CN115169233A - Hypersonic aircraft uncertain trajectory prediction method based on depth Gaussian process - Google Patents
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Abstract
The invention discloses a prediction method of an uncertain track of a hypersonic aircraft based on a depth Gaussian process, which comprises the following steps: acquiring multiple groups of parameter data related to the flight of a hypersonic aerocraft; step two, taking each group of parameter data as an input variable, and constructing a training sample set by matching time numbers corresponding to the input variables; step three, establishing a depth Gaussian process model; step four, based on the training sample set in the step two, adopting a deep Gaussian process model obtained in the step three to establish a mapping relation under the condition probability of the training sample, and obtaining an optimal solution through calculation; and step five, taking the optimal solution obtained in the step four as a weight parameter of the depth Gaussian process model, taking the test samples in the training sample set as model input, and performing trajectory prediction to obtain a prediction result of the trajectory of the hypersonic vehicle under a 95% confidence interval and probability distribution of the trajectory. The invention provides a prediction method for an uncertain track of a hypersonic aircraft based on a depth Gaussian process, which considers historical track errors caused by mismatching of maneuvering modes corresponding to an actual aircraft and training data and inaccurate parameter estimation and has stronger applicability and robustness.
Description
Technical Field
The invention relates to the field of aircraft trajectory prediction, in particular to a prediction method for uncertain trajectories of hypersonic aircrafts.
Background
Hypersonic aircrafts generally have the characteristics of high flying speed (generally more than 5 Ma), long flying distance, strong maneuverability, complex and variable ballistic trajectory and the like. The Hypersonic Glide type aircraft (HGV) reenters at Hypersonic speed, the flying height is about 25 km-120 km, and the flying airspace is located in the adjacent space and is the airspace most beneficial to penetration. The HGV trajectory is difficult to predict compared to conventional ballistic reentry vehicles. The large-range and strong-maneuvering penetration prevention capability of the HGV aircraft in the reentry process brings great difficulty to accurate target interception, and the trajectory prediction model is required to be high in accuracy and strong in real-time performance; due to the fact that the tasks are changed or the aircraft deviates from the nominal track greatly due to deviation and disturbance, the adaptability requirement of the prediction method to various types of tasks is increasing.
The research of the HGV track prediction method has important significance on national defense safety, and becomes one of the core technologies for competing for initiative in adjacent space in countries in the world. The track prediction research of the existing hypersonic flight vehicle predicts the whole track based on the known motion state of the target. For targets with strong maneuverability, the precision of the full-track prediction methods is difficult to guarantee, and the longer the track is, the worse the precision is. When a prediction model is developed by using Deep learning methods such as Deep Belief Networks (DBN), convolutional Neural Networks (CNN), recurrent Neural Networks (RNN), etc., training data is required to cover a state space of a trajectory. When there is not enough training data, or the training data does not cover some part of the state space, the machine learning model also has difficulty in giving accurate results, i.e., the traditional method cannot solve the confidence interval, and the prediction made by the traditional method belongs to uncertain trajectory prediction.
When a prediction model is developed based on a statistical learning method such as an Auto Regression (AR) model, a prediction uncertainty result can be given, but the statistical learning model is difficult to construct, and compared with a deep learning model, the generalization performance is poor.
Disclosure of Invention
An object of the present invention is to solve at least the above problems and/or disadvantages and to provide at least the advantages described hereinafter.
To achieve these objects and other advantages and in accordance with the purpose of the invention, a method for predicting an uncertain trajectory of a hypersonic aircraft based on a depth gaussian process is provided, comprising:
acquiring multiple groups of parameter data related to the flight of a hypersonic aircraft;
step two, taking each group of parameter data as an input variable, and constructing a training sample set by matching time numbers corresponding to the input variables;
step three, establishing a depth Gaussian process model;
step four, based on the training sample set in the step two, adopting a deep Gaussian process model obtained in the step three to establish a mapping relation under the condition probability of the training sample, and obtaining an optimal solution through calculation;
and step five, taking the optimal solution obtained in the step four as a weight parameter of the depth Gaussian process model, taking the test samples in the training sample set as model input, and performing trajectory prediction to obtain a prediction result of the trajectory of the hypersonic vehicle under a 95% confidence interval and probability distribution of the trajectory.
Preferably, in the step one, the parameter data is three-dimensional space coordinate, speed, track inclination angle and track azimuth change data of the hypersonic aerocraft;
the parameter data comprises analog simulation data and actual measurement data, the analog simulation data is random numbers which are normally distributed and generated by using Box-Muller transformation, the random numbers are added into a training sample set to obtain disturbed data, and the amplitude of disturbance is set to be 10% of the maximum amplitude of a track prediction section, so that possible observation errors or large-amplitude random disturbance of an aircraft are simulated;
when the method is applied, the measured data is used as a test sample, and the simulation data is used as a training sample.
Preferably, in the step one, each set of parameter data has a time sequence matched with the corresponding track, and a time number is set in each time sequence;
in step two, the training sample set is D = [ (t) i ，x i )|i＝1，2，L，n]Wherein, t i Is a time number, x i Are input variables.
Preferably, in the second step, the depth gaussian process model includes a plurality of single-layer gaussian process regression models stacked together;
the plurality of single-layer Gaussian process regression models includes: selecting a linear covariance kernel function, a periodic covariance kernel function, a Matern covariance kernel function and an exponential quadratic covariance kernel function as kernel functions of a single-layer GPR model;
mapping is achieved through single shallow layer Gaussian process control between the regression models of each layer of Gaussian process, and each shallow layer Gaussian process has independent hyper-parameters and covariance.
Preferably, in the regression problem of each single-layer gaussian process regression model:
let the output of the training set be y and the output of the test set be y * K is the covariance function, N is the mathematical representation of the distribution, D * To predict the output set, when the expected distribution is 0:
suppose there are n training points, n * Test point, then K (D, D) * ) Representing nxn calculated from all training points and all test points * An order covariance matrix;
knowing the prior obedience of y N (0,K (D, D)), p is the probability, we obtain from the multiplication:
p(y * |D，D * )＝p(y * |D * )；
by using the properties of the blocking matrix, when the prior expectation of the gaussian process is not 0 and the expectation function is μ (·), the joint distribution is:
the corresponding condition distribution is as follows:
the joint distribution of the depth gaussian process model with four hidden layers is represented as:
preferably, the depth Gaussian process model uses a test sample as an input, deduces the relation between the input and the target output based on the mapping relation, and determines the conditional distribution of the target output through the given input;
establishing a regression prediction model according to a training sample set D, wherein g is a Gaussian process and is a mean function M (x) i ) Covariance function K, i.e., g GP (M, K);
according to the definition of Gaussian process, multivariate Gaussian distribution follows multivariate variance normal distribution MVN and satisfies g (t) i )～MVN(M(x i ) K), i =1,2,l, n, converting the problem into a corresponding prediction output by a given set of training samples
In the deep Gaussian process model, the covariance function must meet the condition that each semi-positive definite symmetric function is a kernel function, so the maximum likelihood method can be adopted to self-adaptively obtain the optimal solution of the hyper-parameter phi.
The invention at least comprises the following beneficial effects: the method breaks through the defects of the traditional method in the aspects of mutation trajectory analysis and prediction trajectory uncertainty analysis by establishing a deep Gaussian process model, better solves the problems of complicated maneuvering, inaccurate parameter estimation, trajectory prediction error quantification and the like of the super-target, and has stronger robustness.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a flow chart of a prediction method for uncertain trajectory of a hypersonic vehicle based on a depth Gaussian process according to an embodiment of the invention;
FIG. 2 is an enlarged schematic view of a portion of the training data set of FIG. 1;
FIG. 3 is an enlarged schematic view of a portion of the test data set of FIG. 1;
FIG. 4 is a plot I of simulated trajectory data for a hypersonic aircraft in accordance with an embodiment of the present invention;
FIG. 5 is a second plot of simulated trajectory data for a hypersonic aircraft in accordance with an embodiment of the present invention;
FIG. 6 is a diagram of the prediction result of the uncertainty trajectory altitude of the hypersonic vehicle under the disturbance-free condition according to an embodiment of the invention;
FIG. 7 is a diagram of the prediction result of the uncertainty trajectory altitude of the hypersonic vehicle under the disturbance condition according to an embodiment of the invention.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
The invention complements the advantages of a machine learning model and an uncertain prediction model, develops a model with large state space variance and small learning model confidence coefficient, and effectively predicts the HGV glide track, in particular to the invention provides a hypersonic aircraft uncertain track prediction method based on a depth Gaussian process, which can establish a nonlinear probability statistical model of a time-varying target, breaks through the defects of the traditional method in the aspects of abrupt change track analysis and predicted track uncertainty analysis, better solves the problems of complicated maneuvering, inaccurate parameter estimation, track prediction error quantization and the like of the hypersonic target, and has stronger robustness, and the method comprises the following steps:
s1: acquiring three-dimensional space coordinates, speed, track inclination angle and track azimuth angle change data of the hypersonic aircraft, wherein the three-dimensional space coordinates, speed, track inclination angle and track azimuth angle change data comprise analog simulation data and actual measurement data, the actual measurement data can be directly used as original data, the analog simulation data is that random numbers which are normally distributed are generated by using Box-Muller transformation and are added into original training data, the amplitude of random disturbance is set to be 10% of the maximum amplitude of a track prediction section so as to simulate possible observation errors or large-amplitude random disturbance of the aircraft, in specific application, the analog data are used as training samples, and the actual measurement data are used as test samples;
s2: and constructing a training set sample consisting of a time number in the existing track time sequence and an input variable corresponding to the training data at each moment by using the simulation data, and using the training set sample to construct a track prediction model. Given a training set of existing trajectory components, D = [ (t) i ,x i )|i＝1,2,L,n]Wherein t is i And x i The input variables corresponding to the time numbers in the time sequence and the training data at each moment, namely the data corresponding to the track coordinate value (X, Y, Z), the speed, the trajectory inclination angle or the course angle;
s3: the method comprises the steps of establishing a Deep Gaussian Process (DGP) model, stacking a plurality of Gaussian Process Regression (GPR) models to form the DGP model, respectively selecting a linear covariance kernel function, a periodic covariance kernel function, a Matern covariance kernel function and an exponential quadratic covariance kernel function as kernel functions of a single-layer GPR model, controlling mapping between layers through a single shallow layer Gaussian Process, and enabling each shallow layer Gaussian Process to have independent hyper-parameters and covariance.
For the regression problem: y = f (x);
let the output of the training set be y and the output of the test set be y * When the expectation of the distribution is 0:
suppose there are n training points, n * Test point, then K (D, D) * ) Representing nxn calculated from all training points and all test points * An order covariance matrix. Given the prior obeys N of y (0,K (D, D)), the multiplication formula yields:
p(y * |D,D * )＝p(y * |D * )
using the properties of the blocking matrix, when the a priori expectation of the gaussian process is not 0, and the expectation function is μ (·), the joint distribution is:
the corresponding condition distribution is as follows:
the joint distribution of a depth gaussian process model containing four hidden layers is represented as:
the DGP model has a much stronger a priori construction than the GPR model, so that different properties of the input data can be cross-preserved.
Further, the test sample is used as input, the deep Gaussian process model establishes a mapping relation under the condition probability of the training sample, the relation between the input and the target output is automatically deduced based on the mapping relation, and the condition distribution of the target output is determined through the given input.
Establishing a regression prediction model from a training data set D, wherein g is a Gaussian process, and a mean function M (x) i ) Covariance function K, i.e., g GP (M, K).
According to the definition of Gaussian process, multivariate Gaussian distribution follows Multivariate Variance Normal distribution (MVN), and satisfies g (t) i )～MVN(M(x i ) K), i =1,2,l, n, converting the problem into a prediction output by a given training set
In the deep gaussian process model, the covariance function must satisfy the Mercer condition, i.e., each positive semidefinite symmetry function is a kernel function. Therefore, the maximum likelihood method is adopted to self-adaptively obtain the optimal solution of the over-parameter phi. And putting the input values into a model to obtain a corresponding track prediction result, and giving a high-precision prediction result of the track of the hypersonic vehicle and the probability distribution of the track of the hypersonic vehicle under a 95% confidence interval.
In the practical application, the method of the invention considers the mismatching of the practical aircraft and the maneuver mode corresponding to the training data and the historical track error caused by the inaccurate parameter estimation, and has stronger applicability and robustness.
Example (b):
referring to fig. 1 to 3, a flow of a prediction method for an uncertain trajectory of a hypersonic aircraft based on a depth gaussian process according to an embodiment of the present invention is shown, and an analysis method of the present invention includes the following steps:
referring to fig. 4, in step S1, simulation data of a three-dimensional space coordinate, a speed, a trajectory inclination angle, and a trajectory azimuth of the hypersonic aerocraft are obtained, and meanwhile, a Box-Muller transform is used to generate a normally distributed random number, which is added to original training data. The amplitude of the random disturbance is set to be 10% of the maximum amplitude of the track prediction section so as to simulate possible observation errors or large-amplitude random disturbance of the aircraft.
Referring to fig. 5, S2 constructs a training set sample composed of the time number in the existing trajectory time sequence and the input variable corresponding to the training data at each time, and uses the training set sample for constructing the trajectory prediction model. Given a training set of existing trajectory components, D = [ (t) i ,x i )|i＝1,2,L,n]Wherein t is i And x i And input variables corresponding to the time numbers in the time series and the training data at each moment, namely data corresponding to the track coordinate value (X, Y, Z), the speed, the trajectory inclination angle or the heading angle. And when the track prediction is carried out, the three-dimensional space coordinate value (X, Y, Z), the speed, the trajectory inclination angle and the heading angle of the aircraft are considered, the track between 800s and 900s in the middle section is used as a training sample, and the track of the aircraft in the future 100s is predicted by using the established HGV track prediction method based on the GPR.
Referring to fig. 6, S3 is to establish a Deep Gaussian Process (DGP) model, which is formed by stacking multiple Gaussian Process Regression (GPR) models, and respectively select a linear covariance kernel, a periodic covariance kernel, a Matern covariance kernel, and an exponential quadratic covariance kernel as kernels of a single-layer GPR model, and mapping between each layer is controlled by a single shallow Gaussian Process, and each shallow Gaussian Process has independent hyper-parameters and covariances. Further, a mapping relation under the condition probability of the training sample is established, the relation between the input vector and the target output is automatically deduced, and the condition distribution of the target output is determined through the given input vector. Establishing a regression prediction model from a training data set D, wherein g is a Gaussian process, and a mean function M (x) i ) Covariance function K, i.e., g GP (M, K).And self-adaptively solving the optimal solution of the hyper-parameter phi by adopting a maximum likelihood method. And putting the input values into a model to obtain a corresponding track prediction result, and giving a high-precision prediction result of the track of the hypersonic vehicle and the probability distribution of the track of the hypersonic vehicle under a 95% confidence interval.
The higher the confidence level, the larger the corresponding confidence interval for an estimate for a given situation.
Under the condition of no disturbance, the established model can predict the space coordinates of the test data track more accurately. In the predicted 100s corresponding tracks, the first 50s are taken as short-term prediction segments (corresponding to the tracks within 900s to 950 s), and confidence intervals are more aggregated; at a prediction segment of 50s to 100s (corresponding to a trajectory within 950s to 1000 s), the confidence interval gradually diverges.
Referring to fig. 7, normally distributed random numbers are generated using a Box-Muller transform with low temporal complexity and added to the original training data. The amplitude of the random disturbance is set to 10% of the maximum amplitude of the track prediction section. And (3) establishing a depth Gaussian process model for analysis, wherein from the result, the model established under the condition of large-amplitude random disturbance can still ensure accurate prediction of the aircraft track.
The above scheme is merely illustrative of a preferred example, and is not limiting. In the implementation of the invention, appropriate replacement and/or modification can be carried out according to the requirements of users.
The number of apparatuses and the scale of the process described herein are intended to simplify the description of the present invention. Applications, modifications and variations of the present invention will be apparent to those skilled in the art.
While embodiments of the invention have been disclosed above, it is not intended to be limited to the uses set forth in the specification and examples. It can be applied to all kinds of fields suitable for the present invention. Additional modifications will readily occur to those skilled in the art. It is therefore intended that the invention not be limited to the exact details and illustrations described and illustrated herein, but fall within the scope of the appended claims and equivalents thereof.
Claims (6)
1. A hypersonic aircraft uncertain track prediction method based on a depth Gaussian process is characterized by comprising the following steps:
acquiring multiple groups of parameter data related to the flight of a hypersonic aircraft;
step two, taking each group of parameter data as an input variable, and constructing a training sample set by matching time numbers corresponding to the input variables;
step three, establishing a depth Gaussian process model;
step four, based on the training sample set in the step two, adopting a deep Gaussian process model obtained in the step three to establish a mapping relation under the condition probability of the training sample, and obtaining an optimal solution through calculation;
and step five, taking the optimal solution obtained in the step four as a weight parameter of the depth Gaussian process model, taking the test samples in the training sample set as model input, and performing trajectory prediction to obtain a prediction result of the trajectory of the hypersonic vehicle under a 95% confidence interval and probability distribution of the trajectory.
2. The method for predicting the uncertain trajectory of the hypersonic flight vehicle based on the depth Gaussian process as claimed in claim 1, wherein in the step one, the parameter data are three-dimensional space coordinate, speed, trajectory inclination angle and trajectory azimuth angle change data of the hypersonic flight vehicle;
the parameter data comprise analog simulation data and actual measurement data, the analog simulation data are random numbers which are normally distributed and generated by using Box-Muller transformation, the random numbers are added into a training sample set to obtain disturbed data, and the amplitude of disturbance is set to be 10% of the maximum amplitude of a track prediction section, so that observation errors which possibly exist or large random disturbance of an aircraft can be simulated;
during application, the measured data is used as a test sample, and the simulation data is used as a training sample.
3. The hypersonic aircraft uncertain trajectory prediction method based on the depth Gaussian process as claimed in claim 1, characterized in that in step one, each set of parameter data has a time series matched with the corresponding trajectory, and each time series is provided with a time number;
in step two, the training sample set is D = [ (t) i ，x i )|i＝1，2，L，n]Wherein, t i Is a time number, x i Are input variables.
4. The method for predicting the uncertain trajectory of the hypersonic aircraft based on the depth Gaussian process as claimed in claim 1, wherein in the second step, the depth Gaussian process model comprises a plurality of single-layer Gaussian process regression models which are stacked;
the plurality of single-layer Gaussian process regression models includes: selecting a linear covariance kernel function, a periodic covariance kernel function, a Matern covariance kernel function and an exponential quadratic covariance kernel function as kernel functions of a single-layer GPR model;
mapping is achieved through single shallow layer Gaussian process control between the regression models of the Gaussian processes of each layer, and each shallow layer Gaussian process has independent hyper-parameters and covariance.
5. The method for predicting the uncertain trajectory of the hypersonic flight vehicle based on the depth Gaussian process as claimed in claim 4, wherein in the regression problem of the regression model of each single-layer Gaussian process:
let the output of the training set be y and the output of the test set be y * K is the covariance function, N is the mathematical representation of the distribution, D * To predict the output set, when the expectation of the distribution is 0:
suppose there are n training points, n * Test point, then K (D, D) * ) Representing nxn calculated from all training points and all test points * An order covariance matrix;
given that y is a priori obeyed by N (0,K (D, D)), p is a probability, we obtain from the multiplication formula:
p(y * |D，D * )＝p(y * |D * )；
by using the properties of the blocking matrix, when the prior expectation of the gaussian process is not 0 and the expectation function is μ (·), the joint distribution is:
the corresponding condition distribution is as follows:
the joint distribution of the depth gaussian process model with four hidden layers is represented as:
6. the method for predicting the uncertain trajectory of the hypersonic aircraft based on the depth Gaussian process as claimed in claim 4, wherein the depth Gaussian process model is used for deducing the relation between the input and the target output based on the mapping relation by taking a test sample as the input, and determining the condition distribution of the target output according to the given input;
establishing a regression prediction model according to a training sample set D, wherein g is a Gaussian process and is a mean function M (x) i ) Covariance function K, i.e., g GP (M, K);
according to the definition of Gaussian process, the multivariate Gaussian distribution follows the multivariate variance normal distribution MVN and satisfies g (t) i )～MVN(M(x i ) K), i =1,2,l, n, converting the problem to pass through a given training sampleCollecting corresponding predicted output
In the deep Gaussian process model, the covariance function must meet the condition that each semi-positive definite symmetric function is a kernel function, so the optimal solution of the hyper-parameter phi is obtained in a self-adaptive manner through a maximum likelihood method.
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| CN117874712A (en) * | 2024-03-11 | 2024-04-12 | 四川省光为通信有限公司 | Single-mode non-airtight optical module performance prediction method based on Gaussian process regression |
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