CN107220497A - A kind of Circularity error evaluation method based on packet learning aid algorithm - Google Patents
A kind of Circularity error evaluation method based on packet learning aid algorithm Download PDFInfo
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Abstract
Involved in the present invention is a kind of Circularity error evaluation method based on packet learning aid algorithm, first, according to lowest area principal, sets up the solution mathematical modeling of Circularity error evaluation；Secondly, by obtaining the measurement data of tested circularity key element, and set up mathematical modeling is combined, sets up the object function of problem；Finally, object function is solved using packet learning aid algorithm, key step includes the step such as mutual study between the Parameter Initialization procedure of algorithm, the teaching phase of student performance, student, and it is high for standard learning aid algorithmic procedure solving precision, the problems such as convergence rate is slower, while using population grouping strategy, strengthening the global optimizing ability of algorithm, so as to sufficiently improve computational accuracy, finally solved.Parameter is less needed for this method, algorithm stability is good, surveyed data can be sufficiently applied to, it is more novel in algorithm application, test function is more accurate relative to other algorithms most in use, faster, solution procedure complies fully with the Minimum Area principle in international standard to iteration speed, therefore computational solution precision is higher.
Description
Technical field
It is more particularly to a kind of based on packet learning aid algorithm the invention belongs to the digital measuring field of machine components
Circularity error evaluation method.
Background technology
Deviation from circular from is one of important Form and position error of revolving parts, affects the assembly precision of part and uses the longevity
Life.Therefore, how accurately to obtain the control information of part circularity, it is ensured that the designing quality of engineering goods, be important at this stage
One of research topic.
The national Specification error evaluation method of four kinds of circularity, including minimum circumscribed circle method, maximum inscribed circle method, most
Small square law and minimum area method, wherein least square method and minimum area method is most widely used.For machine components circle
The evaluation algorithm of error is spent, Wang Dongxia etc. is in its document《Application of the differential evolution algorithm in Circularity error evaluation》In employ
Differential evolution algorithm is evaluated to deviation from circular from, and Yue Wuling etc. is in its document《Deviation from circular from based on imitative delta algorithm is fast
Fast accurate evaluation》In employ imitative delta algorithm deviation from circular from evaluated, Chen Sa et al. is in its document《Lost based on improving
The Circularity error evaluation of propagation algorithm》Middle use genetic algorithm is evaluated to flatness error.
In summary, continuing to develop with computer technology and artificial intelligence technology, Circularity error evaluation method is also got over
Come more perfect, precision also more and more higher, and wherein topmost method is exactly that minimum area method is entered with reference to all kinds of optimized algorithms
Row constantly research.Learning aid optimized algorithm is a kind of new global intelligent optimization algorithm proposed in 2012, its algorithm parameter
Seldom, algorithm robustness very well, can further improve arithmetic accuracy by introducing corresponding strategies, be calculated because learning aid optimizes
The calculating performance of method well, has been widely used in all kinds of engineering fields at this stage.
The present invention is on the basis of basic learning aid algorithm, to add grouping strategy to algorithm initialization process, enter one
Step improves the search capability of algorithm, it is to avoid algorithm is absorbed in local optimum, to improve the evaluating precision of part flatness.
The content of the invention
It is an object of the invention to provide a kind of Circularity error evaluation method based on packet learning aid algorithm, to improve circularity
The evaluating precision and computational stability of error.
A kind of Circularity error evaluation method based on packet learning aid algorithm, mainly including herein below：
Step one：The measured circle key element of tested part is determined, the measurement data points of part are obtained by three coordinate measuring machine
For Pi(xi, yi) (i=1,2 ..., n)；
Step 2：According to the lowest area principal of deviation from circular from, shown in the range formula of point to the center of circle, such as formula (1)；Build
The mathematical modeling of vertical deviation from circular from, shown in such as formula (2).Wherein RijFor the distance of measuring point to the center of circle, (xi, yi) sat for measuring point
Mark, (aj, bj) it is concentric circles central coordinate of circle value, f (a`, b`) is deviation from circular from；
F (a ', b ')=min (max (Rij)-min(Rij)) (2)
Step 3：Read measurement data Pi(xi, yi) (i=1,2 ..., n), bring into formula (2), to learning aid algorithm
Parameter initialized, it is main to include initialization student X=(x1, x2..., xi), i=1, wherein 2 ..., N, xiRepresent class
Student i, N in level are student's quantity.For some student xi, there is x againi=(xi1, xi2..., xij), j=1,2 ..., D,
xijThe subject j, D for representing student's i are total subject, and optimal solution is xt, i.e. fitness value is optimal for class's teacher's achievement, religion
Iterations W, ramping constraint iterations w, into step 4 with learning optimized algorithm；
Step 4：It is to strengthen the information interchange ability between student using the purpose of population packet and strategy of shuffling, by building
Vertical new group and the teacher of each group, so as to increase the ability of searching optimum of algorithm, it is to avoid algorithm is precocious.Population point is defined first
Group policy：Determine group's number m in class, every group of number of student n, so that it is determined that produce initial student's number for F (F=m ×
N) fitness of each student is calculated, student is ranked up according to fitness by quality, and record the adaptation of whole population
The optimal student x of angle valuet.Student is grouped by group number m, criteria for classifying is that the student that will be ranked first is put into the 1st
Group, the 2nd student is put into the 2nd group, and m-th of student is put into m-th of group, and m+1 student then is put into the 1st again
Group, by that analogy, the 2m student are put into m-th of group, wherein, q-th of group YqExpression formula is：Yq=x (q+m (p-
1)), p=1 ..., n；Q=1 ... m).Global optimum student x is recorded simultaneouslytWith Straight A x in groupT, m。
Step 5：The fitness function value of each student is calculated, and according to achievement of the formula (3), (4) and (5) to student
It is updated, in formula：X (i, j) ' is the achievement after student i subject j renewals；Before x (i, j) updates for student i subject j
Achievement；Rand is the random number between [0,1]；xt(j) it is the subject j achievements of teacher；T is the teaching factor；X (j) is student section
Mesh j achievement；M (j) is j-th of section's purpose average achievement in class；Round is the bracket function rounded up.Teaching phase
After the completion of, by contrasting the quality of fitness value, the renewal of solution is completed, into step 5；
X (i, j) '=x (i, j)+rand × (xt(j)-tM(j)) (3)
T=round [1+rand (0,1)] (4)
Step 6：Student performance is carried out again " to learn ", concrete mode is by randomly selecting two students, contrasting it
Fitness value obtains size, the carry out study renewal small to fitness value for making fitness value big, and more new formula is such as shown in (6), formula
In：x′aAchievement after learning for student a；xaAchievement before learning for student a；xbAchievement before learning for student b.When learning
After the completion of journey, further with the achievement x of teachertContrasted, the renewal of solution is completed, into step 7；
x′a=xb+rand×|xa-xb| (6)
Step 7：Whether evaluation algorithm is when iteration completion, and after W iteration is met, algorithm is terminated, now globally optimal solution
xtFitness function value be required flatness error value, if algorithm fails to complete W iteration, this iteration is obtained
Globally optimal solution brings next iteration process into as class teacher.
Compared with prior art, the present invention has the advantage that：
By setting up the minimum area method parametric equation of Flatness error evaluation, asking for flatness is more intuitively reflected
Mathematical modeling is solved, is a kind of general mathematical modeling, without the coordinate transformation process in computational geometry and measuring point preprocessing process
Etc. cumbersome modeling process, surveyed data can be sufficiently applied to, and be can apply among substantial amounts of measuring point data,
In algorithm application, the algorithm mutually introduces search by hill climbing strategy twice, entered on the basis of standard learning aid optimized algorithm
One step improves the precision of algorithm, and faster, solution procedure complies fully with the Minimum Area principle in international standard to convergence rate, because
This computational solution precision is higher.
Brief description of the drawings
Fig. 1 is the algorithm flow of the present invention；
Fig. 2 is the deviation from circular from iterative curve map of the present invention.
Embodiment
In order to become apparent from the design and advantage of the specific expression present invention, following processes will be with reference to accompanying drawing to whole
The protocol procedures of evaluation are described in detail.
The invention provides a kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain, it is main include with
Lower content：
Step one：The measured circle key element of tested part is determined, the measurement data points of part are obtained by three coordinate measuring machine
For Pi(xi, yi) (i=1,2 ..., n)；
Step 2：According to the lowest area principal of deviation from circular from, shown in the range formula of point to the center of circle, such as formula (1)；Build
The mathematical modeling of vertical deviation from circular from, shown in such as formula (2).Wherein RijFor the distance of measuring point to the center of circle, (xi, yi) sat for measuring point
Mark, (aj, bj) it is concentric circles central coordinate of circle value, f (a`, b`) is deviation from circular from；
F (a ', b ')=min (max (Rij)-min(Rij)) (2)
Step 3：Read measurement data Pi(xi, yi) (i=1,2 ..., n), bring into formula (2), to learning aid algorithm
Parameter initialized, it is main to include initialization student X=(x1, x2..., xi), i=1, wherein 2 ..., N, xiRepresent class
Student i, N in level are student's quantity.For some student xi, there is x againi=(xi1, xi2..., xij), j=1,2 ..., D,
xijThe subject j, D for representing student's i are total subject, and optimal solution is xt, i.e. fitness value is optimal for class's teacher's achievement, religion
Iterations W, ramping constraint iterations w, into step 4 with learning optimized algorithm；
Step 4：It is to strengthen the information interchange ability between student using the purpose of population packet and strategy of shuffling, by building
Vertical new group and the teacher of each group, so as to increase the ability of searching optimum of algorithm, it is to avoid algorithm is precocious.Population point is defined first
Group policy：Determine group's number m in class, every group of number of student n, so that it is determined that produce initial student's number for F (F=m ×
N) fitness of each student is calculated, student is ranked up according to fitness by quality, and record the adaptation of whole population
The optimal student x of angle valuet.Student is grouped by group number m, criteria for classifying is that the student that will be ranked first is put into the 1st
Group, the 2nd student is put into the 2nd group, and m-th of student is put into m-th of group, and m+1 student then is put into the 1st again
Group, by that analogy, the 2m student are put into m-th of group, wherein, q-th of group YqExpression formula is：Yq=x (q+m (p-
1)), p=1 ..., n；Q=1 ... m).Global optimum student x is recorded simultaneouslytWith Straight A x in groupT, m。
Step 5：The fitness function value of each student is calculated, and according to achievement of the formula (3), (4) and (5) to student
It is updated, in formula：X (i, j) ' is the achievement after student i subject j renewals；Before x (i, j) updates for student i subject j
Achievement；Rand is the random number between [0,1]；xt(j) it is the subject j achievements of teacher；T is the teaching factor；X (j) is student section
Mesh j achievement；M (j) is j-th of section's purpose average achievement in class；Round is the bracket function rounded up.Teaching phase
After the completion of, by contrasting the quality of fitness value, the renewal of solution is completed, into step 5；
X (i, j) '=x (i, j)+rand × (xt(j)-tM(j)) (3)
T=round [1+rand (0,1)] (4)
Step 6：Student performance is carried out again " to learn ", concrete mode is by randomly selecting two students, contrasting it
Fitness value obtains size, the carry out study renewal small to fitness value for making fitness value big, and more new formula is such as shown in (6), formula
In：x′aAchievement after learning for student a；xaAchievement before learning for student a；xbAchievement before learning for student b.When learning
After the completion of journey, further with the achievement x of teachertContrasted, the renewal of solution is completed, into step 7；
x′a=xb+rand×|xa-xb| (6)
Step 7：Whether evaluation algorithm is when iteration completion, and after W iteration is met, algorithm is terminated, now globally optimal solution
xtFitness function value be required roundness error, if algorithm fails to complete W iteration, by this iteration obtain it is complete
Office's optimal solution brings next iteration process into as class teacher.
It is described above, it is only that the present invention teaches good embodiment, but protection scope of the present invention is not limited thereto,
Any one skilled in the art the invention discloses technical scope in, the variations and alternatives that can be readily occurred in,
It should all be included within the scope of the present invention, therefore, protection scope of the present invention should be with scope of the claims
It is defined.
Claims (1)
1. a kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain, it is characterised in that use following steps：
Step one：The measured circle key element of tested part is determined, the measurement data points for obtaining part by three coordinate measuring machine are Pi
(xi, yi) (i=1,2 ..., n)；
Step 2：According to the lowest area principal of deviation from circular from, shown in the range formula of point to the center of circle, such as formula (1)；Set up circle
The mathematical modeling of error is spent, shown in such as formula (2).Wherein RijFor the distance of measuring point to the center of circle, (xi, yi) it is measuring point coordinate, (aj,
bj) it is concentric circles central coordinate of circle value, f (a`, b`) is deviation from circular from；
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F (a ', b ')=min (max (Rij)-min(Rij)) (2)
Step 3：Read measurement data Pi(xi, yi) (i=1,2 ..., n), bring into formula (2), to the ginseng of learning aid algorithm
Number is initialized, main to include initialization student X=(x1, x2..., xi), i=1, wherein 2 ..., N, xiRepresent in class
Student i, N is student's quantity.For some student xi, there is x againi=(xi1, xi2..., xij), j=1,2 ..., D, xijTable
The subject j, D of dendrography life i are total subject, and optimal solution is xt, i.e. fitness value is optimal for class's teacher's achievement, learning aid
The iterations W of optimized algorithm, ramping constraint iterations w, into step 4；
Step 4：It is to strengthen the information interchange ability between student using the purpose of population packet and strategy of shuffling, it is new by setting up
Group and each group teacher, so as to increase the ability of searching optimum of algorithm, it is to avoid algorithm is precocious.Population packet plan is defined first
Slightly：Group's number m in class, every group of number of student n are determined, is counted so that it is determined that producing initial student's number for F (F=m × n)
The fitness of each student is calculated, student is ranked up according to fitness by quality, and records the fitness value of whole population
Optimal student xt.Student is grouped by group number m, it is the 1st small that criteria for classifying is that the student that will be ranked first is put into
Group, the 2nd student is put into the 2nd group, and m-th of student is put into m-th of group, is then again put into m+1 student the 1st small
Group, by that analogy, the 2m student are put into m-th of group, wherein, q-th of group YqExpression formula is：Yq=x (q+m (p-1)), p
=1 ..., n；Q=1 ... m).Global optimum student x is recorded simultaneouslytWith Straight A x in groupT, m。
Step 5：The fitness function value of each student is calculated, and the achievement of student is carried out according to formula (3), (4) and (5)
Update, in formula：X (i, j) ' is the achievement after student i subject j renewals；X (i, j) is the achievement before student i subject j renewals；
Rand is the random number between [0,1]；xt(j) it is the subject j achievements of teacher；T is the teaching factor；X (j) is student's subject j's
Achievement；M (j) is j-th of section's purpose average achievement in class；Round is the bracket function rounded up.Teaching phase is completed
Afterwards, by contrasting the quality of fitness value, the renewal of solution is completed, into step 5；
X (i, j) '=x (i, j)+rand × (xt(j)-tM(j)) (3)
T=round [1+rand (0,1)] (4)
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Step 6：Student performance is carried out again " to learn ", concrete mode is by randomly selecting two students, contrasting its adaptation
Angle value obtains size, the carry out study renewal small to fitness value for making fitness value big, and more new formula is such as shown in (6), in formula：
x′aAchievement after learning for student a；xaAchievement before learning for student a；xbAchievement before learning for student b.Work as learning process
After the completion of, further with the achievement x of teachertContrasted, the renewal of solution is completed, into step 7；
x′a=xb+rand×|xa-xb| (6)
Step 7：Whether evaluation algorithm is when iteration completion, and after W iteration is met, algorithm is terminated, now globally optimal solution xt's
Fitness function value is required flatness error value, if algorithm fails to complete W iteration, the overall situation that this iteration is obtained
Optimal solution brings next iteration process into as class teacher.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108319764A (en) * | 2018-01-15 | 2018-07-24 | 湖北汽车工业学院 | Evaluation method for spatial straightness errors method based on longicorn palpus searching algorithm |
| CN109323677A (en) * | 2018-08-21 | 2019-02-12 | 上海隧道工程有限公司 | Improve the Circularity error evaluation algorithm of cuckoo searching algorithm |
| CN109917647A (en) * | 2019-03-06 | 2019-06-21 | 南京航空航天大学 | One kind optimizing sliding-mode control based on the improved learning aid algorithm of instructional strategies and filled Spacecraft |
| CN110579201A (en) * | 2019-07-25 | 2019-12-17 | 北京航空航天大学 | Flatness evaluation method based on differential evolution algorithm |
-
2017
- 2017-05-26 CN CN201710387364.3A patent/CN107220497A/en active Pending
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108319764A (en) * | 2018-01-15 | 2018-07-24 | 湖北汽车工业学院 | Evaluation method for spatial straightness errors method based on longicorn palpus searching algorithm |
| CN109323677A (en) * | 2018-08-21 | 2019-02-12 | 上海隧道工程有限公司 | Improve the Circularity error evaluation algorithm of cuckoo searching algorithm |
| CN109323677B (en) * | 2018-08-21 | 2020-08-11 | 上海隧道工程有限公司 | Roundness error evaluation algorithm for improved cuckoo search algorithm |
| CN109917647A (en) * | 2019-03-06 | 2019-06-21 | 南京航空航天大学 | One kind optimizing sliding-mode control based on the improved learning aid algorithm of instructional strategies and filled Spacecraft |
| CN109917647B (en) * | 2019-03-06 | 2020-12-11 | 南京航空航天大学 | Teaching and learning algorithm improved based on teaching strategy and liquid-filled spacecraft optimization sliding mode control method |
| CN110579201A (en) * | 2019-07-25 | 2019-12-17 | 北京航空航天大学 | Flatness evaluation method based on differential evolution algorithm |
| CN110579201B (en) * | 2019-07-25 | 2021-06-01 | 北京航空航天大学 | Flatness evaluation method based on differential evolution algorithm |
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Application publication date: 20170929 |