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Решение обратной задачи вихретокового контроля

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9. ?acoeueoaou /eneaiiiai iiaeaee?iaaiey

9.1 Aii?ieneiaoeee i?e /eneaiiii iiaeaee?iaaiee

Aeey iino?iaiey iiaeaeae ?aaeueiuo ?ani?aaeaeaiee YI aiciiaeii
i?eiaiaiea oeaeiai ?yaea aii?ieneiaoeee. Ana iie iiaoo auoue ?acaeaeaiu
ia aeaa eeanna.

1. Aii?ieneiaoeee, no?iyueany ii iaai?o ec i?iecaieueiiai /enea oceia.
Iaeaieaa ?ani?ino?aiaiiua ec ieo: eoni/ii-iinoiyiiay, eoni/ii-eeiaeiay e
nieaeiii. A oneiaeyo iaoae caaea/e oeacaiiua aii?ieneiaoeee eiatho
ianeieueei nouanoaaiiuo iaaeinoaoeia:

?acoeueoaou aii?ieneiaoeee neaai niaeanothony n ?aaeueiinoueth.
Eoni/ii-iinoiyiiay e eoni/ii-eeiaeiay aii?ieneiaoeee i?eioeeieaeueii
yaeythony iaaeaaeeeie, a aii?ieneiaoeey nieaeiii naeaaeeaaao ana, a
?acoeueoaoa /aai aicieeatho cia/eoaeueiua iaiiiioiiiinoe e anieanee.

I?e oaaee/aiee eiee/anoaa oceia aii?ieneiaoeee auno?i ia?anoaao
iaonoie/eainoue i?ioeanna ?aoaiey ia?aoiie caaea/e, aeey
i?ioeaiaeaenoaey eioi?ie o?aaoaony i?eiaiaiea eneonnoaaiiuo i?eaiia, ia
aa?aioe?othueo oniaoa.

A ?aaeueiuo oneiaeyo iu ia eiaai aeinoiaa?iie ai?ei?iie eioi?iaoeee i
aaee/eia YI a oceao aii?ieneiaoeee, ?aniieiaeaiiuo a aeoaeia ieanoeiu.

2. Aii?ieneiaoeee, no?iyueany ii cia/aieyi YI ia aa?oiae e ieaeiae
iiaa?oiinoyo ieanoeiu e ianeieueeei ia?aiao?ai aii?ieneiaoeee. Iaeaieaa
ecaanoiua ec ieo: yeniiiaioeeaeueiay, aeia?aiee/aneei oaiaainii e
aaonnieaeie. Aii?ieneiaoeee eiatho aeae:

– aii?ieneiaoeey aaonnieaeie

aaea

x – eii?aeeiaoa, ?aaia ioeth ia ieaeiae iiaa?oiinoe ieanoeiu e aaeeieoea
ia aa?oiae

(1 – aaee/eia yeaeo?ii?iaiaeiinoe ia aa?oiae iiaa?oiinoe ieanoeiu

(2 – aaee/eia yeaeo?ii?iaiaeiinoe ia ieaeiae iiaa?oiinoe ieanoeiu

( – eiyooeoeeaio, oa?aeoa?ecothuee e?ooecio yeniiiaiou

( – eiyooeoeeaio

( – eiyooeoeeaio, oa?aeoa?ecothuee e?ooecio; (=0 niioaaonoaoao neo/ath
neiy n i?iaiaeeiinoueth (1 e oieueiie ( ia iieoi?ino?ainoaa n
i?iaiaeeiinoueth (2

( – eiyooeoeeaio, oa?aeoa?ecothuee e?ooecio

Aeey iaoae caaea/e iiaeiaiua aii?ieneiaoeee yaeythony
i?aaeii/oeoaeueiuie, iineieueeo iaeaaeatho caiaoiuie aeinoieinoaaie:

Aii?ieneiaoeee yaeythony iiiioiiiuie e aeaaeeeie, /oi oi?ioi
niaeanoaony n oece/aneie ?aaeueiinoueth.

Iieuecoynue oece/anee iainiiaaiiuie ?annoaeaeaieyie iu iiaeai iieo/eoue
iaiaoiaeeioth ai?ei?ioth eioi?iaoeeth i aaee/eiao YI a i?eiiaa?oiinoiuo
neiyo ieanoeiu.

I?ioeann ?aoaiey ia?aoiie caaea/e nouanoaaiii aieaa onoie/ea e
inouanoaeyaony cia/eoaeueii auno?aa

Aeey eeethno?aoeee iaoeo ?annoaeaeaiee i?eaaaeai i?eia? i?eiaiaiey
i?eaaaeaiiuo auoa aii?ieneiaoeee e neo/ath ainnoaiiaeaiey
eoni/ii-eeiaeiie ooieoeee. Ii ine aanoeenn ioeiaeaia ioiineoaeueiay
aeoaeia, ii ine i?aeeiao yeaeo?ii?iaiaeiinoue (INi/i).

Ia a?aoeea iieacaiu aii?ieneiaoeee: eoni/ii iinoiyiiay(SIci),eoni/ii
eeiaeiay(SIli), nieaei(SIs), yeniiiaioeeaeueiay(SIe), aeia?aiee/aneei
oaiaainii (Sith), aaonnieaeie(SIg).

Eaaei caiaoeoue, /oi aii?ieneiaoeey aeia?aiee/aneei oaiaainii oi?ioi
iienuaaao i?eiiaa?oiinoiua eciaiaiey (aiaeiae/ii yeniiiaioeeaeueiie i?e
aieueoii iieacaoaea yeniiiaiou). Aaonnieaea iiaeao auoue eaaei
aini?iecaaaeaia n iiiiuueth yeniiiaioeeaeueiie aii?ieneiaoeee, iiyoiio a
aeaeueiaeoai eniieueciaaia ia aoaeao.

9.2 Iiaeaee ?aaeueiuo ?ani?aaeaeaiee yeaeo?ii?iaiaeiinoe

Iiaeaeue caaea/e aeieaeia iienuaaoue iaeioi?oth ieanoeio, iiaeaa?aioooth
iiaa?oiinoiie ia?aaioea. Aeey ii?aaeaeaiiinoe caaeaaeei oieueio ieanoeiu
?aaiie aeaoi naioeiao?ai. Ia iniiaa aeaiiuo ec I?eeiaeaiey 2 caaeaaeei
cia/aiey YI aaeece ieaeiae e aa?oiae iiaa?oiinoae niioaaonoaaiii 20
(INi/i) e 13 (INi/i).

Aeey ?aoaiey ia?aoiie caaea/e iaiaoiaeeii caaeaoue ai?ei?ioth
eioi?iaoeeth i aaee/eia YI a oceao aii?ieneiaoeee. A ea/anoaa oaeiaie
i?eiai eioa?aae [8,25] (INi/i), iieo/aiiue aianaieai 25% ioeeiiaiey io
n/eoaaiuo enoeiiuie cia/aiee. Yoi ioeeiiaiea iiaeaee?oao iaoi/iinoue
ai?ei?iie eioi?iaoeee.

Ec-ca iniaaiiinoae ?aaeecaoeee aeai?eoia onoie/eainoue ?aoaiey neeueii
caaeneo io oi/iinoe caaeaiey YI a ocea, niioaaonoaothuai ieaeiae
iiaa?oiinoe ieanoeiu, iiyoiio ia?aie/aiea a iai caaeaaeei eioa?aaeii
[19,21] (INi/i).

A iaoai neo/aa ana aiciiaeiua iiaeaee ?ani?aaeaeaiee YI iiaoo auoue
?acaeaeaiu ia aeaa eeanna. ?ani?aaeaeaiey ioiinyueany e ia?aiio ec ieo
oneiaii iaciaai aeoaeiiuie. A ieo YI i?aoa?iaaaao nouanoaaiiua eciaiaiey
ia i?ioyaeaiee anae aeoaeiu ieanoeiu. Aoi?ie eeann ia?acotho
?ani?aaeaeaiey, YI a eioi?uo caiaoii eciaiyaony eeoue a i?eiiaa?oiinoiii
neia aeoaeiie ii?yaeea /aoaa?oe ieanoeiu., iiyoiio iaciaai yoe
?ani?aaeaeaiey iiaa?oiinoiuie.

E?eoa?eai ioee/ey ainnoaiiaeaiiie ooieoeee ?ani?aaeaeaiey YI io
iiaeaeueiie aoaeai n/eoaoue aaee/eio ioiineoaeueiie iia?aoiinoe,
iineieueeo n?aaiaiea ?acoeueoaoia n aa iiiiuueth aiieia aaeaeaaoii
oeaeyi iaoae ?aaiou.

Neaaeoao ioiaoeo, /oi iia?aoiinoue ainnoaiiaeaiey aeey iiaa?oiinoiuo
?ani?aaeaeaiee YI i?aaenoaaeyao i?aeoe/aneee eioa?an a iaeanoe, i?eia?ii
ia?aie/aiiie aeoaeiie ii?yaeea /aoaa?oe ieanoeiu, /oi iaoneiaeaii
oece/aneei niuneii iiaa?oiinoiie ia?aaioee. Iiyoiio aeey neo/aaa
iiaa?oiinoiuo ?ani?aaeaeaiee iniiaiia aieiaiea aoaeai oaeaeyo eiaiii
oeacaiiui aeoaeiai.

Aeey i?iaa?ee aiciiaeiinoe ainnoaiiaeaiey i?eiiaa?oiinoiuo eciaiaiee YI
?anniio?ei aeaa aaciaua iiaeaee iiaa?oiinoiuo ?ani?aaeaeaiee.

Aaciaay iiaeaeue A1.

Aii?ieneiaoeey yeniiiaioie.

I?iaiaeeiinoue (2=20 [INi/i]

I?iaiaeeiinoue (1=13 [INi/i]

Aaciaay iiaeaeue A2

Aii?ieneiaoeey aeia?aiee/aneei oaiaainii.

I?iaiaeeiinoue (2=20 [INi/i]

I?iaiaeeiinoue (1= 6 [INi/i]

Eiyooeoeeaio ( = 1

Eiyooeoeeaio ( = { 0.1, 0.05, 0.02, 0.01 }

Aeey i?iaa?ee aiciiaeiinoe ainnoaiiaeaiey aeoaeiiuo ?ani?aaeaeaiee YI
?anniio?ei aeaa aaciaua iiaeaee aeoaeiiuo ?ani?aaeaeaiee.

Aaciaay iiaeaeue B1

Aii?ieneiaoeey eoni/ii-eeiaeiay.

I?iaiaeeiinoue caaeaaony a oceao n ion/eouaaaiie io aeia ieanoeiu
ioiineoaeueiie aeoaeiie { 0, 0.25, 0.5, 0.75, 1 }.

Oceiaua cia/aiey i?iaiaeeiinoe { 20, 20, 17.6, 15.3, 13 }, {20, 20, 20,
16.5, 13 }, {20,20,20,20,13} [INi/i].

Aaciaay iiaeaeue B2

Aii?ieneiaoeey nieaeiii.

I?iaiaeeiinoue caaeaaony a oceao n ion/eouaaaiie io aeia ieanoeiu
ioiineoaeueiie aeoaeiie { 0, 0.25, 0.5, 0.75, 1 }.

Oceiaua cia/aiey i?iaiaeeiinoe { 20, 20, 17.6, 15.3, 13 }, {20, 20, 20,
16.5, 13 }, {20,20,20,20,13} [INi/i].

Caiaoei, /oi ia i?aeoeea iiaeii inouanoaeoue aeinoaoi/ii oi/iia
ii?aaeaeaiea aaee/eiu YI i?eiiaa?oiinoiuo neiaa iooai ecia?aiee
i?iaiaeeiinoe o?aaeeoeeiiiuie n?aaenoaaie, iiyoiio aeiiieieoaeueii
?anniio?ei iiaeaeueiua caaea/e i?e oneiaee ecaanoiie YI ia aa?oiae, a
oae aea aa?oiae e ieaeiae iiaa?oiinoyo.

Iineieueeo ia i?aeoeea ?acoeueoaou ecia?aiee aiineiiai iai?yaeaiey
eiatho ii?aaeaeaiioth iia?aoiinoue, ana iiaeaee aoaeai ?ann/eouaaoue
yioee?oy iia?aoiinoue (U= 0,1,2,5%.

Aeey enneaaeiaaiey caaeneiinoe ?acoeueoaoia ainnoaiiaeaiey
?ani?aaeaeaiee YI io /anoiou aicaoaeaeaiey ?aciaueai /anoioiue
aeeaiaciia o?e /anoe neaaeothuei ia?acii( aeoaeiu i?iieeiiaaiey
i?eaaaeaiu aeey neo/ay iinoiyiiie YI (=13 INi/i ):

Iiaeaee FA1L, FB1L Iiaeaee FA1M, FB1M Iiaeaee FA1H, FB1H

f , [Aoe] h , [m] f , [EAoe] h , [m] f , [EAoe] h , [m]

1 0.1396 5 0.001974 55 0.0005952

10 0.04414 10 0.001396 60 0.0005699

20 0.03121 15 0.00114 80 0.0004935

50 0.01974 20 0.000987 90 0.0004653

100 0.01396 25 0.0008828 100 0.0004414

200 0.00987 30 0.0008059 200 0.0003121

500 0.006243 35 0.0007461 300 0.0002549

1000 0.004414 40 0.0006979 500 0.0001974

2000 0.003121 45 0.000658 700 0.0001668

5000 0.001974 54.1 0.0006001 1000 0.0001396

Aeey enneaaeiaaiey caaeneiinoe ?acoeueoaoia ainnoaiiaeaiey
?ani?aaeaeaiee YI io /enea ecia?yaiuo aiineiuo iai?yaeaiee N ?anniio?ei
neo/ae N={ 5, 10, 15 }.

Ieceea /anoiou

f , [Aoe] 1, 5, 10, 20, 35, 50, 100, 150, 200, 500, 750, 1000, 2000,
3500, 5000

f , [Aoe] 1, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000

f , [Aoe] 1, 20, 100, 500, 2000

N?aaeiea /anoiou

f , [EAoe] 5, 7.5, 10, 15,17.5, 20, 25, 27.5, 30, 35, 37.5, 40, 45, 50,
54.1

f , [EAoe] 5, 10, 15, 20, 25, 30, 35, 40, 45, 54.1

f , [EAoe] 5, 15, 25, 35, 45

Aunieea /anoiou

f , [EAoe] 55, 57.5, 60, 80, 85, 90,100, 150, 200, 300, 400, 500, 700,
850, 1000

f , [EAoe] 55, 60, 80, 90,100, 200, 300, 500, 700, 1000

f , [EAoe] 55, 80, 100, 300, 700

9.3 I?eioeeieaeueiay aiciiaeiinoue ainnoaiiaeaiey

Aeey enneaaeiaaiey aiciiaeiinoe ainnoaiiaeaiey ?ani?aaeaeaiey YI
?anniio?ei ?acoeueoaou, iieo/aiiua a i?aaeiieiaeaiee iaee/ey oi/iuo
aeaiiuo (iia?aoiinoue ecia?aiey ionoonoaoao). Ia a?aoeeao a ia?auo
/aou?ao ioieoao I?eeiaeaiey 3 ?anniao?eaaaiua caaeneiinoe iieacaiu
e?aniui oeaaoii (enoiaeiua aeaiiua /a?iui). Enoiaey ec ieo iiaeii
naeaeaoue neaaeothuea auaiaeu

Ainnoaiiaeaiea n iiiiuueth aii?ieneiaoeee, eniieueciaaiiie i?e yioeyoeee
ecia?aiee (?aoaiee i?yiie caaea/e), i?eaiaeeo e iia?aoiinoe
ainnoaiiaeaiey ii?yaeea 0.1%.

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n oi?ioae
oi/iinoueth ( iia?aoiinoue 2-5% ) aeey i?eiiaa?oiinoiuo neiaa aeoaeiie
ii?yaeea /aoaa?oe ieanoeiu.

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie aiciiaeii n oi?ioae oi/iinoueth (
iia?aoiinoue 2-3% ). Iia?aoiinoue ainnoaiiaeaiey oaaee/eaaaony n
oiaiueoaieai aeoaeiu.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie i?aeoe/anee iaaiciiaeii. Eiatho ianoi
inoeeeeyoeee, i?eaiaeyuea e iia?aoiinoyi, i?aauoathuei 10%.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n oi?ioae
oi/iinoueth (iia?aoiinoue 2-3%). Iia?aoiinoue ainnoaiiaeaiey
oaaee/eaaaony n oiaiueoaieai aeoaeiu, caieiaaiie ?ani?aaeaeaieai.

9.4 Ainnoaiiaeaiea ii caooieaiiui aeaiiui

?anniio?aiiua a aeaiiii ?acaeaea ?acoeueoaou aeaiiino?e?otho
aiciiaeiinoue ainnoaiiaeaiey ?ani?aaeaeaiee YI a ?aaeueiuo oneiaeyo.
A?aoeee i?aaenoaaeaiu a ia?auo /aou?ao ioieoao I?eeiaeaiey 3.

Ia a?aoeeao ?anniao?eaaaiua caaeneiinoe iieacaiu oeaaoaie: ?acoeueoao
ainnoaiiaeaiey i?e iia?aoiinoe aeaiiuo ?aaiie 1% – aieoaui, ?acoeueoao
ainnoaiiaeaiey i?e iia?aoiinoe aeaiiuo ?aaiie 2% – ei?e/iaaui,
?acoeueoao ainnoaiiaeaiey i?e iia?aoiinoe aeaiiuo ?aaiie 5% – neiei.

Enoiaey ec ieo iiaeii naeaeaoue neaaeothuea auaiaeu:

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n oi?ioae
oi/iinoueth ( iia?aoiinoue 2-8% ) aeey i?eiiaa?oiinoiuo neiaa aeoaeiie
ii?yaeea /aoaa?oe ieanoeiu.

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie cao?oaeiaii( iia?aoiinoue inoeeeee?oao a
i?aaeaeao 0-10% ). Iia?aoiinoue ainnoaiiaeaiey oaaee/eaaaony n
oiaiueoaieai aeoaeiu, caieiaaiie ?ani?aaeaeaieai.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie i?aeoe/anee iaaiciiaeii. Eiatho ianoi
inoeeeeyoeee, i?eaiaeyuea e iia?aoiinoyi, i?aauoathuei 10%.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n oi?ioae
oi/iinoueth (iia?aoiinoue 3-6% aeey iaeiieiaiiuo aii?ieneiaoeee e 7-10%
a i?ioeaiii neo/aa). Iia?aoiinoue ainnoaiiaeaiey oaaee/eaaaony n
oiaiueoaieai aeoaeiu, caieiaaiie ?ani?aaeaeaieai.

9.5 Ainnoaiiaeaiea n o/aoii aeiiieieoaeueiie eioi?iaoeee

N oeaeueth oeo/oaiey ?acoeueoaoia ainnoaiiaeaiey a ?aaeueiie ianoaiiaea,
ineiaeiaiiie iaee/eai caooieaiiuo aeaiiuo, neaaeoao eniieueciaaoue aieaa
aeanoeea ia?aie/aiey ia aaee/eio YI a i?eiiaa?oiinoiuo neiyo.

Aeey eeethno?aoeee i?eaaaeai ianeieueei a?aoeeia, i?aaenoaaeaiiuo a
iyoii ioieoa I?eeiaeaiey 3. Ia a?aoeeao ?anniao?eaaaiua caaeneiinoe
iieacaiu oeaaoaie: aaciaua ia?aie/aiey – ei?e/iaaui, aeanoeea
ia?aie/aiey ia aa?oiae iiaa?oiinoe – aieoaui, aeanoeea ia?aie/aiey ia
iaieo iiaa?oiinoyo – iaeeiiaui.

Enoiaey ec iieo/aiiuo ?acoeueoaoia iiaeii naeaeaoue neaaeothuea auaiaeu

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n
oaeiaeaoai?eoaeueiie oi/iinoueth aeey i?eiiaa?oiinoiuo neiaa aeoaeiie
ii?yaeea /aoaa?oe ieanoeiu. Aeiiieieoaeueiua aeanoeea ia?aie/aiey
?acoeueoaou ainnoaiiaeaiey ia oeo/oatho.

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie cao?oaeiaii. Aeiiieieoaeueiua aeanoeea
ia?aie/aiey ?acoeueoaou ainnoaiiaeaiey ia oeo/oatho.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie i?aeoe/anee iaaiciiaeii. Eiatho ianoi
inoeeeeyoeee, i?eaiaeyuea e iia?aoiinoyi, i?aauoathuei 10%.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n
oaeiaeaoai?eoaeueiie oi/iinoueth (iia?aoiinoue 6-10% ). Iia?aoiinoue
ainnoaiiaeaiey oiaiueoaaony i?e eniieueciaaiee aeiiieieoaeueiua
ia?aie/aiee i?eia?ii aaeaia, iniaaiii a i?eiiaa?oiinoiii neia oieueiie
ii?yaeea 10%.

9.6 Ainnoaiiaeaiea i?e ?acee/iii aicaoaeaeaiee

Aeey auai?a iaiaoiaeeiiai eiee/anoaa ecia?aiee Uai* e niioaaonoaothueo
ei /anoio aicaoaeaeaiey AOI ?anniio?ei o?e aiciiaeiuo aeeaiaciia /anoio,
a eaaeaeii ec eioi?uo enneaaeoai neo/ae iyoe, aeanyoe e iyoiaaeoeaoe
/anoio.

Ia a?aoeeao a oanoii ioieoa I?eeiaeaiey 3 ?anniao?eaaaiua caaeneiinoe
iieacaiu oeaaoaie: 5 /anoio – ei?e/iaaui, 10 /anoio – aieoaui , 15
/anoio – iaeeiiaui.

Iaeanoue ieceeo /anoio

Enoiaey ec iieo/aiiuo ?acoeueoaoia iiaeii naeaeaoue neaaeothuea auaiaeu

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n
oaeiaeaoai?eoaeueiie oi/iinoueth aeey i?eiiaa?oiinoiuo neiaa aeoaeiie
ii?yaeea /aoaa?oe ieanoeiu. Aeey oeo/oaiey ?acoeueoaoia ainnoaiiaeaiey
neaaeoao eniieueciaaoue 10 /anoio a neo/aa iia?aoiinoe aeaiiuo ia aieaa
2% e 15 /anoio a i?ioeaiii neo/aa.

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie cao?oaeiaii. Aeey oeo/oaiey ?acoeueoaoia
ainnoaiiaeaiey a i?eiiaa?oiinoiii neiaa aeoaeiie ii?yaeea /aoaa?oe
ieanoeiu neaaeoao eniieueciaaoue 10 /anoio a neo/aa iia?aoiinoe aeaiiuo
ia aieaa 2% e 15 /anoio a i?ioeaiii neo/aa.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie i?aeoe/anee iaaiciiaeii. Eiatho ianoi
inoeeeeyoeee, i?eaiaeyuea e iia?aoiinoyi, i?aauoathuei 10%.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n
oaeiaeaoai?eoaeueiie oi/iinoueth (iia?aoiinoue 6-8% ). Aeey oeo/oaiey
?acoeueoaoia ainnoaiiaeaiey neaaeoao eniieueciaaoue 10 /anoio a neo/aa
iia?aoiinoe aeaiiuo ia aieaa 2% e 15 /anoio a i?ioeaiii neo/aa.

Iaeanoue n?aaeieo /anoio

Enoiaey ec iieo/aiiuo ?acoeueoaoia iiaeii naeaeaoue neaaeothuea auaiaeu:

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n
oaeiaeaoai?eoaeueiie oi/iinoueth aeey i?eiiaa?oiinoiuo neiaa aeoaeiie
ii?yaeea /aoaa?oe ieanoeiu. Aeey oeo/oaiey ?acoeueoaoia ainnoaiiaeaiey
neaaeoao eniieueciaaoue 10 /anoio a neo/aa iia?aoiinoe aeaiiuo ia aieaa
2% e 15 /anoio a i?ioeaiii neo/aa.

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie i?aeoe/anee iaaiciiaeii. Eiatho ianoi
inoeeeeyoeee, i?eaiaeyuea e iia?aoiinoyi, i?aauoathuei 10%.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie i?aeoe/anee iaaiciiaeii. Eiatho ianoi
inoeeeeyoeee, i?eaiaeyuea e iia?aoiinoyi, i?aauoathuei 10%.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n
oaeiaeaoai?eoaeueiie oi/iinoueth (iia?aoiinoue 6-8% ). Aeey oeo/oaiey
?acoeueoaoia ainnoaiiaeaiey neaaeoao eniieueciaaoue 10 /anoio a neo/aa
iia?aoiinoe aeaiiuo ia aieaa 2% e 15 /anoio a i?ioeaiii neo/aa.

Iaeanoue aunieeo /anoio

Enoiaey ec iieo/aiiuo ?acoeueoaoia iiaeii naeaeaoue neaaeothuea auaiaeu:

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n
oaeiaeaoai?eoaeueiie oi/iinoueth aeey i?eiiaa?oiinoiuo neiaa aeoaeiie
ii?yaeea /aoaa?oe ieanoeiu. Aeey oeo/oaiey ?acoeueoaoia ainnoaiiaeaiey
neaaeoao eniieueciaaoue 15, /oi iicaieyao ainnoaiaaeeaaoue?ani?aaeaeaiey
n iia?aoiinoueth (2-5)%.

Ainnoaiiaeaiea aeoaeiiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie i?aeoe/anee iaaiciiaeii. Eiatho ianoi
inoeeeeyoeee, i?eaiaeyuea e iia?aoiinoyi, i?aauoathuei 10%.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
nieaeiii e eoni/ii-eeiaeiie i?aeoe/anee iaaiciiaeii. Eiatho ianoi
inoeeeeyoeee, i?eaiaeyuea e iia?aoiinoyi, i?aauoathuei 10%.

Ainnoaiiaeaiea iiaa?oiinoiuo ?ani?aaeaeaiee n iiiiuueth aii?ieneiaoeee
yeniiiaioeeaeueiie e aeia?aiee/aneei oaiaainii aiciiaeii n
oaeiaeaoai?eoaeueiie oi/iinoueth. Aeey oeo/oaiey ?acoeueoaoia
ainnoaiiaeaiey neaaeoao eniieueciaaoue 15 /anoio.

10. Caeeth/aiea

Ii ?acoeueoaoai i?iaeaeaiiie ?aaiou iiaeii naeaeaoue neaaeothuea
auaiaeu:

Nouanoaoao i?eioeeieaeueiay aiciiaeiinoue ainnoaiiaeaiey eae
iiaa?oiinoiuo oae e aeoaeiiuo ?ani?aaeaeaiee YI n iia?aoiinoueth, ia
i?aauoathuae (2-3)%. Aeey ainnoaiiaeaiey iiaa?oiinoiuo ?ani?aaeaeaiee
neaaeoao eniieueciaaoue yeniiiaioeeaeueioth e aeia?aiee/aneoth
aii?ieneiaoeee, a aeey aeoaeiiuo nieaei e eoni/ii-iinoiyiioth (aiciiaeii
eniieueciaaiea yeniiiaioeeaeueiie e aeia?aiee/aneie aii?eneiaoeee aeey a
i?eiiaa?oiinoiii neia aeoaeiie ii?yaeea /aoaa?oe ieanoeiu).

Nouanoaaiiia io?eoeaoaeueiia aeeyiea ia ?acoeueoaou ainnoaiiaeaiey
eiatho iia?aoiinoue ecia?aiey Uai* (ia neaaeoao eniieueciaaoue aeaiiua n
iia?aoiinoueth ecia?aiey aieaa 2%) e iaeay aeoaeia ?ani?aaeaeaiey YI
(?ani?aaeaeaiey YI nin?aaeioi/aiiua a i?eiiaa?oiinoiii neia aeoaeiie
iaiaa (3-5)% ainnoaiaaeeaathony ooaea).

Eniieueciaaiea aeanoeeo ia?aie/aiee ia aaee/eio YI a i?eiiaa?oiinoiuo
neiyo ii?aaaeaii i?e ainnoaiiaeaiee iiaa?oiinoiuo ?ani?aaeaeaiee, i?e/ai
i?e iaee/ee aeaiiuo n iia?aoiinoueth, i?aainoiaeyuae 2%, eee iaeie
aeoaeiu ?ani?aaeaeaiey i?aaeii/oeoaeueiaa caaeaaaoue ia?aie/aiey ia
iaaeo iiaa?oiinoyo. I?e caooieaiiinoe aeaiiuo ii?yaeea (1-2)%
aeinoaoi/ii caaeaoue aeanoeea ia?aie/aiey eeoue ia aa?oiae iiaa?oiinoe.

A iaai?a /anoio aicaoaeaeaiey AOI aeieaeiu i?enoonoaiaaoue
iecei/anoioiua ninoaaeythuea, aeeyiea eioi?uo iniaaiii caiaoii i?e
?aaioa n aeoaeiiuie ?ani?aaeaeaieyie e niioaaonoaothueie
aii?ieneiaoeeyie. ?aeiiaiaeoaony eniieueciaaoue ii?yaeea aeanyoe /anoio,
?aaiiia?ii ?ani?aaeaeaiiuo ii /anoioiiio aeeaiaciio (0.001(70)EAoe. A
oneiaeyo aunieie iia?aoiinoe ecia?aiee eee io/aoeeai au?aaeaiiuo
i?eiiaa?oiinoiuo eciaiaieyo YI caiaoiia iieiaeeoaeueiia aeeyiea
ieacuaaao oaaee/aiea /enea /anoio aicaoaeaeaiey AOI (iai?eia?, aei
iyoiaaeoeaoe.).

A i?ioeanna ?aaiou iaae caaea/ae aue i?iaaaeai aiaeec eeoa?aoo?u,
aua?aia iiaeaeue caaea/e e niiniau aa aii?ieneiaoeee. I?e iiiiue
i?ia?aiiu, ?ac?aaioaiiie niaeanii i?aaeeiaeaiiie iiaeaee, auee
i?iaaaeaiu ?an/aou iiaeaeueiuo caaea/ e ?anniio?aiu ?acoeueoaou
ainnoaiiaeaiey ?ani?aaeaeaiee YI a caaeneiinoe io iniiaiuo aeeythueo
oaeoi?ia.

Oaeei ia?acii, oeaee, iinoaaeaiiua a oaoie/aneii caaeaiee, ?aoaiu a
iieiii iauaia.

11. Eeoa?aoo?a

Ia?ac?ooathuee eiio?ieue ea/anoaa ecaeaeee yeaeo?iiaaieoiuie iaoiaeaie,
Aa?aneiia AA, 1978,215

Aeo?aoieiaue eiio?ieue iaeeaaeiuie i?aia?aciaaoaeyie., Aa?aneiia
AA,1985,86

Aeo?aoieiaua iaoiaeu e i?eai?u ia?ac?ooathuaai eiio?iey., ?oaeaeia AI,
1992, 72

Iaeeaaeiua e ye?aiiua aeao/eee., Niaieaa AN, 1967, 144

Oai?ey e ?an/ao iaeeaaeiuo aeo?aoieiauo i?aia?aciaaoaeae., Aeyeei AA,
1981, 135

Iniiau aiaeeca oece/aneeo iieae.,Iie?ianeee AAe, 1982, 89

Aeaoaeoineiiey iaoaeeia., Aeaiaeue AE, 1972, 303

Eiaeoeoeeiiiay no?oeoo?ineiiey., Aei?ioaaa AE,1973,177

No?oeoo?a e naienoaa iaoaeeia e nieaaia.Ni?aai/iee., Oiaoei IA,1987,580

Iaei??aeoiua caaea/e *eneaiiua iaoiaeu e i?eeiaeaiey., Aii/a?neee
AA,1989,198

Iaei??aeoiua caaea/e iaooeceee e aiaeeca., Eaa?aioueaa II,1980,286

Eeiaeiua iia?aoi?u e iaei??aeoiua caaea/e., Eaa?aioueaa II,1991,331

Iaoiaeu ?aoaiey iaei??aeoii iinoaaeaiiuo caaea/ Aeai?eoie/. aniaeo.,
Ii?icia AA, 1992,320

*eneaiiua iaoiaeu ?aoaiey iaei??aeoiuo caaea/., Oeoiiia AI,1990,230

Ia/aea oai?ee au/eneeoaeueiuo iaoiaeia, E?ueia AE,1984,260

Iaoaiaoe/aneia i?ia?aiie?iaaiea a i?eia?ao e caaea/ao., Aeoee/
EE,1993,319

Iaoaiaoe/aneia i?ia?aiie?iaaiea., Ea?iaiia AA,1986,286

Iaoaiaoe/aneia i?ia?aiie?iaaiea., I?aoiaa ?A,1992,290

Iaeeiaeiia i?ia?aiie?iaaiea Oai?ey e aeai?eoiu., Aaca?a I,1982,583

I?eeeaaeiia iaeeiaeiia i?ia?aiie?iaaiea., Oeiiaeueaeao Ae,1975,534

Aaaaeaiea a iaoiaeu iioeiecaoeee., Aiee I,1977,344

Aaaaeaiea a iioeiecaoeeth., Iieye AO,1983,384

Eo?n iaoiaeia iioeiecaoeee., Nooa?aa AA,1986,326

I?aeoe/aneay iioeiecaoeey., Aeee O,1985,509

*eneaiiua iaoiaeu iioeiecaoeee., Iieae Y,1974,367

Aeai?eoiu ?aoaiey yeno?aiaeueiuo caaea/., ?iiaiianeee EA,1977,352

Iaoiaeu ?aoaiey yeno?aiaeueiuo caaea/., Aaneeueaa OI,1981,400

Iaoiaeu ?aoaiey yeno?aiaeueiuo caaea/ e eo i?eiaiaiea a nenoaiao
iioeiecaoeee., Aaoooaiei THA, 1982,432

*eneaiiua iaoiaeu ?aoaiey yeno?aiaeueiuo caaea/., Aaneeueaa OI,1988,549

Aaaaeaiea a au/eneeoaeueioth oeceeo., Oaaei?aiei ?I,1994,526

Iaoiaeu iaoaiaoe/aneie oeceee., A?naiei Ass,1984,283

O?aaiaiey iaoaiaoe/aneie oeceee., Oeoiiia AI,1977

O?aaiaiey iaoaiaoe/aneie oeceee., Aeaaeeie?ia AN,1988,512

Iaoiae eioaa?aeueiuo o?aaiaiee a oai?ee ?annaeaaiey., Eieoii Ae,1987,311

Oai?ey yeaeo?iiaaieoiiai iiey., Iieeaaiia EI,1975,207

Eddy current testing. Manual on eddy current method., Cecco VS,1981,195

Optimization methods with applications for PC., Mistree F,1987,168

Electromagnetic inverse profiling., Tijhuis AG,1987,465

Inverse acoustic and electromagnetic scattering theory., Colton
D,1992,305

( Iaeeaaeiie yeaeo?iiaaieoiue i?aia?aciaaoaeue iaae iauaeoii eiio?iey n
eciaiythueieny ii aeoaeia yeaeo?e/aneeie e iaaieoiuie naienoaaie(,
Eaneiia AA, Eoeaaa THA, (Aeaoaeoineiiey(, 1978, ?6, n81-84

( Aiciiaeiinoe i?eiaiaiey iaoiaeia oai?ee neioaca eceo/athueo nenoai a
caaea/ao yeaeo?iiaaieoiiai eiio?iey (, Eoeaaa THA, 1980, oaiaoe/aneee
nai?iee (O?oaeu IYE(, auione 453, n12-18

( Analitical solutions to eddy-current probe-coil problems ( , Deeds WE,
Dodd CV, (Journal of Applied Phisics(, 1968, vol39, (3, p2829-2838

( General analysis of probe coils near stratified conductors ( , Deeds
WE, Dodd CV,(International Journal of Nondestructive Testing(, 1971,
vol3, (2, p109-130

( Tutorial. A review of least-squares inversion and its application to
geophysical problems (, Lines LR, Treitel S, (Geophysical Prospecting (,
1984, vol32, (2, p159-186

( Eddy current calculations using half-space Green’s functions ( ,
Bowler JR, (Journal of Applied Phisics(, 1987, vol61, (3, p833-839

( Reconstruction of 3D conductivity variations from eddy current(
electromagnetic induction ) data (, Nair SM, Rose JH, ( Inverse
Problems(, 1990, (6, p1007-1030

( Electromagnetic induction (eddy-currents) in a conducting half-space
in the absence and presence of inhomogeneities: a new formalism ( , Nair
SM, Rose JH, (Journal of Applied Phisics(, 1990, vol68, (12, p5995-6009

( Eddy-current probe impedance due to a volumetric flaw ( , Bowler JR,
(Journal of Applied Phisics(, 1991, vol70, (3, p1107-1114

( Theory of eddy current inversion ( , Bowler JR, Norton SJ, (Journal of
Applied Phisics(, 1993, vol73, (2, p501-512

( Impedance of coils over layered metals with continuously variable
conductivity and permeability: Theory and experiment ( , Rose JH,
(Journal of Applied Phisics(, 1993, vol74, (3, p2076

( Eddy-current interaction with ideal crack ( , Bowler JR, (Journal of
Applied Phisics(, 1994, vol75, (12, p8128,8138

( Method of solution of forward problems in eddy-current testing ( ,
Kolyshkin AA, (Journal of Applied Phisics(, 1995, vol77, (10, p4903-4912

I?eeiaeaiea 1. I?ia?aiiiay ?aaeecaoeey

I?ia?aiiiay ?aaeecaoeey eceiaeaiiiai iaoiaea ?aoaiey ia?aoiie caaea/e
AOE inouanoaeaia i?e iiiiue eiiieeyoi?a Borland Pascal 7.0 e ninoieo ec
oanoe iiaeoeae:

ErIn12.pas – eniieiyaiue oaee, inouanoaeyao iniiaiie oeeee i?ia?aiiu

EData.pas – niaea?aeeo aeiaaeueiua aeaiiua e inouanoaeyao /oaiea oaeea
enoiaeiuo aeaiiuo

EFile.pas – niaea?aeeo aniiiiaaoaeueiua ooieoeee e einouanoaeyao
nio?aiaiea ?acoeueoaoia ?an/aoia

EMath.pas – inouanoaeyao iiaeaea?aeeo iia?aoeee n eiiieaeniuie /eneaie

EDirect.pas – inouanoaeyao ?aoaiea i?yiie caaea/e AOE

EMinimum.pas – inouanoaeyao ?aoaiea ia?aoiie caaea/e AOE

I1.1 Enoiaeiua aeaiiua

Enoiaeiua aeaiiua i?ia?aiiu o?aiyony a oaenoiaii oaeea( eiaee?iaea
ASCII, ?anoe?aiea ii oiie/aieth TXT ).

HThick – oieueia ieanoeiu,[ii]

nPoints – eiee/anoai oceia aii?ieneiaoeee yeaeo?ii?iaiaeiinoe aeey
PWL,PWC,SPL aii?ieneiaoeee. A neo/aa EXP,HTG aii?ieneiaoeee au/eneaiea
cia/aiee YI a ieo i?iecaiaeeony ii ieii/aiee ?an/aoia

nLayers – eiee/anoai eioa?aaeia n eoni/ii-iinoiyiiie
yeaeo?ii?iaiaeiinoueth, ia eioi?ua ?acaeaaaony ieanoeia aeey
iaiin?aaenoaaiiiai ?an/aoa aiineiie YAeN ii ?aeeo?aioiui oi?ioeai aeey
iiiaineieiie ieanoeiu

nFreqs – eiee/anoai /anoio aicaoaeaeaiey aa?iiiee aiineiie
ioiineoaeueiie YAeN

nStab – /enei noaaeeece?oaiuo cia/aueo oeeo?

epsU – iia?aoiinoue ecia?aiey

aG – eiyooeoeeaio naeaoey ia?aie/aiee (aG0,
a i?ioeaiii neo/aa eniieuecothony eii?aeeiaou neiaa ec oaeea

I1.2 Eniieuecoaiua aii?ieneiaoeee

I?eia/aiea. Eii?aeeiaoa O([0,1] ion/eouaaaony io aeia ieanoeiu aeey anao
aii?ieneiaoeee.

Nieaei(SPL), eoni/ii-eeiaeiay(PWL), eoni/ii-iinoiyiiay(PWC)
aii?ieneiaoeee.

A i?ioeanna ?an/aoia euoony cia/aiey yeaeo?ii?iaiaeiinoe a oceao
aii?ieneiaoeee, i?e/ai eiee/anoai oceia oaaee/eaaaony io aaeaieeoeu aei
nPoints a oeaeyo nio?aiaiey onoie/eainoe ?aoaiey.

Ia/aeueiua cia/aiey (oceiaua cia/aiey (enoeiiie( YI aeey yioeyoeee
ecia?aiee U*ai) caaeathony a noieaoea (si( oaeea enoiaeiuo aeaiiuo,
ia/aeueiua cia/aiey ia?aie/aiee ia oceiaua cia/aiey YI a noieaoeao
(siMin( e (siMax((aeaeaeaiea ii noieaoeo naa?oo aiec niioaaonoaoao
eciaiaieth eii?aeeiaou io aeia ieanoeiu aei ia?aaaouaaaiie iiaaoiinoe).

Yeniiiaioeeaeueiay aii?ieneiaoeey(EXP)

A neo/aa caaeaiey yeniiiaioeeaeueiie aii?ieneiaoeee caaeneiinoue
yeaeo?ii?aiaeiinoe io oieueiu i?aaenoaaeyaony a aeaea

SIGMA = ( siE-siI )*EXP( -alfa*(1-x) ) + siI

Aa?ue?oaiuie ia?aiao?aie yaeythony yaeo?ii?iaiaeiinoue ia aa?oiae
iiaa?oiinoe siA, yeaeo?ii?iaiaeiinoue “ia aaneiia/iinoe” siI e ia?aiao?
alfa. A oaeea enoiaeiuo aeaiiuo a oaaeeoea ec nPoints no?ie n
iiaecaaieiaeii “si siMin siMax”, eioi?iaoeey ia ia?aie/aieyo ia
ia?aiao?u siE, siI caaeaaony a ia?aie e nPoints-no?iea. Aaee/eia e
ia?aie/aiey aeey ia?aiao?a alfa caaeathony ia?aie no?ieie a “special
approximation parameters”.

Aii?ieneiaoeey aeia?aiee/aneei oaiaainii (HTG)

A neo/aa caaeaiey aii?ieneiaoeee aeia?aiee/aneei oaiaainii caaeneiinoue
yeaeo?ii?aiaeiinoe io oieueiu i?aaenoaaeyaony a aeaea

SIGMA = si2 + ( si1-si2 )/2*{ 1 + th( ( beta-x )/gamma ) }

Aaee/eia e ia?aie/aiey aeey ia?aiao?ia si2,beta,gamma caaeathony ia/eiay
ni aoi?ie no?iee a “special approximation parameters”, aeey si1
aiaeiae/ii siI.

I1.3 ?acoeueoaou ?an/aoa

?acoeueoaou ?an/aoa iiiauathony a oaenoiaue oaee( eiaee?iaea ASCII,
?anoe?aiea ii oiie/aieth LST ), i?e yoii ?acoeueoao eaaeaeie eoa?aoeee
ioa?aaeaaony no?ieie aeaea:

1 0.000353 Rg= 17.003 15.639 9.697

aaea ia?aay oeeo?a (a aeaiiii neo/aa 1) niioaaonoaoao iiia?o oaeouae
aioo?aiiae eoa?aoeee, caoai iinea oaenoa “” eaeao cia/aiea oaeouae
aaniethoiie n?aaeiaeaaae?aoe/iie iaaycee ii anai aa?iiieeai (a aeaiiii
neo/aa 0.000353), caoai iinea oaenoa “Rg= “, eaeoo eneiiua oaeouea
cia/aiey ia?aiaiiuo ieieiecaoeee. A neo/aa SPL,PWL,PWC aii?ieneiaoeee
yoi iaiin?aaenoaaiii oceiaua cia/aiey yeaeo?ii?iaiaeiinoe aeey oaeouaai
eiee/anoaa oceia, a aeey EXP,HTG aii?ieneiaoeee yoi ia?aiao?u { siE,
siI, Alfa } eee { si1, si2, Beta, Gamma}. B ea/anoaa iineaaeiae no?iee
iiiauathony nPoints au/eneaiiuo cia/aiee y/i?iaiaeiinoe a ?aaiiia?ii
?aniieiaeaiiuo oceao ieanoeiu.

I1.4 Iniiaiay i?ia?aiia ErIn

(***********************************************************************
*****)

(* ErIn v1.42
*)

(* Eddy current inverse problem solver.
*)

(* (C) 1999 by Nikita U.Dolgov
*)

(* Moscow Power Engineering Institute , Introscopy dept.
*)

{***********************************************************************
*****}

Program ErIn;{23.02.99}

Uses

DOS,CRT, EData, EMath, EDirect, EFile, EMinimum;

Var

m, mLast, i : byte; {loop
counters}

procedure about; {Let me to introduce
myself}

begin

clrscr;

GetTime( clk1.H, clk1.M, clk1.S, clk1.S100 ); {get start
time}

writeln(‘***********************************************************’);

writeln(‘* ErIn v1.42 Basic *
*’);

writeln(‘***********************************************************’);

end;

procedure initParameters;

var

apDT : byte; {approximation type for direct
task}

begin

apDT := nApprox SHR 4;
{XXXXYYYY->0000XXXX}

fHypTg:=(( apDT AND apHypTg ) = apHypTg);

if fHypTg then

begin

si0[ 1 ]:=si[ 1 ]; {si1 – conductivity about bottom of
slab}

si0[ 2 ]:=par0[ 2 ]; {si2 – conductivity about top of
slab}

si0[ 3 ]:=par0[ 3 ]; {Beta – ratio of approx.}

si0[ 4 ]:=par0[ 4 ]; {Gamma- ratio of approx.}

mCur:=4;

end

else

if(( apDT AND apExp ) = 0 ) then {It’s not an EXP
approx.}

begin

for i:=1 to nPoints do si0[ i ] :=si [ i ]; {SI data from
file}

mCur:=nPoints;

end

else

begin

si0[ 1 ]:=si[ 1 ]; {siI – conductivity about bottom of
slab}

si0[ 2 ]:=si[ nPoints ]; {siE – conductivity about top of
slab}

si0[ 3 ]:=par0[ 1 ]; {Alfa- ratio of approx.}

mCur:=3;

end;

setApproximationType( apDT ); {approx. type for direct
problem}

setApproximationData( si0, mCur ); {approx. data for direct
problem}

nApprox := ( nApprox AND $0F );
{XXXXYYYY->0000YYYY}

fHypTg := (( nApprox AND apHypTg ) = apHypTg );

fMulti := (( nApprox AND apExp ) = 0 ) AND NOT fHypTg; {It’s not
an EXP approx.}

if fMulti then

begin

for i:=1 to nPoints do

begin

Gr[ 1,i ]:=SiMax[ i ];

Gr[ 2,i ]:=SiMin[ i ];

Rg[ i ]:=( Gr[ 1,i ] + Gr[ 2,i ] )/2; {zero estimate
of SI}

Rgs[ i ]:=1E33; {biggest
integer}

end;

mLast:=nPoints; {loop for every node of
approx.}

mCur :=1; {to begin from the only node of
approx}

end

else

if fHypTg then

begin

Gr[ 1,1 ]:= siMax[ 1 ]; Gr[ 2,1 ]:= siMin[ 1 ]; Rgs[ 1
]:=1E33;

Gr[ 1,2 ]:=parMax[ 2 ]; Gr[ 2,2 ]:=parMin[ 2 ]; Rgs[ 2
]:=1E33;

Gr[ 1,3 ]:=parMax[ 3 ]; Gr[ 2,3 ]:=parMin[ 3 ]; Rgs[ 3
]:=1E33;

Gr[ 1,4 ]:=parMax[ 4 ]; Gr[ 2,4 ]:=parMin[ 4 ]; Rgs[ 4
]:=1E33;

for i:=1 to 4 do Rg[ i ]:=( Gr[ 1,i ] + Gr[ 2,i ] )/2;

mLast:=1;

mCur:=4;

end

else

begin

Gr[ 1,1 ]:= siMax[1]; Gr[2,1]:= siMin[1]; Rgs[ 1
]:=1E33;

Gr[ 1,2 ]:= siMax[nPoints]; Gr[2,2]:= siMin[nPoints]; Rgs[ 2
]:=1E33;

Gr[ 1,3 ]:= parMax[1]; Gr[2,3]:= parMin[1]; Rgs[ 3
]:=1E33;

for i:=1 to 3 do Rg[ i ]:=( Gr[ 1,i ] + Gr[ 2,i ] )/2;

mLast:=1;

mCur :=3;

end;

initConst( nLayers, parMaxH, parMaxX , parEps, parEqlB );{set probe
params}

end;

procedure directTask; {emulate voltage measurements [with
error]}

begin

for i:=1 to nFreqs do

begin

getVoltage( freqs[i], Umr[ i ], Umi[ i ] ); {“measured”
Uvn*}

if ( epsU > 0 ) then {add measurement
error}

begin

randomize; Umr[ i ]:=Umr[ i ]*( 1 + epsU*( random-0.5 )
);

randomize; Umi[ i ]:=Umi[ i ]*( 1 + epsU*( random-0.5 )
);

end;

end;

writeln(‘* Voltage measurements have been emulated’);

setApproximationType( nApprox ); {approx. type for inverse
problem}

setApproximationData( Rg, mCur ); {approx. data for inverse
problem}

end;

procedure reduceSILimits; {evaluate SI for m+1 points of approx.
using aG}

var

x0, x1, xL, dx, Gr1, Gr2 : real;

j, k : byte;

begin

{—————————– get SI min/max for m+1 points of
approximation}

dx:=1/( nPoints-1 );

for i:=1 to m+1 do

begin

k:=1;

x1:=0;

x0:=( i-1 )/m;

for j:=1 to nPoints-1 do

begin

xL:=( j-1 )/( nPoints-1 );

if( ( xL Gr[1,i] )then Rg[i]:=Gr[1,i];

if ( Rg[i] 1 then {There’re more than 1 point of
approx.}

begin

Gr1:= Rg[i]+( Gr[1,i]-Rg[i] )*aG; {reduce upper
bound}

Gr2:= Rg[i]-( Rg[i]-Gr[2,i] )*aG; {reduce lower
bound}

if ( Gr1 Gr[2,i] )then Gr[2,i]:=Gr2;

end;

end;

setApproximationData( Rg , m+1 );

end;

procedure resultMessage; {to announce new
results}

begin

if fMulti then

begin

writeln(‘ current nodal values of conductivity’);

write(‘ si : ‘);for i:=1 to m do write(Rg[i] :6:3,’ ‘);writeln;

write(‘ max: ‘);for i:=1 to m do write(Gr[1,i]:6:3,’ ‘);writeln;

write(‘ min: ‘);for i:=1 to m do write(Gr[2,i]:6:3,’ ‘);writeln;

end

else

begin

for i:=1 to nPoints do si[i]:=getSiFunction( ( i-1 )/( nPoints-1
) );

if fHypTg then

saveHypTgResults

else

saveExpResults;

end;

end;

procedure clockMessage; {user-friendly
message}

begin

writeln(‘***********************************************************’);

write( ‘* approximation points number :’,m:3,’ * Time ‘);
clock;

writeln(‘***********************************************************’);

end;

procedure done; {final
message}

begin

Sound(222); Delay(111); Sound(444); Delay(111); NoSound;
{beep}

write(‘* Task processing time ‘); clock; saveTime;

writeln(‘* Status: Inverse problem has been successfully
evaluated.’);

end;

Begin

about;

loadData;

initParameters;

directTask;

for m:=1 to mLast do

begin

if fMulti then

begin

mCur:=m;

clockMessage;

end;

doMinimization; {main part of
work}

setApproximationData( Rg, mCur ); {set new approx.
data}

resultMessage;

if(( fMulti )AND( m ‘, sum:10:7, ‘ Rg=’ );

write( FF , iter:2, ‘ ‘, sum:10:7, ‘ Rg=’);

for i:=1 to mCur do

begin

write( Rg[i]:6:3, ‘ ‘);

write( FF , Rg[i]:6:3, ‘ ‘);

end;

writeln;

writeln( FF );

close( FF );

saveResults:=isStable( ns , Rgs , Rg );

end;

procedure saveExpResults;

begin

assign( FF , outFileName );

append( FF );

writeln( ‘ siE=’,Rg[2]:6:3,’ siI=’,Rg[1]:6:3,’
alfa=’,Rg[3]:6:3);

writeln( FF , ‘ siE=’,Rg[2]:6:3,’ siI=’,Rg[1]:6:3,’
alfa=’,Rg[3]:6:3);

write( ‘ SI: ‘);

write( FF , ‘ SI: ‘);

for i:=1 to nPoints do

begin

write( si[i]:6:3,’ ‘);

write( FF , si[i]:6:3,’ ‘);

end;

writeln;

writeln( FF );

close( FF );

end;

procedure saveHypTgResults;

begin

assign( FF , outFileName );

append( FF );

writeln( ‘ si1=’,Rg[2]:6:3,’ si2=’,Rg[1]:6:3,’
beta=’,Rg[3]:6:3,’ gamma=’,Rg[4]:6:3);

writeln( FF , ‘ si1=’,Rg[2]:6:3,’ si2=’,Rg[1]:6:3,’
beta=’,Rg[3]:6:3,’ gamma=’,Rg[4]:6:3);

write( ‘ SI: ‘);

write( FF , ‘ SI: ‘);

for i:=1 to nPoints do

begin

write( si[i]:6:3,’ ‘);

write( FF , si[i]:6:3,’ ‘);

end;

writeln;

writeln( FF );

close( FF );

end;

procedure clock; {t2 =
t2-t1}

var

H1,M1,S1,H2,M2,S2,sec1,sec2 : longint;

begin

GetTime( clk2.H, clk2.M, clk2.S, clk2.S100 ); {current
time}

H2:=clk2.H; M2:=clk2.M; S2:=clk2.S; H1:=clk1.H; M1:=clk1.M;
S1:=clk1.S;

sec2:= ( H2*60 + M2 )*60 + S2;

sec1:= ( H1*60 + M1 )*60 + S1;

if( sec2 dx ) do

begin

i:=i + 1;

dx:=dx + dh;

end;

siPWConst:=appSigma[ i ];

end;

end;

function siPWLinear( x:real ) : real;{Piecewise linear approximation}

var

dx, dh : real;

i : byte;

begin

if( appCount = 1 )then siPWLinear := appSigma[ 1 ]

else

begin

dh:=1/( appCount-1 );

dx:=0;

i:=1;

repeat

i:=i + 1;

dx:=dx + dh;

until( x maxsteps) );

if( flag )then

begin

eqlComp( result, integ2H );

end

else

begin

writeln(‘Error: Too big number of integration steps.’);

halt(1);

end;

end;

end;

procedure initConst( par1, par2 : integer; par3, par4 : real;
par5:boolean );

var

i : byte;

bThick, dl, x : real;

const

Ri=0.02; hi=0.005; { radius and lift-off of excitation
coil}

Rm=0.02; hm=0.005; { radius and lift-off of measuring
coil}

begin

with cInfo do

begin

Nlay :=par1;

xMax :=par3;

maxsteps:=par2;

R :=sqrt( Ri*Rm );

H :=( hi+hm )/R;

Kr :=sqrt( Ri/Rm );

eps :=par4;

bThick :=hThick*0.002/R; {2*b/R [m]}

for i:=1 to Nlay do m[i]:= mu[i];

if par5 then

begin

bThick:=bThick/NLay;

for i:=1 to Nlay do b[i]:=bThick;

dl:=1/NLay;

x:=dl/2; {x grows up from bottom of slab to
the top}

for i:=1 to Nlay do

begin

zCentre[i]:=x;

x:=x + dl;

end;

end

else

for i:=1 to Nlay do

begin

b[i]:=( zLayer[i+1]-zLayer[i] )*bThick;

zCentre[i]:=( zLayer[i+1]+zLayer[i] )/2;

end;

end;

end;

procedure init( f:real );{get current approach of conductivity values}

var

i : byte;

begin

with cInfo do

begin

w:=PI23*f;

for i:=1 to Nlay do sigma[i]:=getSiFunction( zCentre[i] )*1E6;

end;

end;

procedure getVoltage( freq : real ; var ur,ui : real );

var

U, U0, Uvn, tmp : complex;

begin

init( freq );

integral( funcSimple, U ); { U
=Uvn }

integral( funcMax , U0 ); { U0=Uvn
max }

divComp( U, Leng(U0), Uvn ); {
Uvn=U/|U0| }

mkComp( 0, 1, tmp ); { tmp=(
0+j1 ) }

MulC( tmp, Uvn, U ); { U= j*Uvn =
Uvn* }

ur := U.re;

ui := U.im;

end;

END.

I1.8 Iiaeoeue ?aoaiey ia?aoiie caaea/e AOE aeey IAOI EMinimum

Unit EMinimum;

INTERFACE

Uses EData, Crt, EFile, EDirect;

procedure doMinimization;

IMPLEMENTATION

procedure getFunctional( Reg : byte );

var

ur, ui, dur, dui, Rgt : real;

ur2, ui2: Functionals;

i, j, k : byte;

begin

getApproximationData( si , k );

setApproximationData( Rg, mCur );

case Reg of

0 : for i:=1 to nFreqs do {get functional F
value}

begin

getVoltage( freqs[i], ur, ui );

Uer[ i ]:=ur; {we need it
for dU}

Uei[ i ]:=ui;

Fh[1,i] := SQR( ur-Umr[i] ) + SQR( ui-Umi[i] );

end;

{Right:U'(i)= (U(i+1)-U(i))/h}

1 : for i:=1 to mCur do {get dF/dSI[i]
value}

begin

Rgt:=Rg[i]*( 1+incVal );
{si[i]=si[i]+dsi[i]}

setApproximationItem( Rgt, i ); {set new si[i]
value}

for j:=1 to nFreqs do

begin {get
dUr/dSI,dUi/dSI}

getVoltage( freqs[ j ], ur, ui );

dur:=( ur-Uer[j] )/( Rg[i]*incVal );

dui:=( ui-Uei[j] )/( Rg[i]*incVal );

Fh[i,j]:=2*(dur*(Uer[j]-Umr[j])+dui*(Uei[j]-Umi[j]));

end;

setApproximationItem( Rg[i], i ); {restore si[i]
value}

end;

{Central:U'(i)= (U(i+1)-U(i-1))/2h}

2 : for i:=1 to mCur do {get dF/dSI[i]
value}

begin

Rgt:=Rg[i]*( 1+incVal );
{si[i]=si[i]+dsi[i]}

setApproximationItem( Rgt, i ); {set new si[i]
value}

for j:=1 to nFreqs do getVoltage(
freqs[j],ur2[j],ui2[j] );

Rgt:=Rg[i]*( 1-incVal );
{si[i]=si[i]-dsi[i]}

setApproximationItem( Rgt, i ); {set new si[i]
value}

for j:=1 to nFreqs do

begin {get
dUr/dSI,dUi/dSI}

getVoltage( freqs[ j ], ur, ui );

dur:=( ur2[j]-ur )/( 2*Rg[i]*incVal );

dui:=( ui2[j]-ui )/( 2*Rg[i]*incVal );

Fh[i,j]:=2*(dur*(Uer[j]-Umr[j])+dui*(Uei[j]-Umi[j]));

end;

setApproximationItem( Rg[i], i ); {restore si[i]
value}

end;

end;

setApproximationData( si , k );

end;

procedure doMinimization;

const

mp1Max = maxPAR + 1;

mp2Max = maxPAR + 2;

m2Max = 2*( maxPAR + maxFUN );

m21Max = m2Max + 1;

n2Max = 2*maxFUN;

m1Max = maxPAR + n2Max;

n1Max = n2Max + 1;

mm1Max = maxPAR + n1Max;

minDh : real = 0.001; {criterion of an exit from golden section
method}

var

A : array [ 1 .. m1Max , 1 .. m21Max ] of real;

B : array [ 1 .. m1Max] of real;

Sx: array [ 1 .. m21Max] of real;

Zt: array [ 1 .. maxPAR] of real;

Nb: array [ 1 .. m1Max] of integer;

N0: array [ 1 .. m21Max] of integer;

a1, a2, dh, r, tt, tp, tl, cv, cv1, cl, cp : real;

n2, n1, mp1, mp2, mm1, m1, m2, m21 : integer;

ain : real;

apn : real;

iq : integer;

k1 : integer;

n11 : integer;

ip : integer;

iterI : integer;

i,j,k : integer;

label

102 ,103 ,104 ,105 ,106 ,107 ,108;

begin

n2:=2*nFreqs; n1:=n2+1; m1:=mCur+n2;

mp1:=mCur+1; mp2:=mCur+2; mm1:=mCur+n1;

m2:=2*( mCur+nFreqs ); m21:=m2+1;

for k:=1 to m1Max do

for i:=1 to m21Max do

A[k,i]:=0;

iterI:=0;

102:

iterI:=iterI+1;

getFunctional( 0 );

for i:=1 to nFreqs do b[i]:= -Fh[1,i];

getFunctional( derivType );

for k:=1 to mCur do

begin

Zt[k]:=Rg[k];

for i:=1 to nFreqs do

begin

A[i,k+1]:=Fh[k,i];

A[i+nFreqs,k+1]:=-A[i,k+1];

end;

for i:=1 to nFreqs do B[i]:=B[i]+Rg[k]*A[i,k+1];

end;

for i:=1 to nFreqs do B[i+nFreqs]:=-B[i];

for i:=n1 to m1 do B[i]:=Gr[1,i-n2]-Gr[2,i-n2];

for i:=1 to m1 do

begin

if in2 then

begin

A[i,1]:=0;

for k:=2 to mp1 do

if i-n2=k-1 then A[i,k]:=1

else A[i,k]:=0;

end;

for k:=mp2 to m21 do

if k-mp1=i then A[i,k]:=1

else A[i,k]:=0;

end;

k1:=1;

for k:=1 to n2 do

if B[k1]>B[k] then k1:=k;

for k:=1 to mp1 do A[k1,k]:=-A[k1,k];

A[k1,mCur+1+k1]:=0;

B[k1]:=-B[k1];

for i:=1 to n2 do

if ik1 then

begin

B[i]:=B[i]+B[k1];

for k:=1 to mm1 do A[i,k]:=A[i,k]+A[k1,k];

end;

for i:=mp2 to m21 do

begin

Sx[i]:=B[i-mp1];

Nb[i-mp1]:=i;

end;

for i:=1 to mp1 do Sx[i]:=0;

Sx[1]:=B[k1];

Sx[mp1+k1]:=0;

Nb[k1]:=1;

103:

for i:=2 to m21 do N0[i]:=0;

104:

for i:=m21 downto 2 do

if N0[i]=0 then n11:=i;

for k:=2 to m21 do

if ((A[k1,n11]N0[k])) then n11:=k;

if A[k1,n11]k1 then

begin

if A[i,n11]>0 then

begin

iq:=iq+1;

if iq=1 then

begin

Sx[n11]:=B[i]/A[i,n11]; ip:=i;

end

else

begin

if Sx[n11]>B[i]/A[i,n11] then

begin

Sx[n11]:=B[i]/A[i,n11]; ip:=i;

end;

end;

end

else

if iq=0 then

begin

N0[n11]:=n11;

goto 104;

end;

end;

Sx[Nb[ip]]:=0;

Nb[ip]:=n11;

B[ip]:=B[ip]/A[ip,n11];

apn:=A[ip,n11];

for k:=2 to m21 do A[ip,k]:=A[ip,k]/apn;

for i:=1 to m1 do

if iip then

begin

ain:=A[i,n11];

B[i]:=-B[ip]*ain+B[i];

for j:=1 to m21 do A[i,j]:=-ain*A[ip,j]+A[i,j];

end;

for i:=1 to m1 do Sx[Nb[i]]:=B[i];

goto 103;

105:

for k:=1 to mCur do Sx[k+1]:=Sx[k+1]+Gr[2,k];

a1:=0;

a2:=1.;

dh:=a2-a1;

r:=0.618033;

tl:=a1+r*r*dh;

tp:=a1+r*dh;

j:=1;

108:

if j=1 then tt:=tl else tt:=tp;

106:

for i:=1 to mCur do Rg[i]:=Zt[i]+tt*(Sx[i+1]-Zt[i]);

getFunctional( 0 );

cv:=abs(Fh[1,1]);

if nFreqs>1 then

for k:=2 to nFreqs do

begin

cv1:=abs(Fh[1,k]);

if cvcp then

begin

a1:=tl; dh:=a2-a1; tl:=tp; tp:=a1+r*dh ; tt:=tp; cl:=cp;
j:=4;

end

else

begin

a2:=tp; dh:=tp-a1; tp:=tl; tl:=a1+r*r*dh; tt:=tl; cp:=cl;
j:=3;

end;

goto 106;

107:

if (iterI I?eeiaeaiea 2 - Oaeaeueiay yeaeo?e/aneay i?iaiaeeiinoue iaoa?eaeia I?eaaaeai naiaeeo ni?aai/iuo aeaiiuo niaeanii[7-9]. Iaoa?eae (min ,[INi/i] (max ,[INi/i] Iaiaaieoiua noaee 0.4 1.8 A?iicu (A?A, A?2, A?9) 6.8 17 Eaooie (EN59, EN62) 13.5 17.8 Iaaieaaua nieaau (IE5-IE15) 5.8 18.5 Oeoaiiaua nieaau (IO4, AO3-AO16) 0.48 2.15 Aethieieaaua nieaau (A95, Ae16, Ae19) 15.1 26.9 I?eeiaeaiea 4 - Abst(act The inverse eddy current problem can be described as the task of reconstructing an unknown distribution of electrical conductivity from eddy-current probe voltage measurements recorded as function of excitation frequency. Conductivity variation may be a result of surface processing with substances like hydrogen and carbon or surface heating. Mathematical reasons and supporting software for inverse conductivity profiling were developed by us. Inverse problem was solved for layered plane and cylindrical conductors. Because the inverse problem is nonlinear, we propose using an iterative algorithm which can be formalized as the minimization of an error functional related to the difference between the probe voltages theoretically predicted by the direct problem solving and the measured probe voltages. Numerical results were obtained for some models of conductivity distribution. It was shown that inverse problem can be solved exactly in case of correct measurements. Good estimation of the true conductivity distribution takes place also for measurement noise about 2 percents but in case of 5 percent error results are worse. PAGE 55

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