CN106202709B

CN106202709B - A kind of concentricity assessment method based on maximum solid state

Info

Publication number: CN106202709B
Application number: CN201610535177.0A
Authority: CN
Inventors: 唐哲敏; 黄美发; 秦玲
Original assignee: Individual
Current assignee: Guilin University of Electronic Technology
Priority date: 2016-07-08
Filing date: 2016-07-08
Publication date: 2019-09-10
Anticipated expiration: 2036-07-08
Also published as: CN106202709A

Abstract

The present invention relates to a kind of concentricity assessment methods based on maximum solid state, this method obtains the geometry design parameter of tested part first and judges whether its concentricity tolerance can be evaluated with this method, then the qualification of the measurement data of practical tested part and preliminary assessment tested cylindrical body and reference cylinder is obtained, then the measurement data of reference cylindrical body is fitted and coordinate conversion is carried out to the measurement data for calculating reference cylindrical body and practical tested cylindrical body, then practical tested cylindrical body is calculated for the limit equivalent diameter of reference cylinder the maximum material boundary, it is last to judge whether practical tested part is qualified according to the tolerance for being tested cylindrical body.

Description

A kind of concentricity assessment method based on maximum solid state

Technical field

The invention belongs to delicate meterings and computer application field, a kind of based on the coaxial of maximum solid state with being related to Rapid method for assessment is spent, can be used for being tested cylindrical body has the concentricity tolerance of size requirement, its axis to have maximum material requirement simultaneously And its reference element have size require and maximum material requirement cylindrical geometric product coaxiality error qualification detection and Evaluation, and guidance is provided for the improvement of processing technology.

Background technique

Scale error, Form and position error (abbreviation of form error and location error) directly affect product quality, assembly and its Service life quickly and accurately calculates part error, has great importance.Dimensional tolerance (tolerance, that is, error permission model Enclose) and geometric tolerance between relationship be known as Tolerance Principle, wherein maximum material requirement be embody part assembling capacity one kind Tolerance Principle.

Standard GB/T/T16671-2009, which defines tested cylindrical body, has the concentricity tolerance of size requirement, its axis to have Maximum material requirement and its reference element have the case where size requirement and maximum material requirement, which defines: 1, being tested The maximum solid state of cylindrical body；2, it is tested the range of the local size of cylindrical body；3, it is tested the maximum solid state of cylindrical body Position relation between the maximum solid state of reference cylinder；4, the maximum solid state of reference cylinder and its local ruler Very little range, the axis and benchmark cylinder under least material condition of the tested cylindrical body under additional explanation least material condition Possible coaxiality error between the axis of body, but do not provide specific calculation formula.

Therefore, in order to judge that between maximum material size and least material size, (qualification of scale error detects Method has regulation in standard GB/T/T3177, GB/T1958, GB/T18779.1, GB/T18779.2, is not belonging to the present invention Scope) part above-mentioned concentricity qualification, standard GB/T/T1958-2004 gives using high-precision, ruler Very little constant drift, no-go gage come detection cylinder body above-mentioned concentricity whether He Ge method.However, it is high-precision, size is permanent The manufacturing cost of fixed drift, no-go gage is higher, and measures various sizes of cylindrical part and need using different drifts, only Rule, further increase measurement cost.

Tested cylindrical body has size to require, the concentricity of its axis has maximum material requirement and its reference element is without most In the case where big entity inquiry, cylinder can be tested by three coordinate measuring engine measurement in delicate metering and computer application field Measuring point on body and reference cylinder calculates tested concentricity of the cylindrical body relative to reference cylinder, and judges tested cylinder Whether the concentricity of body is qualified.But there are no mathematical method come come evaluate tested cylindrical body have size require, its axis it is same Axis degree tolerance has maximum material requirement and its reference element has size to require the qualification with the part of maximum material requirement.

Summary of the invention

Technical problem to be solved by the invention is to provide a kind of concentricity rapid evaluation sides based on maximum solid state Method, not only realizing tested cylindrical body has the concentricity tolerance of size requirement, its axis to have maximum material requirement and its base Standard will be known as size and require to detect and evaluate with the qualification of the part of maximum material requirement, and algorithm stability is good, calculates It is high-efficient, can be applied to other element to be measured have size require, its direction and location tolerance have maximum material requirement and Its reference element has in the qualification detection and evaluation of the part of size requirement and maximum material requirement.

To solve the above problems, the present invention is achieved by the following scheme:

Step 1: obtaining tested cylindrical bodyCb, reference cylinderCAGeometry design parameter；If tested cylindrical bodyCb's Concentricity tolerance and reference cylinderCAThere are maximum material requirement, and reference cylinderCAOnly dimensional tolerance --- it can be with Using envelope principle, then jumping to step 2, otherwise terminate this rapid method for assessment, and provides conclusion and " be tested the same of cylindrical body Axis degree tolerance cannot be evaluated with this method ".

The tested cylindrical bodyCbGeometry design parameter include: hole element or axial element, nominal diameterD _b, name Adopted lengthL _b, axis the upper deviationes _bOr the upper deviation in holeES _b, axis lower deviationei _bOr the lower deviation in holeEI _b, concentricity toleranceT _{b, AM, coa}, concentricity tolerance whether mark the reference cylinder of maximum material requirement, concentricity toleranceCAWhether maximum is marked Entity state.

The reference cylinderCAGeometry design parameter include: hole element or axial element, nominal diameterD _A, name Adopted lengthL _A, axis the upper deviationes _AOr the upper deviation in holeES _A, axis lower deviationei _AOr the lower deviation in holeEI _A, dimensional tolerance whether Using envelope principle, other geometric tolerances.

Step 2: obtaining practical tested cylindrical bodyC _b, reference cylindrical bodyC _AMeasurement data；Evaluate reference cylinder BodyC _AScale error and practical tested cylindrical bodyC _bScale error jump to step 3, otherwise if above-mentioned error is all qualified Terminate this rapid method for assessment, and provides conclusion " reference cylindrical bodyC _AAnd/or practical tested cylindrical bodyC _bOther errors It is unqualified ".

Step 3: by reference cylindrical bodyC _AMeasure data fitting be cylindrical bodyCC _A, in the fitting circle of tested cylindrical body Local coordinate system is established on cylinder, and calculates practical tested cylindrical bodyC _b, reference cylindrical bodyC _AMeasurement data in the part Coordinate in coordinate system.

Step 4: with reference cylindrical bodyC _ARelative to cylindrical bodyCC _AMThree-dimensional attitudev _AFor variable, with reality Tested cylindrical bodyC _bRelative to cylindrical bodyCC _AMEquivalent diameterd _{b, AM, coa}=f(v _A) it is objective function, objective optimization is carried out, is obtained To practical tested cylindrical bodyC _bRelative to cylindrical bodyCC _AMLimit equivalent diameterd _{b, AM, coa, mM}。

Wherein,v _AIt is constrained as follows: for arbitrarily without departing from reference cylinderCAThe maximum material boundary cylindrical bodyCC _AM's Cylindrical bodyCC _A, relative to cylindrical bodyCC _AMThree-dimensional attitude can be expressed asv _A；For anyv _A, cylindrical bodyCC _ADo not surpass Reference cylinder outCAThe maximum material boundary cylindrical bodyCC _A。

Step 5: according to tested cylindrical bodyCbMaximum solid virtual sizeD _bMVAnd cylindrical bodyCC _bDiameterd _b, most equivalent Diameterd _{b, AM, min}, judge practical tested cylindrical bodyC _bCoaxiality error it is whether qualified.

For the ease of actual parts are mapped with design configuration, following steps can be embodied as by the present invention:

Cylindrical body is actually tested described in step 2b, reference cylindrical bodyAMeasurement data be measurement space right-angle It is measured in coordinate system, and including following four measuring point data collection:

Reference cylindrical bodyABottom surface on measuring pointP _{measure, A, under, i}Measuring point datap _{measure, A, under, i} (x _{measure, A, under, i}, y _{measure, A, under, i}, z _{measure, A, under, i}),i=1, 2 … I,IFor measure-point amount and it is Positive integer, all measuring point datasp _{measure, A, under, i}(x _{measure, A, under, under, i}, y _{measure, A, under, i},z _{measure, A, under, i}) formation measuring point data collectionp _{measure, A, under, i}}。

Reference cylindrical bodyASide on measuring pointP _{measure, A, n}Measuring point datap _{measure, A, n} (x _{measure, A, n}, y _{measure, A, n}, z _{measure, A, n}),n=1, 2 … N,NIt for measure-point amount and is positive integer, it is all Measuring point datap _{measure, A, n}(x _{measure, A, n}, y _{measure, A, n}, z _{measure, A, n}) form measuring point data collection {p _{measure, A, n}}。

Practical tested cylindrical bodybBottom surface on measuring pointP _{measure, b, under, j}Measuring point datap _{measure, b, under, j} (x _{measure, b, under, j}, y _{measure, b, under, j}, z _{measure, b, under, j}),j=1, 2 … J,JFor measure-point amount and it is Positive integer, all measuring point datasp _{measure, b, under, j}(x _{measure, b, under, under, j}, y _{measure, b, under, j},z _{measure, b, under, j}) formation measuring point data collectionp _{measure, b, under, j}}。

Practical tested cylindrical bodybSide on measuring pointP _{measure, b, m}Measuring point datap _{measure, b, m} (x _{measure, b, m}, y _{measure, b, m}, z _{measure, b, m}),m=1, 2 … M,MIt for measure-point amount and is positive integer, it is all Measuring point datap _{measure, b, m}(x _{measure, b, m}, y _{measure, b, m}, z _{measure, b, m}) form measuring point data collection {p _{measure, b, m}}。

In order to simplify the corresponding process of actual parts and design configuration, practical tested cylindrical body and reality can be reduced to the greatest extent The bottom surface measuring point of reference cylinder, at this point, following steps of the invention can be embodied as:

In step 2, reference cylindrical bodyABottom surface on measuring point numberI=2, and two measuring pointsP _{measure, A, under, 1}、P _{measure,A,under,2}Respectively in reference cylindrical bodyATwo bottom surfaces on.

Practical tested cylindrical bodybBottom surface on measuring point numberJ=2, and two measuring pointsP _{measure, b, under, 1}、P _{measure,b,under,2}Respectively in actually tested cylindrical bodybTwo bottom surfaces on.

In step 3, by reference cylindrical bodyC _AMeasuring point data collectionp _{measure, A, n}It is fitted to cylindrical bodyCC _ASide Face,P _{measure, A, under, 1}、P _{measure,A,under,2}The midpoint of lineP _{measure, A, under, 1/2}In cylindrical bodyCC _ATwo bottom surfaces Symmetrical planePL _{A, 1/2}On, cylindrical bodyCC _ALength be equal to reference cylinderCANominal lengthL _A。

In cylindrical bodyCC _AOn establish local rectangular coordinate systemO _{xyz, A}, coordinate systemO _{xyz, A}Origin and cylindrical bodyCC _AIt is several What centerO _AIt is overlapped, coordinate systemO _{xyz, A}A reference axis and cylindrical bodyCC _AAxis be overlapped, the positive direction vector of the reference axis With vectorO _A P _{measure, b, under, 1/2}Dot product be not less than zero, whereinP _{measure, b, under, 1/2}It isP _{measure, b, under, 1}、P _{measure,b,under,2}The midpoint of line；Define cylindrical bodyCC _AUnit direction vectorn _CCALength be 1, positive direction and the coordinate The positive direction vector of axis is identical.

By reference cylindrical bodyC _AMeasuring point data collectionp _{measure, A, n}And practical tested cylindrical bodyC _bMeasuring point data Collectionp _{measure, b, m}Coordinate conversion is carried out, obtain reference cylindrical bodyC _AWith practical tested cylindrical bodyC _bMeasuring point in coordinate SystemO _{xyz, A}In coordinate setp _{A, n}Andp _{b, m}}。

In order to reduce use difficulty of the invention, and consider contribution of the form error in overall error, the present invention can be with It is embodied as:

The tested cylindrical bodyCbGeometry design parameter include be hole element or axial element, nominal diameterD _b, name Adopted lengthL _b, axis the upper deviationes _bOr the upper deviation in holeES _b, axis lower deviationei _bOr the lower deviation in holeEI _b, concentricity toleranceT _{b, AM, coa}, concentricity tolerance whether mark the reference cylinder of maximum material requirement, concentricity toleranceCAWhether maximum is marked Entity state.

Step 2: obtaining practical tested cylindrical bodyC _b, reference cylindrical bodyC _AMeasurement data, including following four measuring point Data set:

Reference cylindrical bodyC _ATwo measuring pointsP _{measure, A, under, 1}、P _{measure,A,under,2}Respectively in reference circle CylinderC _ATwo bottom surfaces on, the measuring point data of two measuring pointsp _{measure, A, under, 1}(x _{measure, A, under, 1},y _{measure, A, under, 1}, z _{measure, A, under, 1})、p _{measure, A, under, 2}(x _{measure, A, under, 2},y _{measure, A, under, 2}, z _{measure, A, under, 2}) formation measuring point data collectionp _{measure, A, under, i},i=1, 2；Practical base Director circle cylinderC _ASide on measuring pointP _{measure, A, n}Measuring point datap _{measure, A, n}(x _{measure, A, n}, y _{measure, A, n},z _{measure, A, n}),n=1, 2 … N,NIt for measure-point amount and is positive integer, all measuring point datasp _{measure, A, n} (x _{measure, A, n}, y _{measure, A, n}, z _{measure, A, n}) formation measuring point data collectionp _{measure, A, n}}；Practical tested cylindrical bodyC _b Two measuring pointsP _{measure, b, under, 1}、P _{measure,b,under,2}Respectively in actually tested cylindrical bodyC _bTwo bottom surfaces on, two The measuring point data of measuring pointp _{measure, b, under, 1}(x _{measure, b, under, 1}, y _{measure, b, under, 1},z _{measure, b, under, 1})、p _{measure, b, under, 2}(x _{measure, b, under, 2}, y _{measure, b, under, 2},z _{measure, b, under, 2}) formation measuring point data collectionp _{measure, b, under, j},j=1, 2；Practical tested cylindrical bodyC _bSide on Measuring pointP _{measure, b, m}Measuring point datap _{measure, b, m}(x _{measure, b, m}, y _{measure, b, m}, z _{measure, b, m}),m=1, 2 … M,MIt for measure-point amount and is positive integer, all measuring point datasp _{measure, b, m}(x _{measure, b, m}, y _{measure, b, m},z _{measure, b, m}) formation measuring point data collectionp _{measure, b, m}}。

Evaluate reference cylindrical bodyC _AWith practical tested cylindrical bodyC _bScale error it is whether qualified, if above-mentioned error It is all qualified, step 3 is jumped to, this rapid method for assessment is otherwise terminated, and provides conclusion " reference cylindrical bodyC _AAnd/or it is real Border is tested cylindrical bodyC _bOther errors it is unqualified ".

Step 3: calculatingp _{measure, A, under, 1/2}=( p _{measure, A, under, 1}+ p _{measure, A, under, 2})/2。

Obtain in step 2 four measuring point data collection are coordinately transformed, four rough translation data sets are obtained {p _{0, A, under, i}(x _{0, A, under, i}, y _{0, A, under, i}, z _{0, A, under, i})| p _{0, A, under, i} =p _{measure, A, under, i}-p _{measure, A, under, 1/2},i=1, 2}、{p _{0, A, n}(x _{0, A, n}, y _{0, A, n}, z _{0, A, n})|p _{0, A, n} = p _{measure, A, n}-p _{measure, A, under, 1/2},n=1, 2 … N }、{ p _{0, b, under, j}(x _{0, b, under, j},y _{0, b, under, j}, z _{0, b, under, j})| p _{0, b, under, j} = p _{measure, b, under, j}-p _{measure, A, under, 1/2},j=1, 2}、{ p _{0, b, m}(x _{0, b, m}, y _{0, b, m}, z _{0, b, m})| p _{0, b, m} = p _{measure, b, m}-p _{measure, A, under, 1/2},m=1, 2 … M }。

It calculatesp _{0, b, under, 1/2}(x _{0, b, under, 1/2}, y _{0, b, under, 1/2}, z _{0, b, under, 1/2})=(p _{0, b, under, 1}+ p _{0, b, under, 2})/2。

Solve objective optimisation problems 1:

s.t.

Solve optimal solution (x _0,min, y _0,min, α _0,min, β _0,min), i.e. reference cylindrical bodyC _AFitting cylindrical bodyCC _A Corresponding (x ₀, y ₀, α ₀, β ₀) value.

To translate roughly data set p _{0, A, n}(x _{0, A, n}, y _{0, A, n}, z _{0, A, n}) following coordinate transform is carried out,n=1, 2 … N:

Obtain practical tested all measuring points of cylinder relative to reference cylindrical body coordinate set p _{A, n}(_{A, n}, y _{A, n},z _{A, n})}。

To translate roughly data set p _{0, b, m}(x _{0, b, m}, y _{0, b, m}, z _{0, b, m}) following coordinate transform is carried out,m=1, 2 … M:

Obtain practical tested all measuring points of cylinder relative to reference cylindrical body coordinate set p _{b, m}(_{b, m}, y _{b, m},z _{b, m})}。

Step 4: calculating benchmark cylindrical bodyCAThe maximum material boundary cylindrical bodyCC _AMDiameterD _AM, work as reference cylinderCAIt is When axis,D _AM= D _A+ es _A；Work as reference cylinderCAWhen being hole,D _AM= D _A+ EI _A；

Solve objective optimisation problems 2:

s.t.

Solve cylindrical bodyCC _bRelative to cylindrical bodyCC _AMLimit equivalent diameterd _{b, AM, coa, mM}=|min d _{b, AM, coa}|。

Step 5: calculating tested cylindrical bodyCbMaximum solid virtual size: when tested cylindrical bodyCbWhen being axis,D _bMV=D _b+ es _b+T _{b, AM, coa}；When tested cylindrical bodyCbWhen being hole,D _bMV= D _b+ EI _b-T _{b, AM, coa}。

When tested cylindrical bodyCbWhen being axis, if limit equivalent diameterd _{b, AM, coa, mM} ≤ D _bMV, then providing conclusion " practical tested cylindrical bodyC _bCoaxiality error it is qualified ", otherwise provide conclusion " practical tested cylindrical bodyC _bCoaxiality error not It is qualified ".

When tested cylindrical bodyCbWhen being hole, ifD _bMV≤d _{b, AM, coa, mM}, then providing conclusion " practical tested cylindrical bodyC _bCoaxiality error it is qualified ", otherwise provide conclusion " practical tested cylindrical bodyC _bCoaxiality error it is unqualified ".

In part error problem analysis, need to solve some objective optimisation problems, feature includes: to need while considering Error amount and nominal parameter, and the several orders of magnitude of the usual difference of size of these two types of numerical value；Functional value near optimal solution becomes Change and relatively mitigates；Equality constraint usually has determining solution；At least one feasible solution can usually be provided.For these features, this hair It is bright to provide a kind of multilayered particles group algorithm to solve both of the aforesaid objective optimisation problems, it is characterized in that steps are as follows:

Step 01: defining the parameter of multilayered particles group algorithm or use its default value, including resolution ratioT _POS, populationN _P (N _P>=2), internal layer maximum number of iterationsN _i,rd(N _i,rd>=1), outer layer maximum number of iterationsN _o,rd, outer layer minimum iteration time Numbern _o,rd, quality weight factorW, local weight factorC ₁, global weight factorC ₂。

Step 02: definitionN _PA particlep _PSO,k(p _{PSO, k,1}, p _{PSO, k,2}, …, p _{PSO, k,Q}), it is excellent that value corresponds to target In change problem independent variable (x ₁, x ₂, …, x _Q),p _{PSO, k, q}Value interval respectively withx _qValue interval it is identical；k=1, 2 … N _P；q=1, 2 … Q；All particle constituent particle collectionp _PSO,k}；One particle is setp _PSO,1Initial value or use its Default value.

0 is set by the number of iterations of outer layer particle swarm algorithm.

Step 03: existing respectivelyp _{PSO, k, q}Value interval taken at random by being evenly distributed (N _P- 1) a value, building (N _P -1) A particlep _PSO,k；k=2, 3 … N _P；q=1, 2 … Q。

Exist respectivelyp _{PSO, k, q}Value interval taken at random by being evenly distributedN _PA value, buildingN _PA particlep _PSO,kIt is initial Speedv _{PSO, k} (v _{PSO, k,1}, v _{PSO, k,2}, …, v _{PSO, k,q})；All particles speed composition speed collectionv _PSO,k}；k=1, 2 … N _P；q=1, 2 … Q。

DefinitionN _PA particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；k=1, 2 … N _P。

It willp _{PSO, k, q}Value substitute into the variable in objective optimisation problems respectivelyx _qAnd its equality constraint, and calculate corresponding Objective optimization functional valuef _k=f(x ₁, x ₂, …, x _Q)；k=1, 2 … N _P；q=1, 2 … Q。

Record particlep _PSO,kCorresponding local optimumf _k,min=f _k,k=1, 2 … N _P。

Record global optimumf _min=min f _k,min, and record and minf _k,minThe value of corresponding particle is global optimum Solutionp _PSO,min。

0 is set by the number of iterations of internal layer particle swarm algorithm.

Step 04: by particlep _PSO,kValue be updated top _PSO,k+v _{PSO, k},k=1, 2 … N _P。

Enable (x ₁, x ₂, …, x _Q)=p _PSO,k, and substitute into the inequality constraints of objective optimisation problems；If inequality constraints It sets up, then will (x ₁, x ₂, …, x _Q) equality constraint in objective optimisation problems is substituted into, and calculate and update corresponding target Majorized function valuef _k；Iff _k ≤ f _k,min, then more new particlep _PSO,kLocal optimumf _k,min=f _k, and more new particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；Iff _k ≤ f _min, then updating global optimumf _min=f _k, and update Globally optimal solution isp _PSO,min=p _PSO,k；k=1, 2 … N _P；q=1, 2 … Q。

If the local optimum and locally optimal solution of each particle are very close, that is, (| maxf _k,min– min f _k,min| ≤ T _POS) and (|p _{PSO,k,min, mean}– p _PSO,k,min| ≤ T _POS), whereinp _{PSO,k,min, mean}Forp _PSO,k,minArithmetic average Value,k=1, 2 … N _P；So, step 07 is gone to, step 05 is otherwise gone to.

Step 05: by particlep _PSO,kSpeedv _PSO,kValue be updated toW v _PSO,k+ C _rand1 C ₁ (p _PSO,k,min-p _PSO,k) + C _rand2 C ₂ (p _PSO,min- p _PSO,k), whereinC _rand1、C _rand2It is in section [0,1] independently of each other by flat It is distributed two values randomly selected； k=1, 2 … N _P。

Step 06: the number of iterations of one secondary internal layer particle swarm algorithm of accumulation；If the number of iterations of internal layer particle swarm algorithm It is greater thanN _i,rd, then jumping to step 07, otherwise jump to step 04.

Step 07: recording the global optimum for the internal layer particle swarm algorithm that each iteration obtainsf _min,s= f _min, whereinsIt is The number of iterations of outer layer particle swarm algorithm.

By particlep _PSO,1Value be set as current globally optimal solutionp _PSO,min。

When the number of iterations of outer layer particle swarm algorithms > n _o,rdWhen, it enablesg =s -n _o,rd, judge multilayered particles group's algorithm Convergence；If |f _min,s– min f _{min, g} | ≤ T _POS, then, terminate multilayered particles group algorithm and export objective optimization to ask The optimal solution of topicp _PSO,minAnd optimal valuef _min, otherwise, accumulate the number of iterations of an outer layer particle swarm algorithm.

If the number of iterations of outer layer particle swarm algorithm is greater thanN _o,rd, then stopping outer layer particle swarm algorithm and exporting target Optimization problem optimal solution (x ₁, x ₂, …, x _Q)=p _PSO,minWith optimal value minf=f _min, otherwise, more new particlep _PSO,1Just Initial value isp _PSO,minJump to step 03.

For the ease of the use of this method, the default parameters of aforenoted multi-layer particle swarm algorithm can be set as follows:

Resolution ratioT _POSDefault value is 0.00005, populationN _PDefault value is 20, internal layer maximum number of iterationsN _i,rdDefault value It is 100, outer layer maximum number of iterationsN _o,rdDefault value is 100, outer layer minimum the number of iterationsn _o,rdDefault value be 50, quality power because SonWDefault value is 0.5, local weight factorC ₁Default value is 2, global weight factorC ₂Default value is 2；p _PSO,1Initial value be defaulted as Null vector.

In order to improve computational efficiency of the invention, the objective optimisation problems 1 in the present invention can be solved with following methods:

The multilayered particles group's algorithm for solving objective optimisation problems 1 is as follows:

Step 11: defining the parameter of multilayered particles group algorithm or use its default value, including resolution ratioT _POS, populationN _P (N _P>=2), internal layer maximum number of iterationsN _i,rd(N _i,rd>=1), outer layer maximum number of iterationsN _o,rd, outer layer minimum iteration time Numbern _o,rd, quality weight factorW, local weight factorC ₁, global weight factorC ₂。

Step 12: definitionN _PA particlep _PSO,k(p _{PSO, k,1}, p _{PSO, k,2}, p _{PSO, k,3}, p _{PSO, k,4}), value corresponds to mesh Mark optimization problem 1 in variable (x ₀, y ₀, α ₀, β ₀),p _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval point Not withx ₀、y ₀、α ₀、β ₀Value interval it is identical, it may be assumed thatp _{PSO, k,1}、p _{PSO, k,2}∈[-D _A, D _A],p _{PSO, k,3}、p _{PSO, k,4}∈[-π,π]；k=1, 2 … N _P；All particle constituent particle collectionp _PSO,k}；One particle is setp _PSO,1(p _PSO,1,1, p _PSO,1,2,p _PSO,1,3, p _PSO,1,4) initial value be (0,0,0,0).

0 is set by the number of iterations of outer layer particle swarm algorithm.

Step 13: existing respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval taken at random by being evenly distributed (N _P- 1) a value, building (N _P- 1) a particlep _PSO,k；k=2, 3 … N _P。

Exist respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval taken at random by being evenly distributedN _PA value, BuildingN _PA particlep _PSO,kInitial velocityv _{PSO, k} (v _{PSO, k,1}, v _{PSO, k,2}, v _{PSO, k,3}, v _{PSO, k,4})；All particles Speed composition speed collectionv _PSO,k}；k=1, 2 … N _P。

It willp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value substitute into the variable in objective optimisation problems 1 respectivelyx ₀、y ₀、α ₀、β ₀And its equality constraint, and calculate corresponding objective optimization functional valued _1,A,k,k=1, 2 … N _P；That is,

where

Record particlep _PSO,kCorresponding local optimumd _1,A,k,min=d _1,A,k,k=1, 2 … N _P。

Record global optimumd _1,A,min=min d _1,A,k,min, and record and mind _1,A,k,minThe value of corresponding particle is Globally optimal solutionp _PSO,min。

Step 14: by particlep _PSO,kValue be updated top _PSO,k+v _{PSO, k},k=1, 2 … N _P。

Enable (x ₀, y ₀, α ₀, β ₀)=p _PSO,k, and substitute into the inequality constraints of objective optimisation problems 1, i.e., 0≤-x _{0,b,under,1/2}cosα ₀sinβ ₀+ y _{0,b,under,1/2}sinα ₀+ z _{0,b,under,1/2}cosα ₀cosβ ₀,x ₀、y ₀∈[-D _A, D _A],α ₀、β ₀ ∈[-π, π]；If inequality constraints is set up, will (x ₀, y ₀, α ₀, β ₀) substitute into objective optimisation problems 1 in equation about Beam calculates and updates corresponding objective optimization functional valued _1,A,k；Ifd _1,A,k ≤ d _1,A,k,min, then more new particlep _PSO,k's Local optimumd _1,A,k,min=d _1,A,k, and more new particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；Ifd _1,A,k ≤d _1,A,min, then updating global optimumd _1,A,min=d _1,A,k, and update globally optimal solution and bep _PSO,min=p _PSO,k；k=1, 2 …N _P。

If the local optimum and locally optimal solution of each particle are very close, that is, (| maxd _1,A,k,min– mind _1,A,k,min| ≤ T _POS) and (|p _{PSO,k,min, mean}– p _PSO,k,min| ≤ T _POS), whereinp _{PSO,k,min, mean}Forp _PSO,k,min Arithmetic mean of instantaneous value,k=1, 2 … N _P；So, step 17 is gone to, step 15 is otherwise gone to.

Step 15: by particlep _PSO,kSpeedv _PSO,kValue be updated toW v _PSO,k+ C _rand1 C ₁ (p _PSO,k,min-p _PSO,k) + C _rand2 C ₂ (p _PSO,min- p _PSO,k), whereinC _rand1、C _rand2It is in section [0,1] independently of each other by flat It is distributed two values randomly selected； k=1, 2 … N _P；

Step 16: the number of iterations of one secondary internal layer particle swarm algorithm of accumulation；If the number of iterations of internal layer particle swarm algorithm It is greater thanN _i,rd, then jumping to step 17, otherwise jump to step 14.

Step 17: recording the global optimum for the internal layer particle swarm algorithm that each iteration obtainsd _1,A,min,s= d _1,A,min, In,sIt is the number of iterations of outer layer particle swarm algorithm.

When the number of iterations of outer layer particle swarm algorithms > n _o,rdWhen, it enablesg =s -n _o,rd, judge multilayered particles group's algorithm Convergence；If |d _1,A,min,s– min d _{1,A,min, g} | ≤ T _POS, then, terminate multilayered particles group algorithm and exports target The optimal solution of optimization problem 1p _PSO,minAnd optimal valued _1,A,min, otherwise, accumulate the number of iterations of an outer layer particle swarm algorithm.

If the number of iterations of outer layer particle swarm algorithm is greater thanN _o,rd, then stopping outer layer particle swarm algorithm and exporting target Optimization problem 1 optimal solution (x ₀, y ₀, α ₀, β ₀)=p _PSO,minWith optimal value mind _{1, A}=d _1,A,min, otherwise, more new particlep _PSO,1Initial value bep _PSO,minJump to step 13.

In order to improve computational efficiency of the invention, the objective optimisation problems 2 in the present invention can be solved with following methods:

The multilayered particles group's algorithm for solving objective optimisation problems 2 is as follows:

Step 21: defining the parameter of multilayered particles group algorithm or use its default value, including resolution ratioT _POS, populationN _P (N _P>=2), internal layer maximum number of iterationsN _i,rd(N _i,rd>=1), outer layer maximum number of iterationsN _o,rd, outer layer minimum iteration time Numbern _o,rd, quality weight factorW, local weight factorC ₁, global weight factorC ₂。

Step 22: defining particlep _PSO,k(p _{PSO, k,1}, p _{PSO, k,2}, p _{PSO, k,3}, p _{PSO, k,4}) value correspond to objective optimization In problem 2 variable (dx _A, dy _A, drx _A, dry _A),p _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval point Not withdx _A、dy _A、drx _A、dry _AValue interval it is identical,k=1, 2 … N _P；All particle constituent particle collectionp _PSO,k}；Setting One particlep _PSO,1(p _PSO,1,1, p _PSO,1,2, p _PSO,1,3, p _PSO,1,4) initial value be (0,0,0,0).

0 is set by the number of iterations of outer layer particle swarm algorithm.

Step 23: existing respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval in it is random by being evenly distributed Take (N _P- 1) a value, building (N _P- 1) a particlep _PSO,k；k=2, 3 … N _P。

Exist respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval in taken at random by being evenly distributedN _PIt is a Value, buildingN _PA particlep _PSO,kInitial velocityv _{PSO, k} (v _{PSO, k,1}, v _{PSO, k,2}, v _{PSO, k,3}, v _{PSO, k,4})；All grains Son speed composition speed collectionv _PSO,k}；k=1, 2 … N _P。

It willp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value substitute into objective optimisation problems 2 in variabledx _A、dy _A、drx _A、dry _AAnd its equality constraint, and calculate corresponding objective optimization functional valued _b,AM,coa,k,k=1, 2 … N _P。

Record particlep _PSO,kLocal optimumd _{b,AM,coa,k,min}=d _b,AM,coa,k,k=1, 2 … N _P。

Record global optimumd _b,AM,coa,min=min d _{b,AM,coa,k,min}, and record and mind _{b,AM,coa,k,min}It is corresponding The value of particle is globally optimal solutionp _PSO,min。

Step 24: by particlep _PSO,kValue be updated top _PSO,k+v _{PSO, k},k=1, 2 … N _P。

Enable (dx _A, dy _A, drx _A, dry _A)=p _PSO,k, and the inequality constraints of objective optimisation problems 2 is substituted into, if differed Formula constraint is set up, then will (dx _A, dy _A, drx _A, dry _A) substitute into objective optimisation problems 2 equality constraint, calculate and update Corresponding objective optimization functional valued _b,AM,coa,k；Ifd _b,AM,coa,k ≤ d _{b,AM,coa,k,min}, then more new particlep _PSO,kOffice Portion's optimal valued _{b,AM,coa,k,min}=d _b,AM,coa,k, and more new particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；Ifd _b,AM,coa,k ≤ d _b,AM,coa,min, then updating global optimumd _b,AM,coa,min=d _b,AM,coa,k, and update globally optimal solution and bep _PSO,min=p _PSO,k；k=1, 2 … N _P。

If the local optimum and locally optimal solution of each particle are very close, that is, (| maxd _{b,AM,coa,k,min}– mind _{b,AM,coa,k,min}| ≤ T _POS) and (|p _{PSO,k,min, mean}– p _PSO,k,min| ≤ T _POS), whereinp _{PSO,k,min, mean}Forp _PSO,k,minArithmetic mean of instantaneous value,k=1, 2 … N _P；So, step 27 is gone to, step 25 is otherwise gone to.

Step 25: by particlep _PSO,kSpeedv _PSO,kValue be updated toW v _PSO,k+ C _rand1 C ₁ (p _PSO,k,min-p _PSO,k) + C _rand2 C ₂ (p _PSO,min- p _PSO,k), whereinC _rand1、C _rand2It is in section [0,1] independently of each other by flat It is distributed two values randomly selected； k=1, 2 … N _P。

Step 26: the number of iterations of one secondary internal layer particle swarm algorithm of accumulation；If the number of iterations of internal layer particle swarm algorithm It is greater thanN _i,rd, then stopping internal layer particle swarm algorithm and jumping to step 27, otherwise jump to step 24.

Step 27: recording the global optimum for the outer layer particle swarm algorithm that each iteration obtainsd _{b,AM,coa,min,s}=d _b,AM,coa,min, whereinsIt is the number of iterations of outer layer particle swarm algorithm.

When the number of iterations of outer layer particle swarm algorithms > n _o,rdWhen, it enablesg =s -n _o,rd, judge multilayered particles group's algorithm Convergence；If |d _{b,AM,coa,min,s}– min d _{b,AM,coa,min, g} | ≤ T _POS, then, end multilayered particles group algorithm is simultaneously defeated The optimal solution of objective optimisation problems 2 outp _PSO,minAnd optimal valued _b,AM,coa,min, otherwise, accumulate an outer layer particle swarm algorithm The number of iterations.

If the number of iterations of outer layer particle swarm algorithm is greater thanN _o,rd, then stopping outer layer particle swarm algorithm and exporting target Optimization problem 2 optimal solution (dx _A, dy _A, drx _A, dry _A) =p _PSO,minWith optimal value mind _b,AM,coa=d _b,AM,coa,min, no Then, more new particlep _PSO,1Initial value bep _PSO,minAnd jump to step 23.

Detailed description of the invention

Fig. 1, the flow chart of basic skills of the invention.

Fig. 2, the present invention in solve objective optimisation problems multilayered particles group's algorithm basic skills flow chart.

Fig. 3, movement of the axial workpiece relative to the maximum material boundary in step 4.

Fig. 4, the geometry designs figure of experimental subjects.

Specific embodiment

EXPERIMENTAL EXAMPLE:

Step 1: obtaining tested cylindrical bodyb, reference cylinderAGeometry design parameter；Judge tested cylindrical bodybIt is coaxial Whether degree tolerance can be evaluated with this method, if tested cylindrical bodybConcentricity tolerance and reference cylinderAThere is maximum solid It is required that and reference cylinderAOnly size tolerance requirements --- the size tolerance requirements can apply envelope principle, then jumping Step 2 is gone to, this rapid method for assessment is otherwise terminated, and provides conclusion " concentricity tolerance of tested cylindrical body cannot use we Method evaluation ".

The tested cylindrical bodybGeometry design parameter include: hole element or axial element, nominal diameterD _b, name Adopted lengthL _b, axis the upper deviationes _bOr the upper deviation in holeES _b, axis lower deviationei _bOr the lower deviation in holeEI _b, concentricity toleranceT _{b, AM, coa}, concentricity tolerance whether mark the reference cylinder of maximum material requirement, concentricity toleranceAWhether mark maximum real Body state.

The reference cylinderAGeometry design parameter include: hole element or axial element, nominal diameterD _A, name Adopted lengthL _A, axis the upper deviationes _AOr the upper deviation in holeES _A, axis lower deviationei _AOr the lower deviation in holeEI _A, dimensional tolerance whether Using envelope principle, other geometric tolerances.

Step 2: obtaining practical tested cylindrical bodyb, reference cylindrical bodyAMeasurement data, including following four measuring point Data set:

Reference cylindrical bodyATwo measuring pointsP _{measure, A, under, 1}、P _{measure,A,under,2}Respectively in reference circle CylinderATwo bottom surfaces on, the measuring point data of two measuring pointsp _{measure, A, under, 1}(x _{measure, A, under, 1},y _{measure, A, under, 1}, z _{measure, A, under, 1})、p _{measure, A, under, 2}(x _{measure, A, under, 2},y _{measure, A, under, 2}, z _{measure, A, under, 2}) formation measuring point data collectionp _{measure, A, under, i},i=1, 2；Practical base Director circle cylinderASide on measuring pointP _{measure, A, n}Measuring point datap _{measure, A, n}(x _{measure, A, n}, y _{measure, A, n},z _{measure, A, n}),n=1, 2 … N,NIt for measure-point amount and is positive integer, all measuring point datasp _{measure, A, n} (x _{measure, A, n}, y _{measure, A, n}, z _{measure, A, n}) formation measuring point data collectionp _{measure, A, n}}；Practical tested cylindrical bodyb Two measuring pointsP _{measure, b, under, 1}、P _{measure,b,under,2}Respectively in actually tested cylindrical bodybTwo bottom surfaces on, two The measuring point data of measuring pointp _{measure, b, under, 1}(x _{measure, b, under, 1}, y _{measure, b, under, 1},z _{measure, b, under, 1})、p _{measure, b, under, 2}(x _{measure, b, under, 2}, y _{measure, b, under, 2},z _{measure, b, under, 2}) formation measuring point data collectionp _{measure, b, under, j},j=1, 2；Practical tested cylindrical bodybSide on Measuring pointP _{measure, b, m}Measuring point datap _{measure, b, m}(x _{measure, b, m}, y _{measure, b, m}, z _{measure, b, m}),m=1, 2 … M,MIt for measure-point amount and is positive integer, all measuring point datasp _{measure, b, m}(x _{measure, b, m}, y _{measure, b, m},z _{measure, b, m}) formation measuring point data collectionp _{measure, b, m}}。

Evaluate reference cylindrical bodyAWith practical tested cylindrical bodybScale error it is whether qualified, if above-mentioned error is all Qualification jumps to step 3, otherwise terminates this rapid method for assessment, and provides conclusion " reference cylindrical bodyAAnd/or practical quilt Survey cylindrical bodybOther errors it is unqualified ".

Solve objective optimisation problems 1:

s.t.

Step 11: using the default parameters of multilayered particles group's algorithm, including resolution ratioT _POS=0.00005, populationN _P= 20, internal layer maximum number of iterationsN _i,rd=100, outer layer maximum number of iterationsN _o,rd=100, outer layer minimum the number of iterationsn _o,rd=50、 Quality weight factorW=0.5, local weight factorC ₁=2, global weight factorC ₂=2。

Step 12: defining 20 particlesp _PSO,k(p _{PSO, k,1}, p _{PSO, k,2}, p _{PSO, k,3}, p _{PSO, k,4}), value corresponds to mesh Mark optimization problem 1 in variable (x ₀, y ₀, α ₀, β ₀),p _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval point Not withx ₀、y ₀、α ₀、β ₀Value interval it is identical, it may be assumed thatp _{PSO, k,1}、p _{PSO, k,2}∈[-D _A, D _A],p _{PSO, k,3}、p _{PSO, k,4}∈[-π,π]；k=1, 2 … 20；All particle constituent particle collectionp _PSO,k}；One particle is setp _PSO,1(p _PSO,1,1, p _PSO,1,2,p _PSO,1,3, p _PSO,1,4) initial value be (0,0,0,0).

0 is set by the number of iterations of outer layer particle swarm algorithm.

Step 13: existing respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval taken at random by being evenly distributed 19 values, construct 19 particlesp _PSO,k；k=2, 3 … 20。

Exist respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval take 20 values at random by being evenly distributed, Construct 20 particlesp _PSO,kInitial velocityv _{PSO, k} (v _{PSO, k,1}, v _{PSO, k,2}, v _{PSO, k,3}, v _{PSO, k,4})；All particles Speed composition speed collectionv _PSO,k}；k=1, 2 … 20。

Define 20 particlesp _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；k=1, 2 … 20。

It willp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value substitute into the variable in objective optimisation problems 1 respectivelyx ₀、y ₀、α ₀、β ₀And its equality constraint, and calculate corresponding objective optimization functional valued _1,A,k,k=1, 2 … 20；That is,

where

Record particlep _PSO,kCorresponding local optimumd _1,A,k,min=d _1,A,k,k=1, 2 … 20。

Step 14: by particlep _PSO,kValue be updated top _PSO,k+v _{PSO, k},k=1, 2 … 20。

Enable (x ₀, y ₀, α ₀, β ₀)=p _PSO,k, and substitute into the inequality constraints of objective optimisation problems 1, i.e., 0≤-x _{0,b,under,1/2}cosα ₀sinβ ₀+ y _{0,b,under,1/2}sinα ₀+ z _{0,b,under,1/2}cosα ₀cosβ ₀,x ₀、y ₀∈[-D _A, D _A],α ₀、β ₀ ∈[-π, π]；If inequality constraints is set up, will (x ₀, y ₀, α ₀, β ₀) substitute into objective optimisation problems 1 in equation about Beam calculates and updates corresponding objective optimization functional valued _1,A,k；Ifd _1,A,k ≤ d _1,A,k,min, then more new particlep _PSO,k's Local optimumd _1,A,k,min=d _1,A,k, and more new particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；Ifd _1,A,k ≤d _1,A,min, then updating global optimumd _1,A,min=d _1,A,k, and update globally optimal solution and bep _PSO,min=p _PSO,k；k=1, 2 … 20。

If the local optimum and locally optimal solution of each particle are very close, that is, (| maxd _1,A,k,min– mind _1,A,k,min|≤0.00005) and (|p _{PSO,k,min, mean}– p _PSO,k,min|≤0.00005), then, step 17 is gone to, it is no Then go to step 15；Wherein,p _{PSO,k,min, mean}Forp _PSO,k,minArithmetic mean of instantaneous value,k=1, 2 … 20。

Step 15: by particlep _PSO,kSpeedv _PSO,kValue be updated to 0.5v _PSO,k+2C _rand1 (p _PSO,k,min- p _PSO,k) + 2C _rand2 (p _PSO,min- p _PSO,k), whereinC _rand1、C _rand2Be in section [0,1] independently of each other by be evenly distributed with Two values that machine is chosen； k=1, 2 … 20；

Step 16: the number of iterations of one secondary internal layer particle swarm algorithm of accumulation；If the number of iterations of internal layer particle swarm algorithm Greater than 100, then jumping to step 17, step 14 is otherwise jumped to.

When the number of iterations of outer layer particle swarm algorithmsWhen > 50, enableg =s -50, judge the receipts of multilayered particles group's algorithm Holding back property；If |d _1,A,min,s– min d _{1,A,min, g}|≤0.00005, then, terminate multilayered particles group algorithm and exports mesh Mark the optimal solution of optimization problem 1p _PSO,minAnd optimal valued _1,A,min, otherwise, accumulate the number of iterations of an outer layer particle swarm algorithm.

If the number of iterations of outer layer particle swarm algorithm is greater than 100, stops outer layer particle swarm algorithm and export target Optimization problem 1 optimal solution (x ₀, y ₀, α ₀, β ₀)=p _PSO,minWith optimal value mind _{1, A}=d _1,A,min, otherwise, more new particlep _PSO,1Initial value bep _PSO,minJump to step 13.

Solve reference cylindrical bodyAFitting cylindrical bodyCC _ADiameterd _A=|min d _{1, A}| and it is correspondingp _PSO,min's Value (x _0,min, y _0,min, α _0,min, β _0,min)。

Obtain practical tested all measuring points of cylinder relative to reference cylindrical body coordinate set p _{A, n}(x _{A, n}, y _{A, n},z _{A, n})}。

Obtain practical tested all measuring points of cylinder relative to reference cylindrical body coordinate set p _{b, m}(x _{b, m}, y _{b, m},z _{b, m})}。

Step 4: calculating benchmark cylindrical bodyAThe maximum material boundary cylindrical bodyCC _AMDiameterD _AM, work as reference cylinderAIt is axis When,D _AM= D _A+ es _A；Work as reference cylinderAWhen being hole,D _AM= D _A+ EI _A。

Solve objective optimisation problems 2:

s.t.

0 is set by the number of iterations of outer layer particle swarm algorithm.

Step 5: calculating tested cylindrical bodybMaximum solid virtual size: when tested cylindrical bodybWhen being axis,D _bMV= D _b+es _b+T _{b, AM, coa}；When tested cylindrical bodybWhen being hole,D _bMV= D _b+ EI _b-T _{b, AM, coa}。

When tested cylindrical bodyCbWhen being axis, if limit equivalent diameterd _{b, AM, coa, mM}≤ D _bMV, then it is " real to provide conclusion Border is tested cylindrical bodyC _bCoaxiality error it is qualified ", otherwise provide conclusion " practical tested cylindrical bodyC _bCoaxiality error do not conform to Lattice ".

Experimental subjects:

Measured hole has size to require, the same cell size tolerance of its hole line has maximum material requirement and its datum hole has size to want The detection of same cell size error qualification and evaluation of the stepped hole part of summation maximum material requirement:

Step 1: obtaining tested cylindrical body as shown in Figure 4b, reference cylinderAGeometry design parameter (length unit is Millimeter, angular unit are degree, radian 1).

The tested cylindrical bodybGeometry design parameter include: be Kong Yaosu, nominal diameterD _b=24, nominal lengthL _b= 15, the upper deviation in holeES _b=0.4, the lower deviation in holeEI _b=0, with cell size toleranceT _{b, AM, coa}=0.2, maximum with cell size tolerances marking Entity inquiry, with the reference cylinder of cell size toleranceAMark maximum solid state.

The reference cylinderAGeometry design parameter include: be Kong Yaosu, nominal diameterD _A=39, nominal lengthL _A= 22, the upper deviation in holeES _A=0.1, the lower deviation in holeEI _A=0.07, dimensional tolerance application envelope principle, without geometric tolerances requirement.

Tested cylindrical bodybSame cell size tolerance and reference cylinderAThere are maximum material requirement, and reference cylinderA Only size tolerance requirements and apply envelope principle, jump to step 2.

Step 2: obtaining practical tested cylindrical bodyb, reference cylindrical bodyAMeasurement data, including following four measuring point Data set, as shown in table 1:

Reference cylindrical bodyATwo measuring pointsP _{measure, A, under, 1}、P _{measure,A,under,2}Respectively in reference circle CylinderATwo bottom surfaces on, the measuring point data of two measuring points formed measuring point data collectionp _{measure, A, under, i},i=1, 2；It is real Border reference cylinderASide on measuring pointP _{measure, A, n}It is distributed on 3 layers of circumference, 3 points of every layer of circumference, measuring point data Formation measuring point data collectionp _{measure, A, n},n=1, 2 … 9；Practical tested cylindrical bodybTwo measuring pointsP _{measure, b, under, 1}、P _{measure,b,under,2}Respectively in actually tested cylindrical bodybTwo bottom surfaces on, the measuring point of two measuring points Data formation measuring point data collectionp _{measure, b, under, j},j=1, 2；Practical tested cylindrical bodybSide on measuring pointP _{measure, b, m}It is distributed on 3 layers of circumference, 3 points of every layer of circumference, measuring point data formation measuring point data collectionp _{measure, b, m},m= 1, 2 … 9}。

By the measuring point on 3 layers of circumferenceP _{measure, A, n}Be fitted to 3 circles respectively, diameter is respectively 39.086,39.083, 39.099 determining reference cylindrical bodyAScale error it is qualified；By the measuring point on 3 layers of circumferencep _{measure, b, m}It is fitted respectively For 3 circles, diameter is respectively 24.013,24.017,24.021, determines practical tested cylindrical bodybScale error it is qualified；It jumps Go to step 3.

Step 3: calculatingp _{measure, A, under, 1/2}=( p _{measure, A, under, 1}+ p _{measure, A, under, 2})/2= (261.1905, 229.524, -584.6165)。

Obtain in step 2 four measuring point data collection are coordinately transformed, four rough translation data sets are obtained {p _{0, A, under, i}(x _{0, A, under, i}, y _{0, A, under, i}, z _{0, A, under, i})| p _{0, A, under, i} =p _{measure, A, under, i}-p _{measure, A, under, 1/2},i=1,2 }, as shown in table 1；{p _{0, A, n}(x _{0, A, n}, y _{0, A, n},z _{0, A, n})| p _{0, A, n} = p _{measure, A, n}-p _{measure, A, under, 1/2},n=1, 2 … N, as shown in table 1；{p _{0, b, under, j}(x _{0, b, under, j}, y _{0, b, under, j}, z _{0, b, under, j})| p _{0, b, under, j} =p _{measure, b, under, j}-p _{measure, A, under, 1/2},j=1,2 }, as shown in table 1；{ p _{0, b, m}(x _{0, b, m}, y _{0, b, m},z _{0, b, m})| p _{0, b, m} = p _{measure, b, m}-p _{measure, A, under, 1/2},m=1, 2 … M, as shown in table 1.

It calculatesp _{0, b, under, 1/2}=( p _{0, b, under, 1}+ p _{0, b, under, 2})/2=(-23.8675, 3.699, - 18.67)。

Solve objective optimisation problems 1:

s.t.

Step 12: defining 20 particlesp _PSO,k(p _{PSO, k,1}, p _{PSO, k,2}, p _{PSO, k,3}, p _{PSO, k,4}), value corresponds to mesh Mark optimization problem 1 in variable (x ₀, y ₀, α ₀, β ₀),p _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval point Not withx ₀、y ₀、α ₀、β ₀Value interval it is identical, it may be assumed thatp _{PSO, k,1}、p _{PSO, k,2}∈ [- 39,39],p _{PSO, k,3}、p _{PSO, k,4}∈[-π, π]；k=1, 2 … 20；All particle constituent particle collectionp _PSO,k}；One particle is setp _PSO,1(p _PSO,1,1, p _PSO,1,2,p _PSO,1,3, p _PSO,1,4) initial value be (0,0,0,0).

0 is set by the number of iterations of outer layer particle swarm algorithm.

where

Enable (x ₀, y ₀, α ₀, β ₀)=p _PSO,k, and substitute into the inequality constraints of objective optimisation problems 1, i.e., 0≤-x _{0,b,under,1/2}cosα ₀sinβ ₀+ y _{0,b,under,1/2} sinα ₀ + z _{0,b,under,1/2} cosα ₀ cosβ ₀,x ₀、y ₀∈[-39, 39],α ₀、β ₀∈[-π, π]；If inequality constraints is set up, will (x ₀, y ₀, α ₀, β ₀) substitute into objective optimisation problems 1 Equality constraint, calculate and update corresponding objective optimization functional valued _1,A,k；Ifd _1,A,k ≤ d _1,A,k,min, then updating grain Sonp _PSO,kLocal optimumd _1,A,k,min=d _1,A,k, and more new particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；Ifd _1,A,k ≤ d _1,A,min, then updating global optimumd _1,A,min=d _1,A,k, and update globally optimal solution and bep _PSO,min=p _PSO,k；k= 1, 2 … 20.If the local optimum and locally optimal solution of each particle are very close, that is, (| maxd _1,A,k,min– mind _1,A,k,min|≤0.00005) and (|p _{PSO,k,min, mean}– p _PSO,k,min|≤0.00005), whereinp _{PSO,k,min, mean}Forp _PSO,k,minArithmetic mean of instantaneous value,k=1, 2 … 20；So, step 17 is gone to, step 15 is otherwise gone to.

Solve reference cylindrical bodyAFitting cylindrical bodyCC _ADiameterd _A=|min d _{1, A}|=39.099 and correspondingp _PSO,minValue (x _0,min, y _0,min, α _0,min, β _0,min)= (13.9257, 6.4138, 0.012, 0.0149)。

Obtain practical tested all measuring points of cylinder relative to reference cylindrical body coordinate set p _{A, n}(x _{A, n}, y _{A, n},z _{A, n}), as shown in table 1.

Obtain practical tested all measuring points of cylinder relative to reference cylindrical body coordinate set p _{b, m}(x _{b, m}, y _{b, m},z _{b, m}), as shown in table 1.

Step 4: calculating benchmark cylindrical bodyCAThe maximum material boundary cylindrical bodyCC _AMDiameterD _AM, reference cylinderCAIt is Hole,D _AM= D _A+ EI _A=39+0.07=39.07；

Solve objective optimisation problems 2:

s.t.

0 is set by the number of iterations of outer layer particle swarm algorithm.

Solve cylindrical bodyCC _bRelative to cylindrical bodyCC _AMLimit equivalent diameterd _{b, AM, coa, mM}=|min d _{b, AM, coa}|= 23.792。

Step 5: calculating tested cylindrical bodybMaximum solid virtual size: tested cylindrical bodybIt is hole,D _bMV= D _b+EI _b-T _{b, AM, coa}=24+0-0.3=23.7。

Tested cylindrical bodybIt is hole, 23.7=D _bMV≤d _{b, AM, coa, mM}=23.792, provide conclusion " practical tested cylindrical bodyb Coaxiality error it is qualified ".

1 data set of table and coordinate set

Claims

1. a kind of concentricity assessment method based on maximum solid state, which is characterized in that specific step is as follows:

Step 1: obtaining tested cylindrical bodyCb, reference cylinderCAAnd the geometry design parameter between them；If tested cylinder BodyCbConcentricity tolerance and reference cylinderCAThere are maximum material requirement, and reference cylinderCAOnly dimensional tolerance does not have There are geometric tolerances, then jumping to step 2, otherwise terminate this rapid method for assessment, and provides conclusion and " be tested the coaxial of cylindrical body Degree tolerance cannot be evaluated with this method "；

The tested cylindrical bodyCbGeometry design parameter include: hole element or axial element, nominal diameterD _b, name it is long DegreeL _b, axis the upper deviationes _bOr the upper deviation in holeES _b, axis lower deviationei _bOr the lower deviation in holeEI _b, concentricity toleranceT _{b, AM, coa}, concentricity tolerance whether mark the reference cylinder of maximum material requirement, concentricity toleranceCAWhether maximum is marked Entity state；

The reference cylinderCAGeometry design parameter include: hole element or axial element, nominal diameterD _A, name it is long DegreeL _A, axis the upper deviationes _AOr the upper deviation in holeES _A, axis lower deviationei _AOr the lower deviation in holeEI _A, whether dimensional tolerance apply Envelope principle, form tolerance, orientation of related features, position of related features, run-out tolerance；

The tested cylindrical bodyCbWith reference cylinderCABetween geometry design parameter be tested cylindrical bodyCbGeometry in The heart and reference cylinderCAGeometric center between nominal distanceL _Ab；

Step 2: obtaining practical tested cylindrical bodyC _b, reference cylindrical bodyC _AMeasurement data；Evaluate reference cylindrical bodyC _A Scale error and practical tested cylindrical bodyC _bScale error jump to step 3 if above-mentioned error is all qualified, otherwise tie This rapid method for assessment of beam, and provide conclusion " reference cylindrical bodyC _AAnd/or practical tested cylindrical bodyC _bOther errors not It is qualified "；

Step 3: by reference cylindrical bodyC _AMeasure data fitting be cylindrical bodyCC _A, in the fitting cylindrical body of tested cylindrical body On establish local coordinate system, and calculate practical tested cylindrical bodyC _b, reference cylindrical bodyC _AMeasurement data in the local coordinate Coordinate in system；

Step 4: with reference cylindrical bodyC _ARelative to cylindrical bodyCC _AMThree-dimensional attitudev _AFor variable, with practical measured circle CylinderC _bRelative to cylindrical bodyCC _AMEquivalent diameterd _{b, AM, coa, mM}=f(v _A) it is objective function, objective optimization is carried out, reality is obtained Border is tested cylindrical bodyC _bRelative to cylindrical bodyCC _AMLimit equivalent diameterd _{b, AM, coa, mM}；

Wherein,v _AIt is constrained as follows: for arbitrarily without departing from reference cylinderCAThe maximum material boundary cylindrical bodyCC _AMCylinder BodyCC _A, relative to cylindrical bodyCC _AMThree-dimensional attitude can be expressed asv _A；For anyv _A, cylindrical bodyCC _AWithout departing from base Director circle cylinderCAThe maximum material boundary cylindrical bodyCC _AM；

Step 5: according to tested cylindrical bodyCbMaximum solid virtual sizeD _bMVWith practical tested cylindrical bodyC _bLimit equivalent it is straight Diameterd _{b, AM, coa, mM}, judge practical tested cylindrical bodyC _bCoaxiality error it is whether qualified.

2. a kind of concentricity assessment method based on maximum solid state according to claim 1, it is characterized in that:

Cylindrical body is actually tested described in step 2C _b, reference cylindrical bodyC _AMeasurement data be measurement rectangular space coordinate It is measured in system, and including following four measuring point data collection:

Reference cylindrical bodyC _ABottom surface on measuring pointP _{measure, A, under, i}Measuring point datap _{measure, A, under, i} (x _{measure, A, under, i}, y _{measure, A, under, i}, z _{measure, A, under, i}),i=1, 2 …I,IFor measure-point amount and it is Positive integer, all measuring point datasp _{measure, A, under, i}(x _{measure, A, under, under, i}, y _{measure, A, under, i},z _{measure, A, under, i}) formation measuring point data collectionp _{measure, A, under, i}}；

Reference cylindrical bodyC _ASide on measuring pointP _{measure, A, n}Measuring point datap _{measure, A, n}(x _{measure, A, n},y _{measure, A, n}, z _{measure, A, n}),n=1, 2 …N,NIt for measure-point amount and is positive integer, all measuring point datasp _{measure, A, n}(x _{measure, A, n}, y _{measure, A, n}, z _{measure, A, n}) formation measuring point data collectionp _{measure, A, n}}；

Practical tested cylindrical bodyC _bBottom surface on measuring pointP _{measure, b, under, j}Measuring point datap _{measure, b, under, j} (x _{measure, b, under, j}, y _{measure, b, under, j}, z _{measure, b, under, j}),j=1, 2 …J,JFor measure-point amount and it is Positive integer, all measuring point datasp _{measure, b, under, j}(x _{measure, b, under, under, j}, y _{measure, b, under, j},z _{measure, b, under, j}) formation measuring point data collectionp _{measure, b, under, j}}；

Practical tested cylindrical bodyC _bSide on measuring pointP _{measure, b, m}Measuring point datap _{measure, b, m}(x _{measure, b, m},y _{measure, b, m}, z _{measure, b, m}),m=1, 2 …M,MIt for measure-point amount and is positive integer, all measuring point datasp _{measure, b, m}(x _{measure, b, m}, y _{measure, b, m}, z _{measure, b, m}) formation measuring point data collectionp _{measure, b, m}}。

3. a kind of concentricity assessment method based on maximum solid state according to claim 2, it is characterized in that:

In step 2, reference cylindrical bodyC _ABottom surface on measuring point numberI=2, and two measuring pointsP _{measure, A, under, 1}、P _{measure,A,under,2}Respectively in reference cylindrical bodyC _ATwo bottom surfaces on；

Practical tested cylindrical bodyC _bBottom surface on measuring point numberJ=2, and two measuring pointsP _{measure, b, under, 1}、P _{measure,b,under,2}Respectively in actually tested cylindrical bodyC _bTwo bottom surfaces on；

In step 3, by reference cylindrical bodyC _AMeasuring point data collectionp _{measure, A, n}It is fitted to cylindrical bodyCC _ASide,P _{measure, A, under, 1}、P _{measure,A,under,2}The midpoint of lineP _{measure, A, under, 1/2}In cylindrical bodyCC _ATwo bottom surfaces Symmetrical planePL _{A, 1/2}On, cylindrical bodyCC _ALength be equal to reference cylinderCANominal lengthL _A；

In cylindrical bodyCC _AOn establish local rectangular coordinate systemO _{xyz, A}, coordinate systemO _{xyz, A}Origin and cylindrical bodyCC _AGeometry in The heartO _AIt is overlapped, coordinate systemO _{xyz, A}A reference axis and cylindrical bodyCC _AAxis be overlapped, the positive direction vector of the reference axis with to AmountO _A P _{measure, b, under, 1/2}Dot product be not less than zero, whereinP _{measure, b, under, 1/2}It isP _{measure, b, under, 1}、P _{measure,b,under,2}The midpoint of line；Define cylindrical bodyCC _AUnit direction vectorn _CCALength be 1, positive direction and the coordinate The positive direction vector of axis is identical；

By reference cylindrical bodyC _AMeasuring point data collectionp _{measure, A, n}And practical tested cylindrical bodyC _bMeasuring point data collection {p _{measure, b, m}Coordinate conversion is carried out, obtain reference cylindrical bodyC _AWith practical tested cylindrical bodyC _bMeasuring point in coordinate systemO _{xyz, A}In coordinate setp _{A, n}Andp _{b, m}}。

4. a kind of concentricity assessment method based on maximum solid state according to claim 3, it is characterized in that:

Step 1: obtaining tested cylindrical bodyCb, reference cylinderCAAnd the geometry design parameter between them；If tested cylinder BodyCbConcentricity tolerance and reference cylinderCAThere are maximum material requirement, and reference cylinderCAOnly dimensional tolerance, Or otherwise only dimensional tolerance and envelope principle then jumping to step 2 terminates this rapid method for assessment, and provide conclusion " concentricity tolerance of tested cylindrical body cannot be evaluated with this method "；

The tested cylindrical bodyCbGeometry design parameter include be hole element or axial element, nominal diameterD _b, nominal lengthL _b, axis the upper deviationes _bOr the upper deviation in holeES _b, axis lower deviationei _bOr the lower deviation in holeEI _b, concentricity toleranceT _{b, AM, coa}, concentricity tolerance whether mark the reference cylinder of maximum material requirement, concentricity toleranceCAWhether maximum is marked Entity state；

Step 2: obtaining practical tested cylindrical bodyC _b, reference cylindrical bodyC _AMeasurement data, including following four measuring point data Collection:

Reference cylindrical bodyC _ATwo measuring pointsP _{measure, A, under, 1}、P _{measure,A,under,2}Respectively in reference cylindrical bodyC _ATwo bottom surfaces on, the measuring point data of two measuring pointsp _{measure, A, under, 1}(x _{measure, A, under, 1},y _{measure, A, under, 1}, z _{measure, A, under, 1})、p _{measure, A, under, 2}(x _{measure, A, under, 2},y _{measure, A, under, 2}, z _{measure, A, under, 2}) formation measuring point data collectionp _{measure, A, under, i},i=1, 2；Practical base Director circle cylinderC _ASide on measuring pointP _{measure, A, n}Measuring point datap _{measure, A, n}(x _{measure, A, n}, y _{measure, A, n},z _{measure, A, n}),n=1, 2 …N,NIt for measure-point amount and is positive integer, all measuring point datasp _{measure, A, n} (x _{measure, A, n}, y _{measure, A, n}, z _{measure, A, n}) formation measuring point data collectionp _{measure, A, n}}；Practical tested cylindrical bodyC _b Two measuring pointsP _{measure, b, under, 1}、P _{measure,b,under,2}Respectively in actually tested cylindrical bodyC _bTwo bottom surfaces on, two The measuring point data of measuring pointp _{measure, b, under, 1}(x _{measure, b, under, 1}, y _{measure, b, under, 1},z _{measure, b, under, 1})、p _{measure, b, under, 2}(x _{measure, b, under, 2}, y _{measure, b, under, 2},z _{measure, b, under, 2}) formation measuring point data collectionp _{measure, b, under, j},j=1, 2；Practical tested cylindrical bodyC _bSide on Measuring pointP _{measure, b, m}Measuring point datap _{measure, b, m}(x _{measure, b, m}, y _{measure, b, m}, z _{measure, b, m}),m=1, 2 …M,MIt for measure-point amount and is positive integer, all measuring point datasp _{measure, b, m}(x _{measure, b, m}, y _{measure, b, m},z _{measure, b, m}) formation measuring point data collectionp _{measure, b, m}}；

Evaluate reference cylindrical bodyC _AWith practical tested cylindrical bodyC _bScale error it is whether qualified, if above-mentioned error is all closed Lattice jump to step 3, otherwise terminate this rapid method for assessment, and provide conclusion " reference cylindrical bodyC _AAnd/or practical quilt Survey cylindrical bodyC _bOther errors it is unqualified "；

Step 3: calculatingp _{measure, A, under, 1/2}=( p _{measure, A, under, 1}+ p _{measure, A, under, 2})/2；

Obtain in step 2 four measuring point data collection are coordinately transformed, four rough translation data sets are obtained {p _{0, A, under, i}(x _{0, A, under, i}, y _{0, A, under, i}, z _{0, A, under, i})| p _{0, A, under, i} =p _{measure, A, under, i}-p _{measure, A, under, 1/2},i=1, 2}、{p _{0, A, n}(x _{0, A, n}, y _{0, A, n}, z _{0, A, n})|p _{0, A, n} = p _{measure, A, n}-p _{measure, A, under, 1/2},n=1, 2 …N }、{ p _{0, b, under, j}(x _{0, b, under, j},y _{0, b, under, j}, z _{0, b, under, j})| p _{0, b, under, j} = p _{measure, b, under, j}-p _{measure, A, under, 1/2},j=1, 2}、{ p _{0, b, m}(x _{0, b, m}, y _{0, b, m}, z _{0, b, m})| p _{0, b, m} = p _{measure, b, m}-p _{measure, A, under, 1/2},m=1, 2 …M}；

It calculatesp _{0, b, under, 1/2}(x _{0, b, under, 1/2}, y _{0, b, under, 1/2}, z _{0, b, under, 1/2})=( p _{0, b, under, 1}+p _{0, b, under, 2})/2；

Solve objective optimisation problems 1:

s.t.

Solve optimal solution (x _0,min, y _0,min, α _0,min, β _0,min), i.e. reference cylindrical bodyC _AFitting cylindrical bodyCC _AIt is corresponding (x ₀, y ₀, α ₀, β ₀) value；

To translate roughly data set p _{0, A, n}(x _{0, A, n}, y _{0, A, n}, z _{0, A, n}) following coordinate transform is carried out,n=1, 2 …N:

Obtain practical tested all measuring points of cylinder relative to reference cylindrical body coordinate set p _{A, n}(x _{A, n}, y _{A, n},z _{A, n})}；

To translate roughly data set p _{0, b, m}(x _{0, b, m}, y _{0, b, m}, z _{0, b, m}) following coordinate transform is carried out,m=1, 2 …M:

Obtain practical tested all measuring points of cylinder relative to reference cylindrical body coordinate set p _{b, m}(x _{b, m}, y _{b, m},z _{b, m})}；

Step 4: calculating benchmark cylindrical bodyCAThe maximum material boundary cylindrical bodyCC _AMDiameterD _AM, work as reference cylinderCAWhen being axis,D _AM= D _A+ es _A；Work as reference cylinderCAWhen being hole,D _AM= D _A+ EI _A；

Solve objective optimisation problems 2:

s.t.

Solve practical tested cylindrical bodyC _bLimit equivalent diameterd _{b, AM, coa, mM}=|min d _{b, AM, coa}|；

Step 5: calculating tested cylindrical bodyCbMaximum solid virtual size: when tested cylindrical bodyCbWhen being axis,D _bMV= D _b+es _b+T _{b, AM, coa}；When tested cylindrical bodyCbWhen being hole,D _bMV= D _b+ EI _b-T _{b, AM, coa}；

When tested cylindrical bodyCbWhen being axis, if limit equivalent diameterd _{b, AM, coa, mM}≤D _bMV, then providing conclusion " practical quilt Survey cylindrical bodyC _bCoaxiality error it is qualified ", otherwise provide conclusion " practical tested cylindrical bodyC _bCoaxiality error it is unqualified "；

When tested cylindrical bodyCbWhen being hole, ifD _bMV≤ limit equivalent diameterd _{b, AM, coa, mM}, then providing conclusion " practical quilt Survey cylindrical bodyC _bCoaxiality error it is qualified ", otherwise provide conclusion " practical tested cylindrical bodyC _bCoaxiality error it is unqualified ".

5. a kind of concentricity assessment method based on maximum solid state according to claim 4, it is characterized in that:

The step of solution of the objective optimisation problems, is as follows:

Step 01: defining the parameter of multilayered particles group algorithm or use its default value, including resolution ratioT _POS, populationN _P, internal layer Maximum number of iterationsN _i,rd, outer layer maximum number of iterationsN _o,rd, outer layer minimum the number of iterationsn _o,rd, quality weight factorW, part power The factorC ₁, global weight factorC ₂；N _P>=2,N _i,rd≥ 1；

Step 02: definitionN _PA particlep _PSO,k(p _{PSO, k,1}, p _{PSO, k,2}, …, p _{PSO, k,Q}), value corresponds to objective optimisation problems In independent variable (x ₁, x ₂, …, x _Q),p _{PSO, k, q}Value interval respectively withx _qValue interval it is identical；k=1, 2 …N _P；q=1, 2 …Q；All particle constituent particle collectionp _PSO,k}；One particle is setp _PSO,1Initial value or use its default value；

0 is set by the number of iterations of outer layer particle swarm algorithm；

Step 03: existing respectivelyp _{PSO, k, q}Value interval taken at random by being evenly distributed (N _P- 1) a value, building (N _P- 1) a grain Sonp _PSO,k；k=2, 3 …N _P；q=1, 2 …Q；

Exist respectivelyp _{PSO, k, q}Value interval taken at random by being evenly distributedN _PA value, buildingN _PA particlep _PSO,kInitial velocityv _{PSO, k} (v _{PSO, k,1}, v _{PSO, k,2}, …, v _{PSO, k,q})；All particles speed composition speed collectionv _PSO,k}；k=1, 2 …N _P；q=1, 2 …Q；

DefinitionN _PA particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；k=1, 2 …N _P；

It willp _{PSO, k, q}Value substitute into the variable in objective optimisation problems respectivelyx _qAnd its equality constraint, and calculate corresponding target Majorized function valuef _k=f(x ₁, x ₂, …, x _Q)；k=1, 2 …N _P；q=1, 2 …Q；

Record particlep _PSO,kCorresponding local optimumf _k,min=f _k,k=1, 2 …N _P；

Record global optimumf _min=min f _k,min, and record and minf _k,minThe value of corresponding particle is globally optimal solutionp _PSO,min；

0 is set by the number of iterations of internal layer particle swarm algorithm；

Step 04: by particlep _PSO,kValue be updated top _PSO,k+v _{PSO, k},k=1, 2 …N _P；

Enable (x ₁, x ₂, …, x _Q)=p _PSO,k, and substitute into the inequality constraints of objective optimisation problems；If inequality constraints is set up, So incite somebody to action (x ₁, x ₂, …, x _Q) equality constraint in objective optimisation problems is substituted into, and calculate and update corresponding objective optimization Functional valuef _k；Iff _k≤f _k,min, then more new particlep _PSO,kLocal optimumf _k,min=f _k, and more new particlep _PSO,kOffice Portion's optimal solution isp _PSO,k,min=p _PSO,k；Iff _k≤f _min, then updating global optimumf _min=f _k, and update globally optimal solution Forp _PSO,min=p _PSO,k；k=1, 2 …N _P；q=1, 2 …Q；

If the local optimum and locally optimal solution of each particle are very close, that is, | maxf _k,min– min f _k,min| ≤T _POS And |p _{PSO,k,min, mean}–p _PSO,k,min| ≤T _POS, whereinp _{PSO,k,min, mean}Forp _PSO,k,minArithmetic mean of instantaneous value,k=1, 2 …N _P；So, step 07 is gone to, step 05 is otherwise gone to；

Step 05: by particlep _PSO,kSpeedv _PSO,kValue be updated toW v _PSO,k+ C _rand1 C ₁ (p _PSO,k,min- p _PSO,k) +C _rand2 C ₂ (p _PSO,min- p _PSO,k), whereinC _rand1、C _rand2It is random by being evenly distributed independently of each other in section [0,1] Two values chosen； k=1, 2 …N _P；

Step 06: the number of iterations of one secondary internal layer particle swarm algorithm of accumulation；If the number of iterations of internal layer particle swarm algorithm is greater thanN _i,rd, then jumping to step 07, otherwise jump to step 04；

Step 07: recording the global optimum for the internal layer particle swarm algorithm that each iteration obtainsf _min,s= f _min, whereinsIt is outer layer The number of iterations of particle swarm algorithm；

By particlep _PSO,1Value be set as current globally optimal solutionp _PSO,min；

When the number of iterations of outer layer particle swarm algorithms > n _o,rdWhen, it enablesg =s -n _o,rd, judge the convergence of multilayered particles group's algorithm Property；If |f _min,s– min f _{min, g} | ≤T _POS, then, terminate multilayered particles group algorithm and exports objective optimisation problems most Excellent solutionp _PSO,minAnd optimal valuef _min, otherwise, accumulate the number of iterations of an outer layer particle swarm algorithm；

If the number of iterations of outer layer particle swarm algorithm is greater thanN _o,rd, then stopping outer layer particle swarm algorithm and exporting objective optimization Problem optimal solution (x ₁, x ₂, …, x _Q)=p _PSO,minWith optimal value minf=f _min, otherwise, more new particlep _PSO,1Initial value Forp _PSO,minJump to step 03.

6. a kind of concentricity assessment method based on maximum solid state according to claim 5, it is characterized in that:

The resolution ratio of the multilayered particles group algorithmT _POSDefault value is 0.00005, populationN _PDefault value is that 20, internal layer maximum changes Generation numberN _i,rdDefault value is 100, outer layer maximum number of iterationsN _o,rdDefault value is 100, outer layer minimum the number of iterationsn _o,rdDefault Value is 50, quality weight factorWDefault value is 0.5, local weight factorC ₁Default value is 2, global weight factorC ₂Default value is 2；p _PSO,1Initial value be defaulted as null vector.

7. a kind of concentricity assessment method based on maximum solid state according to claim 5, it is characterized in that:

Step 11: defining the parameter of multilayered particles group algorithm or use its default value, including resolution ratioT _POS, populationN _P, internal layer Maximum number of iterationsN _i,rd, outer layer maximum number of iterationsN _o,rd, outer layer minimum the number of iterationsn _o,rd, quality weight factorW, part power The factorC ₁, global weight factorC ₂；N _P>=2,N _i,rd≥ 1；

Step 12: definitionN _PA particlep _PSO,k(p _{PSO, k,1}, p _{PSO, k,2}, p _{PSO, k,3}, p _{PSO, k,4}), it is excellent that value corresponds to target In change problem 1 variable (x ₀, y ₀, α ₀, β ₀),p _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval respectively withx ₀、y ₀、α ₀、β ₀Value interval it is identical, it may be assumed thatp _{PSO, k,1}、p _{PSO, k,2}∈[-D _A, D _A],p _{PSO, k,3}、p _{PSO, k,4}∈[-π, π]；k=1, 2 …N _P；All particle constituent particle collectionp _PSO,k}；One particle is setp _PSO,1(p _PSO,1,1, p _PSO,1,2,p _PSO,1,3, p _PSO,1,4) initial value be (0,0,0,0)；

0 is set by the number of iterations of outer layer particle swarm algorithm；

Step 13: existing respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval taken at random by being evenly distributed (N _P - 1) a value, building (N _P- 1) a particlep _PSO,k；k=2, 3 …N _P；

Exist respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval taken at random by being evenly distributedN _PA value, buildingN _P A particlep _PSO,kInitial velocityv _{PSO, k} (v _{PSO, k,1}, v _{PSO, k,2}, v _{PSO, k,3}, v _{PSO, k,4})；The velocity group of all particles At speed collectionv _PSO,k}；k=1, 2 …N _P；

It willp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value substitute into the variable in objective optimisation problems 1 respectivelyx ₀、y ₀、α ₀、β ₀ And its equality constraint, and calculate corresponding objective optimization functional valued _1,A,k,k=1, 2 …N _P；That is,

where

Record particlep _PSO,kCorresponding local optimumd _1,A,k,min=d _1,A,k,k=1, 2 …N _P；

Record global optimumd _1,A,min=min d _1,A,k,min, and record and mind _1,A,k,minThe value of corresponding particle be it is global most Excellent solutionp _PSO,min；

Step 14: by particlep _PSO,kValue be updated top _PSO,k+v _{PSO, k},k=1, 2 …N _P；

Enable (x ₀, y ₀, α ₀, β ₀)=p _PSO,k, and substitute into the inequality constraints of objective optimisation problems 1, i.e., 0≤-x _{0,b,under,1/2}cosα ₀sinβ ₀+ y _{0,b,under,1/2}sinα ₀+ z _{0,b,under,1/2}cosα ₀cosβ ₀,x ₀、y ₀∈[-D _A, D _A],α ₀、β ₀∈[-π, π]；Such as Fruit inequality constraints is set up, then will (x ₀, y ₀, α ₀, β ₀) substitute into objective optimisation problems 1 in equality constraint, calculate and more New corresponding objective optimization functional valued _1,A,k；Ifd _1,A,k≤d _1,A,k,min, then more new particlep _PSO,kLocal optimumd _1,A,k,min=d _1,A,k, and more new particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；Ifd _1,A,k≤d _1,A,min, then Update global optimumd _1,A,min=d _1,A,k, and update globally optimal solution and bep _PSO,min=p _PSO,k；k=1, 2 …N _P；

If the local optimum and locally optimal solution of each particle are very close, that is, | maxd _1,A,k,min– min d _1,A,k,min| ≤T _POSAnd |p _{PSO,k,min, mean}–p _PSO,k,min| ≤T _POS, whereinp _{PSO,k,min, mean}Forp _PSO,k,minArithmetic mean of instantaneous value,k= 1, 2 …N _P；So, step 17 is gone to, step 15 is otherwise gone to；

Step 15: by particlep _PSO,kSpeedv _PSO,kValue be updated toW v _PSO,k+ C _rand1 C ₁ (p _PSO,k,min- p _PSO,k) +C _rand2 C ₂ (p _PSO,min- p _PSO,k), whereinC _rand1、C _rand2It is random by being evenly distributed independently of each other in section [0,1] Two values chosen； k=1, 2 …N _P；

Step 16: the number of iterations of one secondary internal layer particle swarm algorithm of accumulation；If the number of iterations of internal layer particle swarm algorithm is greater thanN _i,rd, then jumping to step 17, otherwise jump to step 14；

Step 17: recording the global optimum for the internal layer particle swarm algorithm that each iteration obtainsd _1,A,min,s= d _1,A,min, whereins It is the number of iterations of outer layer particle swarm algorithm；

When the number of iterations of outer layer particle swarm algorithms > n _o,rdWhen, it enablesg =s -n _o,rd, judge the convergence of multilayered particles group's algorithm Property；If |d _1,A,min,s– min d _{1,A,min, g} | ≤T _POS, then, terminate multilayered particles group algorithm and export objective optimization to ask The optimal solution of topic 1p _PSO,minAnd optimal valued _1,A,min, otherwise, accumulate the number of iterations of an outer layer particle swarm algorithm；

If the number of iterations of outer layer particle swarm algorithm is greater thanN _o,rd, then stopping outer layer particle swarm algorithm and exporting objective optimization Problem 1 optimal solution (x ₀, y ₀, α ₀, β ₀)=p _PSO,minWith optimal value mind _{1, A}=d _1,A,min, otherwise, more new particlep _PSO,1's Initial value isp _PSO,minJump to step 13.

8. a kind of concentricity assessment method based on maximum solid state according to claim 5, it is characterized in that:

Step 21: defining the parameter of multilayered particles group algorithm or use its default value, including resolution ratioT _POS, populationN _P, internal layer Maximum number of iterationsN _i,rd, outer layer maximum number of iterationsN _o,rd, outer layer minimum the number of iterationsn _o,rd, quality weight factorW, part power The factorC ₁, global weight factorC ₂；N _P>=2,N _i,rd≥ 1；

Step 22: defining particlep _PSO,k(p _{PSO, k,1}, p _{PSO, k,2}, p _{PSO, k,3}, p _{PSO, k,4}) value correspond to objective optimisation problems In 2 variable (dx _A, dy _A, drx _A, dry _A),p _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval respectively withdx _A、dy _A、drx _A、dry _AValue interval it is identical,k=1, 2 …N _P；All particle constituent particle collectionp _PSO,k}；Setting one Particlep _PSO,1(p _PSO,1,1, p _PSO,1,2, p _PSO,1,3, p _PSO,1,4) initial value be (0,0,0,0)；

0 is set by the number of iterations of outer layer particle swarm algorithm；

Step 23: existing respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval in taken at random by being evenly distributed (N _P - 1) a value, building (N _P- 1) a particlep _PSO,k；k=2, 3 …N _P；

Exist respectivelyp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value interval in taken at random by being evenly distributedN _PA value, buildingN _PA particlep _PSO,kInitial velocityv _{PSO, k} (v _{PSO, k,1}, v _{PSO, k,2}, v _{PSO, k,3}, v _{PSO, k,4})；The speed of all particles Composition speed collectionv _PSO,k}；k=1, 2 …N _P；

It willp _{PSO, k,1}、p _{PSO, k,2}、p _{PSO, k,3}、p _{PSO, k,4}Value substitute into objective optimisation problems 2 in variabledx _A、dy _A、drx _A、dry _AAnd its equality constraint, and calculate corresponding objective optimization functional valued _b,AM,coa,k,k=1, 2 …N _P；

Record particlep _PSO,kLocal optimumd _{b,AM,coa,k,min}=d _b,AM,coa,k,k=1, 2 …N _P；

Record global optimumd _b,AM,coa,min=min d _{b,AM,coa,k,min}, and record and mind _{b,AM,coa,k,min}Corresponding particle Value is globally optimal solutionp _PSO,min；

Step 24: by particlep _PSO,kValue be updated top _PSO,k+v _{PSO, k},k=1, 2 …N _P；

Enable (dx _A, dy _A, drx _A, dry _A)=p _PSO,k, and the inequality constraints of objective optimisation problems 2 is substituted into, if inequality is about Shu Chengli, then will (dx _A, dy _A, drx _A, dry _A) equality constraint that substitutes into objective optimisation problems 2, it calculates and updates corresponding Objective optimization functional valued _b,AM,coa,k；Ifd _b,AM,coa,k≤d _{b,AM,coa,k,min}, then more new particlep _PSO,kLocal optimum Valued _{b,AM,coa,k,min}=d _b,AM,coa,k, and more new particlep _PSO,kLocally optimal solution bep _PSO,k,min=p _PSO,k；Ifd _b,AM,coa,k≤d _b,AM,coa,min, then updating global optimumd _b,AM,coa,min=d _b,AM,coa,k, and update globally optimal solution and bep _PSO,min=p _PSO,k；k=1, 2 …N _P；

If the local optimum and locally optimal solution of each particle are very close, that is, | maxd _{b,AM,coa,k,min}– mind _{b,AM,coa,k,min}| ≤T _POSAnd |p _{PSO,k,min, mean}–p _PSO,k,min| ≤T _POS, whereinp _{PSO,k,min, mean}Forp _PSO,k,minCalculation Art average value,k=1, 2 …N _P；So, step 27 is gone to, step 25 is otherwise gone to；

Step 25: by particlep _PSO,kSpeedv _PSO,kValue be updated toW v _PSO,k+ C _rand1 C ₁ (p _PSO,k,min- p _PSO,k) +C _rand2 C ₂ (p _PSO,min- p _PSO,k), whereinC _rand1、C _rand2It is random by being evenly distributed independently of each other in section [0,1] Two values chosen； k=1, 2 …N _P；

Step 26: the number of iterations of one secondary internal layer particle swarm algorithm of accumulation；If the number of iterations of internal layer particle swarm algorithm is greater thanN _i,rd, then stopping internal layer particle swarm algorithm and jumping to step 27, otherwise jump to step 24；

Step 27: recording the global optimum for the outer layer particle swarm algorithm that each iteration obtainsd _{b,AM,coa,min,s}= d _b,AM,coa,min, Wherein,sIt is the number of iterations of outer layer particle swarm algorithm；

When the number of iterations of outer layer particle swarm algorithms > n _o,rdWhen, it enablesg =s -n _o,rd, judge the convergence of multilayered particles group's algorithm Property；If |d _{b,AM,coa,min,s}– min d _{b,AM,coa,min, g} | ≤T _POS, then, terminate multilayered particles group algorithm and exports target The optimal solution of optimization problem 2p _PSO,minAnd optimal valued _b,AM,coa,min, otherwise, accumulate the iteration time of an outer layer particle swarm algorithm Number；

If the number of iterations of outer layer particle swarm algorithm is greater thanN _o,rd, then stopping outer layer particle swarm algorithm and exporting objective optimization Problem 2 optimal solution (dx _A, dy _A, drx _A, dry _A) =p _PSO,minWith optimal value mind _b,AM,coa=d _b,AM,coa,min, otherwise, More new particlep _PSO,1Initial value bep _PSO,minAnd jump to step 23.