A method for predicting trajectory parameters of rotating projectiles based on reduced-order model and multi-layer perceptron

Abstract

A method for predicting the trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron is provided, which belongs to the field of flight mechanics and artificial intelligence technology, and includes generating a rotating projectile trajectory sample data set; reducing the order of the rotating projectile trajectory sample data to obtain the fundamental mode of the trajectory parameters and the corresponding modal coefficient information; using a multi-layer perceptron to establish a prediction model from the initial launch state to the fundamental modal coefficient of the trajectory parameters; using the constructed model for the prediction of the fundamental modal coefficient of the trajectory parameters, and combining the obtained fundamental mode to achieve rapid prediction of the trajectory parameters of the rotating projectile. The present invention is based on model reduction technology and combined with a multi-layer perceptron neural network, which can well learn the characteristics of the trajectory parameters, achieve rapid and accurate prediction of the trajectory parameters, and reduce the time consumption of large-scale high-precision trajectory calculations. When establishing the prediction model, the present invention first performs clustering processing on the initial state parameters to improve the modeling accuracy and reduce the prediction error.

Description

Technical Field

[0001] The invention belongs to the technical field of missile trajectory parameter prediction, and in particular relates to a method for predicting the trajectory parameters of a rotating missile based on a reduced-order model and a multi-layer perceptron. Background Art

[0002] In the design and development stage of rotating projectiles, a large number of time-consuming and high-precision CFD / RBD coupling simulation tests are required to evaluate the aerodynamic characteristics, stability, flight trajectory and other performance parameters of the designed rotating projectile shape. When the initial state of the rotating projectile changes, the CFD / RBD coupling calculation needs to be re-executed, resulting in low efficiency in design and evaluation; in fact, the ballistic parameters of the rotating projectile obtained under different initial states have similar physical characteristics, and the use of reduced-order models and neural networks can capture and learn these characteristics and achieve rapid prediction of ballistic parameters. Therefore, it is necessary and widely needed to develop a method for rapid prediction of the ballistic parameters of rotating projectiles under different initial states. Summary of the invention

[0003] The technical problem solved by the present invention is: to provide a method for predicting the ballistic parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron, so as to extract the ballistic parameter characteristics of a rotating projectile with a variable initial state, realize rapid and accurate prediction of the ballistic parameters of a rotating projectile under different initial states, reduce the time-consuming problem of a large number of CFD / RBD coupling calculations caused by the change of initial state parameters in the design and performance evaluation of the rotating projectile, and improve the calculation efficiency.

[0004] The technical solution adopted by the present invention is a method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron, comprising the following steps:

[0005] 1) Generate a sample data set of rotating projectile trajectories under different initial states; the specific steps are as follows:

[0006] 1-1): Select a rotating missile configuration and generate the aerodynamic calculation grid of the rotating missile;

[0007] 1-2): Determine the initial state parameter design space of the rotating projectile, including 9 state parameters including three-axis velocity, angular velocity and attitude angle, and use Latin hypercube sampling method to obtain 150 initial state parameter samples;

[0008] 1-3): Using the aerodynamic calculation grid in step 1-1), the initial state parameter sample obtained in step 1-2) is subjected to computational fluid dynamics CFD / rigid body dynamics RBD coupling simulation calculation to obtain a rotating projectile trajectory sample data set;

[0009] 2): The rotating projectile trajectory sample data in step 1-3) is reduced in order using the intrinsic orthogonal decomposition (POD) method to obtain the fundamental mode of each parameter and its corresponding fundamental mode coefficient;

[0010] 3): Cluster the initial state parameter samples obtained in step 1-2) and divide them into 15 categories;

[0011] 4): Using a multi-layer perceptron neural network MLP, a prediction model is established from the initial state parameter data after clustering in step 3) to the fundamental modal coefficient data of the ballistic parameters in step 2), and the POD-MLP model for rapid prediction of ballistic parameters is completed;

[0012] 5): The POD-MLP model in step 4) is used to quickly predict the trajectory parameters of a rotating projectile whose initial state parameters have changed; the specific steps are as follows:

[0013] 5-1): Give the new initial state parameters of the rotating projectile;

[0014] 5-2): The initial state parameters in step 5-1) are used as the input of the POD-MLP model trained in step 4) to predict the fundamental modal coefficients of the trajectory parameters;

[0015] 5-3): Using the fundamental mode coefficients predicted in step 5-2) and the fundamental modes obtained in step 2), the ballistic parameter data to be predicted are reconstructed.

[0016] In the above step 1-1), the rotating missile configuration is an ARL tail rotating missile; the aerodynamic calculation grid is an unstructured hybrid grid, and the whole set of grids contains 20816 surface grids and 811923 individual grids; the boundary layer grid uses triangular prism units, the first layer height is 1e-6m, there are 25 layers in total, and the growth rate is 1.2; tetrahedral units are used in other areas.

[0017] In the above steps 1-2), the total number of samples obtained using Latin hypercube sampling is 150, of which 90% are used for training and 10% are used for testing; the initial state parameters are the three-axis speed, angular velocity and attitude angle of the rotating missile, wherein the pitch angle value range is -8 to 8°, the roll angle value range is 0 to 15°, the yaw angle value range is -3 to 3°, the roll angular velocity value range is 300 to 3000 rad / s, the pitch angular velocity value range is -65 to 85 rad / s, the yaw angular velocity value range is -60 to 60 rad / s, the axial velocity value range is 981 to 1030 m / s, the normal velocity value range is -225 to 190 m / s, and the lateral velocity value range is -200 to 145 m / s.

[0018] In the above steps 1-3), the spatial discretization of the fluid mechanics CFD calculation adopts the Roe format, and the turbulence model is the SA model; the six-degree-of-freedom equation is solved using the fourth-order variable step Adams estimation correction method; a total of 1000 steps of fluid mechanics CFD / rigid body dynamics RBD coupling calculation are performed, and each state parameter includes 150×1000 data points.

[0019] In the above step 2), each state parameter in the rotating projectile trajectory sample data is reduced to a lower order by using the proper orthogonal decomposition (POD) method to obtain the fundamental mode of each parameter and its corresponding fundamental mode coefficient, a total of 9 groups of fundamental modes and corresponding fundamental mode coefficients.

[0020] In the above step 3), the 150 initial state parameters in steps 1-2) are divided into 15 categories using the k-means clustering algorithm.

[0021] In the above step 4), a total of 9 parameters of the initial state parameters after clustering processing in step 3) are used as the input of the multi-layer perceptron neural network MLP, and the fundamental mode coefficients obtained by reducing the order of each state parameter in the rotating projectile trajectory sample data in step 2) by the proper orthogonal decomposition POD method are used as the output of the multi-layer perceptron neural network MLP. A POD-MLP rotating projectile trajectory parameter prediction model is established for each ballistic state parameter and trained, and a total of 9 prediction models are established.

[0022] The advantages of the present invention compared with the prior art are:

[0023] 1. This technical solution combines the POD reduction model and the MLP neural network to learn the characteristics of the trajectory parameters, realize the rapid and accurate prediction of the trajectory parameters of the rotating projectile under different initial states, and improve the calculation efficiency;

[0024] 2. The ballistic parameter rapid prediction model proposed in this technical solution is suitable for predicting the ballistic parameters when the initial state parameters of a rotating projectile change significantly, and has a high model generalization ability;

[0025] 3. Before using the MLP neural network to establish the prediction model, this technical solution clusters the model input, namely 150 groups of initial state parameters, which can effectively improve the modeling accuracy and reduce the prediction error of the trajectory parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A flowchart of the modeling process of the trajectory parameter prediction model of a rotating projectile based on a reduced-order model and a multi-layer perceptron neural network in the present invention;

[0027] Figure 2Schematic diagram of the geometric shape and aerodynamic calculation grid of the rotating projectile in the present invention, a is the geometric shape diagram of the rotating projectile, and b is the aerodynamic calculation grid of the rotating projectile;

[0028] Figure 3 It is a diagram of the energy proportion of each modal order of the state parameters of the rotating missile in the present invention, a is the energy proportion of the first 5 fundamental modes of the pitch angle, and b is the energy proportion of the first 20 fundamental modes of the pitch angular velocity;

[0029] Figure 4 are the prediction results of trajectory parameters in the present invention, a is the comparison between the actual and predicted results of pitch angle under three different initial states, b is the prediction error diagram of pitch angle under three different initial states, c is the comparison between the actual and predicted results of pitch angular velocity under three different initial states, and d is the prediction error diagram of pitch angular velocity under three different initial states. DETAILED DESCRIPTION

[0030] The following will be combined with the embodiments of the present invention Figure 1-4 , the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. 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.

[0031] It should be noted that, in this article, the terms "include", "comprises" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions. The elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0032] See also Figure 1 , details the embodiments of the present invention

[0033] The method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron includes the following steps:

[0034] 1) Generate a sample data set of rotating projectile trajectories under different initial states; the specific steps are as follows:

[0035] 1-1): This embodiment selects the ARL tail rotating bomb configuration, and the geometrical shape diagram is as follows Figure 2 As shown; the aerodynamic calculation grid used is an unstructured hybrid grid, such as Figure 3As shown in the figure, the whole set of grids contains 20816 surface grids and 811923 body grids; the boundary layer grid uses triangular prism elements, the first layer height is 1e-6m, there are 25 layers in total, and the growth rate is 1.2; tetrahedral elements are used in other areas;

[0036] 1-2): Determine the initial state parameter design space of the rotating missile, including 9 state parameters including three-axis velocity, angular velocity and attitude angle, among which the pitch angle ranges from -8 to 8°, the roll angle ranges from 0 to 15°, the yaw angle ranges from -3 to 3°, the roll angular velocity ranges from 300 to 3000 rad / s, the pitch angular velocity ranges from -65 to 85 rad / s, the yaw angular velocity ranges from -60 to 60 rad / s, the axial velocity ranges from 981 to 1030 m / s, the normal velocity ranges from -225 to 190 m / s, and the lateral velocity ranges from -200 to 145 m / s. The total number of samples is 150, of which 90% are used for training and 10% are used for testing;

[0037] 1-3): Using the aerodynamic calculation grid in step 1-1), the initial state parameter sample obtained in step 1-2) is subjected to computational fluid dynamics CFD / rigid body dynamics RBD coupling simulation calculation to obtain a rotating projectile trajectory sample data set; wherein, the spatial discretization in fluid dynamics CFD calculation adopts the Roe format, and the turbulence model is the SA model; the four-order variable step Adams estimation correction method is adopted to solve the six-degree-of-freedom equation; a total of 1000 steps of fluid dynamics CFD / rigid body dynamics RBD coupling calculation are performed, and each state parameter includes 150×1000 data points;

[0038] 2): Use the intrinsic orthogonal decomposition POD to establish a POD reduction model for each state parameter (speed, angular velocity, attitude angle) in the rotating ballistic sample data in steps 1-3), select the number of fundamental modes corresponding to the fundamental mode energy ratio greater than 99% after analysis, and the number of fundamental modes selected for different state parameters is different, and the reduced fundamental modes and corresponding coefficients, sample means, and mapping matrix data are obtained. In this embodiment, the pitch angle and pitch angular velocity are taken as examples, and the number of fundamental modes can be selected as 5 and 20 respectively. Figure 3 In the figure, a) is the energy proportion of the first 5 fundamental modes of pitch angle, and b) is the energy proportion of the first 20 fundamental modes of pitch angular velocity;

[0039] 3): The initial state parameter samples obtained in step 1-2) are clustered using the k-means clustering algorithm and divided into 15 categories;

[0040] 4): Use a multi-layer perceptron neural network MLP to establish a prediction model from the initial state parameter data after clustering in step 3) to the fundamental modal coefficient data of the ballistic parameters in step 2), and complete the construction of the POD-MLP model for rapid prediction of ballistic parameters; specifically, the initial state parameters after clustering in step 3) totaling 9 parameters are used as the input of the multi-layer perceptron neural network MLP, and the fundamental modal coefficients obtained by reducing the order of each state parameter in the rotating projectile ballistic sample data in step 2) by the intrinsic orthogonal decomposition POD method are used as the output of the multi-layer perceptron neural network MLP. A POD-MLP rotating projectile ballistic parameter prediction model is established for each ballistic state parameter and trained, and a total of 9 prediction models are established.

[0041] 5): The POD-MLP model in step 4) is used to quickly predict the trajectory parameters of a rotating projectile whose initial state parameters have changed; the specific steps are as follows:

[0042] 5-1): Give the new initial state parameters of the rotating projectile;

[0043] 5-2): The initial state parameters in step 5-1) are used as the input of the POD-MLP model trained in step 4) to predict the fundamental modal coefficients of the trajectory parameters;

[0044] 5-3): Reconstruct the trajectory parameter data to be predicted using the fundamental mode coefficients predicted in step 5-2) and the fundamental mode obtained in step 2); Figure 4 The prediction results of the pitch angle and pitch angular velocity parameters of a rotating missile under three different initial states are given, where a is the comparison between the actual and predicted results of the pitch angle under three different initial states, b is the prediction error diagram of the pitch angle under three different initial states, c is the comparison between the actual and predicted results of the pitch angular velocity under three different initial states, and d is the prediction error diagram of the pitch angular velocity under three different initial states.

[0045] The technical solution combines the POD reduced-order model and the MLP neural network, which can well learn the ballistic parameter characteristics, realize rapid and accurate prediction of the ballistic parameters of rotating projectiles under different initial states, and improve calculation efficiency; the ballistic parameter rapid prediction model proposed in the present invention is suitable for the prediction of ballistic parameters when the initial state parameters of rotating projectiles change greatly, and has a high model generalization ability; before using the MLP neural network to establish the prediction model, the present invention performs clustering processing on the input of the model, that is, 150 groups of initial state parameters, which can effectively improve the modeling accuracy and reduce the prediction error of the trajectory parameters.

[0046] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0047] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron, characterized in that The following steps are involved: 1) Generate a sample data set of rotating projectile trajectories under different initial states; the specific steps are as follows: 1-1): Select a rotating missile configuration and generate the aerodynamic calculation grid of the rotating missile; 1-2): Determine the initial state parameter design space of the rotating projectile, including 9 state parameters including three-axis velocity, angular velocity and attitude angle, and use Latin hypercube sampling method to obtain 150 initial state parameter samples; 1-3): Using the aerodynamic calculation grid in step 1-1), a computational fluid dynamics (CFD) / rigid body dynamics (RBD) coupling simulation calculation is performed on the initial state parameter sample obtained in step 1-2) to obtain a rotating projectile trajectory sample data set; 2): The rotating ballistic sample data in step 1-3) is reduced in order using the proper orthogonal decomposition (POD) method to obtain the fundamental mode of each parameter and its corresponding fundamental mode coefficient; 3): Cluster the initial state parameter samples obtained in step 1-2) and divide them into 15 categories; 4): Using a multi-layer perceptron neural network MLP, a prediction model is established from the initial state parameter data after clustering in step 3) to the fundamental modal coefficient data of the ballistic parameters in step 2), and the POD-MLP model for rapid prediction of ballistic parameters is completed; 5): The POD-MLP model in step 4) is used to quickly predict the trajectory parameters of a rotating projectile whose initial state parameters have changed; the specific steps are as follows: 5-1): Give the new initial state parameters of the rotating projectile; 5-2): The initial state parameters in step 5-1) are used as the input of the POD-MLP model trained in step 4) to predict the fundamental modal coefficients of the trajectory parameters; 5-3): Using the fundamental mode coefficients predicted in step 5-2) and the fundamental modes obtained in step 2), the ballistic parameter data to be predicted are reconstructed.

2. The method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron according to claim 1, characterized in that: In the above step 1-1), the rotating missile configuration is an ARL tail rotating missile; the aerodynamic calculation grid is an unstructured hybrid grid, and the whole set of grids contains 20816 surface grids and 811923 individual grids; the boundary layer grid uses triangular prism units, the first layer height is 1e-6m, there are 25 layers in total, and the growth rate is 1.2; tetrahedral units are used in other areas.

3. The method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron according to claim 1, characterized in that: In the above steps 1-2), the total number of samples obtained using Latin hypercube sampling is 150, of which 90% are used for training and 10% are used for testing; the initial state parameters are the three-axis speed, angular velocity and attitude angle of the rotating missile, wherein the pitch angle value range is -8 to 8°, the roll angle value range is 0 to 15°, the yaw angle value range is -3 to 3°, the roll angular velocity value range is 300 to 3000 rad / s, the pitch angular velocity value range is -65 to 85 rad / s, the yaw angular velocity value range is -60 to 60 rad / s, the axial velocity value range is 981 to 1030 m / s, the normal velocity value range is -225 to 190 m / s, and the lateral velocity value range is -200 to 145 m / s.

4. The method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron according to claim 1, characterized in that: In the above steps 1-3), the spatial discretization of the fluid mechanics (CFD) calculation adopts the Roe format, and the turbulence model is the SA model; the six-degree-of-freedom equation is solved using the fourth-order variable step Adams estimation correction method; a total of 1000 steps of fluid mechanics (CFD) / rigid body dynamics (RBD) coupling calculations are performed, and each state parameter includes 150×1000 data points.

5. The method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron according to claim 1, characterized in that: In the above step 2), each state parameter in the rotating projectile trajectory sample data is reduced to a lower order by using the proper orthogonal decomposition (POD) method to obtain the fundamental mode of each parameter and its corresponding fundamental mode coefficient, a total of 9 groups of fundamental modes and corresponding fundamental mode coefficients.

6. The method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron according to claim 1, characterized in that: In the above step 3), the 150 initial state parameters in steps 1-2) are divided into 15 categories using the k-means clustering algorithm.

7. The method for predicting trajectory parameters of a rotating projectile based on a reduced-order model and a multi-layer perceptron according to claim 1, characterized in that: In the above step 4), the fundamental mode coefficients obtained by reducing the order of the initial characteristic orthogonal decomposition POD method after clustering in step 3) are used as the multi-layer perceptron state parameters, a total of 9 parameters, as the input of the multi-layer perceptron neural network MLP. Each state parameter in the rotating projectile trajectory sample data in step 2) is output through the local neural network MLP. A POD-MLP rotating projectile trajectory parameter prediction model is established for each trajectory state parameter and trained. A total of 9 prediction models are established.

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