CN108562258A - A kind of maximum inscribed circle column diameter assessment method of fast steady letter - Google Patents
A kind of maximum inscribed circle column diameter assessment method of fast steady letter Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/10—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring diameters
Abstract
The invention belongs to delicate metering and computer application field, have be related to a kind of stabilization, quickly, the simple maximum inscribed circle column diameter assessment method of form, comprise the steps of：Step 1：Measuring point collection is obtained, and feature row vector collection, boundary element collection and state elements collection are established according to measuring point collection；Step 2：It takes state elements to integrate the corresponding measuring point of minimum value as key point, and its measuring point serial number is added to key point and is concentrated；Step 3：Analysis matrix and analysis column vector are established according to crucial point set；Step 4：Rank analysis is carried out to analysis matrix and augmentation analysis matrix, continues optimizing to determine, reject key point or terminator and obtains optimal value；Step 5：It solves analysis matrix and analysis column vector obtains search direction；Step 6：To come up with the new key point of problem solving, measuring point state set is updated, and enter and recycle next time；Step 7, terminator and optimal value is obtained.
Description
Technical field
The invention belongs to delicate metering and computer application field, have be related to a kind of stabilization, quickly, form simply most
Body diameter assessment method inscribed greatly, the evaluation of the maximum inscribed circle column diameter for the parts that can be used for having rotary structure, and
Guidance is provided for the improvement of its processing technology.
Background technology
Scale error, Form and position error（The abbreviation of form error and site error）Directly affect product quality, assembly and its
Service life quickly and accurately calculates part error, has great importance.Maximum is given in national standard and iso standard
The definition of inscribed body diameter and method of discrimination, but do not provide the side that maximum inscribed cylinder diameter value is calculated by measurement data
Method.Currently, the assessment method of maximum inscribed circle column diameter is a research hotspot of academia, it is broadly divided into following five classes evaluation
Method.
The first kind, special geometry assessment method.Using the geometric properties of cylinder, according to inscribed cylinder and/or circumcircle
The translation of column and deformation strategy, the maximum for gradually finding the definition and/or criterion that meet national standard and iso standard are inscribed
Body diameter.Such methods speed, but the form of mathematical model is more complex, is not easy to promote the use of.
Second class, convex closure or class convex closure assessment method.Convex closure or class convex closure are built using the property of convex closure, obtains and effectively surveys
Measure data, diminution wait for assessment of data scale, eventually by enumerative technique obtain meet national standard and iso standard definition and/or
The maximum inscribed circle column diameter of criterion.Such methods have apparent advantage when handling medium-scale measuring point data.Data are advised
The larger occasion of mould, data scale can be reduced by building convex closure by remaining on.But what such methods were used to directly evaluate
Efficiency has but seemed insufficient.
Third class builds objective optimization function linearly or nonlinearly, and optimizes solution using common optimum method,
The optimal value of objective optimization function is as maximum inscribed circle column diameter.Such methods are easily understood, and are realized in many softwares
Standard solution, thus, it is easy to promote.Due to there is no that the geometrical feature of maximum inscribed circle column diameter evaluation is added, and do not examine
Consider larger this case of data scale in evaluation task, such methods are generally inefficient.
4th class, artificial intelligence/biological intelligence algorithm.Such methods are to analyze compared to the advantage of third class method
" there is complicated gradient analytic expression or the object function without apparent analytic expression " and find " global optimum ".Such methods are current
Also standard solution is realized in many softwares, therefore, is also easy to promote.Although current such methods are burning hoter, it is used in
Maximum inscribed circle column diameter is less suitable when evaluating.This is because the gradient of the object function of maximum inscribed circle column diameter evaluation is
The sum of a large amount of simple analytic expressions, and " local optimum " of object function is exactly " global optimum ".Therefore, such methods are not
There is advantage more apparent than third class method.
5th class, active set m ethod.Active set m ethod is a kind of method of special disposal Large-scale programming problem, and feature is
Reduce the processing to " inactivce constraints " to the greatest extent in searching process.When being evaluated applied to maximum inscribed circle column diameter, efficiency and the
A kind of method is suitable, and algorithm maturity and Integrated Simulation degree are suitable with third class, the 4th class method, be it is current than faster, letter
Single maximum inscribed circle column diameter assessment method.But this method is very sensitive to initial value, being not can be steadily complete
Task is evaluated at maximum inscribed circle column diameter.
In conclusion still lack at present a kind of stabilization, quickly, form simple maximum inscribed circle column diameter evaluation side
Method.
Invention content
The purpose of the present invention is：
The present invention existing described problem in view of the prior art, provide a kind of stabilization, quickly, the simple maximum inscribed circle of form
Column diameter assessment method, the evaluation of the maximum inscribed circle column diameter for the parts that can be used for having rotary structure, and processed for it
The improvement of technique provides guidance.
The scheme that the present invention uses is：
A kind of maximum inscribed circle column diameter assessment method of fast steady letter is through the following steps that realize：
Step 1：Acquisition measuring point collectionp i , and according top i Establish feature row vector collectionA i , boundary element collectionb i And state member
Element collectiont i , wherein：
i=1, 2, 3, …, N；iFor measuring point serial number,NFor measuring point sum；
p i ={x i , y i , z i It is measuring pointiPlane rectangular coordinates, and the axis of tested cylinder is close to coordinate systemzAxis,
XOY plane of the central plane of two bottom surfaces of tested cylinder close to coordinate system；
t i =, all state elementst i Collection be combined into state elements collectiont i }；
A i =([x i , y i , -y i z i , x i z i ])/t i , it is a feature row vector, all feature row vectorsA i Collection be combined into spy
Sign row vector collectionA i }；
b i =b, it is a real number more than 0, all boundary elementsb i Collection be combined into boundary element collectionb i }。
Step 2 is carried out after step 1.
Step 2：It takest i Minimum valuet minCorresponding measuring pointp l1For key point, and by its measuring point serial numberl 1It is added to key point
CollectionlIn.
Step 3 is carried out after step 2.
Step 3：According to crucial point setlEstablish analysis matrixAWith analysis column vectorb, wherein：
A=[…, A j T, …, A k T, …]T, it isLThe matrix that row 4 arranges,LFor crucial point setlIn element number,j, k
For crucial point setlIn element；
b=[…, b, …]T, it isLCapable column vector.
Step 4 is carried out after step 3.
Step 4：To analysis matrixAAnd augmentation analysis matrix [A, b] carry out rank analysis.
It calculatesr A =rank(A),r Ab =rank（[A, b]）, and comparer A Withr Ab , only following two situations：
Situation one：Ifr A =r Ab , then, optimizing should be continued, jump to step 5；
Situation two：Ifr A < r Ab , then, it attempts from analysis matrixAWith analysis column vectorbIn delete crucial point setlIn
Some elementlCorresponding row obtains reducing matrixA l- With diminution column vectorb l- , seek linear equationA l- v l- = b l- Solutionv l- =v l-0 , then calculateb l- =A l v l-0 ；If key point setlIn element all attempted, and do not obtain any oneb l-
>b, then, optimizing should be terminated, jump to step 7；If attempt crucial point setlIn elementlWhen, it obtainsb l- >b, that
, matrix will be reducedA l- With diminution column vectorb l- Respectively asAMatrix and analysis column vectorb, by elementlRemove crucial point set
{l, and jump to step 5；Wherein,v l- =[v l-,1, v l-,2, v l-,3, v l-,4]T,v l-0 =[v l-0,1, v l-0,2, v l-0,3,v l-0,4]T。
Step 5：Seek linear equationAv= bSolutionv=v 0 , whereinv=[v 1, v 2, v 3, v 4]T,v 0 =[v 0,1, v 0,2,v 0,3, v 0,4]T。
Step 6 is carried out after step 5.
Step 6：It calculatesv i =A i v 0 , then calculateτ i =(t i – t min)÷(b - v i ).It takesτ i In more than zero part in
Minimum valueτ minCorresponding measuring pointp l2For new key point, and by its measuring point serial numberl 2Be added to crucial point setlIn.
To ownt i It is updated tot i + τ min∙ v i ,t minIt is updated tot i Minimum value.
An optimizing is completed after step 6, carries out step 3.
Step 7：It calculatest=2 t min Maximum inscribed circle column diameter required by being exactly.
In order in easily obtaining step 1 measuring point collectionp i , can by general measurement datap i * By following but
Unlimited following methods are handled, and obtain axis close to coordinate systemzAxis is tested two bottom center's plane of cylinder close to coordinate system
XOY plane measuring point collectionp i }：One, it is moved by the average value of coordinate；Two, it is moved by the extreme value of coordinate；Three, it presses and sits
Target root mean square minimum principle is moved.
More accurate solution in order to obtain, can be optimized as follows：
In step 6, ifτ min∙ v i Single value or the accumulated value ∑ of iteration for several timesτ min∙ v i More than given threshold valueq,
So, by measuring point collectionp i Be updated top i + τ min∙vOrp i +∑τ min∙v, and by the formula more new feature row vector in step 1
CollectionA i , boundary element collectionb i And state elements collectiont i }。
For the ease of numerical computations, Ke YilingbA specific numerical value more than 0 is taken, can be, but not limited to 1.
The beneficial effects of the invention are as follows：
1, fully consider therefore the geometrical feature of inscribed body diameter, simplified evaluation form are easier to than first kind assessment method
It promotes.2, fully consider that the geometrical feature of inscribed body diameter, each iteration all obtain one more by ripe linear operation
Excellent value, and minimum inscribed body diameter can be finally obtained, therefore, this algorithm comparison is stablized, and there is no the 5th class methods
Initial value tender subject.The fact that 3, imply " most of measuring point is invalid measurement point " in inscribed body diameter evaluation, these are invalid
Iteration will not be added in measuring point, and therefore, iterations of the invention are less, with first kind assessment method and the 5th class assessment method phase
When.4, when calculating search direction, the crucial point set of considerationlCorresponding measuring point, therefore, the operand of each iteration is smaller,
It is suitable with the 5th class assessment method.5, since the operand of less, each iteration of iterations is smaller, total arithmetic speed
It is suitable with first kind assessment method and the 5th class assessment method.
The present invention provides a kind of maximum inscribed circle column diameter assessment method, this method is stable, quick, form is simple, can
Evaluation for there is the maximum inscribed circle column diameter of the parts of rotary structure, and provide finger for the improvement of its processing technology
It leads, therefore has industrial possibility.
Description of the drawings
Fig. 1 is the flow chart of the present invention.
Specific implementation mode
The following is specific embodiments of the present invention, and with reference to attached drawing, the solution of the present invention is further described, but this hair
It is bright to be not limited to these examples.
Evaluation measuring point collectionp i Maximum inscribed circle column diameter.
Step 1：Acquisition measuring point collectionp i As follows：
| i | x i | y i | z i |
| 1 | 9.5285 | 3.1018 | -44.9417 |
| 2 | 5.8950 | -8.0895 | -39.9115 |
| 3 | -5.8697 | -8.0894 | -34.9254 |
| 4 | -9.5075 | 3.0930 | -29.9394 |
| 5 | 0.0051 | 10.0065 | -24.9598 |
| 6 | 9.5187 | 3.0979 | -19.9390 |
| 7 | 5.8812 | -8.0864 | -14.9905 |
| 8 | -5.8714 | -8.0748 | -9.9766 |
| 9 | -9.4958 | 3.1040 | -4.9176 |
| 10 | 0.0166 | 10.0059 | 0.0309 |
| 11 | 9.5210 | 3.0967 | 5.0832 |
| 12 | 5.8941 | -8.0790 | 10.0263 |
| 13 | -5.8642 | -8.0855 | 15.0456 |
| 14 | -9.5029 | 3.1009 | 20.0992 |
| 15 | 0.0151 | 10.0196 | 25.0235 |
| 16 | 9.5211 | 3.0912 | 30.0757 |
| 17 | 5.8899 | -8.0730 | 35.0988 |
| 18 | -5.8593 | -8.0820 | 40.0000 |
| 19 | -9.4997 | 3.0943 | 45.0219 |
| 20 | 0.0065 | 10.0019 | 50.0748 |
Establish state elements collectiont i As follows：
| i | t i |
| 1 | 10.0207 |
| 2 | 10.0095 |
| 3 | 9.9946 |
| 4 | 9.9980 |
| 5 | 10.0065 |
| 6 | 10.0101 |
| 7 | 9.9989 |
| 8 | 9.9838 |
| 9 | 9.9902 |
| 10 | 10.0059 |
| 11 | 10.0120 |
| 12 | 10.0006 |
| 13 | 9.9882 |
| 14 | 9.9960 |
| 15 | 10.0196 |
| 16 | 10.0104 |
| 17 | 9.9933 |
| 18 | 9.9825 |
| 19 | 9.9910 |
| 20 | 10.0019 |
Establish feature row vector collectionA i As follows：
Establish boundary element collectionb i As follows：
{b i }=[1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1]T。
Step 2 is carried out after step 1.
Step 2：It takest i Minimum valuet min=9.9825 corresponding measuring pointsp 18For key point, and its measuring point serial number 18 is added
To crucial point setlIn so thatl}={18}.Step 3 is carried out after step 2.
Step 3：According to crucial point setlEstablish analysis matrixAWith analysis column vectorb, wherein：
A=A 18=[- 0.5870,0.8096,32.3848, -23.4783] are a matrixes for 1 row 4 row, crucial point setl}
Element number in={ 18 } is 1, element 18；
b=1, it is the column vector of 1 row, single-element can also be regarded as.
Step 4 is carried out after step 3.
Step 4：To analysis matrixAAnd augmentation analysis matrix [A, b] carry out rank analysis.
It calculatesr A =rank(A)=1,r Ab =rank（[A, b]）=1, and comparer A Withr Ab .Becauser A =r Ab , so should be after
Continuous optimizing, jumps to step 5.
Step 5：Seek linear equationAv= bSolutionv=v 0 =[0.0000 , 0.0000 , 0.0309 , 0.0000]T。
Step 6 is carried out after step 5.
Step 6：It calculatesv i =A i v 0 , as a result as follows：
| i | v i |
| 1 | 0.4296 |
| 2 | -0.9960 |
| 3 | -0.8729 |
| 4 | 0.2860 |
| 5 | 0.7707 |
| 6 | 0.1905 |
| 7 | -0.3744 |
| 8 | -0.2492 |
| 9 | 0.0472 |
| 10 | -0.0010 |
| 11 | -0.0485 |
| 12 | 0.2501 |
| 13 | 0.3761 |
| 14 | -0.1925 |
| 15 | -0.7727 |
| 16 | -0.2868 |
| 17 | 0.8756 |
| 18 | 1.0000 |
| 19 | -0.4306 |
| 20 | -1.5462 |
Then it calculatesτ i =( t i –t min)÷(b - v i ), the result that record is wherein more than 0 is as follows：
| i | τ i |
| 1 | 0.0669 |
| 2 | 0.0135 |
| 3 | 0.0065 |
| 4 | 0.0217 |
| 5 | 0.1048 |
| 6 | 0.0342 |
| 7 | 0.0120 |
| 8 | 0.0010 |
| 9 | 0.0081 |
| 10 | 0.0234 |
| 11 | 0.0281 |
| 12 | 0.0241 |
| 13 | 0.0092 |
| 14 | 0.0114 |
| 15 | 0.0210 |
| 16 | 0.0217 |
| 17 | 0.0866 |
| 19 | 0.0060 |
| 20 | 0.0076 |
Wherein minimum valueτ min=0.0010 corresponding measuring pointp 8For new key point, its measuring point serial number 8 is added to crucial point set
{lIn so that crucial point setl}={18,8}。
To ownt i It is updated tot i +τ min∙ v i ,t minIt is updated tot i Minimum value.
An optimizing is completed after step 6, carries out step 3.
And so on, after carrying out the 7th optimizing, crucial point setl} ={18,20,5,6,17}。
At this point, first carrying out step 3：According to crucial point setl}={ 18,20,5,6,17 } establish analysis matrixAIt is arranged with analysis
Vectorb, wherein：
b=[1,1,1,1,1]T。
Step 4 is carried out after step 3.
Step 4：To analysis matrixAAnd augmentation analysis matrix [A, b] carry out rank analysis.
It calculatesr A =rank(A)=4,r Ab =rank（[A, b]）=5, r A < r Ab .First, it attempts from analysis matrixAWith point
Analyse column vectorbIn delete crucial point setl}={ 18,20,5,6,17 } in first element, 18 corresponding row, obtain reduction square
Battle arrayA 18- ：
Withb 18- Column vector：b 18- =[1,1,1,1]T。
Acquire linear equationA 18- v 18- = b 18- Solutionv 18- =v 18-0 =[1.5734 , 0.9990 , 0.0000 ,
0.0425]T, then calculateb 18- =A 18 v 18-0 =-2.7289<1=b.It is similar, it can be in the hope of：b 20- =-1.6596 <1=b,b 5- =
-11.4667 <1=b,b 6- = 68.9453 >1=b。
It willA 6- Matrix andb 6- Matrix respectively asAMatrix andbMatrix, by element 6 remove crucial point setlSo thatl}=
{ 18,20,5,17 }, and jump to step 5.
It is similar, after next 8th optimizing, crucial point setl} ={18,20,5,17,9}。
At this point, first carrying out step 3：According to crucial point setl}={ 18,20,5,17,9 } establish analysis matrixAIt is arranged with analysis
Vectorb.Wherein：
b=[1,1,1,1,1]T。
Step 4 is carried out after step 3.
Step 4：To analysis matrixAAnd augmentation analysis matrix [A, b] carry out rank analysis.
It calculatesr A =rank(A)=4,r Ab =rank（[A, b]）=5, r A < r Ab .As previously mentioned, can be in the hope of：b 18- =A 18 v 18-0 =-2.8788<1=b；b 20- =A 20 v 20-0 = -1.7390<1=b；b 5- =A 5 v 5-0 = -13.2907<1=b；b 17- =A 17 v 17-0 =
-2.4762 <1=b；b 9- =A 9 v 9-0 = -50.3836<1=b.Jump to step 7.
Step 7：It calculatest=2 t min =2 × 9.9945=19.9890 be exactly required maximum inscribed circle column diameter.
In the above description, the present invention is illustrated by specific embodiment, but it should be understood by those skilled in the art that not
It is detached from the thought invented in right and can carry out various transformations and deformation in field.
Claims (5)
1. a kind of maximum inscribed circle column diameter assessment method of fast steady letter, which is characterized in that comprise the steps of：
Step 1：Acquisition measuring point collectionp i , and according top i Establish feature row vector collectionA i , boundary element collectionb i And state member
Element collectiont i , wherein：
i=1, 2, 3, …, N；iFor measuring point serial number,NFor measuring point sum；
p i ={x i , y i , z i It is measuring pointiPlane rectangular coordinates, and the axis of tested cylinder is close to coordinate systemzAxis, quilt
The central plane of two bottom surfaces of cylinder is surveyed close to the XOY plane of coordinate system；
t i =, all state elementst i Collection be combined into state elements collectiont i }；
A i =([x i , y i , -y i z i , x i z i ])/t i , it is a feature row vector, all feature row vectorsA i Collection be combined into spy
Sign row vector collectionA i }；
b i =b, it is a real number more than 0, all boundary elementsb i Collection be combined into boundary element collectionb i }；
Step 2 is carried out after step 1；
Step 2：It takest i Minimum valuet minCorresponding measuring pointp l1For key point, and by its measuring point serial numberl 1Be added to crucial point setl}
In；
Step 3 is carried out after step 2；
Step 3：According to crucial point setlEstablish analysis matrixAWith analysis column vectorb, wherein：
A=[…, A j T, …, A k T, …]T, it isLThe matrix that row 2 arranges,LFor crucial point setlIn element number,j, k
For crucial point setlIn element；
b=[…, b, …]T, it isLCapable column vector；
Step 4 is carried out after step 3；
Step 4：To analysis matrixAAnd augmentation analysis matrix [A, b] carry out rank analysis；
It calculatesr A =rank(A),r Ab =rank（[A, b]）, and comparer A Withr Ab , only following two situations：
Situation one：Ifr A =r Ab , then, optimizing should be continued, jump to step 5；
Situation two：Ifr A < r Ab , then, it attempts from analysis matrixAWith analysis column vectorbIn delete crucial point setlIn
Some elementlCorresponding row obtains reducing matrixA l- With diminution column vectorb l- , seek linear equationA l- v l- = b l- Solutionv l- =v l-0 , then calculateb l- =A l v l-0 ；If key point setlIn element all attempted, and do not obtain any oneb l-
>b, then, optimizing should be terminated, jump to step 7；If attempt crucial point setlIn elementlWhen, it obtainsb l- >b, that
, matrix will be reducedA l- With diminution column vectorb l- Respectively asAMatrix and analysis column vectorb, by elementlRemove crucial point set
{l, and jump to step 5；Wherein,v l- =[v l-,1, v l-,2, v l-,3, v l-,4]T,v l-0 =[v l-0,1, v l-0,2, v l-0,3,v l-0,4]T；
Step 5：Seek linear equationAv= bSolutionv=v 0 , whereinv=[v 1, v 2, v 3, v 4]T,v 0 =[v 0,1, v 0,2, v 0,3,v 0,4]T；
Step 6 is carried out after step 5；
Step 6：It calculatesv i =A i v 0 , then calculateτ i =(t i – t min)÷(b - v i )；It takesτ i In more than zero part in most
Small valueτ minCorresponding measuring pointp l2For new key point, and by its measuring point serial numberl 2Be added to crucial point setlIn；
To ownt i It is updated tot i + τ min∙ v i ,t minIt is updated tot i Minimum value；
An optimizing is completed after step 6, carries out step 3；
Step 7：It calculatest=2 t min Maximum inscribed circle column diameter required by being exactly.
2. a kind of maximum inscribed circle column diameter assessment method of fast steady letter as described in claim 1, which is characterized in that will be general
Measurement datap i * Converted by ordinary coor, axis is obtained close to coordinate systemzAxis, two bottom center's plane of tested cylinder
Close to coordinate system XOY plane measuring point collectionp i }。
3. a kind of maximum inscribed circle column diameter assessment method of fast steady letter as claimed in claim 2, which is characterized in that described normal
Advise coordinate transform, moved for one, by the average value of coordinate or two, moved by the extreme value of coordinate or three, by coordinate
Root mean square minimum principle moved.
4. a kind of maximum inscribed circle column diameter assessment method of fast steady letter as described in claim 1, which is characterized in that in step
In 6, ifτ min∙ v i Single value or the accumulated value ∑ of iteration for several timesτ min∙ v i More than given threshold valueq, then, by measuring point
Collectionp i Be updated top i + τ min∙vOrp i +∑τ min∙v, and by step 1 formula more new feature row vector collectionA i , boundary
Element setb i And state elements collectiont i }。
5. a kind of maximum inscribed circle column diameter assessment method of fast steady letter as described in claim 1, which is characterized in thatb=1。
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