in step 1.3, the network is trained using a 4-layer ANN and a back propagation algorithm.
In the step 2, the structure and parameters of the neural network are directly inherited from the step 1.3 to obtain a result;
for aircraft with similar trajectory, the corresponding type of neural network which is pre-selected and connected is selected as an initialization model, then according to the method of step 1.2, the loss function is reconstructed according to a new trajectory equation, and the method of step 1.3 is used again for training.
The method for reconstructing the loss function comprises the following steps:
and changing the attack angle function of the aircraft, wherein the change of the attack angle function causes the corresponding change of the regularization term of the loss function.
Has the beneficial effects that:
the aircraft trajectory simulation method based on the neural network realizes solving precision similar to that of the traditional numerical solving method by means of the universal approximation property of the neural network based on the neural network algorithm method. Meanwhile, due to the reusability of the neural network method, the trained optimization model can continuously reuse the ballistic equation solving neural network of the existing aircraft, purposeful initialization of the ballistic equation solving neural network is realized, the neural network model for solving the original ballistic equation is used as an initialization model, the training time of the neural network for solving a new aircraft ballistic motion equation is greatly shortened, and the solving speed of the ballistic equation is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of a neural network structure constructed using the tensflow architecture of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
In the aircraft trajectory simulation method based on the neural network, the trajectory motion equation of the aircraft is integrated into the training process of the neural network, so that the input and the output of the neural network meet the objective physical knowledge expressed by the trajectory motion equation, and the solution of the aircraft trajectory equation by using the neural network is realized. In addition, aiming at the problem that the trajectory of the aircraft needs to be calculated repeatedly, the training process of the neural network is divided into two parts of off-line pre-training and on-line parameter fine-tuning (here, the weight and the bias of the neural network). The neural network parameter optimization process with large calculation amount is placed in an off-line pre-training stage, the establishment of a neural network structure and the initialization of network parameters are mainly realized, the neural network takes time as input, and the output is the performance parameters of the missile, such as speed, trajectory inclination angle, displacement and the like of the aircraft. The purpose of this stage is to obtain a neural network with higher precision for solving the equation set after the pre-training is finished, and to provide an initialization model for the subsequent on-line training process. Then, the online parameter fine tuning part uses the neural network trained in the first stage, and can perform secondary training on the basis of the pre-trained neural network for other aircrafts meeting the same type of ballistic motion equation. The secondary training process is to multiplex a pre-trained neural network model, perform small-amplitude parameter adjustment on the model aiming at a new ballistic equation set, realize solution of the new equation set, reduce the optimization times of neural network weight and bias parameters, avoid a large number of random search processes in the prior period, greatly improve the training efficiency of the neural network, only need to perform local adjustment on the neural network parameters according to an updated ballistic equation, and greatly shorten the solution time of the ballistic equation by multiplexing the neural network structure and the parameters.
Compared with the traditional ballistic equation numerical solution, the ballistic equation solving method based on the neural network has reusability, and the neural network which is trained in the pre-training stage can be saved, so that the neural network can be directly called in the secondary training stage of the neural network, the neural network early-stage parameter optimization which consumes the most time is put in the off-line training stage, the target aircraft ballistic equation can be quickly solved in the on-line training stage, and the requirements of quickness and accuracy in the aircraft ballistic equation solving are met.
The flow of the aircraft trajectory simulation method based on the neural network is shown in fig. 1, and the method specifically comprises the following steps:
step 1, solving offline pre-training of a neural network of a ballistic equation:
the whole model training and using steps start from the stage of 'neural network off-line pre-training for solving ballistic equations'. The part mainly comprises the construction of a neural network and the fusion of a differential equation of the trajectory motion of the aircraft into the neural network, wherein the goal of the fusion stage of the differential equation is to express the trajectory equation of the aircraft into a regularization term of a loss function of the neural network, and the regularization term can be connected with a neural network structure, so that the training error generated because the input-output relation does not meet the trajectory motion equation is gradually reduced in the training process of the neural network. This stage is mainly composed of 3 large core elements, including: "neural network", "differential equation", and "initial condition". The method specifically comprises the following substeps:
step 1.1, constructing a neural network;
an Artificial Neural Network (ANN) is a calculation model based on the structure and the function of a biological neural network, is a machine learning algorithm with the widest application range at present, and is commonly used for fitting various complex functions due to the universal approximation property. The method takes the neural network as a tool for solving the ballistic differential equation, the training process of the neural network is a process that the neural network gradually approaches the solution of the aircraft ballistic equation, and the ballistic motion equation of the aircraft aims to input a certain time in the motion process of the aircraft into the trained neural network, so that the motion state of the aircraft at the moment can be rapidly acquired.
The input of the network is the motion time t of the aircraft, and the output is the aircraft speed v (t), the aircraft trajectory inclination angle theta (t), the aircraft x-axis displacement x (t) and the aircraft y-axis displacement y (t) which are obtained by network calculation;
the neural network structure constructed by using a Tensorflow architecture is shown in figure 2 and comprises an input layer, 4 hidden layers and an output layer, wherein the number of nodes of the input layer is 1, the number of nodes of the output layer is 4, the number of nodes of the hidden layers is 10, a ReLu function is used as an activation function, and AdamaOptizer is used as an optimizer of the neural network. Details of the neural network hyper-parameters are shown in table 1:
TABLE 1 neural network hyperparameters
Since the regularization term of the loss function needs to be constructed in the next step, and derivation needs to be carried out on the output layer of the neural network at this time, the invention introduces an automatic differentiation method tf of Tensorflow. For the whole framework, the automatic differentiation is also a link connecting the neural network and the differential equation, so that the basis for constructing the loss function of the neural network is stated, and the specific construction method thereof will be described in detail in the next step.
Step 1.2, constructing a loss function;
the loss function is used for calculating the difference between the forward calculation result of each iteration of the neural network and the true value so as to guide the next training to be carried out in the correct direction. In the invention, the loss function realizes the integration of a differential equation and a neural network, and is used for solving the loss function of the neural network of the ballistic equation. The loss function of the invention comprises two parts, namely a data item and a regularization item. The data item part of the loss function adopts the mean square error MSE which is the same as that of the traditional neural network to express the difference value between the first value of each dimensionality output by the neural network and the initial value of the differential equation set, and the regularization part is obtained according to the deformation of each differential equation in the ballistic motion differential equation set to express the coincidence degree of the input-output relation of the neural network and the differential equation.
Training the neural network according to the loss function as a guide, wherein when the input-output relationship of the neural network does not satisfy the ballistic motion equation, the regularization term of the loss function generates an error, the weight and the bias of the neural network are forced to explore in a direction in which the error is reduced, and finally the input-output relationship of the neural network satisfies the differential equation, so that the solution of fitting the differential equation by using the neural network is realized, namely, the ballistic simulation of the aircraft by using the neural network is realized.
The form of the breeze equation for ballistic motion of a certain aircraft is assumed as follows:
and assuming the initial conditions:
| parameter(s) | Numerical value | Unit of |
| t 0 | 6 | Second of |
| xd 0 | 0.004 | Kilometer in length |
| yd 0 | 161.320 | Kilometer in length |
| vd 0 | 54.604 | Meter per second |
| θd 0 | 1.5707 | Arc degree |
The data item of the neural network loss function is used for determining the position of the fitting function of the neural network, and the data item of the neural network loss function constructed by the initial condition of the bitor equation is as follows:
i 1 ＝(vd-vd 0 )
i 2 ＝(θd-θd 0 )
i 3 ＝(xd-xd 0 )
i 4 ＝(yd-yd 0 )
in the above formula, vd, θ d, xd and yd are outputs of 4 dimensions of the neural network, respectively.
The data item of the loss function determines the shape of the fitting function of the neural network, and the regularization item form of the loss function of the neural network constructed according to the ballistic equation is as follows:
the integrity loss function of a neural network can be expressed as:
step 1.3, training a neural network:
the training process of the neural network is a process in which the input and output relations of the neural network gradually satisfy a differential equation. The aim of the training of the neural network is to find suitable parameters so that the value of the loss function is as small as possible. The invention uses the tenarflow self-carried Adam optimizer to optimize the neural network, and the optimizer can adaptively adjust the learning rate of the neural network in the training process of the neural network, so that the adjustment step length of the parameters is gradually reduced along with the training process, and the optimal solution of the parameters can be found more favorably. In this embodiment, the network is trained using a 4-layer ANN and a back propagation algorithm.
The training process of the neural network can reduce the data item and the regularization item of the loss function at the same time, and the process enables the neural network to gradually approximate the special solution of the aircraft trajectory motion equation.
Step 2, integrating the neural network of the trajectory equation to train on line
The online training process is a secondary training process aiming at the ballistic equation of the aircraft of a specific model on the basis of a neural network model obtained by offline training. Compared with the step 1, the step 2 does not need to reconstruct the neural network, and the structure and the parameters of the neural network directly inherit the result obtained after the step 1.3 is finished. As the trajectory motion equations followed by different types of aircrafts are relatively fixed, for the aircrafts with similar trajectories, only the corresponding type of neural network which is pre-selected and connected is selected as an initialization model, then the loss function is reconstructed according to the new trajectory equation according to the method in the step 1.2, the attack angle function of the aircraft is mainly changed, the regularization term of the loss function is correspondingly changed due to the change of the attack angle function, and the method in the step 1.3 is used again for training.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. An aircraft trajectory simulation method based on a neural network is characterized by comprising the following steps:
step 1, solving offline pre-training of a neural network of a ballistic equation: the method comprises the steps of constructing a neural network and fusing an aircraft trajectory motion differential equation into the neural network;
the objective of integrating the aircraft trajectory motion differential equation into the neural network is to express the aircraft trajectory equation into a regularization term of a neural network loss function, and the regularization term is connected with a neural network structure to ensure that training errors generated due to the fact that the input-output relation does not meet the trajectory motion equation are gradually reduced in the training process of the neural network;
step 2, on-line training of a neural network fused into a ballistic equation: performing secondary training aiming at a ballistic equation of an aircraft of a specific model on the basis of a neural network model obtained by offline training;
the step 1 specifically comprises the following substeps:
step 1.1, constructing a neural network;
the neural network structure comprises an input layer, an output layer and 4 hidden layers, wherein the number of nodes of the input layer is 1, the number of nodes of the output layer is 4, the number of nodes of the hidden layers are all 10, a ReLu function is used as an activation function, and AdamaOptizer is used as an optimizer of the neural network;
the input parameter of the neural network is the motion time t of the aircraft, and the output parameter is the aircraft speed v (t), the aircraft trajectory inclination angle theta (t), the aircraft x-axis displacement x (t) and the aircraft y-axis displacement y (t) which are obtained by network calculation;
step 1.2, constructing a loss function;
the loss function is used for calculating the difference between the forward calculation result of each iteration of the neural network and the true value to generate gradient information;
the loss function comprises a data term and a regularization term; the data item part adopts the mean square error MSE which is the same as that of the traditional neural network, and the regularization part is obtained according to the deformation of each differential equation in the ballistic motion differential equation set;
and 1.3, training a neural network to enable the neural network to gradually approximate to a special solution of an aircraft trajectory motion equation, so as to obtain an optimal solution of the parameters enabling the value of the loss function to be as small as possible.
2. The method for simulating the aircraft trajectory based on the neural network according to claim 1, characterized in that in step 1.3, the neural network is optimized using a tena optimizer of self-contained tenorflow.
3. The method for aircraft trajectory simulation based on neural networks as claimed in claim 1, characterized in that in step 1.3, 4-layer ANN and back propagation algorithm are used to train the network.
4. The aircraft trajectory simulation method based on the neural network as claimed in claim 1, wherein in the step 2, the structure and the parameters of the neural network are directly inherited to obtain the result after the step 1.3 is finished;
for aircraft with similar trajectory, selecting a pre-trained neural network of a corresponding type as an initialization model, then reconstructing a loss function according to a new trajectory equation according to the method of step 1.2, and training again by using the method of step 1.3.
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