CN107403048A - Collision probability computational methods based on cube models - Google Patents
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Abstract
Present disclose provides a kind of collision probability computational methods based on cube models, terrestrial space are divided into cube grid, and cube is numbered；Calculate position and its residing cube numbering of space object；Space object is matched, using the space object in adjacent and identical cube as pairing target；Calculate the collision probability between pairing target.The disclosure compensate for the defects of original cube models may omit collision situation by increasing the consideration to the collision possibilities of adjacent cube space objects so that the cube models after improvement more meet that physics is true, and analysis result is more reasonable credible.
Description
Technical field
This disclosure relates to space object collision probability calculating field, more particularly to a kind of collision probability based on cube models
Computational methods.
Background technology
The increasing of space junk has triggered the research on space environment long-time stability in the world.And computer skill
The development of art to emulate the long-term evolution of N systems system., it is necessary to consider fragment in space junk phylogeny
Increase mechanism and reduce mechanism, it is corresponding, it is necessary to which a kind of can utilize the fragment orbital data of continuous renewal be touched
Hit the algorithm of probability calculation.NASA have developed a kind of collision probability algorithm for being referred to as " Cube " model.Cube moulds
The core concept of type is, in space junk system long-term evolution, at regular intervals dt to systematic sampling once, sampling when
Carve, whole terrestrial space is divided into length h small cubes, the moment each space is calculated using the orbital data of renewal
Position where object, then find out in same cubical space object, calculate its collision probability between any two, if
There was only an object in one cube, then do not consider its collision probability with object in other cubes.Cube models it is excellent
Point is quickly to match N body fragment systems by dividing cube to space, greatly reduces amount of calculation；It is lacked
Point is then to miss the calculating to collision probability between the space object in neighboring cubes, the even meeting of this collision probability
More than the collision probability between two objects in same cube.
The content of the invention
(1) technical problems to be solved
The disclosure, which is intended to make up, does not account in neighboring cubes lacking for collision probability between space object in Cube models
Fall into, propose a kind of collision probability computational methods based on cube models.
(2) technical scheme
Present disclose provides a kind of collision probability computational methods based on cube models, including：Terrestrial space division is vertical
Cube grid, and cube is numbered；Calculate position and its residing cube numbering of space object；To space object
Matched, using the space object in adjacent and identical cube as pairing target；And between calculating pairing target
Collision probability.
It is described that terrestrial space is divided into cube grid in some embodiments of the present disclosure, and cube is compiled
Number include：Using the earth's core as coordinate origin, cartesian coordinate system is established, terrestrial space is divided into cube grid, and to every
Individual cube is numbered in units of the length of side.
In some embodiments of the present disclosure, the numbering is expressed as (x, y, z), and x, y, z represents cube in x-axis respectively
The numbering in direction, y-axis direction and z-axis direction.
In some embodiments of the present disclosure, the position for calculating space object and its residing cube numbering bag
Include：Position according to where the orbital tracking after the renewal of each space object calculates it, searches the cube residing for the position,
And cubical numbering residing for recording.
It is described that space object is matched in some embodiments of the present disclosure, adjacent and identical cube will be in
Interior space object includes as pairing target：Respectively in three change in coordinate axis direction, stood as residing for numeric order by space object
The numbering of cube is ranked up, obtain with object space object residing for cubical numbering it is adjacent and be identically numbered；With it is described
Space object sequence number corresponding to numbering in cube forms the space object sequence number collection of three change in coordinate axis direction；Calculate three seats
The common factor of the space object sequence number collection in parameter direction, obtain with object space object residing for cube is adjacent and identical cube
Space object sequence number collection；The Euclidean distance of space object and object space object that space object sequence number is concentrated is traveled through, is retained
Euclidean distance is in the space object less than threshold value as pairing target.
In some embodiments of the present disclosure, using dichotomy as residing for numeric order by space object cubical numbering
It is ranked up.
In some embodiments of the present disclosure, the threshold value takes the cube length of side to be multiplied by
In some embodiments of the present disclosure, the collision probability calculated between pairing target includes：To in adjacent
With the space object in identical cube, space object i and j mean number of collisions are：
C=SiSjVimpAcdUdt
Collision probability is：
pij=1-exp (- c)
Wherein, dU is volume elements；Dt is time sampling interval；Si、SjPoints of the representation space object i and j in volume elements dU respectively
Cloth density；VimpIt is space object i and j relative impact velocity；AcFor space object i and j collision cross-section.
In some embodiments of the present disclosure, the volume elements dU be the Euclidean distance using between space object i and j threshold value as
The spheroid volume of radius.
In some embodiments of the present disclosure, wherein,
Space object is uniformly distributed in volume elements dU,
Si=Sj=1/dU
Wherein, dcThe threshold value of Euclidean distance between space object i and j；H is the cube length of side.
(3) beneficial effect
It can be seen from the above technical proposal that collision probability computational methods of the disclosure based on cube models have and following had
Beneficial effect：
(1) disclosure compensate for original cube by increasing the consideration to the collision possibility of adjacent cube space objects
Model may omit the defects of collision situation so that it is true that the cube models after improvement more meet physics, analysis result more adduction
Manage credible.
(2) disclosure is applied to assessment of the space junk system during long-term evolution to collision probability, is advantageous to carry
The reasonability and confidence level of high spatial fragment long-term evolution model.And the research to space junk long-term evolution model can be to not
Come China and active fragment removing offer analysis of strategies and model support are provided.
Brief description of the drawings
Fig. 1 is the flow chart of the collision probability computational methods based on cube models of the embodiment of the present disclosure.
Embodiment
The disclosure is by the quick pairing of space object, calculating the collision probability between space object.This method is applied to
Assessment of the space junk system during long-term evolution to collision probability.In the disclosure, touching between consideration extraterrestrial target
Hit, the collision that can be regarded as between air molecule, the collision probability between extraterrestrial target is assessed according to aerodynamics.Air
Intermolecular collision probability obeys Poisson distribution.
For the purpose, technical scheme and advantage of the disclosure are more clearly understood, below in conjunction with specific embodiment, and reference
Accompanying drawing, the disclosure is further described.
The embodiment of the present disclosure provides a kind of collision probability computational methods based on cube models, referring to Fig. 1, including：
Step S1：Terrestrial space is divided into cube grid, and cube is numbered.
The step specifically includes：In sampling instant, using the earth's core as coordinate origin, cartesian coordinate system is established, by the earth
Around terrestrial space be divided into the length of side be h it is cube shaped into grid, and to each cube by length of side h multiple carry out
Numbering, i.e., be numbered in units of length of side h.
Cubical numbering is expressed as (x, y, z), and x, y, z represents cube in x-axis direction, y-axis direction, z-axis side respectively
To numbering；X-axis direction numbering represents that the cube is in the position of x-th of unit of x-axis, and similarly, y-axis direction numbering represents
The cube is in the position of y-th of unit of y-axis, and y-axis direction numbering represents that the cube is in z-th of unit of z-axis
Position.
Step S2：Calculate the position of space object and its residing cubical numbering.
The step specifically includes：In sampling instant, the orbital tracking after being updated according to each space object calculates its place
Position, search the cube residing for the position, and cubical numbering residing for recording.In this step can be first to space object
It is ranked up, for serial number i space object, its position coordinates is expressed as (Xi, Yi, Zi), cubical volume residing for the position
Number it is expressed as (xi, yi, zi)。
Step S3：Space object is matched, using the space object in adjacent and identical cube as pairing
Target.
The step is in sampling instant, by the way that cubical numbering residing for all space objects is compared, is found out
Extraterrestrial target in adjacent or identical cube.
Specifically,
First, respectively in three change in coordinate axis direction, cubical numbering carries out two as residing for numeric order by space object
Point-score sorts, obtain with object space object residing for cubical numbering it is adjacent and be identically numbered.
Space object sequence number in cube corresponding with above-mentioned numbering forms the space object sequence of three change in coordinate axis direction
Number collection.
In one example, can the first spatially numeric order of object, by cubical x-axis residing for each space object
Direction numbering carries out dichotomy sequence, obtains cubical x-axis direction numbering collection residing for space object, record x-axis direction numbering
Concentration is adjacent with cubical x-axis direction numbering residing for space object i and identical x-axis direction is numbered, and obtains and these x-axis sides
To cubical set corresponding to numbering, the space object sequence number in the cube in the set forms x-axis director space object
Sequence number collection Mx。
Dichotomy sequence herein specifically includes：Carried out to cubical x-axis direction numbering residing for k-th of space object
During sequence, cubical x-axis direction numbering sequences sequence according to x-axis and forms array residing for k-1 space object before
Nk-1, now first with cubical x-axis direction numbering residing for k-th of space object of binary search in array Nk-1Position,
Then by cubical x-axis direction numbering insertion N residing for k-th of space objectk-1Correspondence position obtain array Nk.
Equally, cubical y-axis direction numbering carries out dichotomy sequence as residing for numeric order by space object, obtains sky
Between cubical y-axis direction numbering collection residing for object, record y-axis direction numbering concentrate with space object i residing for cubical y-axis
Direction numbering is adjacent and identical y-axis direction is numbered, and obtains cubical set corresponding with these y-axis direction numberings, the collection
Space object sequence number in cube in conjunction forms y-axis director space object sequence number collection My.By numeric order by space object
Residing cubical z-axis direction numbering carries out dichotomy sequence, obtains cubical z-axis direction numbering collection residing for space object,
Cubical z-axis direction residing for recording z-axis direction numbering concentration and space object i is numbered adjacent and identical z-axis direction and numbered,
Obtain cubical set corresponding with these z-axis direction numberings, the space object sequence number in the cube in the set forms z
Direction of principal axis space object sequence number collection Mz。
In other examples, the sequence in y-axis direction or z-axis direction can also first be carried out.
Then, the common factor M of the space object sequence number collection of three change in coordinate axis direction is calculatedi=Mx∩My∩Mz, obtain and space
The adjacent and identical cubical space object sequence number collection M of cube residing for object ii。
Finally, space object sequence number collection M is traveled throughiIn space object and space object i Euclidean distance, retain it is European away from
From less than threshold value dcSpace object as pairing target.
In one example, threshold value dcTake
Step S4：Calculate the collision probability between pairing target.
To the space object in adjacent and identical cube, it is general that its collision between any two is calculated by the following method
Rate：
According to aerodynamics, in volume elements dU, within the dt times, space object i and j mean number of collisions are：
C=SiSjVimpAcdUdt (1)
Collision frequency obeys Poisson statistics, therefore collision probability is：
pij=1-exp (- c) (2)
Wherein, Si、SjDistribution density of the two spaces object in volume elements dU, V are represented respectivelyimpIt is two spaces object
With respect to impact velocity, AcFor the collision cross-section of two spaces object.Collision cross-sectionAc1、
Ac2It is the respective sectional area of two spaces object.
The pairing target considered in this method is Euclidean distance in dcWithin space object, therefore dU is no longer cubical
Volume, but with dcFor the spheroid volume of radius, i.e.,
Space object is uniformly distributed in volume elements dU simultaneously, therefore
Si=Sj=1/dU (4)
Time sampling interval dt is set to 5 days, and the collision probability p between space object i and j can be calculatedij。
In summary, the collision probability method that the disclosure is developed based on cube models, it is empty to adjacent cube by increase
Between object collision possibility consideration, compensate for the defects of original cube models may omit collision situation so that after improvement
Cube models more to meet physics true, analysis result is more rationally credible.The disclosure is applied to space junk system long-term
To the assessment of collision probability in evolutionary process, be advantageous to improve the reasonability and confidence level of space junk long-term evolution model.And
Research to space junk long-term evolution model can carry out active fragment to following China and remove offer analysis of strategies and model
Support.
So far, the present embodiment is described in detail combined accompanying drawing.According to above description, those skilled in the art
There should be clear understanding to the disclosure.
It should be noted that in accompanying drawing or specification text, the implementation that does not illustrate or describe is affiliated technology
Form known to a person of ordinary skill in the art, is not described in detail in field.In addition, above-mentioned definition to each element and not only limiting
Various concrete structures, shape or the mode mentioned in embodiment, those of ordinary skill in the art can be carried out simply more to it
Change or replace, such as：
(1) direction term mentioned in embodiment, such as " on ", " under ", "front", "rear", "left", "right" etc., only it is ginseng
The direction of accompanying drawing is examined, is not used for limiting the protection domain of the disclosure；
(2) consideration that above-described embodiment can be based on design and reliability, the collocation that is mixed with each other uses or and other embodiment
Mix and match uses, i.e., the technical characteristic in different embodiments can freely form more embodiments.
Particular embodiments described above, the purpose, technical scheme and beneficial effect of the disclosure are carried out further in detail
Describe in detail bright, should be understood that the specific embodiment that the foregoing is only the disclosure, be not limited to the disclosure, it is all
Within the spirit and principle of the disclosure, any modification, equivalent substitution and improvements done etc., the guarantor of the disclosure should be included in
Within the scope of shield.
Claims (10)
1. a kind of collision probability computational methods based on cube models, including：
Terrestrial space is divided into cube grid, and cube is numbered；
Calculate position and its residing cube numbering of space object；
Space object is matched, using the space object in adjacent and identical cube as pairing target；And
Calculate the collision probability between pairing target.
It is described that terrestrial space is divided into cube grid 2. collision probability computational methods as claimed in claim 1, and to cube
Body be numbered including：
Using the earth's core as coordinate origin, cartesian coordinate system is established, terrestrial space is divided into cube grid, and to each vertical
Cube is numbered in units of the length of side.
3. collision probability computational methods as claimed in claim 2, the numbering is expressed as (x, y, z), and x, y, z represents vertical respectively
Numbering of the cube in x-axis direction, y-axis direction and z-axis direction.
4. collision probability computational methods as claimed in claim 1, the position for calculating space object and its residing cube
Body numbering includes：
Position according to where the orbital tracking after the renewal of each space object calculates it, searches cube residing for the position
Body, and cubical numbering residing for record.
5. collision probability computational methods as claimed in claim 1, described that space object is matched, adjacent and phase will be in
Include with the space object in cube as pairing target：
Respectively in three change in coordinate axis direction, cubical numbering is ranked up as residing for numeric order by space object, obtain with
Cubical numbering is adjacent residing for object space object and is identically numbered；
Space object sequence number in cube corresponding with the numbering forms the space object sequence number collection of three change in coordinate axis direction；
Calculate three change in coordinate axis direction space object sequence number collection common factor, obtain with object space object residing for cube it is adjacent
With the cubical space object sequence number collection of identical；
Travel through the Euclidean distance of space object and object space object that space object sequence number is concentrated, retain Euclidean distance less than
The space object of threshold value is as pairing target.
6. collision probability computational methods as claimed in claim 5, stood using dichotomy as residing for numeric order by space object
The numbering of cube is ranked up.
7. collision probability computational methods as claimed in claim 5, the threshold value take the cube length of side to be multiplied by
8. collision probability computational methods as claimed in claim 1, the collision probability calculated between pairing target includes：
To the space object in adjacent and identical cube, space object i and j mean number of collisions are：
C=SiSjVimpAcdUdt
Collision probability is：
pij=1-exp (- c)
Wherein, dU is volume elements；Dt is time sampling interval；Si、SjDistributions of the representation space object i and j in volume elements dU is close respectively
Degree；VimpIt is space object i and j relative impact velocity；AcFor space object i and j collision cross-section.
9. collision probability computational methods as claimed in claim 8, the volume elements dU be between space object i and j it is European away from
From threshold value be radius spheroid volume.
10. collision probability computational methods as claimed in claim 9, wherein,
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<mrow>
<mn>4</mn>
<mi>&pi;</mi>
</mrow>
<mn>3</mn>
</mfrac>
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<mi>d</mi>
<mi>c</mi>
<mn>3</mn>
</msubsup>
<mo>=</mo>
<mn>4</mn>
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</msqrt>
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1
Space object is uniformly distributed in volume elements dU,
Si=Sj=1/dU
Wherein, dcThe threshold value of Euclidean distance between space object i and j；H is the cube length of side.
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