2007 3 3 :100026788 (2007) 0320098207 1,2, 1, 3 (11, 230009 ;21, 475001 ; 31, 332005) :,,. (FLS - SVM),,.,,,.,,,,,. : ;;; ; : O213 : A Intelligent Prediction Method for Small2Batch Producing Quality based on Fuzzy Least Square SVM DOG Hua 1,2, YAG Shi2yuan 1, WU De2hui 3 (11Hefei University of Technology, Hefei 230009,China ; 21He nan University, Kaifeng 475001,China ; 31Jiujiang University, Jiujiang 332005,China) Abstract : A quality intelligent prediction model for small2batch producing process was proposed in the paper, after comparing with the common used approaches of procedure intelligent prediction and their characteristics. The prediction process and algorithm were presented too. The model takes fuzzy least square support vector machine ( FLS2 SVM) as the intelligent kernel. On one hand, it can solve the small2batch learning better and avoid the disadvantages, such as over2trainning, weak normization capability, etc., of artificial neural networks prediction. On the other hand, it makes samples fuzzy by membership function to choose optimum samples and make history data farther is more weight. After doing lots of prediction experiments and comparing with other common prediction methods, the method proposed in the paper proved to be good normization capability, more rapidly built, and more easily realized. It offers feasibility to predict and control small2batch machining process online. Key words : small2batch ; support vector machine (SVM) ; fuzzy least square support vector machine ( FLS2SVM) ; intelligent prediction ; quality control 1 (SPC),, [1 ]. ( 6. ),,. [2,3 ],SPC :2006201204 : (70672096) : (1975 - ),(),,,;(1940 - ), (),,,;(1975 - ),(),,,.
3 99.,,,;,,,.,, [4 ], (4M1E),,.,,(Artificial eural etwork, A). A.,. A. [5 ],. (Support Vector Machine, SVM) (Structural Risk Minimization, SRM),,A, A [6,7 ],SVM,,. (Least Square SVM, LS - SVM) SVM,,, SVM, [8,9 ].,.,,., LS2SVM, (Fuzzy LS2SVM,FLS2SVM).,,.,,. 2 { x i, y i }, (,2,, ), x i R n n, y i R. SVM :( ) n F, f ( x) = T ( x) + b, (1) SVM, : min 1 2 T + c ( i + 3 i ), s. t. c,1, i, 3 i. 2 Lagrange : l (, b,, 3 ) = 1 2 T + c ( i, 3 i 0, i, 3 i 0,,2,,. y i - T ( x i ) - b + i T ( x i ) + b - y i + 3 i i 0, 3 i 0,,,, (2), i + 3 i ) - i (+ i + y i - T ( x i ) - b) - 3 i (+ 3 i + y i - T ( x i ) - b) - ( i i + i 3 3 i ), (3) (3),, ( a i - a 3 i ) 0 x i ;
100 2007 3,( ).,SVM,. ( ), (3) : max J = - 1 a, a 3 s. t. 2 ( 3 i i, j = 1 - i ) ( 3 j ( x i, x j ) = ( x i ) T ( x j ), (4) j ) ( x i, x j ) - ( 3 i - + i ) + y i ( 3 i - i ), ( i - 3 i ) = 0, (5) i, 3 i [0, c ] (5), SVM : b = x j, x k. y ( x) = ( a i - a 3 i ) ( x i, x) + b, SV S ( a i - a 3 i ) [ ( x j, x i ) + ( x k - x i ) ], (6) LS2SVM SVM, i,: min 1 2 T + 1 2 2, i s. t. y i = T ( x i ) + b + i,,2,,, (7),,,,. LS2SVM SVM,. Lagrange : L (, b,, a) = 1 2 T + 2 i -, a i, (,, ) Lagrange. a b KKT : 5 = 0 = 5 b = 0 a i = 0 5 = 0 a i,: a i ( x i ) = i 5 a = 0 ( x i ) + b + i - y i = 0 0 T + - 1 I b a = 0 y a i [( x i ) + b + i - y i ], (8), (9), (10), y = [ y 1,, y ] T,= [1,,1 ] T, a = [ a 1,, a n ] T,, i j ij = ( x i, x j ) =( x i ) T ( x j ) (( ) Mercer ). a b,ls2svm : y ( x) = a i ( x i, x) + b, (11) SVM,Lin SVM,, (FSVM) [10 ]. LS2SVM,LS2SVM i,
3 101 { x i, y i, i }, (,2,, ),0 i 1. (7) : LS2SVM, Lagrange : 2 i min 1 2 T + 1 2 i s. t. y i = T ( x i ) + b + i,,2,,, (12) L (, b,, a) = 1 2 T +,: i 0 T + ( i ) - 1 I 2 i - a i [( x i ) + b + i - y i ], (13) b a = 0 y, y, a,, I LS2SVM., (14) (14) LS2SVM. (10), (14) i,(fls2svm). 3 FLS2SVM 311 SPC. 2050, (),,., ( ),., n (2050 38 ),. :,.,,,, n,, n. i, x i i i + n - 1, y i = z i + n. { x i + 1, y i + 1 }, LS2SVM, a, b.,a, b LS2SVM,, z z + n - 1 x ^y, + n ^z + n. ^z + n + n, + n + 1. LS2SVM 1. 312,.,,,,,,,.,,,. : i = (1 - ) - i, (15) 1 FLS2SVM
102 2007 3,,0 << 1,,2,,. i : i = + i (1 - )Π, (16) (14), i,.,,;,.,. 4,28,. 1,90 + 0145 + 0130. D smaxs., ( ), ( ). 1 :mm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 D smaxs 0. 38 0. 37 0. 38 0. 39 0. 42 0. 41 0. 40 0. 38 0. 36 0. 42 0. 44 0. 40 0. 37 0. 40 15 16 17 18 19 20 21 22 23 24 25 26 27 28 D smaxs 0. 42 0. 45 0. 42 0. 41 0. 40 0. 42 0. 41 0. 44 0. 43 0. 43 0. 42 0. 43 0. 44 0. 46 BP LS2SVM FLS2SVM 1, D smaxs 25,26,27,28. 3 4, Matlab polyfit ;BP LS2SVM FLS2 SVM n 5, BP Matlab A,= 011, 10000,6,10.LS2SVM FLS2SVM,500,RBF :( x, y) = exp ( - ( x - y) ( x - y) T Π 2 2 ), 011, FLS2SVM, 013. n, MS E = ( ^y i - y i ) 2 n, ^y i, y i, n. Pentium M2112G CPU,128M,2. 2 BP LS2SVM FLS2SVM 3 BP(6,1) BP(10,1) LS2SVM FLS2SVM CPU 0. 1s 60. 3s 64. 3s 0. 6s 0. 6s MSE 3. 5e24 2. 7e24 1. 3e24 1. 0e25 4. 3e25 2,LS2SVM,FLS2SVM,BP 12.,,LS2SVM FLS2SVM, B P,60. BP LS2SVM FLS2SVM 128 2.
3 103 2 BP LS2SVM FLS2SVM,.,,,, 525, 2628. 2 : 1),. 2) BP. 3)LS2SVM,,3 ( 2628), BP. 4) FLS2SVM D smaxs,,,3., FLS2SVM,,,,,,. 5,,, ;,,,.,,. LS2SVM,LS2SVM,., LS2SVM,. : [ 1 ] Shewhart M. Interpreting statistical process control ( SPC) charts using machine learning and expert system techniques [ C ]ΠΠ Proceedings of the IEEE 1992 ational Aerospace and Electronics Conference, 1992. [ 2 ]. [J ].,1998,19 (3) :183-188. Zhang Linna. Research on machining error and forecasting model[j ]. Acta Metrologica Sinica, 1998,19 (3) :183-188. [ 3 ],. [J ].,2003,14 (13) :1130-1132. Li Jian, Liu Hongxing. Systematic error modeling in part machining processes based on genetic algorithm [J ]. China Machine
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