CN106971087A - A kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain - Google Patents

Abstract

Involved in the present invention is a kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain, and first, according to lowest area principal, sets up the solution mathematical modeling of Flatness error evaluation；Secondly, by obtaining the measurement data of tested flat elemental, and set up mathematical modeling is combined, sets up the object function of problem；Finally, object function is solved using secondary learning aid algorithm of climbing the mountain, key step includes the Parameter Initialization procedure of algorithm, the mutually step such as study, and not high for standard learning aid algorithmic procedure solving precision between the teaching phase of student performance, student, the problems such as convergence rate is slower, simultaneously using the local optimal searching ability and quickening convergence rate of two benches hill-climbing algorithm enhancing algorithm, so as to sufficiently improve computational accuracy, finally solved.Parameter is less needed for this method, algorithm stability is good, surveyed data can be sufficiently applied to, it is more novel in algorithm application, test function is more accurate relative to other algorithms most in use, faster, solution procedure complies fully with the Minimum Area principle in international standard to iteration speed, therefore computational solution precision is higher.

Description

A kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain

Technical field

It is more particularly to a kind of based on secondary learning aid calculation of climbing the mountain the invention belongs to the digital measuring field of machine components The Flatness error evaluation method of method.

Background technology

Flatness error is one of basic Form and position error of machine components, affects the assembly precision of part and uses the longevity Life.Therefore, how further to improve the evaluating precision of part flatness, it is ensured that the designing quality of engineering goods, be heavy at this stage One of research direction wanted.

The national Specification error evaluation method of four kinds of flatnesses, including line-of-sight course, diagonal method, least square method And minimum area method, wherein least square method and minimum area method is most widely used.For machine components flatness error Evaluation algorithm, Wang Zhijian etc. is in its document《Flatness error is solved with least square method》In employ least square method to flat Face degree error is evaluated, and Wen Xiulan etc. is in its document《Flatness error evaluation based on evolution strategy》In employ evolution Algorithm is evaluated to flatness error, and Yue Wuling et al. is in its document《Rapid evaluation-increasing of flatness and straightness error Quantity algorithm》Middle use delta algorithm is evaluated to flatness error.

In summary, continuing to develop with computer technology and artificial intelligence technology, Flatness error evaluation method It is more and more perfect, precision also more and more higher, and wherein topmost method is exactly to minimum area method with reference to all kinds of optimized algorithms Constantly studied.Learning aid optimized algorithm is a kind of new global intelligent optimization algorithm proposed in 2012, its algorithm ginseng Number is seldom, and algorithm robustness very well, can further improve arithmetic accuracy, due to learning aid by introducing local searching strategy The calculating performance of optimized algorithm well, has been widely used in all kinds of engineering fields at this stage.

The present invention is that on the basis of basic learning aid algorithm, search by hill climbing strategy is introduced twice, further improves and calculates The search capability of method, to improve the evaluating precision of part flatness.

The content of the invention

It is an object of the invention to provide a kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain, to carry The evaluating precision and computational stability of high flatness error.

A kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain, mainly including herein below：

Step one：The tested flat elemental of tested part is determined, the plane survey of part is obtained by three coordinate measuring machine Data point is P_i(x_i, y_i, z_i) (i=1,2 ..., n)；

Step 2：According to the lowest area principal of flatness error, with reference to any datum plane equation Z in space, such as formula (1) shown in；Spatial point to plane range formula, such as shown in formula (2)；Set up the mathematical modeling of flatness error, such as formula (3) shown in.Wherein A, B are respectively the directioin parameter of datum plane, and C is the location parameter of plane, (x_i, y_i, z_i) it is measuring point P_i's Coordinate parameters, d_iFor measuring point P_iTo datum plane equation Z distance, f is required flatness error, and obtains A, B, C tri- simultaneously The value of parameter；

Z=Ax+By+C (1)

F=min (max (d_i)-min(d_i)) (3)

Step 3：Read measurement data P_i(x_i, y_i, z_i) (i=1,2 ..., n), are brought into formula (3), and learning aid is calculated The parameter of method is initialized, main to include initialization student X=(x₁, x₂..., x_i), i=1,2 ..., N, wherein x_iRepresent Student i, N in class are student's quantity.For some student x_i, there is x again_i=(x_i1, x_i2..., x_ij), j=1,2 ..., D, x_ijThe subject j, D for representing student's i are total subject, and optimal solution is x_t, i.e. fitness value is optimal for class's teacher's achievement, religion Iterations W, ramping constraint iterations w, into step 4 with learning optimized algorithm；

Step 4：The fitness function value of each student is calculated, and according to achievement of the formula (4), (5) and (6) to student It is updated, in formula：X (i, j) ' is the achievement after student i subject j renewals；Before x (i, j) updates for student i subject j Achievement；Rand is the random number between [0,1]；x_t(j) it is the subject j achievements of teacher；T is the teaching factor；X (j) is student section Mesh j achievement；M (j) is j-th of section's purpose average achievement in class；Round is the bracket function rounded up.Teaching phase After the completion of, by contrasting the quality of fitness value, the renewal of solution is completed, into step 5；

X (i, j) '=x (i, j)+rand × (x_t(j)-tM(j)) (4)

T=round [1+rand (0,1)] (5)

Step 5：Using hill climbing, search by hill climbing is carried out again to each student, concrete mode is to exchange any two Section's purpose achievement, then contrast exchanges the fitness before and after subject, selects smaller as after hill climbing maneuver of fitness value Achievement is generated, this time iteration is needed w times, after the completion of iteration, and the replacement of student performance is carried out again, and records globally optimal solution x_t, into step 6；

Step 6：Student performance is carried out again " to learn ", concrete mode is by randomly selecting two students, contrasting it Fitness value obtains size, the carry out study renewal small to fitness value for making fitness value big, and more new formula is such as shown in (7), formula In：x′_aAchievement after learning for student a；x_aAchievement before learning for student a；x_bAchievement before learning for student b.When learning After the completion of journey, further with the achievement x of teacher_tContrasted, the renewal of solution is completed, into step 7；

x′_a=x_b+rand×|x_a-x_b| (7)

Step 7：It is the achievement x of teacher to globally optimal solution again_tHill climbing maneuver is carried out, as shown in step 5, is entered again The renewal of row globally optimal solution.Evaluation algorithm whether when iteration complete, after W iteration is met, algorithm terminate, now the overall situation most Excellent solution x_tFitness function value be required flatness error value, if algorithm fails to complete W iteration, this iteration is obtained The globally optimal solution arrived brings next iteration process into as class teacher.

Compared with prior art, the present invention has the advantage that：

By setting up the minimum area method parametric equation of Flatness error evaluation, asking for flatness is more intuitively reflected Mathematical modeling is solved, is a kind of general mathematical modeling, without the coordinate transformation process in computational geometry and measuring point preprocessing process Etc. cumbersome modeling process, surveyed data can be sufficiently applied to, and be can apply among substantial amounts of measuring point data, In algorithm application, the algorithm mutually introduces search by hill climbing strategy twice, entered on the basis of standard learning aid optimized algorithm One step improves the precision of algorithm, and faster, solution procedure complies fully with the Minimum Area principle in international standard to convergence rate, because This computational solution precision is higher.

Brief description of the drawings

Fig. 1 is the algorithm flow chart of the present invention；

Fig. 2 is the flatness error iterative curve map of the present invention.

Embodiment

In order to become apparent from the design and advantage of the specific expression present invention, following processes will be with reference to accompanying drawing to whole The protocol procedures of evaluation are described in detail.

The invention provides a kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain, it is main include with Lower content：

Step one：The tested flat elemental of tested part is determined, the plane survey of part is obtained by three coordinate measuring machine Data point is P_i(x_i, y_i, z_i) (i=1,2 ..., n)；

Step 2：According to the lowest area principal of flatness error, with reference to any datum plane equation Z in space, such as formula (1) shown in；Spatial point to plane range formula, such as shown in formula (2)；Set up the mathematical modeling of flatness error, such as formula (3) shown in.Wherein A, B are respectively the directioin parameter of datum plane, and C is the location parameter of plane, (x_i, y_i, z_i) it is measuring point P_i's Coordinate parameters, d_iFor measuring point P_iTo datum plane equation Z distance, f is required flatness error, and obtains A, B, C tri- simultaneously The value of parameter；

Z=Ax+By+C (1)

F=min (max (d_i)-min(d_i)) (3)

Step 3：Read measurement data P_i(x_i, y_i, z_i) (i=1,2 ..., n), are brought into formula (3), and learning aid is calculated The parameter of method is initialized, main to include initialization student X=(x₁, x₂..., x_i), i=1,2 ..., N, wherein x_iRepresent Student i, N in class are student's quantity.For some student x_i, there is x again_i=(x_i1, x_i2..., x_ij), j=1,2 ..., D, x_ijThe subject j, D for representing student's i are total subject, and optimal solution is x_t, i.e. fitness value is optimal for class's teacher's achievement, religion Iterations W, ramping constraint iterations w, into step 4 with learning optimized algorithm；

Step 4：The fitness function value of each student is calculated, and according to achievement of the formula (4), (5) and (6) to student It is updated, in formula：X (i, j) ' is the achievement after student i subject j renewals；Before x (i, j) updates for student i subject j Achievement；Rand is the random number between [0,1]；x_t(j) it is the subject j achievements of teacher；T is the teaching factor；X (j) is student section Mesh j achievement；M (j) is j-th of section's purpose average achievement in class；Round is the bracket function rounded up.Teaching phase After the completion of, by contrasting the quality of fitness value, the renewal of solution is completed, into step 5；

X (i, j) '=x (i, j)+rand × (x_t(j)-tM(j)) (4)

T=round [1+rand (0,1)] (5)

Step 5：Using hill climbing, search by hill climbing is carried out again to each student, concrete mode is to exchange any two Section's purpose achievement, then contrast exchanges the fitness before and after subject, selects smaller as after hill climbing maneuver of fitness value Achievement is generated, this time iteration is needed w times, after the completion of iteration, and the replacement of student performance is carried out again, and records globally optimal solution x_t, into step 6；

Step 6：Student performance is carried out again " to learn ", concrete mode is by randomly selecting two students, contrasting it Fitness value obtains size, the carry out study renewal small to fitness value for making fitness value big, and more new formula is such as shown in (7), formula In：x′_aAchievement after learning for student a；x_aAchievement before learning for student a；x_bAchievement before learning for student b.When learning After the completion of journey, further with the achievement x of teacher_tContrasted, the renewal of solution is completed, into step 7；

x′_a=x_b+rand×|x_a-x_b| (7)

Step 7：It is the achievement x of teacher to globally optimal solution again_tHill climbing maneuver is carried out, as shown in step 5, is entered again The renewal of row globally optimal solution.Evaluation algorithm whether when iteration complete, after W iteration is met, algorithm terminate, now the overall situation most Excellent solution x_tFitness function value be required flatness error value, if algorithm fails to complete W iteration, this iteration is obtained The globally optimal solution arrived brings next iteration process into as class teacher.Algorithm whole flow process is as shown in figure 1, algorithm iteration Curve is as shown in Figure 2.

It is described above, it is only that the present invention teaches good embodiment, but protection scope of the present invention is not limited thereto, Any one skilled in the art the invention discloses technical scope in, the variations and alternatives that can be readily occurred in, It should all be included within the scope of the present invention, therefore, protection scope of the present invention should be with scope of the claims It is defined.

Claims (1)

1. a kind of Flatness error evaluation method based on secondary learning aid algorithm of climbing the mountain, it is characterised in that use following steps：

Step one：The tested flat elemental of tested part is determined, the plane survey data of part are obtained by three coordinate measuring machine Point is P_i(x_i, y_i, z_i) (i=1,2 ..., n)；

Step 2：According to the lowest area principal of flatness error, with reference to any datum plane equation Z in space, such as formula (1) institute Show；Spatial point to plane range formula, such as shown in formula (2)；The mathematical modeling of flatness error is set up, such as formula (3) institute Show.Wherein A, B are respectively the directioin parameter of datum plane, and C is the location parameter of plane, (x_i, y_i, z_i) it is measuring point P_iCoordinate Parameter, d_iFor measuring point P_iTo datum plane equation Z distance, f is required flatness error, and obtains A, B, tri- parameters of C simultaneously Value；

Z=Ax+By+C (1)

$d_i=\frac{z_i-{\mathrm{Ax}}_i-{\mathrm{By}}_i-c}{\sqrt{1+A^2+B^2}}---\left(2\right)$

F=min (max (d_i)-min(d_i)) (3)

Step 3：Read measurement data P_i(x_i, y_i, z_i) (i=1,2 ..., n), bring into formula (3), to learning aid algorithm Parameter is initialized, main to include initialization student X=(x₁, x₂..., x_i), i=1, wherein 2 ..., N, x_iRepresent class In student i, N is student's quantity.For some student x_i, there is x again_i=(x_i1, x_i2..., x_ij), j=1,2 ..., D, x_ij The subject j, D for representing student's i are total subject, and optimal solution is x_t, i.e. fitness value is optimal for class's teacher's achievement, religion with Learn the iterations W, ramping constraint iterations w, into step 4 of optimized algorithm；

Step 4：The fitness function value of each student is calculated, and the achievement of student is carried out according to formula (4), (5) and (6) Update, in formula：X (i, j) ' is the achievement after student i subject j renewals；X (i, j) is the achievement before student i subject j renewals； Rand is the random number between [0,1]；x_t(j) it is the subject j achievements of teacher；T is the teaching factor；X (j) is student's subject j's Achievement；M (j) is j-th of section's purpose average achievement in class；Round is the bracket function rounded up.Teaching phase is completed Afterwards, by contrasting the quality of fitness value, the renewal of solution is completed, into step 5；

X (i, j) '=x (i, j)+rand × (x_t(j)-tM(j)) (4)

T=round [1+rand (0,1)] (5)

$M\left(j\right)=\frac{1}{N}\underset{j=1}{\overset{N}{\Σ}}x\left(j\right)---\left(6\right)$

Step 5：Using hill climbing, search by hill climbing is carried out again to each student, concrete mode is to exchange any two subject Achievement, then contrast exchange subject before and after fitness, selection the smaller student as after hill climbing maneuver of fitness value into Achievement, this iteration is needed w times, after the completion of iteration, and the replacement of student performance is carried out again, and records globally optimal solution x_t, enter Enter step 6；

Step 6：Student performance is carried out again " to learn ", concrete mode is by randomly selecting two students, contrasting its adaptation Angle value obtains size, the carry out study renewal small to fitness value for making fitness value big, and more new formula is such as shown in (7), in formula： x′_aAchievement after learning for student a；x_aAchievement before learning for student a；x_bAchievement before learning for student b.Work as learning process After the completion of, further with the achievement x of teacher_tContrasted, the renewal of solution is completed, into step 7；

x′_a=x_b+rand×|x_a-x_b| (7)

Step 7：It is the achievement x of teacher to globally optimal solution again_tHill climbing maneuver is carried out, as shown in step 5, is carried out again complete The renewal of office's optimal solution.Whether evaluation algorithm is when iteration completion, and after W iteration is met, algorithm is terminated, now globally optimal solution x_tFitness function value be required flatness error value, if algorithm fails to complete W iteration, this iteration is obtained Globally optimal solution brings next iteration process into as class teacher.