Stratospheric airship flight trajectory envelope prediction method based on uncertainty model

Abstract

The invention belongs to the technical field of flight path envelope prediction, and relates to a stratospheric airship flight path envelope prediction method based on an uncertainty model, and the method comprises the steps: obtaining a work task of a stratospheric airship, and building a flight path envelope prediction scene of the stratospheric airship; forecast wind field data are obtained, wind field information in a working area during the stratospheric airship air staying period is determined, and a wind field uncertainty model is obtained; according to the working scene and the scene information of the stratospheric airship, a working strategy of the stratospheric airship is formulated; according to the working strategy of the stratospheric airship, the three-degree-of-freedom kinematics model, the aerodynamic model, the wind field uncertainty model and the flight path envelope prediction scene, generating a flight path point set of the stratospheric airship in different limit scenes; and carrying out contour extraction on the flight path point set of the stratospheric airship in different limit scenes to obtain a flight path envelope. The method can predict the flight path envelope of the stratospheric airship.

Description

Technical Field

[0001] The present application relates to the technical field of flight trajectory envelope prediction, and particularly to a method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model. Background Art

[0002] With the development of technology and the progress of techniques, stratospheric airships have received increasing attention and research.

[0003] The prediction of the flight envelope of a stratospheric airship is an important research direction in the field of flight control. The purpose is to predict the trajectory of the aircraft in the future time period and determine its movement range. For aircraft such as stratospheric airships whose flight trajectories are easily affected by the wind field, reliable flight trajectory envelope prediction technology can effectively support the formulation of flight test plans and the analysis of test risks.

[0004] In the prior art, researchers' research on aircraft trajectory envelopes or similar mainly focuses on traditional aircraft such as hypersonic aircraft, launch vehicles, and satellites. However, the current research on the flight trajectory envelope of stratospheric airships is almost blank. This is because stratospheric airships have the characteristics of low dynamics, large inertia, long time delay, and being greatly affected by the environment, and their flight principles are very different from those of traditional aircraft. If relying on relevant methods or literature for traditional aircraft trajectory envelope prediction, large deviations often occur, resulting in inaccurate predictions. Summary of the Invention

[0005] Based on this, it is necessary to provide a method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model to accurately predict the flight trajectory envelope of the stratospheric airship for the above technical problems.

[0006] The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model includes:

[0007] Obtain the work tasks of the stratospheric airship, and determine the working parameters, working scenarios, and scenario information of the stratospheric airship to establish a flight trajectory envelope prediction scenario for the stratospheric airship;

[0008] Obtain the predicted wind field data during the time period when the stratospheric airship executes the work tasks, and determine the wind field information in the working area during the hovering period of the stratospheric airship;

[0009] According to the wind field information in the working area during the hovering period of the stratospheric airship, obtain a wind field uncertainty model;

[0010] According to the working parameters of the stratospheric airship, a three-degree-of-freedom kinematic model of the stratospheric airship is established; considering the change of the wind field, an aerodynamic model of the stratospheric airship is established; according to the working scenario of the stratospheric airship and the scenario information, a working strategy of the stratospheric airship is formulated; according to the working strategy, the three-degree-of-freedom kinematic model, the aerodynamic model, the wind field uncertainty model and the flight trajectory envelope prediction scenario of the stratospheric airship, a set of flight trajectory points of the stratospheric airship under different extreme scenarios is generated.

[0011] Extract the contour of the set of flight trajectory points of the stratospheric airship under different extreme scenarios to obtain the flight trajectory envelope.

[0012] In one embodiment, after obtaining the trajectory envelope, it further includes:

[0013] Adopt the kernel density estimation method, select the two-dimensional Gaussian kernel distribution as the kernel function, and consider the adaptive bandwidth of the kernel function to calculate the distribution probability density of each trajectory point in the flight trajectory point set.

[0014] According to the distribution probability density of each trajectory point, calculate the distribution probability of the entire trajectory to obtain the distribution characteristics and distribution laws of the trajectory.

[0015] In one embodiment, obtain the predicted wind field data during the period when the stratospheric airship performs its work tasks, and determine the wind field information in the working area during the hovering period of the stratospheric airship, including:

[0016] Obtain the predicted wind field data during the period when the stratospheric airship performs its work tasks, perform interpolation processing on the predicted wind field data to obtain the wind field data at the working altitude of the stratospheric airship.

[0017] Perform interpolation processing on the wind field data at the working altitude of the stratospheric airship to obtain the meridional wind speed and zonal wind speed at any point on the horizontal plane where the working altitude of the stratospheric airship is located.

[0018] According to the meridional wind speed and zonal wind speed, calculate the wind field direction data and wind field speed data, and use the wind field direction data and wind field speed data as the wind field information in the working area during the hovering period of the stratospheric airship.

[0019] In one embodiment, according to the wind field information in the working area during the hovering period of the stratospheric airship, obtain the wind field uncertainty model, including:

[0020] According to the wind field direction data in the wind field information in the working area during the hovering period of the stratospheric airship, construct a wind direction uncertainty model.

[0021] According to the wind field speed data in the wind field information in the working area during the hovering period of the stratospheric airship, construct a wind speed uncertainty model.

[0022] Based on the wind direction uncertainty model and the wind speed uncertainty model, a wind field uncertainty model is obtained.

[0023] In one embodiment, the wind direction uncertainty model is described using the Von Mises distribution, and its probability density function is expressed as:

[0024]

[0025] In the formula, is the wind direction probability density, θ i is the wind direction, is the wind direction in the predicted wind field data, κ is the concentration degree of the wind direction, and I0(κ) is the Bessel modified function of order 0;

[0026] The wind speed uncertainty model is described using the Gaussian distribution, and its probability density is expressed as:

[0027]

[0028] Wherein,

[0029]

[0030] In the formula, is the wind speed probability density, w i is the wind speed, is the magnitude of the wind speed in the predicted wind field data, σ i is the standard deviation of the Gaussian distribution, and ρ is the parameter of the distribution amplitude.

[0031] In one embodiment, the set of flight trajectory points of the stratospheric airship under different extreme scenarios refers to: the set of trajectory points generated when the stratospheric airship flies according to the flight strategy when taking the limit values in different directions with different uncertainties of the wind field uncertainty model.

[0032] In one embodiment, the working scenarios of the stratospheric airship include: the regional residence scenario or the transfer flight scenario.

[0033] In one embodiment, contour extraction is performed on the set of flight trajectory points of the stratospheric airship under different extreme scenarios to obtain a flight trajectory envelope, including:

[0034] Using the Alpha-Shapes method, a circle that rolls along the edge of the set of flight trajectory points and does not fall into the set of trajectory points is determined as the rolling circle;

[0035] Taking any point in the set of flight trajectory points as the starting point, a neighborhood point set is composed of all points whose distance from the starting point is not greater than twice the radius of the circle;

[0036] Take any point in the neighborhood point set as the trajectory point, and calculate the rolling circle determined by the starting point and the trajectory point;

[0037] According to the rolling circle, extract the contour of the flight trajectory point set of the stratospheric airship under different extreme scenarios to obtain the flight trajectory envelope.

[0038] In one embodiment, the kernel density estimation method is adopted, the two-dimensional Gaussian kernel distribution is selected as the kernel function, and the adaptive bandwidth of the kernel function is considered to calculate the distribution probability density of each trajectory point in the flight trajectory point set, including:

[0039]

[0040] In the formula, f(x i ,y i ) is the distribution probability density of each trajectory point in the flight trajectory point set, (x i ,y i ) is the i-th trajectory point in the flight trajectory point set, μ1 is the average value of x i , σ1 is the variance of x i , σ2 is the variance of y i , r h is the distance to the trajectory point (x i ,y i ), h i is the bandwidth of the i-th trajectory point.

[0041] The above method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model generates a flight trajectory point set of the stratospheric airship under different extreme scenarios according to the working strategy, three-degree-of-freedom kinematic model, aerodynamic model, wind field uncertainty model, and flight trajectory envelope prediction scenario of the stratospheric airship, so as to predict the flight trajectory envelope of the stratospheric airship, can determine the boundary of the flight trajectory of the stratospheric airship under different working scenarios, generate the flight trajectories under four 3-Sigma uncertainty limit scenarios, and extract the flight trajectory envelope of the stratospheric airship according to the trajectory point set. Moreover, the flight trajectory envelope of the stratospheric airship is accurate, reasonable, and effective, and is applicable to determining the boundary of the flight area of the stratospheric airship before it executes a flight mission, providing strong support for the formulation of the flight test plan and flight risk assessment of the stratospheric airship, and ensuring the safety of the stratospheric airship in performing tasks. Brief Description of the Drawings

[0042] Figure 1 is a schematic flow chart of a method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment;

[0043] Figure 2 is for a method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment in the wind direction When, the distribution probability density diagrams of the downwind direction under different κ values (κ representing the concentration degree of the wind direction distribution takes 0, 0.5, 1, 2, 4, 8 respectively);

[0044] Figure 3 For the prediction method of the flight trajectory envelope of a stratospheric airship based on an uncertainty model in a wind direction in one embodiment When, the distribution probability density diagrams of the downwind direction under different κ values (κ representing the concentration degree of the wind direction distribution takes 0, 0.5, 1, 2, 4, 8 respectively);

[0045] Figure 4 For the prediction method of the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment when the wind speed magnitude in the predicted wind field is The wind speed probability density diagrams corresponding to different σ values (σ represents the variance of the wind speed distribution) when ρ = 0.2;

[0046] Figure 5 Schematic diagram of the regional residence strategy of the prediction method of the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment;

[0047] Figure 6 Prediction result diagram of the flight trajectory envelope with a regional residence scenario duration of 10 days for the prediction method of the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment;

[0048] Figure 7 Contour map of the flight trajectory distribution probability of the regional residence scenario of the prediction method of the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment;

[0049] Figure 8 Prediction result diagram of the flight trajectory envelope of the transition flight scenario of the prediction method of the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment;

[0050] Figure 9 Contour map of the flight trajectory distribution probability of the transition flight scenario of the prediction method of the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment;

[0051] Figure 10 Structure block diagram of the prediction device of the flight trajectory envelope of a stratospheric airship based on an uncertainty model in one embodiment. Specific implementation manner

[0052] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0053] In addition, in the present application, descriptions such as "first" and "second" are only for descriptive purposes and cannot be construed as indicating or implying their relative importance or implicitly indicating the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include at least one such feature. In the description of the present application, the meaning of "multiple groups" is at least two groups, such as two groups, three groups, etc., unless otherwise specifically defined.

[0054] In the present application, unless otherwise clearly specified and limited, terms such as "connection" and "fixation" shall be understood in a broad sense. For example, "fixation" may be a fixed connection, a detachable connection, or integrated; it may be a mechanical connection, an electrical connection, a physical connection or a wireless communication connection; it may be directly connected, or indirectly connected through an intermediate medium, and may be the communication inside two components or the interaction relationship between two components, unless otherwise clearly limited. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific circumstances.

[0055] In addition, the technical solutions between various embodiments of the present application can be combined with each other, but it must be based on the fact that those of ordinary skill in the art can implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present application.

[0056] The present application provides a method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model. As Figure 1 shown in the schematic flowchart, in one embodiment, it includes the following steps.

[0057] Step 101: Obtain the working task of the stratospheric airship, and determine the working parameters, working scenarios and scenario information of the stratospheric airship to establish a flight trajectory envelope prediction scenario for the stratospheric airship.

[0058] Specifically:

[0059] Obtain the working task of the stratospheric airship, and determine the working parameters of the stratospheric airship: the mass m of the stratospheric airship, the volume U, the axial added mass coefficient k1, the lateral added mass coefficient k2, the axial drag coefficient C d1 and the lateral drag coefficient Cd2 , the yaw ability ω of the stratospheric airship max , the average wind resistance speed v ave , the maximum wind resistance speed v max ;

[0060] Obtain the work tasks of the stratospheric airship and determine the work scenarios of the stratospheric airship: area residence scenario or transfer flight scenario;

[0061] According to the work scenarios of the stratospheric airship, determine the scenario information of the stratospheric airship. Specifically: if the work scenario of the stratospheric airship is the area residence scenario, it is necessary to obtain the longitude and latitude coordinates of the area residence center, the area residence radius, and the residence strategy; if the work scenario of the stratospheric airship is the transfer flight scenario, it is necessary to obtain the longitude and latitude coordinates of the transfer starting position, the longitude and latitude coordinates of the transfer target position, and the flight strategy;

[0062] According to the work parameters, work scenarios, and scenario information of the stratospheric airship, establish a flight trajectory envelope prediction scenario for the stratospheric airship.

[0063] In this step, how to establish a flight trajectory envelope prediction scenario for the stratospheric airship according to the work parameters, work scenarios, and scenario information of the stratospheric airship belongs to the prior art and will not be elaborated here.

[0064] Step 102, obtain the predicted wind field data during the period when the stratospheric airship executes the work tasks, and determine the wind field information in the work area during the hovering period of the stratospheric airship.

[0065] Specifically:

[0066] Obtain the predicted wind field data during the period when the stratospheric airship executes the work tasks, and perform interpolation processing on the predicted wind field data to obtain the wind field data at the working height of the stratospheric airship;

[0067] Perform interpolation processing on the wind field data at the working height of the stratospheric airship to obtain the meridional wind speed and zonal wind speed at any point on the horizontal plane where the working height of the stratospheric airship is located;

[0068] According to the meridional wind speed and zonal wind speed, calculate the wind field wind direction data and wind field wind speed data, and use the wind field wind direction data and wind field wind speed data as the wind field information in the work area during the hovering period of the stratospheric airship.

[0069] More specifically:

[0070] Obtain the predicted wind field data during the period when the stratospheric airship executes the work tasks, and the predicted wind field data includes the meridional wind speed and zonal wind speed of different altitude wind layers;

[0071] Interpolate the meridional wind speed and zonal wind speed of different altitude wind layers respectively. Use Spline interpolation between wind layers to obtain the wind field data at the working altitude of the stratospheric airship;

[0072] In the horizontal plane, perform bilinear interpolation on the wind field data at the working altitude of the stratospheric airship to obtain the meridional wind speed v windv and the zonal wind speed v windu at any point in the horizontal plane where the stratospheric airship works, which are used as the wind field information at the position of the stratospheric airship;

[0073] According to the meridional wind speed v windv and the zonal wind speed v windu , calculate the wind field wind direction data:

[0074]

[0075] where θ w is the wind field wind direction data, v windv is the meridional wind speed, and v windu is the zonal wind speed;

[0076] According to the meridional wind speed v windv and the zonal wind speed v windu , calculate the wind field wind speed data:

[0077]

[0078] where v w is the wind field wind speed data, v windu is the zonal wind speed, and v windv is the meridional wind speed;

[0079] Use the wind field wind direction data and the wind field wind speed data as the wind field information in the working area during the hovering of the stratospheric airship.

[0080] In this step, the specific interpolation process belongs to the prior art and will not be elaborated here.

[0081] Step 103: Obtain the wind field uncertainty model according to the wind field information in the working area during the hovering of the stratospheric airship.

[0082] Specifically:

[0083] Construct a wind direction uncertainty model according to the wind field wind direction data in the wind field information in the working area during the hovering of the stratospheric airship;

[0084] Construct a wind speed uncertainty model according to the wind field wind speed data in the wind field information in the working area during the hovering of the stratospheric airship;

[0085] Based on the wind direction uncertainty model and the wind speed uncertainty model, a wind field uncertainty model is obtained.

[0086] More specifically:

[0087] Based on the wind direction data in the wind field information within the working area during the hovering of the stratospheric airship, a wind direction uncertainty model is constructed. The wind direction uncertainty model is described by the Von Mises distribution, and its probability density function is expressed as:

[0088]

[0089] In the formula, is the wind direction probability density; θ i is the wind direction; is the wind direction in the predicted wind field data, and its value range is [0, 2π]; κ is the concentration degree of the wind direction. When κ → 0, the wind direction distribution is more dispersed. When κ → ∞, the wind direction distribution is more concentrated; I0(κ) is the Bessel modified function of the 0th order;

[0090] Based on the wind speed data in the wind field information within the working area during the hovering of the stratospheric airship, a wind speed uncertainty model is constructed. The wind speed uncertainty model is described by the Gaussian distribution, and its probability density is expressed as:

[0091]

[0092] Among them,

[0093]

[0094] In the formula, is the wind speed probability density; w i is the wind speed; is the wind speed magnitude in the predicted wind field data; σ i is the standard deviation of the Gaussian distribution; ρ is the parameter of the distribution amplitude, which can be determined according to the wind field data within the flight area;

[0095] Based on the wind direction uncertainty model and the wind speed uncertainty model, a wind field uncertainty model is obtained.

[0096] In this step, the Von Mises distribution, the Gaussian distribution, and the Bessel modified function are all existing technologies and will not be elaborated here.

[0097] Step 104: Establish a three-degree-of-freedom kinematic model of the stratospheric airship according to its operating parameters; establish an aerodynamic model of the stratospheric airship considering the change of the wind field; formulate an operating strategy for the stratospheric airship according to its operating scenario and scenario information; generate a set of flight trajectory points of the stratospheric airship under different limit scenarios according to the operating strategy, three-degree-of-freedom kinematic model, aerodynamic model, wind field uncertainty model and flight trajectory envelope prediction scenario of the stratospheric airship.

[0098] Specifically:

[0099] Establish a three-degree-of-freedom kinematic model of the stratospheric airship according to its operating parameters:

[0100]

[0101] Among them,

[0102] λ 11 = k 11 m

[0103] λ 22 = k 22 m

[0104] λ 66 = k 66 m

[0105] In the formula, m is the mass of the stratospheric airship; k 11 , k 22 , k 66 are different inertia factors related to the external dimensions of the stratospheric airship; is the change rate of the axial velocity of the stratospheric airship, is the change rate of the lateral velocity of the stratospheric airship, is the change rate of the yaw angular velocity of the stratospheric airship, u is the axial velocity of the stratospheric airship, v is the lateral velocity of the stratospheric airship, ω is the yaw angular velocity of the stratospheric airship, F T is the thrust received by the stratospheric airship, [F wind-x , F wind-y , τ wind = F wind is the interference force and moment caused by the wind field, X w is the aerodynamic force component in the X-axis, Y w is the aerodynamic force component in the Y-axis, N w is the rotational component of the aerodynamic force on the Z-axis, I z is the moment of inertia of the airship about the Z-axis of the body coordinate system, τ is the moment received by the stratospheric airship, is the velocity of the stratospheric airship in the x direction, is the velocity of the stratospheric airship in the y direction, is the yaw angular velocity of the stratospheric airship, and ψ is the yaw angle of the stratospheric airship;

[0106] Considering the change of the wind field, an aerodynamic model of the stratospheric airship is established:

[0107]

[0108] In the formula, ρ air is the air density, u is the axial velocity of the stratospheric airship, v is the lateral velocity of the stratospheric airship, S h is the reference area of the stratospheric airship, C d1 is the axial drag coefficient, C d2 is the lateral drag coefficient;

[0109] According to the regional loitering scenario of the stratospheric airship and the corresponding scenario information, a regional loitering strategy for the stratospheric airship is formulated; specifically: in the regional loitering mission, in order to achieve energy consumption optimization and the best operating performance, the concepts of a rigid loitering area and a flexible loitering area are introduced as the constraints of the loitering mission; taking the loitering target point of the stratospheric airship as the center, the distance from the flexible loitering area to the loitering center point is r, and the distance from the rigid loitering area to the loitering center point is R. Different areas are divided into a level-I working area, a level-II working area, and a level-III working area. Different working strategies are set in different working areas, and different control instructions are executed to achieve the regional loitering mission; the level-I working area is the flexible loitering area of the stratospheric airship. In this area, the stratospheric airship does not precisely control its own position, but adjusts its heading through propeller differential to make the bow point to the loitering center point, allowing the airship position to freely drift within this area; the level-II working area is between the flexible loitering area and the rigid loitering area. In this area, the stratospheric airship is still within the rigid loitering area. To meet the energy consumption requirements, it is set that the stratospheric airship flies towards the loitering center with a constant thrust; the level-III working area is outside the rigid loitering area. When the stratospheric airship is in this area, it has deviated from the effective mission loitering area and needs to return to the rigid loitering area as soon as possible. Therefore, when the airship is in the level-III working area, it is set to fly towards the loitering center at the maximum flight speed; the regional loitering strategy is specifically expressed as:

[0110]

[0111] In the formula, v air is the airspeed, v max is the maximum wind resistance speed, v ave is the average wind resistance speed, R is the distance from the rigid loitering area to the loitering center point, r is the distance from the flexible loitering area to the loitering center point, and dis is the distance between the stratospheric airship and the loitering center;

[0112] According to the transfer flight scenario of the stratospheric airship and the corresponding scenario information, formulate the transfer flight strategy of the stratospheric airship; specifically: during the flight, adjust the yaw angle of the airship to point to the target point and maintain flight at the average wind resistance speed;

[0113] According to the working strategies of the stratospheric airship (including: regional residence strategy, transfer flight strategy), three-degree-of-freedom kinematic model, aerodynamic model, wind field uncertainty model, and flight trajectory envelope prediction scenario, generate the flight trajectory point set Ω of the stratospheric airship under different limit scenarios.

[0114] In this step, the Von Mises distribution of the wind field uncertainty model can be regarded as the Gaussian distribution on the circle. Therefore, the flight trajectory point set of the stratospheric airship under different limit scenarios refers to: when taking the limit values in different directions of different uncertainties of the wind field uncertainty model, the trajectory point set generated by the stratospheric airship flying according to the flight strategy. The limit values are taken as the limit values under the 3σ uncertainty condition, and four limit scenarios are obtained, as shown in Table 1. Among them, v w is the wind field wind speed data, represents the standard deviation of the wind speed, σ θ represents the standard deviation of the wind direction, and θ represents the wind direction.

[0115] Table 1: Scenarios

[0116]

[0117] Step 105, perform contour extraction on the flight trajectory point set of the stratospheric airship under different limit scenarios to obtain the flight trajectory envelope.

[0118] Specifically:

[0119] Adopt the Alpha-Shapes method (a method for describing the geometric structure of the boundary of a given point set) to determine the circle that rolls along the edge of the flight trajectory point set Ω and does not fall into the flight trajectory point set Ω as the rolling circle, with a radius of α. α determines the fineness of the generated boundary contour. The larger the α value, the closer the generated shape is to the convex hull. The smaller the α value, the more the generated shape can fit the contour of the flight trajectory point set. The two points included in the rolling circle are the points on the edge contour of the flight trajectory point set Ω, and the line segment between the two points is the boundary line segment;

[0120] Take any point P i (x1, y1) in the flight trajectory point set as the starting point, and use all points whose distance from the starting point P i is not greater than twice the circle radius, that is, 2α, to form the neighborhood point set R b ;

[0121] Take any point P b in the neighborhood point set R r(x2, y2) is used as a trajectory point to calculate the starting point P i and the trajectory point P r to determine the rolling circle;

[0122] The center of the rolling circle is P0(x3, y3), and the center coordinates are calculated according to the rear distance method:

[0123]

[0124] wherein,

[0125]

[0126] in the formula, H is the parameter to be solved;

[0127] According to the rolling circle, the contour of the flight trajectory point set of the stratospheric airship under different limit scenarios is extracted to obtain the flight trajectory envelope of the stratospheric airship.

[0128] In this step, the Alpha-Shapes method is a prior art and will not be elaborated here.

[0129] In this embodiment, after obtaining the trajectory envelope, it further includes:

[0130] Adopt the kernel density estimation method, select the two-dimensional Gaussian kernel distribution as the kernel function, and consider the adaptive bandwidth selection of the kernel function to calculate the distribution probability density of each trajectory point in the flight trajectory point set;

[0131] According to the distribution probability density of each trajectory point, calculate the distribution probability of the entire trajectory to obtain the distribution characteristics and distribution laws of the trajectory, and then intuitively describe the distribution of the trajectory during the in-air operation of the stratospheric airship to support the formulation of the flight test mission and safety risk analysis.

[0132] Specifically:

[0133] Adopt the kernel density estimation method to calculate the trajectory distribution probability, that is: select the two-dimensional Gaussian (Gaussian) kernel distribution as the kernel function, and assume that the coordinates of the i-th trajectory point in the trajectory point set are (x i , y i ), then (x i , y i ) follows the two-dimensional Gaussian distribution with parameters (μ1, μ2, σ1, σ2, ρ), and its probability density can be expressed as:

[0134]

[0135] In the formula, f(x i , y i ) is the distribution probability density of each trajectory point in the flight trajectory point set, (x i,y i ) is the i-th trajectory point in the flight trajectory point set, σ1 is the variance of x i , and σ2 is the variance of y i , μ1 is the mean of x i , and μ2 is the mean of y i , ρ xy is the correlation coefficient of x i and y i , and it can take 0;

[0136] Adopt the method of adaptive bandwidth to determine the kernel function bandwidth h, that is, the influence range of the probability distribution of each trajectory point:

[0137] h i = (g -1 · f(x i ,y i )) -a

[0138] Among them,

[0139]

[0140] In the formula, h i is the bandwidth of the i-th trajectory point (x i ,y i ); a is the bandwidth sensitivity parameter, and its value range is [0,1], that is, the larger a is, the more sensitive the bandwidth is to the value of f(x i,t ,y i,t ). When a = 0, the kernel density estimation with adaptive bandwidth becomes the kernel density estimation with fixed bandwidth; g is the geometric mean; n is the number of trajectory points;

[0141] Adopt the adaptive bandwidth kernel density estimation method (that is, the method that improves the kernel density estimation method by using adaptive bandwidth) to calculate the distribution probability density of each trajectory point in the flight trajectory point set:

[0142]

[0143] In the formula, r h is the distance to the trajectory point (x i ,y i ); h i is the bandwidth of the i-th trajectory point (x i ,y i );

[0144] Calculate the distribution probability of the entire trajectory based on the distribution probability density of each trajectory point (specifically: since the trajectory points are independently distributed, it can be considered that the bandwidths of the kernel functions of all trajectory points are equal, and adding the distribution probability densities of all trajectory points can obtain the distribution probability of the entire trajectory), so as to obtain the distribution characteristics and distribution laws of the trajectory.

[0145] The above-mentioned method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model generates a set of flight trajectory points of the stratospheric airship under different limit scenarios according to the working strategy, three-degree-of-freedom kinematic model, aerodynamic model, wind field uncertainty model, and flight trajectory envelope prediction scenario of the stratospheric airship, so as to predict the flight trajectory envelope of the stratospheric airship. It can determine the boundaries of the flight trajectories of the stratospheric airship under different working scenarios, generate flight trajectories under four 3-Sigma uncertainty limit scenarios, and extract the flight trajectory envelope of the stratospheric airship according to the set of trajectory points. Moreover, the flight trajectory envelope of the stratospheric airship is accurate, reasonable, and effective, and is applicable to determining the boundary of its flight area before the stratospheric airship executes a flight mission, providing strong support for formulating the flight test plan and evaluating the flight risk of the stratospheric airship, and ensuring the safety of the stratospheric airship in performing tasks.

[0146] As Figure 2 shown, κ represents the degree of concentration of the wind direction distribution; when κ → 0, the wind direction distribution is more dispersed; when κ → ∞, the wind direction distribution is more concentrated.

[0147] As Figure 3 shown, κ represents the degree of concentration of the wind direction distribution; when κ → 0, the wind direction distribution is more dispersed; when κ → ∞, the wind direction distribution is more concentrated.

[0148] As Figure 4 shown, the predicted wind speed magnitude of the wind field is w i = 5 m / s, when ρ = 0.2, the distribution probability density of the wind speed satisfies the distribution as shown in the figure.

[0149] As Figure 5 shown, the area residence strategy introduces the concepts of a rigid residence area and a flexible residence area as the constraint conditions for the residence mission; taking the residence target point of the stratospheric airship as the center, the distance from the flexible residence area to the residence center point is r, and the distance from the rigid residence area to the residence center point is R. Different areas are divided into a Class I working area, a Class II working area, and a Class III working area, and different working strategies are set in different working areas to execute different control instructions to achieve the area residence mission.

[0150] As Figure 6As shown, the dashed circle represents the flight trajectory envelope of the stratospheric airship, the solid circle represents the rigid residence area, and the four legends represent the trajectories under four extreme scenarios. It can be seen that this method can make reasonable predictions for the flight trajectory envelope according to the regional residence strategy of the stratospheric airship.

[0151] As Figure 7 shown, it can be seen that the adaptive bandwidth kernel density estimation method proposed in this patent can intuitively describe the distribution characteristics of the flight trajectory, which helps to analyze the working characteristics of the stratospheric airship under different working scenarios.

[0152] As Figure 8 shown, the dashed line represents the flight trajectory envelope of the stratospheric airship, and the four legends represent the trajectories under four extreme scenarios. It can be seen that this method can make reasonable predictions for the flight trajectory envelope according to the regional transfer flight strategy of the stratospheric airship.

[0153] As Figure 9 shown, it can be seen that the adaptive bandwidth kernel density estimation method proposed in this patent can intuitively describe the distribution characteristics of the flight trajectory, which helps to analyze the working characteristics of the stratospheric airship under different working scenarios.

[0154] It should be understood that although Figure 1 the steps in the flowchart are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, there is no strict order limit for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 at least a part of the steps in

[0155] This application also provides a device for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model. As Figure 10 shown, in one embodiment, it includes: a first module 1001, a second module 1002, a third module 1003, a fourth module 1004, and a fifth module 1005, where:

[0156] The first module 1001 is used to obtain the working tasks of the stratospheric airship, and determine the working parameters, working scenarios, and scenario information of the stratospheric airship, so as to establish a prediction scenario for the flight trajectory envelope of the stratospheric airship.

[0157] The second module 1002 is used to obtain the predicted wind field data during the working task period of the stratospheric airship, and obtain the wind field direction data and the wind field speed data;

[0158] The third module 1003 is used to construct a wind direction uncertainty model according to the wind field direction data; construct a wind speed uncertainty model according to the wind field speed data; and obtain a wind field uncertainty model according to the wind direction uncertainty model and the wind speed uncertainty model;

[0159] The fourth module 1004 is used to establish a three-degree-of-freedom kinematic model of the stratospheric airship according to the working parameters of the stratospheric airship; establish an aerodynamic model of the stratospheric airship considering the wind field change; formulate a working strategy of the stratospheric airship according to the working scenario and scenario information of the stratospheric airship; and generate a set of flight trajectory points of the stratospheric airship in different limit scenarios according to the working strategy, the three-degree-of-freedom kinematic model, the aerodynamic model, the wind field uncertainty model and the flight trajectory envelope prediction scenario;

[0160] The fifth module 1005 is used to perform contour extraction on the set of flight trajectory points of the stratospheric airship in different limit scenarios to obtain a trajectory envelope.

[0161] For the specific limitations of the device for predicting the flight trajectory envelope of the stratospheric airship based on the uncertainty model, reference may be made to the limitations of the method for predicting the flight trajectory envelope of the stratospheric airship based on the uncertainty model in the above text, which will not be elaborated here. Each module in the above device can be implemented in whole or in part by software, hardware and their combinations. The above modules can be embedded in the processor of the computer device in hardware form or independent of it, or stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above modules.

[0162] The content not described in detail in this specification belongs to the prior art well known to those skilled in the art.

[0163] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0164] The above-described embodiments only represent several implementation manners of the present application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model, characterized in that: include: Obtaining the work tasks of the stratospheric airship, and determining the work parameters, work scenarios and scenario information of the stratospheric airship, so as to establish the flight trajectory envelope prediction scenario of the stratospheric airship; Obtain the forecast wind field data during the time period when the stratospheric airship performs its work mission, and determine the wind field information in the working area during the stratospheric airship's stay in the air; According to the wind field information in the working area during the stay of the stratospheric airship, the wind field uncertainty model is obtained; According to the working parameters of the stratospheric airship, a three-degree-of-freedom kinematic model of the stratospheric airship is established; considering the changes in the wind field, an aerodynamic model of the stratospheric airship is established; according to the working scene and scene information of the stratospheric airship, a working strategy of the stratospheric airship is formulated; according to the working strategy of the stratospheric airship, the three-degree-of-freedom kinematic model, the aerodynamic model, the wind field uncertainty model and the flight trajectory envelope prediction scenario, a flight trajectory point set of the stratospheric airship under different extreme scenarios is generated; The flight trajectory point set of the stratospheric airship in different extreme scenarios is extracted to obtain the flight trajectory envelope.

2. The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model according to claim 1, characterized in that: After obtaining the trajectory envelope, it also includes: The kernel density estimation method is adopted, two-dimensional Gaussian kernel distribution is selected as the kernel function, and the adaptive bandwidth of the kernel function is considered to calculate the distribution probability density of each trajectory point in the flight trajectory point set; According to the distribution probability density of each trajectory point, the distribution probability of the entire trajectory is calculated to obtain the distribution characteristics and distribution laws of the trajectory.

3. The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model according to claim 2, characterized in that: Obtain the forecast wind field data during the time period when the stratospheric airship performs its work mission, and determine the wind field information in the working area during the stratospheric airship's stay in the air, including: Obtain the forecast wind field data during the time period when the stratospheric airship performs the work mission, perform interpolation processing on the forecast wind field data, and obtain the wind field data at the working altitude of the stratospheric airship; Interpolate the wind field data at the working altitude of the stratospheric airship to obtain the meridional wind speed and zonal wind speed at any point on the horizontal plane where the working altitude of the stratospheric airship is located; The wind field direction data and the wind field speed data are calculated according to the longitudinal wind speed and the latitudinal wind speed, and the wind field direction data and the wind field speed data are used as the wind field information in the working area during the stratospheric airship's stay in the air.

4. The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model according to claim 3, characterized in that: According to the wind field information in the working area during the stratospheric airship's stay in the air, the wind field uncertainty model is obtained, including: According to the wind field and direction data in the wind field information in the working area during the stratospheric airship's stay in the air, a wind direction uncertainty model is constructed; According to the wind field speed data in the wind field information in the working area during the stratospheric airship's stay in the air, a wind speed uncertainty model is constructed; According to the wind direction uncertainty model and the wind speed uncertainty model, a wind field uncertainty model is obtained.

5. The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model according to claim 4, characterized in that: The wind direction uncertainty model is described by Von Mises distribution, and its probability density function is expressed as: In the formula, is the probability density of wind direction, θ i For wind direction, is the wind direction in the forecast wind field data, κ is the concentration of wind direction, and I0(κ) is the Bessel correction function of order 0; The wind speed uncertainty model is described using Gaussian distribution, and its probability density is expressed as: in, In the formula, is the wind speed probability density, w i is the wind speed, is the wind speed of the forecast wind field data, σ i is the standard deviation of the Gaussian distribution, and ρ is the parameter of the distribution amplitude.

6. The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model according to any one of claims 1 to 5, characterized in that: The flight trajectory point set of the stratospheric airship in different extreme scenarios refers to the set of trajectory points generated by the stratospheric airship flying according to the flight strategy when the wind field uncertainty model takes extreme values ​​in different directions of different uncertainties.

7. The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model according to any one of claims 1 to 5, characterized in that: The working scenarios of the stratospheric airship include: regional residence scenarios or transition flight scenarios.

8. The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model according to any one of claims 1 to 5, characterized in that: The flight trajectory point set of the stratospheric airship in different extreme scenarios is extracted to obtain the flight trajectory envelope, including: The Alpha-Shapes method is used to determine the circle that rolls along the edge of the flight trajectory point set and does not fall into the trajectory point set as the rolling circle; Take any point in the flight trajectory point set as the starting point, and use all points whose distance from the starting point is not greater than twice the radius of the circle to form a neighborhood point set; Take any point in the neighborhood point set as a trajectory point and calculate the rolling circle determined by the starting point and the trajectory point; According to the rolling circle, the flight trajectory point set of the stratospheric airship in different extreme scenarios is contour extracted to obtain the flight trajectory envelope.

9. The method for predicting the flight trajectory envelope of a stratospheric airship based on an uncertainty model according to any one of claims 2 to 5, characterized in that: The kernel density estimation method is used, a two-dimensional Gaussian kernel distribution is selected as the kernel function, and the kernel function adaptive bandwidth is considered to calculate the distribution probability density of each trajectory point in the flight trajectory point set, including: In the formula, f(x i ,y i ) is the distribution probability density of each trajectory point in the flight trajectory point set, (x i ,y i ) is the i-th trajectory point in the flight trajectory point set, μ1 is x i The average value of i The variance of y i The variance, r h To the trajectory point (x i ,y i ), h i is the bandwidth of the ith trajectory point.

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