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This is an author’s version published in: http://oatao.univ-toulouse.fr/21325
To cite this version:
Dawoua Kaoutoing, Maxime
and Houé Ngouna, Raymond
and
Pantalé, Olivier
and Beda, Tibi
Anomaly detection in
orthogonal metal cutting based on autoencoder method. In: 9th
international Conference on Intelligent Systems 2018, 25 September
2018 - 27 September 2018 (Madeira, Portugal).
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&",6(,&%7&",G8%0I'1(,-'%K)Z,1()K%,'%7=8c% % % % 3&!' , . .4567% % % %%%%%%%%%7!8% % % % 89+%&!' ,5577:5456767% % %%%%%%%%%7=8% OG)%.+()'(%Y+*,+J.)%G%,5%6+ZZ)K%J+1R%,'(-%+%*)1-'5(*I1(,-'% Y)1(-*%!; " #$%,'%(G)%-I(ZI(%.+4)*%I5,'2%(G)%0-*6I.+%,'%7b8c% % % !; , -<&/<%&!' 0 1<'% % %%%%%%%%%7b8% LG)*)%/<" #(2$%+'K%1<" #$%G+Y)%(G)%5+6)%6)+','25%+5%,'% 7#8%*)2+*K,'2%(G)%-I(ZI(%.+4)*P%+'K%-<%,5%+'%-I(ZI(%0I'1(,-'%70-*% ,'5(+'1)P%(G)%5,26-,K%0I'1(,-'%0-*%1.+55,0,1+(,-'%Z*-J.)65P%-*%(G)% .,')+*%,K)'(,(4%0I'1(,-'%0-*%*)2*)55,-'%Z*-J.)658A% OM! NG()2("%,',6)E%$0(77) D5%,'%+'4%')I*+.%')(L-*R%6-K).P%.)+*','2%L,..%-11I*%LG)'% (G)% L),2G(5% Z+*+6)()*5% +*)% +K+Z()K% (-% 6,',6,a)% +% 0I'1(,-'% =&!> -<&-.&!'''A%=%,5% +% .-55% 0I'1(,-'% Z)'+.,a,'2%-<&-.&!''%0-*%
J),'2% K,00)*)'(% 0*-6%! A% D'% )N+6Z.)P% 1-66-'.4% I5)K% ,'% *)2*)55,-'%Z*-J.)6%+5%,'%(G)%1-'()N(%-0%(G)%Z*)5)'(%5(IK4P%,5%(G)% 6)+'%5]I+*)K%)**-*P%LG,1G%*)Z*)5)'(5%+'%+Y)*+2)%*)1-'5(*I1(,-'% )**-*A%OG)%-Z(,6,a)K%Z+*+6)()*%? , &/.> /<> 1.> 1<'%,5%-J(+,')K% +0()*% 6,',6,a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i)/I'%+'K%1-;L-*R)*5`%+1G,)Y)6)'(5%^!=_c%
1.! Initialize the weights (Wj) and the biases (bj) 2.! Iterate until convergence criterion is reached:
a.! Get the training sample
b.! Update all weights and biases as in (5) and (6):
@ABC , @ABD EF=&/> G'F@
AB HHHHHHHHHHHHHHHHHHHHHHHHHHHHH&I'% 1ABC , 1ABD EF=&/> G'F1
AB HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH&J'%
OG)% 1-'5(+'(%E%,5% (G)% 2("%,',6) %"&(P% LG,1G% 1-'(*-.5% G-L% 6I1G%(G)%+.2-*,(G6%+KeI5(%(G)%L),2G(5%7,A)A%(G)%.-L)*%(G)%Y+.I)P% (G)%5.-L)*%(G)%+.2-*,(G6%(*+Y).5%+.-'2%(G)%.-55%2*+K,)'(8A%
D%L)..;R'-L'%Z*-J.)6P%LG)'%+ZZ.4,'2%+I(-)'1-K)*%,5%(G+(P% ,(%1+'%0+,.%(-%.)+*'%+'4(G,'2%,0%(G)%)'1-K)*%-.%+'K%(G)%K)1-K)*%-<% +*)%2,Y)'%(--%6I1G%1+Z+1,(4%^!b_c%,'%5I1G%+%1+5)P%(G)%6-K).%6+4% eI5(% R))Z% *)Z*-KI1,'2% (G)% 5+6)% ,'ZI(% Y+.I)5% +(% (G)% -I(ZI(A% O-%
+Y-,K% (G,5P% 5)Y)*+.% Z)'+.(4% 0I'1(,-'5% 1+'% J)% +KK)K% (-% (G)% .-55% 0I'1(,-'P% LG,1G% +*)% 1+..)K% l*)2I.+*,a+(,-'l% 0I'1(,-'5P% +6-'2% LG,1G% (G)% 7E"%7'&D) E(,"2&D%K&%'A%D5%'-()K%,'%^!b_P%(*+,','2%+% 6-K).%L,(G%5Z+*5,(4%Z)'+.(4%+..-L5%(-%Z)*0-*6%+%6-K).%(G+(%G+5% .)+*')K%I5)0I.%0)+(I*)5%+5%U")#DE%$-/0&UA%
D'%,55I)%G)*)%,5%(-%K)0,')%(G)%+ZZ*-Z*,+()%5Z+*5)%Z)'+.(4%,'% -*K)*%0-*%(G)%6-K).%(-%Z)*0-*6%L)..A%D%.-55%0I'1(,-'%L,(G%5Z+*5)% Z)'+.(4%.--R5%.,R)%7:8c%
% =&?' , = L!> -<M-.&!'NO 0 K&%'% % %%%%%%%%%7:8% %
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