Floating-point heredity algorithm measures medium application in radius of workpiece circular arc

The mathematical model of radius of circular arc of 1 drift concave side uses traditional method to measure radius of circular arc of drift concave side (see figure) when, need to stop machine the 3 ～ that measure drift concave side to go up measure a place 4 times, seek an its radius measure through computation next. Because form of the existence in the process is processed in drift concave side error, because this presses place choosing,be being measured to nod gotten radius is not optimum solution certainly. For affirmatory and best measure a place, but the question that the measurement of radius of drift concave side translate into begs region of the least value. Set the concave side that be measured is nod group of ranges be includinged that make by a large number of disperse, in these homocentric circles, total presence radius differs a pair of the smallest circles, can turn into the problem beg a group of variable R1, r2, ... , the region of the least value in Rn. Right now, the nominal radius dimension of circular arc of concave side of the drift that be measured is R, radius dimension public errand is δ , it is facilitating computation, distributing tolerancepublic errand semmetry, the size of circular arc radius that measures namely is R ± δ / 2. The mathematical model that can get circular arc radius from this is δ =min | Ri-Rj | (In 1)R=(Ri-Rj)/2(2) type, ri, rj is measured to include respectively outline is homocentric round radius, be measured namely homocentric circle plants outline group in I with J round radius (I=1, 2, ... , n: J=1, 2, ... , m) . 3.

The 2 methods that seek solution and measure basis afore-mentioned mathematical models, radius of concave side of the drift that seek solution is best the value can divide a measure to undertake, beg the coordinate of the centre of a circle that gives circular arc and circularity error δ above all, beg radius of solution circular arc next optimal value. Beg what the coordinate of the centre of a circle of drift circular arc sets drift concave side to go up to be measured to nod for M{(Xj, yj) | J=1, 2, ... , m} , the M that measure a place distributings in circular arc concave side circumferential on, xj, yj is value of the coordinate that measure a place respectively. Satisfy on this groups of coordinate most of zonule law include the value region of homocentric round Q is the outline that be measured {(Xo, yo) | Xmax of ≤ of Xmin ≤ Xo, ≤ of Ymin ≤ Yo Ymax}(3) agrees to make data processing standard maintains, take ≤ of 0 ≤ Xoi 1, ≤ of 0 ≤ Yoi 1. Accordingly, measure M(Xj with coordinate law, the mathematical model that Yjj) begs Q of coordinate of the centre of a circle of the arc that solve a circle is type of Y(4) of δ of {Xo=Xmin-Xoi δ XYo=Ymin-Yoi in, the error of X coordinate is δ X=Xmax-Xmin, the error of Y coordinate is δ Y=Ymax-Ymin. After the circularity error that begs drift circular arc builds initiative maths model, can use the circularity error of circular arc of drift of genetic and algorithmic computation, computational move is as follows: Decide kind of group of dimensions, probability and developmental algebra are chosen plant N=50 of group of initiative scale number, alternate probability Pc=0.

9, mutation probability Pm=0.

02, t=100 of the biggest developmental algebra. Kind group initialization uses floating-point heredity algorithm, make (Xo, the limits finding actor of Yo) includes whole and optimum solution feasible region, in solution feasible decide N each form randomly inside the country (the likelihood solves) , form initiative kind group (T=0) is P(ot)={(Xtoi, ytoi) | I=1, 2, ... , n}(5) fitness function consults type (=min of δ of 1) maths model | Ri-Rj | , the homocentric round radius that target function is correspondence of place of N each body is poor (individual and measurable spend function) , namely δ (Xtoi, ytoi)=Rtmaxi-Rtmini(i=1, 2, ... , in N)(6) type, rtmaxi, rtmini is the M{(Xj that measure a place respectively, yj) | J=1, 2, ... , m} arrives individual (Xtoi, the two homocentric round the centre of a circle of Ytoi) correspondence (Xsub>o, the largest space of Ysub>o) and the least space. The metabolic way that takes a cost as a result of target function δ and fitness are contrary, namely target function value is less, corresponding individual fitness is bigger. For this, the map relationship that establishs fitness function and target function is (- Xtoi, δ of Ytoi)= δ Max- (Xtoi, in Ytoi)(7) type, δ Max is plant now the target function maximum of group of place correspondence. Choice strategy is calculated each live individually probability Ptl, devise strategy of a random selection next, make each individual (Xtoi, ytoi) is undertaken by the choice progenitive probability is Ptl, namely Ptl=f(Xtoi, ytoi)/mf(Xtoi, ytoi) Σ J=1(8) will be planted group medium individual by fitness by arrive greatly small have sort, next the basis is onefold and individual (Xtoi, the in copulatory pool probability after the fitness of Ytoi) correspondence decides its are progenitive, onefold and individual (Xtoi, the in copulatory pool amount after Ytoi) is progenitive is Nti=ptin. Be like Nti ≥ 1, individual the amount in copulatory pool takes integer: Be like Nti<1, individual the size order that presses fitness in the amount in copulatory pool is taken respectively 1, till till copulatory pool medium amount achieves N. After the course is progenitive, the N in copulatory pool new individual for A1(t)={(Xto1i, yto1i) | I=i, 2, ... , n}(9) arithmetical across holds the arithmetical across functor in action FGA to beg radius of circular arc of Jie Chong head. Arithmetical across operation is to press across of model of the following maths to arise new child individual process: {Ri= α Ri+(1- α ) RjRj=(1- α ) in Ri+ α Rj(10) type, ri, rj is Ri of two father body, of the generation after Rj passes across two stature is individual, α is a real number that be given beforehand or selects randomly (1) of ≤ of 0 ≤ α . Repeat this one process, till form new transition to plant group of A2(t)={(Xto2i, yto2i) | I=1, 2, ... , n}(11) sheet weighs gauss mutation functor to choose an argument Xtoni randomly by even distributinging means, add it an obedient gauss (normal state) distributinging N(0, of σ 2) disturb ξ , have Ai={Ai+ ξ namely (be like I=j, j ∈ {1, 2, ... , n})Ai(other) (12) new generation is planted group the new generation that computational classics gets after progenitive, across, mutation is planted group for At+13={(Xt+1o3i, yt+1o3i) | I=1, 2, ... , n}(13) new generation is planted group in the target function value of each individual correspondence and fitness computation formula are δ (Xt+1o3i, yt+1o3i)=Rt+1maxi-Rt+1mini(i=1, 2, ... , n)(14)f(Xt+1o3i, δ of Yt+1o3i)= δ T+1max- (Xt+1o3i, yt+1o3i)(i=1, 2, ... , in N)(15) type, rt+1maxi, rt+1mini, it is the M{(Xj that measure a place respectively, yj) | J=1, 2, ... , m} arrives individual (Xt+1o3i, the X of δ of Q(Xmin+Xt+1o3i of two homocentric round the centre of a circle of Yt+1o3i) correspondence, of Ymin+Yt+1o3i δ Y) the biggest with the least space, rt+1max is planted for new generation the maximum of group of corresponding target function. For accommodate sex best individual save come down to be not sent missing, should will go up generation is planted group in the individual reservation with the biggest fitness is planted to next generation group in, replace next generation to plant group in fitness is the smallest individual. For this, need to find out fitness the biggest individual (Xt+1o3i, the target function of Yt+1o3i) correspondence is worth δ (Xt+1o3i, yt+1o3i) . After begging radius of drift circular arc to decide target function is worth δ , can beg a M{(Xj that measure a place, yj) | J=1, 2, ... , the M} the largest space to this individual and corresponding two homocentric round the centre of a circle Rt+1maxk and Rt+1mink of the least space, right now, attainable measure δ of radius R=[(Rt+1maxk+Rt+1mink)/2] ± / 2 right now, need to examine kind group whether to achieve the biggest developmental algebra, if already was achieved, plant right now group in the measurement of the individual correspondence with the biggest fitness radius R is overall situation namely optimum solution, the circular arc that begs namely measures radius: Otherwise, the measure C in needing to change the circularity that begs drift circular arc to the error has consideration afresh. Subordinate list is measured to nod data to measure bit of XY to measure bit of XY112.

0100000.

0000006-8.

5060008.

4815160211.

2308004.

2498477-10.

0000006.

6603479310.

1145096.

4943928-12.

0180000.

249262040.

00500012.

00500093.

00450011.

61778705-5.

50600010.

682523109.

4500007.

41199004 computation example uses floating-point heredity algorithm to measured radius to undertake emulation computation to circular arc of drift concave side. The measurement that drift is measured to nod data sees subordinate list. Emulation computation eventuate: R=12.

010100 ± 0.

008200mm. Computation makes clear as a result, the circular arc of genetic and algorithmic computation that uses solid numeric code measures radius to be able to be obtained with be measured the overall situation that actual condition conform to suits outline is best solution. 5 epilogue use circular arc of computation of floating-point heredity algorithm to measure radius to have relatively high accuracy, can satisfy most law of packet look area criterion for evaluation, obtain overall situation optimum solution. This algorithm applies to the disperse that is not workpiece of dimension of whole circular arc, large size to measure data processing and computation of dimension of three dimensional space. CNC Milling CNC Machining