CN107274487A - The evaluation method of safe flight envelope curve - Google Patents
The evaluation method of safe flight envelope curve Download PDFInfo
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- CN107274487A CN107274487A CN201710369195.0A CN201710369195A CN107274487A CN 107274487 A CN107274487 A CN 107274487A CN 201710369195 A CN201710369195 A CN 201710369195A CN 107274487 A CN107274487 A CN 107274487A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/10—Constructive solid geometry [CSG] using solid primitives, e.g. cylinders, cubes
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
Abstract
The invention discloses a kind of evaluation method of safe flight envelope curve, the mode for carrying out plane fitting by using least square method calculates the law vector of cloud data, by using the method for being most worth optimization, the computation complexity of local least square method fitting process is improved, so as to optimize the calculating time of least square fitting method；Pass through the k neighborhoods of query point cloud, corresponding topological structure is set up, the section under least square method is fitted on the basis of topological structure, so as to estimate the surface method arrowhead amount of a cloud, the algorithm has higher accuracy, can be suitably used for the application environment higher to required precision；The safe flight envelope curve calculated using this evaluation method has that precision is high, fireballing feature, possesses the prospect of wide popularization and application.
Description
Technical field
The present invention relates to the processing of cloud data, more particularly to a kind of evaluation method of safe flight envelope curve.
Background technology
Flight envelope is the closed geometry figure using flying speed, height and overload etc. as boundary, to represent aircraft
Flight range and flight restriction condition.By taking permanent forward flight envelope curve as an example, by abscissa of speed, be highly vertical
In the two-dimentional quadrant of coordinate, all speed and height for maintaining normal flight are marked, an irregular quadrangle is formed.The left side
Minimum speed limitation is represented, the right represents that maximal rate is limited, flying height limitation shown above.
At present, aircraft can be navigated using three-dimensional data map, and the three-dimensional data of surrounding terrain environment is swept in advance
Retouch to form cloud data, and be fabricated to three-dimensional data map.Aircraft rises in flight course with the height of surrounding terrain environment
Volt, it is necessary to calculate safe flight envelope curve, so as to be that control air speed and height provide real-time instruction in real time.
Point cloud scanning is an important branch of three-dimensional measurement, by the sea for scanning the actual object that can be obtained and landform
Measure 3D information.Therefore, the processing of cloud data has and its important in geography information, spatial analysis, environmental analysis etc. direction
Effect.
In the feature extraction of cloud data, the geometric attribute such as law vector and curvature is the important ginseng of reflection point cloud characteristic
The precision of number, law vector and curvature will directly reflect the accuracy of cloud data.Therefore, how effectively, exactly to calculate
Go out law vector and curvature these geometric parameters, be the key point solved the problems, such as.
The content of the invention
In view of this, it is an object of the invention to provide a kind of evaluation method of safe flight envelope curve, its can effectively, it is accurate
Really calculate law vector.
The technical proposal of the invention is realized in this way：The invention provides a kind of evaluation method of safe flight envelope curve,
It is characterized in that：Comprise the following steps,
S1, obtains the three-dimensional data coordinate of surrounding terrain environmental model, forms cloud data, obtains position of aircraft and sits
Mark, the direction of motion, speed and enroute I. F. R. altitude；
S2, estimates the surface law vector of cloud data；
S3, according to the surface law vector of the obtained cloud datas of step S2, position of aircraft coordinate, the direction of motion, speed
And enroute I. F. R. altitude calculates safe flight envelope curve.
On the basis of above technical scheme, it is preferred that the step S2 includes,
S2-1, reads in cloud data, and obtain a cloud number n；
S2-2, appoints from cloud data concentration and takes a point Pi；
S2-3, sets up PiK- neighborhoods；
S2-4, carries out surface fitting with least square method by this k+1 point, obtains the section of fitting surface；
S2-5, regards point P by the law vector in obtained curved surface sectioniNormal, then inspection technique direction vector one
Cause property, is consistent, by obtained law vector if pointing to viewpointStore；If it is not, then being carried out to law vector direction
Upset, then by obtained law vectorStore.
S2-6, the institute that traversal cloud data is concentrated a little, repeats the above steps.
It is further preferred that the step S2-4 comprises the following steps,
To n obtained cloud data, PiIt is the certain point in measurement data, to try to achieve the normal at the point, first sets flat
Face equation is：
Ax+by+cz+d=0 (1)
In formula (1), a2+b2+c2=1, plane parameter a, b, c, d can be obtained so that k neighbor point to the plane away from
From quadratic sum it is minimum, the fit Plane of acquisition is optimal, that is, meets formula (2)：
Wherein, diIt is any point Pi (x in cloud datai,yi,zi) to this plane apart from di=| axi+byi+czi-
d|
Extreme value is solved using method of Lagrange multipliers, formula (3) is obtained
Local derviation is sought into d on formula (3) both sides, and makes partial derivative be zero, is obtained：
OrderBarycenter is
di=| a Δs xi+bΔyi+cΔzi| (5)
A is asked to formula (3) both sides again, b, c partial derivative is obtained：
Above-mentioned equation group constitutive characteristic value equation is obtained：
Ax=λ x (7)
In formula (7),
So, plane parameter a, b, c are solved, is exactly the characteristic value and characteristic vector of solution matrix, but because A is that 3 ranks are real
Symmetrical matrix, it can be seen from the knowledge of matrix, for real symmetric matrix, characteristic value can be solved using formula (7), be obtained：
In constraints a2+b2+c2Under=1, it can obtainSo, e is most
Small value is exactly the minimal eigenvalue of matrix A, and corresponding characteristic vector is plane parameter a, b, c, and d can be tried to achieve using barycenter.
Still more preferably, the step S2-5 includes,
The uniformity in direction is first judged, if it is known that actual view Vp, it is only necessary to all law vectorsDirection all point to
Vision pointpDirection, it is consistent to be considered as direction, that is, meets formula (9)：
If being unsatisfactory for formula (9), i.e. point PiNormal vectorWith point PiTo vision pointpRay angle be more than 90 °,Should be by
Reversely.
Still further preferably, the step S2-5 also includes,
If setting measuring point Pi, PjBe that distance is close on curved surface 2 points, the then dot product of corresponding law vectorOtherwise,
OrIt should be reversed.
The evaluation method of the safe flight envelope curve of the present invention has the advantages that relative to prior art：
(1) mode for carrying out plane fitting by using least square method calculates the law vector of cloud data, by using
Most it is worth the method for optimization, improves the computation complexity of local least square method fitting process, so as to optimizes least square fitting method
The calculating time；
(2) by the k- neighborhoods of query point cloud, corresponding topological structure is set up, is fitted most on the basis of topological structure
Section under small square law, so as to estimate the surface method arrowhead amount of a cloud, the algorithm has higher accuracy, can be suitably used for
The application environment higher to required precision；
(3) the safe flight envelope curve calculated using this evaluation method has that precision is high, fireballing feature, possesses and pushes away extensively
The prospect extensively applied.
Embodiment
Below in conjunction with embodiment of the present invention, technical solution of the present invention is clearly and completely described, it is clear that institute
The embodiment of description is only a part of embodiment of the invention, rather than whole embodiments.Based in the present invention
Embodiment, the every other embodiment party that those of ordinary skill in the art are obtained under the premise of creative work is not made
Formula, belongs to the scope of protection of the invention.
The evaluation method of the safe flight envelope curve of the present invention, comprises the following steps,
S1, obtains the three-dimensional data coordinate of surrounding terrain environmental model, forms cloud data, obtains position of aircraft and sits
Mark, the direction of motion, speed and enroute I. F. R. altitude.
S2, estimates the surface law vector of cloud data.Specifically, including,
S2-1, reads in cloud data, and obtain a cloud number n.
S2-2, appoints from cloud data concentration and takes a point Pi。
S2-3, sets up PiK- neighborhoods.When estimating a cloud plane normal, it should opened from the neighborhood around the point
Begin, find k nearest point adjacent with the point, that is, described k- neighborhoods.By the way that topological relation between points is built
Erect and, can effectively reduce data processing scope, improve efficiency of algorithm.Known sample point cloud data point set a Pt's, k takes
It is worth to be much, the radius r of this neighborhood is much in other words, is worth thinking.K choosing value can not it is much can not be too small, if k
When excessive, neighborhood coverage is too wide, causes the amount of calculation of surface fitting too big, this point feature it is possible that distortion
Distortion；If k is too small, the feature of the point can not sufficiently be reflected by fitting the curved surface come, reduce the precision of feature.
S2-4, carries out surface fitting with least square method by this k+1 point, obtains the section of fitting surface.
To n obtained cloud data, PiIt is the certain point in measurement data, to try to achieve the normal at the point, first sets flat
Face equation is：
Ax+by+cz+d=0 (1)
In formula (1), a2+b2+c2=1, plane parameter a, b, c, d can be obtained so that k neighbor point to the plane away from
From quadratic sum it is minimum, the fit Plane of acquisition is optimal, that is, meets formula (2)：
Wherein, diIt is any point Pi (x in cloud datai,yi,zi) to this plane apart from di=| axi+byi+czi-
d|
Extreme value is solved using method of Lagrange multipliers, formula (3) is obtained
Local derviation is sought into d on formula (3) both sides, and makes partial derivative be zero, is obtained：
OrderBarycenter is
di=| a Δs xi+bΔyi+cΔzi| (5)
A is asked to formula (3) both sides again, b, c partial derivative is obtained：
Above-mentioned equation group constitutive characteristic value equation is obtained：
Ax=λ x (7)
In formula (7),
So, plane parameter a, b, c are solved, is exactly the characteristic value and characteristic vector of solution matrix, but because A is that 3 ranks are real
Symmetrical matrix, it can be seen from the knowledge of matrix, for real symmetric matrix, characteristic value can be solved using formula (7), be obtained：
In constraints a2+b2+c2Under=1, it can obtainSo, e is most
Small value is exactly the minimal eigenvalue of matrix A, and corresponding characteristic vector is plane parameter a, b, c, and d can be tried to achieve using barycenter.
S2-5, regards point P by the law vector in obtained curved surface sectioniNormal, then inspection technique direction vector one
Cause property, is consistent, by obtained law vector if pointing to viewpointStore；If it is not, then being carried out to law vector direction
Upset, then by obtained law vectorStore.
The direction of normal vector that directly obtains is calculated using above method it is possible that it is inconsistent the problem of.To make direction
Being consistent property, it should be adjusted to the direction of normal.The uniformity in direction is first judged, if it is known that actual view Vp, only
Need all law vectorsDirection all point to vision pointpDirection, it is consistent to be considered as direction, that is, meets formula (9)：
If being unsatisfactory for formula (9), i.e. point PiNormal vectorWith point PiTo vision pointpRay angle be more than 90 °,Should be by
Reversely.
If setting measuring point Pi, PjBe that distance is close on curved surface 2 points, the then dot product of corresponding law vectorOtherwise,
OrIt should be reversed.
S2-6, the institute that traversal cloud data is concentrated a little, repeats the above steps.
S3, according to the surface law vector of the obtained cloud datas of step S2, position of aircraft coordinate, the direction of motion, speed
And enroute I. F. R. altitude calculates safe flight envelope curve.
The better embodiment of the present invention is the foregoing is only, is not intended to limit the invention, it is all the present invention's
Within spirit and principle, any modification, equivalent substitution and improvements made etc. should be included in the scope of the protection.
Claims (5)
1. a kind of evaluation method of safe flight envelope curve, it is characterised in that：Comprise the following steps,
S1, obtains the three-dimensional data coordinate of surrounding terrain environmental model, forms cloud data, obtains position of aircraft coordinate, fortune
Dynamic direction, speed and enroute I. F. R. altitude；
S2, estimates the surface law vector of cloud data；
S3, according to the surface law vector of the obtained cloud datas of step S2, position of aircraft coordinate, the direction of motion, speed and
Enroute I. F. R. altitude calculates safe flight envelope curve.
2. the evaluation method of safe flight envelope curve as claimed in claim 1, it is characterised in that：The step S2 includes,
S2-1, reads in cloud data, and obtain a cloud number n；
S2-2, appoints from cloud data concentration and takes a point Pi；
S2-3, sets up PiK- neighborhoods；
S2-4, carries out surface fitting with least square method by this k+1 point, obtains the section of fitting surface；
S2-5, regards point P by the law vector in obtained curved surface sectioniNormal, then inspection technique direction vector uniformity,
It is consistent, by obtained law vector if pointing to viewpointStore；If it is not, then law vector direction is overturn,
Again by obtained law vectorStore.
S2-6, the institute that traversal cloud data is concentrated a little, repeats the above steps.
3. the evaluation method of safe flight envelope curve as claimed in claim 2, it is characterised in that：The step S2-4 includes following
Step,
To n obtained cloud data, PiIt is the certain point in measurement data, to try to achieve the normal at the point, first sets plane equation
For：
Ax+by+cz+d=0 (1)
In formula (1), a2+b2+c2=1, plane parameter a, b, c, d can be obtained so that the distance of k neighbor point to the plane
Quadratic sum is minimum, and the fit Plane of acquisition is optimal, that is, meets formula (2)：
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Wherein, diIt is any point Pi (x in cloud datai,yi,zi) to this plane apart from di=| axi+byi+czi-d|
Extreme value is solved using method of Lagrange multipliers, formula (3) is obtained
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A is asked to formula (3) both sides again, b, c partial derivative is obtained：
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Above-mentioned equation group constitutive characteristic value equation is obtained：
Ax=λ x (7)
In formula (7),
So, plane parameter a, b, c are solved, is exactly the characteristic value and characteristic vector of solution matrix, but because A is that 3 ranks are symmetrical in fact
Matrix, it can be seen from the knowledge of matrix, for real symmetric matrix, characteristic value can be solved using formula (7), be obtained：
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In constraints a2+b2+c2Under=1, it can obtainSo, e minimum value
It is exactly the minimal eigenvalue of matrix A, corresponding characteristic vector is plane parameter a, b, c, and d can be tried to achieve using barycenter.
4. the evaluation method of safe flight envelope curve as claimed in claim 3, it is characterised in that：The step S2-5 includes,
The uniformity in direction is first judged, if it is known that actual view Vp, it is only necessary to all law vectorsDirection all point to viewpoint
VpDirection, it is consistent to be considered as direction, that is, meets formula (9)：
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If being unsatisfactory for formula (9), i.e. point PiNormal vectorWith point PiTo vision pointpRay angle be more than 90 °,It should be reversed.
5. the evaluation method of safe flight envelope curve as claimed in claim 4, it is characterised in that：The step S2-5 also includes,
If setting measuring point Pi, PjBe that distance is close on curved surface 2 points, the then dot product of corresponding law vectorOtherwise,OrIt should be reversed.
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| CN109507877A (en) * | 2018-11-22 | 2019-03-22 | 北京航空航天大学 | Flight Vehicle Trajectory plans security assessment method |
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Application publication date: 20171020 |