. , , ,

,,,

—

() () . , (, ). , . , . , . .

: 35 , 20 , 4 , 2 .


.

[1] , , -. , . . , , . .

[2] , , , ( ) . , .

() () , , , , . . , , . , , .

, , , , , . . , .

.


2.

2.1

: .

, , . (-) . , , , , . .

( ) . , , , .

1.


, , . - , . , , , . . .1 . . .

, , . , , ( ).

2.2 ()

, ( .2) , () : , . , , , . .2, , . .

2.

, , . , , , , .

( ).

2.3

, , . . , , , . - , - . , , . , . , .3, . , .

3. ,

2.4

, .

, ( ) (.4).


4.

, . . , , . , , , .

, , . .


3.

3.1

.

5.

, . , , .

, , , , , , . , , .

, .

. , , , , . , .

, , , ( ).

4.2 COMSOL Multiphysics

COMSOL Multiphysics - (PDE) [3]. , ( ) . . , PDE , : , , , .. . . (GUI), COMSOL Script MATLAB.

. :

          , ;

          , ;

          (Weak form), PDE , , .

, , :

          ;

          ;

          .

PDE, COMSOL Multiphysics . . PDE, : , , , , , , , , , , .

, (coupling variables) .

:

1.         , , ;

2.         ;

3.         , ;

4.         ;

5.         ;

6.         , ;

7.         , ;

8.         ;

9.         .

3.3 COMSOL Multiphysics

(. 6). , . (r, z, φ).


6.

3.4

. 7 .

7.

COMSOL Multiphysics .


8. COMSOL Multiphysics

3.5

, .1

, (μr)

,

(σ, /)

,

(J, /2)
1 2 0
1 0 1

.

25, 100, 200 400, .

3.6

, r = 0 (. 8), , , , r = 0, z.

. continuity.

3.7 .

, , . , .

9.

r- (.10 .11). .


10. ( ) 100

11. ( ) 100


4.

4.1

. .

COMSOL Multiphysics, , , .

:

-

- , COMSOL Multiphysics

:

- ,

: , , . 400. MatLab, COMSOL Multiphysics, . 1.


4.2

, 25, 100, 200, 400, (0.4, 0.6, 0.8, 1.0, 1.2 ), (0.1)

12.

: ,


, 25, 100, 200, 400, (0.1, 0.3, 0.5, 0.7, 0.9 ), (0.4)

13.

: ,

( , ) .

, 25


14.

: , .

( , ) .

, 25


15.

: ,

4.3

:

          F1 ;

          F2 ;

          F3 ;

          F4 - ;

          F5 ;

          F6 , ;

          F7 ;

          F8 ;

          F9 ;

          F10 / ;

          F11 / .

. 16 . [5]

16.

MatLab , . 2.

, , , .


5.

5.1

Statistica.

Statistica - , . (, , ). , , .. STATISTICA Visual Basic, 10000 . Basic' Microsoft Visual Basic. STATISTICA - , : - 100 , - , - , - , - , - , , - , - , - T- ( ), - , , , - , - .

. 2 ,

frequency 25
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11
width 0,49 -0,26 0,65 -0,23 0,63 -0,22 0,03 0,01 -0,04 0,81 0,63
depth 0,58 -0,69 0,54 -0,85 0,54 -0,84 -0,42 0,33 0,57 0,34 0,55
frequency 100
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11
width 0,72 -0,20 0,46 -0,25 0,59 -0,14 0,05 0,07 0,05 0,70 0,59
depth 0,49 -0,89 0,59 -0,83 0,54 -0,90 -0,35 0,46 -0,56 0,50 0,56
frequency 200
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11
width 0,57 -0,13 0,47 -0,10 0,54 -0,13 0,04 0,08 -0,06 0,63 0,54
depth 0,57 -0,92 0,43 -0,76 0,54 -0,93 -0,33 0,48 -0,70 0,55 0,56
frequency 400
F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11
width 0,38 -0,07 0,51 -0,08 0,44 -0,07 0,03 0,08 -0,09 0,51 0,44
depth 0,54 -0,92 0,48 -0,90 0,53 -0,94 -0,33 0,47 0,57 0,55 0,56

. 2 , .

F1, F5, F10 F11. F2, F4, F6 F9.

5.2

, . - . .

- , . , . , . , ( ), . , " ", . .

, . , , . , , - , , , , , , , , .

:

1.        

2.        

3.        

4.        

5.        

6.        

7.        

8.         ,

9.        

. .

. . . , , , . , , . . : , .

. , , , , , . , , . , .

, . , . , , . , , . , , , , , ).

. , . . , , , . , , , , . ; . , ( ). , , . , , , . . .

, , , . , , , , .

, , , . .

5.3


6:6-9-1:1

17.

0,193377
0,190212
0,054221
0,055778
6
(1) 9
(2) 0
0,000800
. 0,000283
-0,000001
. 0,000055
0,000043
. 0,193778
0,981070

, :

 

1 0,000786 0,000700
2 0,000752 0,000700
3 0,000806 0,000900
4 0,000845 0,000900
5 0,000749 0,000700

8:8-7-1:1

 

18.

0,281847
0,180694
0,078536
0,051684
8
(1) 7
(2) 0

0,000500
. 0,000283
-0,000002
. 0,000070
0,000054
. 0,245855
0,969317

 

 

1 0,000419 0,000400
2 0,000419 0,000400
3 0,000763 0,000600
4 0,000409 0,000400
5 0,000678 0,000600

6.

:

         

         

         

         

: , , , , , .

, , (, 0,5 /). , .

, , . , .

, . .

:

         

         

         

.

.

19

(. 19) , . , .

. 3 , . 100 .

error pers rbf orns
average 0,054 0,061 0,063
max 0,238 0,253 0,4
min 0,001 0 0

.

20

(.20) , . , 8 , 62 1 2 2 . , , , , . .

. 4 , . 100 .

error pers rbf orns
average 0,043 0,052 0,04
max 0,144 0,251 0,205
min 0 0,002 0

, , . , .

, , . , , .

, . , .

. .

, .


1. Brudar B. How to Distinguish Surface and Subsurface Cracks // Electromagnetic NDT Methods: NDT International, Vol. 17, August 1984, p 221-223.

2. Brudar B. Magnetic Leakage Fields Calculated by the Method of Finite Differences// Electromagnetic NDT Methods: NDT International, Vol. 18, No.6, December 1985, p 353-357.

3. .. . . -, 2006.

4. .. . MATLAB 2006a . . .. , 2006.

5. Song S-J. Model-based interpretation of experimental eddy current signals obtained from steam generator tubes by bobbin probe. // Insight. 2003. 5.


1

, MatLab .

%

air1H=10e-3; %

L=50e-3; %

air2H=6.5e-3; %

OKH=1.5e-3; %

OKD=8e-3; %

H_k=2e-3; %

l_k=3e-3; %

delta_k=1e-3; %

D_k = 3e-3; %

delta_izm=0.5e-3; %

r=0.01; %

%

ld_def=1e-3; %

x_def=(L/2)-ld_def; %

hd_def=1e-3; %

fd_def=1; % -

%fd = 1 - ,

%1<fd<0.01 -

%fd<0.001 ->

%

x_start=20e-3; %

x_end=0e-3; %

x_step=-0.5e-3; %

hd_start=0.4e-3; %

hd_end=1.2e-3; %

hd_step=0.2e-3; %

ld_start=0.1e-3; %

ld_end=1.0e-3; %

ld_step=0.2e-3; %

fd=[1,0.01,0.3,0.7]; %

f=[25e3,100e3,200e3,400e3]; %,

f_ind=1;

x_size=size((x_start:x_step:x_end)');

x_size=x_size(1);

clear data

%figure;GEOMPLOT(fem);

%

clear data

data_ind=1;

for fd_ind = 1:size(fd')

for ld = ld_start:ld_step:ld_end

for hd = hd_start:hd_step:hd_end

for f_ind = 1:size(f')

data(data_ind,1)=data_ind;

data(data_ind,2)=fd(fd_ind);

data(data_ind,3)=ld;

data(data_ind,4)=hd;

data(data_ind,5)=f(f_ind);

x_ind=1

for x = x_start:x_step:x_end

flclear fem

% Application mode 1

clear appl

appl.mode.class = 'AzimuthalCurrents';

appl.mode.type = 'axi';

appl.module = 'ACDC';

appl.assignsuffix = '_emqa';

clear prop

prop.analysis='transient';

appl.prop = prop;

clear pnt

pnt.I0 = {};

pnt.name = {};

pnt.ind = [];

appl.pnt = pnt;

clear bnd

bnd.chsrcdst = {};

bnd.murbnd = {};

bnd.sigmabnd = {};

bnd.eta = {};

bnd.d = {};

bnd.index = {};

bnd.Esphi = {};

bnd.pertype = {};

bnd.type = {};

bnd.A0phi = {};

bnd.name = {};

bnd.H0 = {};

bnd.Js0phi = {};

bnd.epsilonrbnd = {};

bnd.murext = {};

bnd.ind = [];

appl.bnd = bnd;

clear equ

equ.Vloop = {};

equ.Sd = {};

equ.magconstrel = {};

equ.srcpnt = {};

equ.M = {};

equ.S0 = {};

equ.Pphi = {};

equ.gporder = {};

equ.coordOn = {};

equ.sigma = {};

equ.name = {};

equ.epsilonr = {};

equ.rOn = {};

equ.dr = {};

equ.cporder = {};

equ.mur = {};

equ.normfH = {};

equ.Br = {};

equ.init = {};

equ.Stype = {};

equ.Drphi = {};

equ.R0 = {};

equ.elconstrel = {};

equ.fH = {};

equ.v = {};

equ.Jephi = {};

equ.usage = {};

equ.srcaxis = {};

equ.user = {};

equ.ind = [];

appl.equ = equ;

fem.appl{1} = appl;

fem.sdim = {'r','z'};

fem.frame = {'ref'};

fem.border = 1;

clear units;

units.basesystem = 'SI';

fem.units = units;

air1 = rect2(air1H,L,'base','center', 'pos', [air1H/2+OKD 0]);

OK = rect2(OKH,L,'base','center','pos', [-(OKH/2)+OKD 0]);

air2 = rect2(air2H,L, 'base','center','pos', [-(OKH+air2H/2)+OKD 0]);

kat1 = rect2(H_k,l_k, 'base','center','pos', [delta_k+(H_k/2)+OKD -((D_k/2)+(l_k/2))]);

kat2 = rect2(H_k,l_k, 'base','center','pos', [delta_k+(H_k/2)+OKD ((D_k/2)+(l_k/2))]);

p1=point2(OKD+delta_izm,0);

defect = geomcoerce('solid',{curve2([0+OKD-OKH 0+OKD-OKH],[x-(ld/2) x+(ld/2)]),...

curve2([0+OKD-OKH hd+OKD-OKH],[x+(ld/2) x+(ld*fd(fd_ind)/2)]),...

curve2([hd+OKD-OKH hd+OKD-OKH],[x+(ld*fd(fd_ind)/2) x-(ld*fd(fd_ind)/2)]),...

curve2([hd+OKD-OKH 0+OKD-OKH],[x-(ld*fd(fd_ind)/2) x-(ld/2)])});

clear s p

p.objs={p1};

p.name={'p1'};

s.objs={air1,air2,OK,kat1,kat2,defect};

s.name={'air1','air2','OK','kat1','kat2','defect'};

draw=struct('s',s,'p',p);

fem.geom = geomcsg(draw);

fem.mesh=meshinit(fem,...

'hmax',0.5e-3,...

'hmaxvtx',[11,0.05e-3],...

'hmaxedg',[4,0.2e-3,6,0.0001,7,0.0001,8,0.2e-3,9,0.0001,11,0.0001,12,0.2e-3,15,0.0001,16,0.0001,17,0.0001,18,0.0001,19,0.0001,20,0.0001,21,0.0001,22,0.0001],...

'hmaxsub',[2,0.2e-3]);

% Application mode 1

clear appl

appl.mode.class = 'AzimuthalCurrents';

appl.mode.type = 'axi';

appl.dim = {'Aphi','redAphi'};

appl.sdim = {'x','z','y'};

appl.module = 'ACDC';

appl.sshape = 2;

appl.assignsuffix = '_emqa';

clear prop

prop.analysis='harmonic';

appl.prop = prop;

clear bnd

bnd.type = {'A0','cont','ax'};

bnd.ind = [3,1,1,2,1,2,2,2,2,1,2,2,1,1,2,2,2,2,2,2,2,2,1];

appl.bnd = bnd;

clear equ

equ.sigma = {0,2e6,0,0};

equ.Jephi = {0,0,1e6,1e6};

equ.ind = [1,2,1,1,3,4];

appl.equ = equ;

appl.var = {'nu',f(f_ind)};

fem.appl{1} = appl;

fem.border = 1;

% Multiphysics

fem=multiphysics(fem);

% Extend mesh

fem.xmesh=meshextend(fem);

% Solve problem

fem.sol=femstatic(fem,...

'solcomp',{'Aphi'},...

'outcomp',{'Aphi'},...

'blocksize','auto',...

'ntol',1e-012);

% Integrate

data(data_ind,5+x_ind)=-postint(fem,'Br_emqa',...

'unit','T',...

'recover','off',...

'dl',11,...

'edim',0)*i*2*pi*data(data_ind,5)*pi*r^2;

data(data_ind,5+(2*x_size)-x_ind)=-data(data_ind,5+x_ind);

x_ind=x_ind+1;

end

data_ind

end

end

end

end


2

, MatLab .

function [y] = prizn (P)

for k=1:5

for w=1:100

y(k,w)=P(k,w);

end;

end;

% k-ctro4ki

% w-ctolbci

for k=6:46

for w=1:100

Z(k,w)=P(k,w);

end;

end;

for w=1:100

for k=6:46

g(k)=Z(k,w);

end;

rez=real(g);

imz=imag(g);

rez=abs(rez);

imz=abs(imz);

mre=max(rez); %mre - max resistanse

for k=6:46

if mre==rez(k)

mr=k; %mr - max resistance index

k=46;

end

end

maxres=g(mr); %maxres - max resistance point (F1)

mrea=angle(maxres);

mrea=(180/pi)*mrea; %mrea - max resistance angle (F2)

y(6,w)=mre;

y(7,w)=mrea;

mim=max(imz); %max reactance

for k=6:46

if mim==imz(k)

mi=k; %mi - max reactance index

k=46;

end

end

maxreact=g(mi); %maxreact - max reactance point (F3)

mima=angle(maxreact);

mima=(180/pi)*mima; %mima - max reactance angle (F4)

y(8,w)=mim;

y(9,w)=mima;

absz=abs(g);

maxz=max(absz); %mabs - max impedance

for k=6:46

if maxz==absz(k)

mz=k; %mz - max impedance index

k=46;

end

end

maximp=g(mz); %maximp - max impedance point (F5)

mimpa=angle(maximp);

mimpa=(180/pi)*mimpa; %mimpa - max impedance angle (F6)

y(10,w)=maxz;

y(11,w)=mimpa;

stang=angle(g(6));

stang=(180/pi)*stang; %stang - starting angle (F7)

endang=angle(g(46));

endang=(180/pi)*endang; %endang - ending angle (F8)

y(12,w)=stang;

y(13,w)=endang;

c=sqrt( ( (real(g(mz))-real(g(mz-1)) )^2) +((imag(g(mz))-imag(g(mz-1)))^2));

b=sqrt(((real(g(mz+1))-real(g(mz)))^2)+((imag(g(mz+1))-imag(g(mz)))^2));

a=sqrt(((real(g(mz+1))-real(g(mz-1)))^2)+((imag(g(mz+1))-imag(g(mz-1)))^2));

turnang=acos(((b^2)+(c^2)-(a^2))/(2*b*c));

turnang=(180/pi)*turnang;

% turnang - turning fase angle at the point of max impedance (F9)

y(14,w)=turnang;

L(1)=sqrt( ((real(g(6)))^2) +((imag(g(6)))^2));

for k=7:46

L(k)=sqrt( ( (real(g(k))-real(g(k-1)) )^2) +((imag(g(k))-imag(g(k-1)))^2));

end

L(47)=sqrt( ( (real(g(46)))^2) +((imag(g(46)))^2));

for k=1:mr

L1(k)=L(k);

end

mrlen=sum(L1); %mrlen - length up to the max resistance point (F10)

totlen=sum(L); %totlen - total length (F11)

y(15,w)=mrlen;

y(16,w)=totlen;

end;

() () .

 

 

 

! , , , .
. , :