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Source text - French Messages
84
Supprimer : lorsque le téléphone affiche un
message vous demandant de confirmer la
suppression, appuyez sur la touche écran Oui. Pour
annuler la suppression, appuyez sur la touche écran
Non.
Messages préenregistrés (Menu 1.4)
Ce menu vous permet d'enregistrer jusqu'à neuf
messages utilisés fréquemment. Lorsque vous
accédez à ce menu, la liste des messages
préenregistrés s'affiche.
1. Faites défiler l'écran jusqu'au message voulu ou
jusqu'à une entrée vide en appuyant sur la
touche Haut ou Bas.
2. Appuyez sur la touche écran Sélect. et saisissez
un nouveau message ou modifiez l'ancien
message.
Pour plus d'informations sur la saisie des
caractères, reportez-vous à la page 39.
3. Appuyez sur la touche écran Ok pour enregistrer
le message.
Diffusion (Menu 1.5)
Ce service réseau vous permet de recevoir des
messages texte sur différents sujets, tels que la
météo ou la circulation. Les messages sont affichés
dès leur réception, sous réserve que :
• le téléphone soit en mode veille ;
• l'option Recevoir (Menu 1.5.2) soit réglée sur
Activé ;
• le canal des messages soit activé dans la liste des
canaux.
Messages
85
Lorsque vous obtenez des messages diffusion,
vous pouvez les consulter en mode veille. S'il s'agit
d'un message texte, vous pouvez vous reporter à
l'écran ; sinon, appuyez sur la touche écran CB
pour lire le message.
Dans l'option de menu Diffusion, les options
suivantes sont disponibles.
Lire : vous permet de lire les messages de diffusion
reçus.
Messages enregistrés : affiche la liste des messages
que vous avez enregistrés à partir de la liste des
messages actuels.
Messages actuels : affiche les derniers messages.
Ces messages sont supprimés lorsque le téléphone
est éteint.
S'il s'agit d'un message long, appuyez sur la touche
Haut ou Bas.
Lorsque vous lisez un message, appuyez sur la
touche écran Options pour accéder aux options
suivantes.
Couper numéro : affiche la liste des numéros inclus
dans le message.
Enregistrer : (messages actuels uniquement)
enregistre ce message dans la liste des archives.
Supprimer : supprime ce message.
Supprimer tout : supprime tous les messages de la
liste.
Recevoir : vous permet d'activer ou de désactiver
la réception des messages diffusés.
Canal : la coche devant Tous indique l'activation
du canal.
Pour activer ou désactiver ce canal, appuyez sur la
touche écran Sélect., puis sélectionnez Activer ou
Désactiver.
Translation - Romanian Ştergere: când telefonul afişează un mesaj cerând confirmarea ştergerii, apăsaţi tasta soft Da. Pentru a anula ştergerea, apăsaţi tasta soft Nu.
Mesaje predefinite (Meniu 1.4)
Acest meniu permite înregistrarea a până la nouă mesaje utilizate frecvent. La accesarea acestui meniu, se afişează lista mesajelor predefinite.
1. Parcurgeţi lista până la mesajul dorit sau până la o nouă înregistrare apăsând tasta Sus sau Jos.
2. Apăsaţi tasta soft Select. pentru a introduce un nou mesaj sau pentru a-l modifica pe cel deja existent.
Pentru informaţii suplimentare despre introducerea caracterelor, vezi pag. 39.
3. Apăsaţi tasta soft Ok pentru a salva mesajul.
Centru de informare (Meniu 1.5)
Această reţea de servicii permite primirea mesajelor text cu diferite subiecte, cum ar fi informaţiile meteo sau despre trafic. Mesajele sunt afişate încă de la primire, cu excepţia cazurilor când:
• telefonul este setat în modul inactiv;
• este activată opţiunea Primire (Meniu 1.5.2);
• canalul de mesaje este activat în lista canalelor.
După obţinerea mesajelor de informare consultarea acestora poate fi efectuată în modul inactiv. În cazul unui mesaj text puteţi reveni la ecran; în caz contrar apăsaţi tasta soft CB pentru a citi mesajul.
Pentru funcţia Centru de informare din meniu sunt disponibile următoarele opţiuni:
Citire: vă permite citirea mesajelor de difuzare primite.
Mesaje salvate: afişează lista mesajelor salvate începând cu lista mesajelor recente.
Mesaje recente: afişează ultimele mesaje. Aceste mesaje sunt şterse când telefonul este oprit. În cazul unui mesaj lung, apăsaţi tasta Sus sau Jos.
La citirea unui mesaj, apăsaţi tasta soft Opţiuni pentru a selecta următoarele opţiuni.
Extragere număr: afişează lista numerelor incluse în mesaj.
Salvare: (doar mesaje recente) salvează acest mesaj în arhivă.
Ştergere: şterge mesajul.
Ştergere toate: şterge toate mesajele de pe listă.
Primire : vă permite activarea sau dezactivarea primirii mesajelor de informare.
Canal : selectarea opţiunii Toate indică activarea canalului.
Pentru activarea sau dezactivarea acestui canal, apăsaţi tasta soft Select., apoi selectaţi Activare sau Dezactivare.
English to Romanian: Food Industry
Source text - English We have key members of staff from several nationalities and cultural backgrounds which helps us to understand and serve our partners in the best possible way. We are working closely with VF International in Paris and Brazil, and we are mainly focused on import into Europe and worldwide food and meat trading.
Our product range includes:
Pork; Fresh, cured, smoked and processed products, chilled and frozen.
Poultry; Chicken and Turkey, fresh, cooked, peppered and salted, chilled and frozen.
Beef; Fresh chilled and frozen cuts for retail and production use.
French fries, frozen.
Vegetables, frozen.
We build partnerships with our suppliers and give them the best possible sales channels and opportunities to discover and enter new markets with their products. We work closely together in order for them to understand our customer’s needs and to maintain a regular quality in each delivery.
Translation - Romanian Membrii cheie ai personalului nostru sunt de diverse naţionalităţi şi provin din medii culturale diferite, lucru ce ne permite să înţelegem şi să ne servim partenerii de afaceri în modul cel mai eficient posibil. Colaborăm îndeaproape cu VF International din Paris şi Brazilia, punând accentul îndeosebi pe importul în Europa şi comerţul global de produse alimentare şi carne.
Gama noastră de produse include:
• Produse din carne de porc: produse proaspete, sărate, afumate, refrigerate şi congelate.
• Produse din carne de pasăre: pui şi curcan proaspăt, gătit, piperat şi sărat, refrigerat şi congelat.
• Produse din carne de vită: bucăţi porţionate proaspăt refrigerate şi congelate pentru producţie şi comerţ cu amănuntul.
• Cartofi prăjiţi, congelaţi.
• Legume, congelate.
Încheiem parteneriate cu furnizorii noştri şi le oferim cele mai bune căi de vânzare precum şi oportunităţi de a descoperi şi de a pătrunde pe noi pieţe cu produsele lor. Colaborăm strâns împreună pentru ca ei să înţeleagă nevoile clientului şi pentru a menţine o calitate constantă pentru fiecare livrare.
Romanian to English: Electrotechnics: Research Project
Source text - Romanian Pentru inginer, una din motivaţiile fundamentale, în cadrul unei activităţi de cercetare, trebuie să fie dată de posibilitatea aplicării concrete şi cu utilitate a obiectului său de studiu şi activitate. Este motivul pentru care înainte de a începe descrierea domeniului vizat de mine, voi face o scurtă enumerare a ariilor de aplicabilitate pe care teoria problemelor electromagnetice inverse, şi rău definite, le materializează. În acest mod, îmi consider pe deplin justificată ingresiunea, cu urme benefice, în cadrul parcursului teoretic.
Construcţia aparatelor de zbor, a navelor maritime, a podurilor de metal, a reactoarelor nucleare, a conductelor de transport gaze naturale, toate necesită şi un proces de verificare, de testare a calităţii fabricatelor din procesele tehnologice. Mai exact, depistarea defectelor care, în cazul agravării lor în timpul funcţionării efective, ar putea conduce la efecte nefaste – şi aici e destul să fie amintite deteriorarea fuselajelor avioanelor în timpul zborului, scăparea de sub control a reactoarelor nucleare, sau transportul, cu pierderi, de fluide inflamabile.
Astfel, o modalitate de depistare a defectelor de material (crack detecting), printr-o tehnică neinvazivă, provine din aplicarea teoriei câmpului electromagnetic. Detectarea formei şi localizarea defectelor de material [H1], se poate realiza prin injecţia unor curenţi turbionari în corpurile materiale supuse studiului şi măsurarea modificării impedanţei [L2], sau măsurarea câmpului din jurul corpului [S2], ori modelarea defectelor ca şi dipoli electrici [P2], ori a incluziunilor sferice din materialele feromagnetice ca şi dipoli magnetici [B4]. Localizarea defectelor de material este o problemă intens cercetată, după criterii de clasificare a materialelor, a defectelor, a variantelor de modelare, a metodelor de calcul [C7], [H1]. Există astfel o bogată bibliografie dedicată: [I1], [A3], [A4], [R3], [T4], [T6], [T7], [T9], [B9], [B8].
Controlul automat al zborului unui aparat, predicţia traiectoriei acestuia, identificarea orientării faţă de un reper, devin realizabile prin scanări radar electromagnetice [K1]. Stabilirea profilului unui câmp magnetic care controlează un flux de plasmă, dintr-un anume proces tehnologic, în condiţiile în care temperaturile foarte ridicate nu permit măsurători directe [C5], [C6], sau mai mult, identificarea fluxului de plasmă într-un plasmatron [C3], localizarea submarinelor prin măsurători ale câmpului magnetic terestru [K2] sunt doar câteva exemple de identificare de obiecte (formă, poziţie, orientare, viteză), în medii inaccessibile (detecţia minelor, inspecţia subterană ori subacvatică, prospectarea geofizică), de configuraţii de câmpuri, de asemenea cu succes cercetate şi aplicate: [R3], [F1], [B7], [Ş1], [O2].
Încălzirea controlată a unor plăci subţiri [L1], sau într-un context mai general, prelucrarea complexă a prefabricatelor prin încălzire locală, constă în a determina un curent electric de inducţie care să realizeze o anumită distribuţie de temperatură corespunzătoare unui proces tehnologic. Determinarea distribuţiei de curent electric într-un film conductor, sau căutarea surselor de câmp în dispozitivele electronice constituie probleme de compatibilitate electromagnetică de sporit interes în asigurarea bunei funcţionări a echipamentelor electronice finale [T5]. Reconstrucţia formei de undă a curentului de întoarcere a trăznetelor din măsurători ale câmpului radiat de canalul de descărcare este o metodă de evaluare a perturbaţiilor electromagnetice, produse de trăznete, cu efect imediat simţit în supratensiuni induse în liniile de transport a energiei electrice, şi deci în menţinerea în parametrii nominali ai alimentării cu energie electrică [D2]. Evaluarea riscului magnetic pe care îl prezintă o navă maritimă (de a fi detectată) se face prin calculul magnetizării acesteia [C8], [C9], [C10]. Cunoaşterea distribuţiei curenţilor dintr-un cablu supraconductor care face parte dintr-un sistem pentru aplicaţii ale fuziunii nucleare, unde densităţiile de energie sunt foarte mari, devine posibilă prin măsurători de câmp în jurul acestui cablu [F1]. Eliminarea pericolului de explozie a conductelor de transport de fluide inflamabile, generat de încărcarea cu sarcină electrică a acestor conducte datorită curgerii fluidelor, se poate de asemenea înfăptui prin estimarea distribuţiei de sarcină electrică de încărcare şi anularea acesteia cu surse electrice corespunzatoare.
Evaluarea surselor de câmp neuromagnetic pentru înţelegerea activităţilor electrice neuronale din creierul uman [I1] sau a surselor de câmp bioelectromagnetic pentru înţelegerea activităţii electrice a inimii [B5], tratamentul medical al cancerului prin injecţia locală a unor câmpuri controlate [W1], obţinerea unei configuraţii optime a sistemului de curenţi care generează un câmp de formă şi valori exact prescrise pentru aplicaţiile medicale de tomografie [T2], diagnosticarea aritmiilor cardiace prin aflarea secvenţelor de activare cardiacă, făcută prin măsurători de potenţial electric de suprafaţă, o tehnică neinvazivă [W2], [W5], prevenirea infarctului miocardic, prin determinarea densităţii de curent pe suprafaţa epicardială a inimii [S7], exprimarea stării de hidratare a corpului uman prin calculul conductivităţii complexe a acestuia [W3], [W4], [B10], [W6], se constituie toate ca exemplificări esenţiale ale efectelor aplicative benefice, pe care ingineria biomedicală le produce, atunci când tratează probleme electromagnetice inverse.
Stabilirea gradului de coroziune al oţelului din structurile de fier – beton ale construcţiilor civile sau industriale, cu impact direct asupra duratei de viaţă, asupra consolidărilor necesare, asupra efectelor pe care curenţii vagabonzi le au, ţine de o tehnică de reconstrucţie a permeabilităţii magnetice prin tomografiere [S8]. De asemenea, reconstrucţia permitivităţii şi conductivităţii unor profile de materiale, situate în zone inaccesibile sau cu structură neomogenă [E3], [L3], ori determinarea distribuţiei de material fluid într-o conductă tehnologică sunt posibilităţi puse în aplicare prin apelul la modelarea electromagnetică inversă.
Optimizarea construcţiei unor dispozitive electromagnetice pentru obţinerea unor mărimi electrice dorite [E5], determinarea configuraţiei optime a spirelor unei bobine din ansamblul unui sistem de rezonanţă magnetică în imagistică [M2], dimensionarea unor generatoare de câmpuri magnetice variabile (configuraţia bobinelor şi variaţia curenţilor) [B9] sunt iarăşi aplicaţii îndeplinite din prisma problemelor inverse.
Materializarea tuturor acestor aplicaţii are la bază un trunchi comun, matematic şi electromagnetic. Mai precis, modelarea fenomenologică se foloseşte de instrumentele teoriei câmpului electromagnetic, iar soluţionarea problemei matematizate urmăreşte un set de principii, care se particularizează de la caz la caz.
Conceptul de problemă inversă, într-o descriere relativ simplă, poate fi redus la a determina mărimi geometrice, proprietăţi de material, sau mărimi electrice din cunoaşterea unor mărimi electrice măsurate. Ulterior, vor fi date definiri mai cuprinzătoare, fiind făcute şi trimiteri spre surse bibliografice bine conturate [M2], [H1], [G3].
În afara aplicaţiilor legate fenomenologic de electrotehnică, teoria problemelor inverse îşi extinde ramurile în arii vaste de acţiune: analiza seismică, detectarea tsunami-urilor [S4], tomografia geofizică, radioastronomie, reconstrucţia 3D din imagini 2D [B2], optica moleculară [S6],etc.
În termeni specifici teoriei câmpului electromagnetic, problemele inverse, primesc denumirea generică de probleme de sinteză, deşi nu există o conceptualizare standardizată în acest sens. Iar problema de sinteză este indisolubil legată de formularea problemei de analiză a câmpului electromagnetic.
Problema sintezei de câmp electromagnetic presupune că sunt cunoscute sau impuse următoarele condiţii:
1) câmpul electric şi/sau magnetic pe întreg domeniul sau pe un subdomeniu.
2) domeniul întreg sau o parte din domeniu (în sensul că se poate cere configuraţia frontierei pentru care anumite condiţii impuse să fie satisfăcute).
3) condiţiile de material pe întreg domeniul sau pe o parte a domeniului (condiţiile necunoscute intrând în categoria mărimilor ce urmează a fi determinate).
4) condiţiile la limită pe toate frontierele care mărginesc domeniul, sau numai pe o porţiune a lor, celelalte urmând a fi determinate.
5) condiţiile de surse în totalitate, parţial sau deloc.
În ipoteza că cele de mai sus sunt date, prin sinteza de proiectare se pot cere :
1) configuraţia optimă a frontierei necunoscute (precizăm că pe această frontieră condiţiile pot fi sau nu cunoscute apriori).
2) condiţiile de material pe anumite subdomenii.
3) condiţiile la limită pe unele frontiere.
4) condiţiile de surse, în totalitate sau parţial.
Nu prezintă o dificultate trasarea unor corelaţii între ipotezele şi cerinţele problemei de sinteză şi exemplificările practice enumerate în primul paragraf.
Orice problemă inversă a câmpului electromagnetic presupune parcurgerea unor etape specifice în procesul de rezolvare. Ponderea fiecărei etape în acest proces, ca şi gradul de dificultate pe care îl comportă diferă de la o problemă la alta. Aceste etape sunt prezentate pe scurt în cele ce urmează.
1. Stabilirea modelului fenomenologic (modelului fizic)
Această etapă presupune precizarea condiţiilor de unicitate cunoscute, precum şi a câmpului cunoscut (impus), de unde să rezulte cu claritate mărimile necunoscute care se cer a fi determinate în procesul sintezei. Asupra condiţiilor de unicitate ce trebuie impuse, domeniul de cercetare este în continuare deschis.
2. Stabilirea modelului matematic
Modelul matematic se formulează prin aplicarea legilor şi teoremelor câmpului electromagnetic. Astfel dacă legile câmpului electromagnetic sunt folosite sub forma lor diferenţială atunci se spune că modelul matematic este diferenţial, dacă legilor li se asociază funcţionale energetice echivalente, care urmează a fi minimizate, modelul se numeşte variaţional, iar dacă legile sunt folosite sub forma lor integrală se spune că modelul matematic este integral. Unui model fenomenologic i se poate aplica orice model matematic, dar în general există criterii obiective (legate de tipul problemei), sau subiective (legate de afinitatea rezolvitorului faţă de un anumit model) care fac ca un model să fie preferat.
3. Stabilirea metodei de prelucrare a modelului matematic
Metoda de prelucrare a modelului matematic poate fi analitică sau numerică. Metoda analitică se aplică prin rezolvarea efectivă a ecuaţiilor modelului matematic (în general diferenţial), fiind posibil de abordat doar probleme cu o anumită simetrie. Metoda de rezolvare cea mai adecvată este metoda separării variabilelor. [M2]
Metoda numerică de prelucrare este strâns legată de modelul matematic ales. Modelul matematic diferenţial presupune aplicarea metodei diferenţelor finite sau metodei Monte Carlo. Aplicaţii ale metodei Monte Carlo în mediu omogen şi neomogen sunt prezentate în [M2]. Metoda diferenţelor finite constă în aproximarea derivatelor cu mărimi computaţionale. Modelarea este facilă, însă efortul de calcul poate deveni costisitor în multe cazuri.
Modelul matematic variaţional impune folosirea ca metodă de prelucrare a metodei elementelor finite, în acest sens existând o metodă de trecere de la modelul de analiză la modelul de sinteză. Exemple în care se aplică cu succes metoda elementelor finite sunt pe direcţia identificării defectelor de material [H1].
Modelul matematic integral o dată ales, metoda de prelucrare numerică va fi metoda elementelor de frontieră [B12]. Utilizarea metodei elementelor de frontieră se aplică în problemele inverse de optimizare [E5], cu următoarele avantaje: modificarea formelor în procesele de optimizare implică doar modificarea nodurilor de frontieră; se poate obţine o relaţie directă între mărimile electrice sau magnetice de sintetizat şi valorile care se modifică prin optimizare, din ecuaţiile integrale de frontieră; efectele unor mici modificări ale nodurilor de frontieră asupra distribuţiei erorilor de calcul în zonele considerate sunt neglijabile. Se menţionează o aplicaţie de identificare a defectelor de material [T7] care se foloseşte de modelarea cu metoda elementelor de frontieră.
Prin raportare la terminologia de la teoria analizei [M4] se poate afirma că modelul matematic împreună cu metoda de prelucrare numerică formează modelul numeric de sinteză [M2].
Prin aplicarea modelului numeric de sinteză (oricare ar fi acesta) se ajunge la un sistem de ecuaţii liniare: [W1], [E4], [C4], [D3], [B4], [S6], [M2] sau neliniare: [A4], [H2], [B2], [R3], [B3]. Datorită faptului că matricea coeficienţilor conţine termeni foarte asemănători, în cazul sistemelor de ecuaţii liniare, sau vectorul efectelor – mărimilor măsurate, conţine termeni cvasi-identici, sau proporţionali, în ambele cazuri, caracterul problemelor este şi mai evident ca incorect formulat, sau rău condiţionat, cu soluţii neunice şi instabile.
4. Stabilirea metodei de sinteză
Metoda de sinteză se alege în funcţie de tipul sistemului rezultat după etapele anterioare. Când se ajunge la sisteme liniare de ecuaţii, soluţiile pot fi unice, dar inacceptabile în majoritatea cazurilor (nu se pot realiza fizic) sau pot fi o infinitate de soluţii. O tratare substanţială a metodelor de rezolvare a sistemelor de ecuatii liniare, pentru obţinerea pseudosoluţiilor se găseşte în [M2]. Dacă aceste variante de rezolvare a sistemelor de ecuaţii liniare nu dau rezultatele scontate, se recurge la regularizare [T1].
Regularizarea constă într-o echivalare a sistemului modelului matematic iniţial (sistem de ecuaţii) cu un model matematic sub formă de funcţională de minimizat şi care înglobează un parametru, numit de regularizare. O mare densitate a efortului de soluţionare se concentrează în acest punct, iar deschiderea cercetării este încă cerută. Metoda regularizării face un compromis între norma erorii sistemului (precizie) şi norma soluţiei (realizabilitate, stabilitate). În cazul sistemelor neliniare de ecuaţii, regularizarea ia forma unei metode iterative adaptate.
S-a făcut o descriere sumară a nivelului aplicativ şi a aparatului teoretic pe care acest nivel se fundamentează, în domeniul problemelor inverse electromagnetice. Până în prezent, aplicaţii de tipul celor exemplificate mai sus, se abordează din prisma urmăririi structurii de modelare în etapele de sinteză menţionate. O atenţie deosebită se îndreaptă asupra procesului matematic de regularizare efectivă, de soluţionare într-un sens tehnic optim a sistemelor de ecuaţii. Nu se neglijează însă deloc nici punerea condiţiilor de unicitate, în etapa construirii modelului fenomenologic, alegerea adecvată şi implementarea eficientă computaţional a metodei de prelucrare a modelului matematic. În aceste direcţii alternativele de acţiune se pretează încă cercetării continue. Identificarea de noi aplicaţii, în domeniul sintezei circuitelor electrice, a sintezei cuadripolilor diporţi apare iarăşi o poartă deschisă studiului creativ.
În contextul în care deja am abordat un spectru bibliografic cuprinzând peste 80 de articole I.E.E.E, COMPEL, S.I.A.M., Inverse Problems, şi mai multe cărţi de referinţă care tratează orientat rezolvarea problemelor inverse incorect formulate, o primă contribuţie asumată va fi aceea a realizării unei monografii teoretice care să cuprindă, în mod original aspecte esenţiale întâlnite în aparatul matematic al problemelor inverse electromagnetice incorect formulate. Se va încerca o construcţie cu caracter unitar, care să servească drept ghid în parcursul teoretic de rezolvare a problemelor din domeniu.
Pe măsura conturării demersului anterior se are în vedere introducerea elementelor regularizante în faza de modelare matematică, când această modelare se reduce la ecuaţii integrale Fredholm de speţa întâi. În acest fel, apar ca alternative directe de continuare a rezolvării o serie de metode numerice clasice, fără a se mai face apel la metodele de prelucrare numerică de tipul celor menţionate în primul capitol, care au un cost computaţional ridicat.
În etapa efectivă de regularizare a sistemelor de ecuaţii liniare se va propune o extindere a aplicării filtrului Tikhonov. Ideea porneşte de la acceptarea ca validă a combinaţiei metodelor de descompunere după valorile proprii şi a regularizării Tikhonov clasice. Pentru testare se vor alege mai multe aplicaţii din cele enumerate în primul capitol.
O altă temă vizată este aceea a întăririi punţii de legătură între funcţionala regularizantă exprimată matriceal şi cea recent propusă ca fiind echivalenta ei statistică [B13]. Atât pe calea matriceală, cât şi pe cea de calcul statistic se va re-evalua inventarul de metode numerice posibile de folosit, pe baza constatării că o atenţie mai puţin intensă a fost acordată până acum spre această chestiune.
Contribuţia întrevăzută a fi cea mai importantă se va axa pe construirea unui sistem expert, care să conţină metodele actuale de alegere a parametrului de regularizare (principiul discrepanţei, criteriul de cvasi-optimalitate, validarea în cruce, criteriul curbei L şi variantele conexe, funcţionala Miller, metoda coeficienţilor binomiali), principii verificate experimental de selecţie a uneia dintre metode, în funcţie de modelul numeric de prelucrare, în funcţie de clasa de aplicaţie, în funcţie de efortul computaţional. Se va căuta şi demonstrarea posibilităţii de combinare a unora dintre metodele de alegere a parametrului de regularizare. De asemenea, atât cu apel la paleta alternativă larg denunţată de calcul al parametrului de regularizare, cât şi pe cale ideatică se va demonstra avantajul existenţei acestui parametru ca un factor de control, ca un mod flexibil de soluţionare optimă a problemelor electromagnetice inverse incorect formulate.
Mai departe, în sfera problemelor neliniare, problema filtrului regularizant, va fi abordată din perspectiva rezolvării succesive a unor probleme liniare, aspect încă puţin dezbătut.
Se observă că preponderenţa contribuţiilor potenţial asumate se situează într-o delimitare teoretică. Ar fi greşit să se creadă însă că parcursul proiectului va fi lipsit de testări aplicative, de incursiuni concrete în probleme practice cu finalitate. În conştienţă cu baza materială real existentă şi cu previziuni de îmbunătăţire a ei, se vor aborda probleme de identificare de defecte de material, probleme de identificare a efectelor trăznetelor asupra liniilor de transport a energiei electrice, probleme de sinteză a unor dispozitive de câmp şi proiectare adaptată a unor cuadripoli din instalaţiile de simetrizare şi compensare a energiei electrice reactive.
Rezultatele cercetării propuse în cadrul acestui proiect trebuie să se dovedească utile, să servească unor scopuri întruchipate de aplicaţii practice ale problemelor electromagnetice inverse incorect formulate. Aşa cum s-a arătat în obiectivele şi activităţile propuse pentru desfăşurarea proiectului, caracterul teoretic al cercetării se încearcă a fi apropiat de necesităţile concrete de rezolvare prin implementări soft. Ţine de autorul proiectului această înclinaţie înspre abordarea teoretică, însă îşi gaseşte justificare solidă în perspectivele deschise şi încă inconsistent fundamentate, pe care teoria problemelor inverse electromagnetice le oferă.
Documentarea pentru înţelegerea şi însuşirea stadiului actual al cunoaşterii în domeniu, aşa cum s-a precizat anterior, a avut în vedere un spectru bibliografic de nivel înalt, iar parcursul abordării a fost permanent însoţit de încercări şi tratări alternative ale celor studiate – aspecte materializate în discuţii colegiale, lucrări propuse studenţilor pentru simpozioane adresate lor, trei articole trimise la conferinţe de prestigiu şi poate cea mai importantă chestiune, stabilirea de contacte cu personalităţi de referinţă din domeniu.
Se intenţionează păstrarea aceluiaşi spirit de acţiune. În continuare, discuţiile în Catedră vor fi forma primară de dezbatere a ideilor în lucru, puntea de propulsie pentru publicarea de lucrări ştiinţifice, sprijinul în derularea activităţilor practice propuse. Se consideră înţeles implicit faptul că orice finalizare a unui obiectiv, dintre cele menţionate, va fi însoţită de câte un raport tehnic asupra conţinutului şi modului de abordare. Nu se va renunţa la colaborarea şi îndrumarea studenţilor interesaţi, această activitate fiind generatoare de mari satisfacţii şi cu un potenţial formativ ridicat.
Terminarea cu succes a propunerilor vizate în acest proiect va impulsiona promovarea obiectelor cercetării, în mediul academic prin notificări şi rapoarte, în mediul industrial potenţial interesat prin prezentări orientate. Se va încerca întărirea legăturii cu cercetătorii de referinţă din domeniu şi lansarea unor direcţii de colaborare. Proiectul şi rezultatele obţinute trebuie să crească prestigiul instituţiei la care autorul aparţine.
Efortul desăvârşirii unei teze de doctorat va fi bine susţinut de activitatea asumată pentru realizarea prezentului proiect, însă în nici un caz nu se va opri o dată cu predarea acestei teze. Implicarea în domeniul soluţionării problemelor inverse poate şi se vrea a fi continuată pe termen lung.
Ca şi până acum, rezultatele cercetării vor fi înglobate în lucrări ştiinţifice adresate unor conferinţe cu tematică mai largă şi amplasare locală, însă ca ţinte principale vor fi urmărite acele conferinţe specifice domeniului, acele publicaţii de specialitate, în care aprecierea lucrărilor să fie just exprimată, şi pentru care pregătirea necesită experienţa lucrărilor şi articolelor de dinainte (IEEE Transaction on Magnetics, Inverse Problems, COMPEL, Revue Roumaine des sciences techniques, Analele Universitatii din Oradea, Acta Electrotehnica Cluj-Napoca).
În dimensionarea bugetului au fost luate în considerare sume minime pentru retribuţia muncii de cercetare, în favoarea cheltuielilor de valorificare a rezultatelor, de publicare de articole, de editarea unor broşuri informative prin care să se promoveze rezultatele în mediul industrial potenţial interesat. De asemenea, o componentă de cost substanţială a fost alocată achiziţionării materialelor care vor face obiectul testării algoritmilor propuşi, precum şi consilierii software pentru punerea în aplicare a sistemului expert de alegere a parametrului de regularizare.
Instituţia aparţinătoare, Universitatea Tehnică din Cluj-Napoca, Departamentul de Electrotehnică, deţine o bază materială suficient de echipată cu mijloace şi personal ajutător, astfel încât să nu fie necesare, pe durată desfăşurării proiectului, achiziţii în domeniu. Eventuale rezultate băneşti acele obiectelor acestui proiect, vor viza şi achiziţii pentru dotarea ulterioară a laboratoarelor. Se dă o listă a echipamentelor existente în laboratoarele de Electrotehnică, din instituţia menţionată, şi la care accesul doctoranzilor aparţinători este nelimitat:
Implicarea colegilor din colectivul Catedrei, precum şi din celelalte colective va consta în cercuri de discuţii periodice, în colaborări pentru scrierea unor articole în care domeniile de competenţă se intersectează şi pot interacţiona activ şi util.
Prezenta propunere de proiect are stabilite ca obiective realizarea a trei produse. Primul obiect, nematerial, dar cuantifiabil, ar fi acela a realizării unei structuri de teoretice de calcul, prin care pornind de la modelul ecuaţiei integrale Fredholm, să se aplice direct un porces de regularizare, fără a mai apela ca etapă intermediară la o funcţională regularizantă. Acesta ar fi un modul implementabil de soluţionare alternativă a problemelor electromagnetice inverse care se reduc la ecuaţii integrale Fredholm.
Al doilea obiect, de data aceasta material, ar fi construcţia teoretică şi soft a unui sistem expert de alegere a parametrului de regularizare, după condiţii multicriteriale, bazate pe experienţa anterioară a aplicării metodelor de selectare a parametrului. Tot în cadrul obiectivului propus pentru realizarea acestui al doilea obiect, se va încerca sinteza de câmp magnetic a unui dispozitiv din sistemele de rezonanţă magnetică în imagistică. Acest dispozitiv, va fi un obiect palpabil al rezultatelor cercetării, cu rol de prototip de promovare în primul rând a metodei de soluţionare prin sistemul expert; va fi un garant al reuşitei sistemului expert.
Cercetarea ştiinţifică trebuie să aibă ca scop final, mai apropiat sau mai îndepărtat, aplicarea în practică a rezultatelor obţinute. În domeniul electrotehnic materializarea unor teorii rezultate prin cercetare ştiinţifică se face prin activitatea de proiectare. Cel care proiectează dispozitive electrotehnice trebuie să aibă la dispoziţie algoritmi bine determinaţi şi siguri pentru orice situaţie. La nivelul actual al tehnicii de calcul activitatea de proiectare este în strânsă legătură cu sinteza câmpului electromagnetic, în sensul că foarte multe probleme de proiectare sunt formulate în termeni specifici sintezei de câmp electromagnetic.
Mediul de lucru se va caracteriza printr-o atmosferă deosebit de cooperantă şi cordială, fapt care va influenţa pozitiv rezultatele obtinute.
Toate sursele cercetate vor fi referite corespunzator în bibliografii, fără ca vreun singur element străin activităţii de cercetare propuse să fie asumat.
Translation - English The prospect of practical applications of study must be one of the primary motivations of an engineer while conducting research work. It is the reason why, before proceeding to the description of my designated field, I will make a short list of applicability areas materialized by the inverse, and ill-defined, electromagnetic problem theory. Thus, I consider my ingression as fully justified, with beneficial outcomes throughout the theoretical course.
The construction of aircrafts, ships, metal bridges, nuclear reactors, or gas pipes, all require a verifying process, the quality testing of technological products. More precisely, it is necessary to detect flaws that, in case of worsening during their use, could lead to ill-fated consequences – and it suffices to take into account the deterioration of plane fuselage during flight, the loss of control over nuclear reactors, or the transport, with leaks, of inflammable fluids.
Thus, a non invasive method of crack detecting comes from applying the electromagnetic field theory. The detection of the form and the localization of material flaws [H1] can be achieved by injecting eddy currents in the material objects under study and by measuring the impedance variation [L2], or the field surrounding the object [S2], or by modeling the flaws as electrical dipoles [P2], or by spherical insertions of ferromagnetic material, such as magnetic dipoles. [B4]. Crack detecting is a highly researched problem, under the criteria of classification of materials, defects, modeling options, and calculation methods [C7], [H1]. Therefore, there is an extended bibliography dedicated to it: [I1], [A3], [A4], [R3], [T4], [T6], [T7], [T9], [B9], [B8].
The automatic control over the flight of an aircraft, the prediction of its trajectory, and the identification of its course toward a certain point of reference – all can be achieved with the help of electromagnetic radar scanning [K1]. Establishing the profile of a magnetic field controlling a plasma flux, in a certain technical process, when extremely high temperatures do not allow direct measurements [C5], [C6], or more, the identification of the plasma flux in a plasmatron [C3], the detection of submarines by measuring the terrestrial magnetic field [K2] are just a few examples of the identification of objects (form, location, course, speed), in inaccessible environments (mine detecting, underground or underwater inspection, geophysical prospecting), and of field configurations, also successfully researched and applied: [R3], [F1], [B7], [Ş1], [O2].
The controlled heating of thin plates [L1], or in a more general context, the complex manufacture of prefabs using local heating, resides in establishing inductive currents that would achieve a certain temperature distribution adequate to a technical process. To determine the power distribution in a conductive film, or to search field generators in electronic devices, amounts to electromagnetic compatibility problems of high interest to ensuring the good function of final electronic equipment [T5]. Reshaping the wave of a lightning return stroke from measurements of the field radiated by the discharge channel is a method of evaluating electromagnetic disturbances caused by lightning, with the immediate consequence of high tensions inducted in the power lines, and therefore in maintaining nominal parameters of the power supply [D2]. The evaluation of the magnetic risk of a ship (of being detected) is made by the calculation of its magnetization C8], [C9], [C10]. Knowledge of the power distribution in a superconductor cable, part of an application system of nuclear fusion, where energy densities are very high, becomes possible by running field measurements around this cable [F1]. The risk of explosion of inflammable fluid conduits, generated by the electric charge of these pipes due to the flow of the fluids, can also be eliminated by estimating the distribution of the loading charge and by canceling it using adequate electric generators.
The evaluation of neuromagnetic field generators from the human brain [I1] or of the bioelectromagnetic field generators for understanding the electric activity of the heart [B5], the medical treatment of cancer by the local injection of controlled fields [W1], obtaining the optimum configuration of a system of currents generating a field of rigorously prescribed form and values for medical tomography applications [T2], the diagnose of cardiac arrhythmias by finding out the cardiac activation sequences, achieved by measuring the electric surface potential, a non invasive technique [W2], [W5], the prevention of myocardic infarction by determining the power density on the epicardic surface of the heart [S7], the expression of the degree of hydration of the human body by calculating its complex conductivity [W3], [W4], [B10], [W6], all constitute essential examples of beneficial applicative consequences produced by biomedical engineering, when dealing with inverse electromagnetic problems.
Establishing the corrosion degree of steel in reinforcing iron structures of civil or industrial buildings, with direct impact on durability, on necessary consolidations, on the effects of errant currents, is connected to a reconstruction technique of magnetic permeability by tomography [S8]. Also, the reconstruction of the permissiveness and conductivity of some material profiles situated in inaccessible areas or with an inhomogeneous structure [E3], [L3], or the determination of fluid matter distribution in a conduit, are solutions applied by using inverse electromagnetic modeling.
The optimization of the construction or electromagnetic devices for obtaining the required electric values [E5], the determination of the optimum configuration of the spires of a coil in the ensemble of a magnetic resonance system in Imagistic [M2], the shaping of variable magnetic field generators (the coil configuration and the current variation) [B9] are again applications carried out from the perspective of inverse problems.
The materialization of all these applications is based on a common mathematic and electromagnetic foundation. More precisely, phenomenological modeling uses the instruments of electromagnetic field theory, and the solving of the mathematized problem follows a set of principles, particularized according to the circumstances.
The concept of inverse problem, in a relatively simple description, can be reduced to determining geometrical values, material properties, or electrical values on the basis of given data. Subsequently, more comprehensive definitions will be given, also by making references to well outlined bibliographical sources [M2], [H1], [G3].
Other than the applications phenomenologically linked to Electrotechnics, the inverse problem theory branches out in vast areas of action such as seismic analysis, tsunami detection, geophysical tomography, radioastronomy, 3D reconstruction from 2D images [B2], molecular optics [S6], etc.
In terms specific to electromagnetic field theory, inverse problems acquire the generic name of synthesis problems, although there is no standard conceptualization in this respect. And the synthesis problem is indissolubly connected to formulating the electromagnetic field analysis problem.
The electromagnetic field synthesis problem requires that the following conditions are known or mandatory:
1) electric and/or magnetic field on the entire domain or subdomain.
2) entire domain or a part of the domain (in the sense that one can ask for the frontier configuration for which certain mandatory conditions are to be met).
3) material conditions on the entire domain or part of it (indefinite conditions fit in the category of measurements to be determined).
4) limit conditions on all frontiers of the domain, or just on a portion of them, the rest are to be determined.
5) source conditions totally, partially or not at all.
Presuming that the above data is given, the project synthesis can ask for:
1) optimum configuration of the indefinite frontier (to be noted that the conditions on this frontier may or may not be known apriori).
2) material conditions on certain subdomains.
3) limit conditions on some frontiers.
4) source conditions, totally or partially.
There is no difficulty in correlating the hypotheses and cerinte of the synthesis problem with the practical examples listed in the first paragraph.
Any inverse problem of the electromagnetic field requires certain specific stages during the solving process. The weight of every stage in this process, as the difficulty degree that it involves, differs from one problem to another. These stages are shortly presented in what follows.
1. Establishing the phenomenological model (the physical model)
This stage requires stating the given conditions of uniqueness, as well as of the given (mandatory) field, from which the indefinite values that need to be determined throughout the synthesis process clearly result. The research field is still open on the mandatory uniqueness conditions.
2. Establishing the mathematic model
The mathematic model is formulated by applying electromagnetic field laws and theorems. Thus, if the electromagnetic field laws are used under their differential form, then it is said that the mathematic model is differential. If energetic equivalent functionals to be minimized are associated to the laws, the model is called variational. And if the laws are used in their integral form, it is said that the mathematic model is integral. Any mathematic model can apply to a phenomenological one, but generally there are objective criteria (having to do with the type of problem), or subjective ones (having to do with the affinity of the solver towards a certain model) that make a certain model to be preferred.
3. Establishing the processing method of the mathematic model
The processing method of the mathematic model can be analytic or numeric. The analytic method is applied by actually solving the equations of the mathematic model (generally differential), allowing only the approach of problems with a certain symmetry. The most adequate solving method is the variables separation method. [M2]
The numeric processing method is closely linked to the chosen mathematic model. The differential mathematic model requires applying the finite differences method or the Monte Carlo method. Applications of the Monte Carlo method in homogenous and inhomogeneous environments are presented in [M2]. The finite differences method resides in approximating the derivatives with computational values. Modeling is trouble-free, but the calculation effort can become costly in a lot of cases.
The variational mathematic model requires the use of the finite elements method as a processing method; in this respect, there is a method of shifting from the analysis model to the synthesis model. Examples of the successful application of the finite elements method are in the direction of crack detecting [H1].
The integral mathematic model once chosen, the numeric processing method will be the frontier element method [B12]. The usage of the frontier element method applies in the inverse problems of optimization [E5], with the following advantages: the modification of forms in optimization processes involves only the modification of the frontier nods; one can obtain a direct relation between the electric or magnetic values modified through optimization, from the frontier integral equations; the effects of slight changes of frontier nods over the calculation errors distribution in the considered areas are negligible noted that there is a crack detecting application [T7] used in modeling with the frontier elements method.
By reference to the analysis theory terminology [M4] it can be stated that the mathematic model together with the numeric processing method form the numeric synthesis model [M2].
By applying the numeric synthesis model (whichever that is) one obtains a linear equations system: [W1], [E4], [C4], [D3], [B4], [S6], [M2] or a non linear equations system: [A4], [H2], [B2], [R3], [B3]. Due to the fact that the coefficient matrix contains very similar terms, in the case of linear equations, or the effect vector of the given measurements contains quasi-identical or proportional terms, in both situations, the characteristic of the problem is even more obviously ill-defined, or badly conditioned, resulting in unstable non exclusive solutions.
4. Establishing the synthesis method
The synthesis method is chosen according to the type of system resulted after the previous stages. When the result is a linear system of equations, the solutions can be unique, but unacceptable in most cases (they are not physically viable) or there can be an infinity of solutions. A substantial treatment of solving methods of linear equations systems to obtain pseudosolutions can be found in [M2]. If these solving options of linear equations systems do not provide the expected results, one resorts to regularization [T1].
Regularization resides in equivalating the system (of equations) of the initial mathematic model with a mathematic model under the form of a functional to minimize and that contains a parameter, called regularization. A great density of solving effort is focused on this point and the opening of research is still on demand. The regularizationmethod compromises between the system error norm (precision) and the solution norm (viability, stability). In the case of non linear systems of equations, regularization takes the form of an adapted iterative method.
A brief description has been made of the applicative level and of the theoretical apparatus on which this level is based, in the field of inverse electromagnetic problems. Up to the present moment, applications such as the ones given as examples above are approached from the perspective of following the modeling structure in the mentioned synthesis stages. Special attention is given to the mathematic process of actual regularization, of solving equation systems in a optimum technical direction. However, the meeting of the uniqueness conditions in the stage of the construction of the phenomenological model, or the adequate choice and the computationally efficient implementation of the mathematic model processing method, are far from being neglected. In these directions alternatives of action still allow continuous research. Identifying new applications in the field of electric circuits synthesis or quadripole synthesis appears again to be an open gate to creative study.
In the context where a large bibliographical spectrum comprising over 80 I.E.E.E, COMPEL, S.I.A.M., Inverse Problems articles, and several reference books that treat the solving of ill-defined inverse problems in an oriented manner has already been approached, a first assumed contribution will be the writing of a theoretical monography that would comprise, in an original way, essential aspects of the mathematic apparatus or ill-defined inverse electromagnetic problems. An attempt will be made to devise it as a unitary construction, which would serve as guide in the theoretical course of solving the problems in the field.
While working to achieve the precedent goal, an introduction of regularizing elements in the stage of mathematic modelling is envisaged, when this modelling comes down to first class Fredholm integral equations. Thus, a series of classical numeric methods appear as direct alternatives of continuing to solve the problem, without having to resort to the numeric processing methods mentioned in the first chapter, which have a high computational cost.
In the actual regularization stage of the linear equation systems an extension of the Tikhonov filter application will be recommended. The idea comes from accepting as valid the combination of decomposition methods according to proper values and the classical Tikhonov regularization. For testing, several applications will be chosen out of those mentioned in the first chapter.
Another envisaged theme is that of consolidating the link between the regularizing functional expressed by a matrix and the one recently put forward as being its statistic equivalent [B13]. A re-evalution of the inventory of possible useful numeric methods will be made, both following the matrix way and that of statistic calculation, on basis of the finding that less attention has been given to this issue.
The contribution foreseen as being the most important will be centred on devising an expert system, comprising the actual methods of choosing the regularization parameter (the discrepancy principle, the quasi-optimality criterion, the cross validation, the L curve criterion and the connected variants, the Miller functional, the binomial coefficients method), principles of method selection experimentally verified, according to the numeric processing model, according to the application class, and to the computational effort. An attempt will be made to demonstrate the possibility of combining some of the methods of choosing the regularization parameter. Also, the advantage of this parameter’s existence as a control factor will be demonstrated, both by resorting to the wide range of mentioned calculation alternatives of the regularization parameter, and via the ideatic approach, as a flexible means of optimum solving of ill-defined inverse electromagnetic problems.
Furthermore, in the field of non linear problems, the regularizing filter problem will be approached from the perspective of successive solving of linear problems, aspect that has yet been less debated upon.
It is noted that a large part of the potentially assumed contributions lie within a theoretical limit. Nonetheless, it would be a mistake to assume that the project course will lack applicative testings, concrete incursions in problems that have a practical aim. In accordance to the real material basis and to previsions of its improvement, problems of crack detecting, of the identification of thunderbolt effects over electric wires, of synthesizing field devices and adapted projection of quadripoles from reactive energy symmetrization and compensation equipment installation devices will be approached.
The results of the research undertaken during this project must prove useful, serving aims embodied by practical applications of ill-defined inverse electromagnetic problems. As shown by the objectives and activities put forward for the development of the project, the theoretical characteristic of the research tries to approach the concrete solving necessities by soft implementations. This inclination towards a theoretical approach belongs to the author of the project, but it is highly justified in the open and still inconsistently established perspectives provided by the inverse electromagnetic problem theory.
As previously stated, the documenting process for understanding and appropriating the current stage if knowledge in the field has had in view a bibliographical spectrum of high level, and the course of the approach has been permanently accompanied by alternative attempts and treatment of the studied material – aspects materialized in collegial debates, in papers recommended to students for symposiums addressed to them, in three articles sent to prestigious conferences and, perhaps the most important issue, in making contacts with personalities of reference in the field.
It is intended to keep the same spirit of action. To continue with, Chair discussions will make up the prime form of debating ideas in progress, the propulsion means for publishing scientific papers, and the support in the implementation of the nominated practical activities. That any completion of a mentioned objective will be accompanied by a technical report over its content and approach method is considered to be implicit. Collaboration and guiding interested students will not be given up upon, this activity generating great satisfaction and having a high formative potential.
The successful accomplishment of the propositions made in this project will stimulate the promotion of the objects of study, in the academic environment by reports and notifications, and in the potentially interested by oriented demonstrations. Attempts will be made to fasten the bond with reference researchers in the field and to initiate further collaborations. The project and its results must increase the prestige of the institution to which the author belongs.
The effort of completing a doctoral thesis will be well supported by the activity undertaken to accomplish the present project, but under no circumstances will it end once this thesis is handed in. The involvement in the field of inverse problem solving can and is desired to be continued on a long term.
As before, the research results will be incorporated in scientific papers that target local conferences with wider thematic, but the main targets will be those field specific conferences, those specialist publications where the evaluation of the works would be fairly expressed and for the preparation of which the experience of previous researches and articles would be necessary (IEEE Transaction on Magnetics, Inverse Problems, COMPEL, Revue Roumaine des sciences techniques, Analele Universitatii din Oradea, Acta Electrotehnica Cluj-Napoca).
Minimum sums of money have been taken into consideration for the retribution of research work, in favor of expenses for turning the results into account, article publishing, and the editing of informative brochures that would promote the results in the potentially interested industrial environment. Likewise, a substantial part of the cost was allocate for the acquisition of the materials that will constitute the object of testing of the nominated algorithms, as well as for the software advisers for the application of the expert system of regularizing parameter selection.
The affiliated institution, the Technical University in Cluj-Napoca, the Electrotehnics Departament, holds a material basis sufficiently equipped with auxiliary means and personel so that further aquisitions in the field would not become necessary. Possible financiary outcomes of the objects of this project will furthermore have in view acquisitions for the subsequent endowment of laboratories. A list of existing equipment in the electrotehnica laboratories of the mentioned institution, to which doctorands have a limited access, is given.
The involvement of the colleagues from the Chair staff, and from the other staffs as well will reside in periodical debate cercles, in collaborations in the writing of articles where the fields of competence intersect and can actively and usefully interact.
The present project proposition has set as objectives the accomplishment of three products. The first immaterial but quantifiable object would be the creation of a theoretical calculation structure, by which, using the Fredholm integral equation model, a direct regularization process could be applied, without resorting to a regularizing functional as an intermediate stage. This would be an implementable module of alternative solving of inverse electromagnetic problems that are reduced to Fredholm integral equations.
The second object, this time a material one, would be the soft and theoretical devise of an expert selection system of the regularizing parameter, under multicriterial conditions, based on the previous experience of applying parameter selection methods. Within the same objective an attempt will be made to synthesize the magnetic field of a device from the magnetic resonance systems in Imagistic. This device will be a palpable object resulted from the research, that would function as a prototype promoting first of all the expert system solving method; it will be a guarantee of the success of the expert system.
Scientific research must have as final, more or less immediate goal, the practical application of the results. In the field of Electrotechnics the materialization of theories obtained through scientific research is achieved through the designing activity. The designer of electrotechnical devices must have at hand well determined and safe algorithms for any situation. At the present level of computer technology the designing activity is closely related to the electromagnetic field synthesis, in that a lot of designing problems are formulated in terms specific to the electromagnetic field synthesis.
The work environment will be characterized by an extremely cooperant and cordial atmosphere, which will have a positive influence over the results.
All researched sources will be adequately referred to in bibliographies, without claming a single element that has not been discovered in the course of the designated research.
The prospect of practical applications of study must be one of the primary motivations of an engineer while conducting research work. It is the reason why, before proceeding to the description of my designated field, I will make a short list of applicability areas materialized by the inverse, and ill-defined, electromagnetic problem theory. Thus, I consider my ingression as fully justified, with beneficial outcomes throughout the theoretical course.
The construction of aircrafts, ships, metal bridges, nuclear reactors, or gas pipes, all require a verifying process, the quality testing of technological products. More precisely, it is necessary to detect flaws that, in case of worsening during their use, could lead to ill-fated consequences – and it suffices to take into account the deterioration of plane fuselage during flight, the loss of control over nuclear reactors, or the transport, with leaks, of inflammable fluids.
Thus, a non invasive method of crack detecting comes from applying the electromagnetic field theory. The detection of the form and the localization of material flaws [H1] can be achieved by injecting eddy currents in the material objects under study and by measuring the impedance variation [L2], or the field surrounding the object [S2], or by modeling the flaws as electrical dipoles [P2], or by spherical insertions of ferromagnetic material, such as magnetic dipoles. [B4]. Crack detecting is a highly researched problem, under the criteria of classification of materials, defects, modeling options, and calculation methods [C7], [H1]. Therefore, there is an extended bibliography dedicated to it: [I1], [A3], [A4], [R3], [T4], [T6], [T7], [T9], [B9], [B8].
The automatic control over the flight of an aircraft, the prediction of its trajectory, and the identification of its course toward a certain point of reference – all can be achieved with the help of electromagnetic radar scanning [K1]. Establishing the profile of a magnetic field controlling a plasma flux, in a certain technical process, when extremely high temperatures do not allow direct measurements [C5], [C6], or more, the identification of the plasma flux in a plasmatron [C3], the detection of submarines by measuring the terrestrial magnetic field [K2] are just a few examples of the identification of objects (form, location, course, speed), in inaccessible environments (mine detecting, underground or underwater inspection, geophysical prospecting), and of field configurations, also successfully researched and applied: [R3], [F1], [B7], [Ş1], [O2].
The controlled heating of thin plates [L1], or in a more general context, the complex manufacture of prefabs using local heating, resides in establishing inductive currents that would achieve a certain temperature distribution adequate to a technical process. To determine the power distribution in a conductive film, or to search field generators in electronic devices, amounts to electromagnetic compatibility problems of high interest to ensuring the good function of final electronic equipment [T5]. Reshaping the wave of a lightning return stroke from measurements of the field radiated by the discharge channel is a method of evaluating electromagnetic disturbances caused by lightning, with the immediate consequence of high tensions inducted in the power lines, and therefore in maintaining nominal parameters of the power supply [D2]. The evaluation of the magnetic risk of a ship (of being detected) is made by the calculation of its magnetization C8], [C9], [C10]. Knowledge of the power distribution in a superconductor cable, part of an application system of nuclear fusion, where energy densities are very high, becomes possible by running field measurements around this cable [F1]. The risk of explosion of inflammable fluid conduits, generated by the electric charge of these pipes due to the flow of the fluids, can also be eliminated by estimating the distribution of the loading charge and by canceling it using adequate electric generators.
The evaluation of neuromagnetic field generators from the human brain [I1] or of the bioelectromagnetic field generators for understanding the electric activity of the heart [B5], the medical treatment of cancer by the local injection of controlled fields [W1], obtaining the optimum configuration of a system of currents generating a field of rigorously prescribed form and values for medical tomography applications [T2], the diagnose of cardiac arrhythmias by finding out the cardiac activation sequences, achieved by measuring the electric surface potential, a non invasive technique [W2], [W5], the prevention of myocardic infarction by determining the power density on the epicardic surface of the heart [S7], the expression of the degree of hydration of the human body by calculating its complex conductivity [W3], [W4], [B10], [W6], all constitute essential examples of beneficial applicative consequences produced by biomedical engineering, when dealing with inverse electromagnetic problems.
Establishing the corrosion degree of steel in reinforcing iron structures of civil or industrial buildings, with direct impact on durability, on necessary consolidations, on the effects of errant currents, is connected to a reconstruction technique of magnetic permeability by tomography [S8]. Also, the reconstruction of the permissiveness and conductivity of some material profiles situated in inaccessible areas or with an inhomogeneous structure [E3], [L3], or the determination of fluid matter distribution in a conduit, are solutions applied by using inverse electromagnetic modeling.
The optimization of the construction or electromagnetic devices for obtaining the required electric values [E5], the determination of the optimum configuration of the spires of a coil in the ensemble of a magnetic resonance system in Imagistic [M2], the shaping of variable magnetic field generators (the coil configuration and the current variation) [B9] are again applications carried out from the perspective of inverse problems.
The materialization of all these applications is based on a common mathematic and electromagnetic foundation. More precisely, phenomenological modeling uses the instruments of electromagnetic field theory, and the solving of the mathematized problem follows a set of principles, particularized according to the circumstances.
The concept of inverse problem, in a relatively simple description, can be reduced to determining geometrical values, material properties, or electrical values on the basis of given data. Subsequently, more comprehensive definitions will be given, also by making references to well outlined bibliographical sources [M2], [H1], [G3].
Other than the applications phenomenologically linked to Electrotechnics, the inverse problem theory branches out in vast areas of action such as seismic analysis, tsunami detection, geophysical tomography, radioastronomy, 3D reconstruction from 2D images [B2], molecular optics [S6], etc.
In terms specific to electromagnetic field theory, inverse problems acquire the generic name of synthesis problems, although there is no standard conceptualization in this respect. And the synthesis problem is indissolubly connected to formulating the electromagnetic field analysis problem.
The electromagnetic field synthesis problem requires that the following conditions are known or mandatory:
1) electric and/or magnetic field on the entire domain or subdomain.
2) entire domain or a part of the domain (in the sense that one can ask for the frontier configuration for which certain mandatory conditions are to be met).
3) material conditions on the entire domain or part of it (indefinite conditions fit in the category of measurements to be determined).
4) limit conditions on all frontiers of the domain, or just on a portion of them, the rest are to be determined.
5) source conditions totally, partially or not at all.
Presuming that the above data is given, the project synthesis can ask for:
1) optimum configuration of the indefinite frontier (to be noted that the conditions on this frontier may or may not be known apriori).
2) material conditions on certain subdomains.
3) limit conditions on some frontiers.
4) source conditions, totally or partially.
There is no difficulty in correlating the hypotheses and cerinte of the synthesis problem with the practical examples listed in the first paragraph.
Any inverse problem of the electromagnetic field requires certain specific stages during the solving process. The weight of every stage in this process, as the difficulty degree that it involves, differs from one problem to another. These stages are shortly presented in what follows.
1. Establishing the phenomenological model (the physical model)
This stage requires stating the given conditions of uniqueness, as well as of the given (mandatory) field, from which the indefinite values that need to be determined throughout the synthesis process clearly result. The research field is still open on the mandatory uniqueness conditions.
2. Establishing the mathematic model
The mathematic model is formulated by applying electromagnetic field laws and theorems. Thus, if the electromagnetic field laws are used under their differential form, then it is said that the mathematic model is differential. If energetic equivalent functionals to be minimized are associated to the laws, the model is called variational. And if the laws are used in their integral form, it is said that the mathematic model is integral. Any mathematic model can apply to a phenomenological one, but generally there are objective criteria (having to do with the type of problem), or subjective ones (having to do with the affinity of the solver towards a certain model) that make a certain model to be preferred.
3. Establishing the processing method of the mathematic model
The processing method of the mathematic model can be analytic or numeric. The analytic method is applied by actually solving the equations of the mathematic model (generally differential), allowing only the approach of problems with a certain symmetry. The most adequate solving method is the variables separation method. [M2]
The numeric processing method is closely linked to the chosen mathematic model. The differential mathematic model requires applying the finite differences method or the Monte Carlo method. Applications of the Monte Carlo method in homogenous and inhomogeneous environments are presented in [M2]. The finite differences method resides in approximating the derivatives with computational values. Modeling is trouble-free, but the calculation effort can become costly in a lot of cases.
The variational mathematic model requires the use of the finite elements method as a processing method; in this respect, there is a method of shifting from the analysis model to the synthesis model. Examples of the successful application of the finite elements method are in the direction of crack detecting [H1].
The integral mathematic model once chosen, the numeric processing method will be the frontier element method [B12]. The usage of the frontier element method applies in the inverse problems of optimization [E5], with the following advantages: the modification of forms in optimization processes involves only the modification of the frontier nods; one can obtain a direct relation between the electric or magnetic values modified through optimization, from the frontier integral equations; the effects of slight changes of frontier nods over the calculation errors distribution in the considered areas are negligible noted that there is a crack detecting application [T7] used in modeling with the frontier elements method.
By reference to the analysis theory terminology [M4] it can be stated that the mathematic model together with the numeric processing method form the numeric synthesis model [M2].
By applying the numeric synthesis model (whichever that is) one obtains a linear equations system: [W1], [E4], [C4], [D3], [B4], [S6], [M2] or a non linear equations system: [A4], [H2], [B2], [R3], [B3]. Due to the fact that the coefficient matrix contains very similar terms, in the case of linear equations, or the effect vector of the given measurements contains quasi-identical or proportional terms, in both situations, the characteristic of the problem is even more obviously ill-defined, or badly conditioned, resulting in unstable non exclusive solutions.
4. Establishing the synthesis method
The synthesis method is chosen according to the type of system resulted after the previous stages. When the result is a linear system of equations, the solutions can be unique, but unacceptable in most cases (they are not physically viable) or there can be an infinity of solutions. A substantial treatment of solving methods of linear equations systems to obtain pseudosolutions can be found in [M2]. If these solving options of linear equations systems do not provide the expected results, one resorts to regularization [T1].
Regularization resides in equivalating the system (of equations) of the initial mathematic model with a mathematic model under the form of a functional to minimize and that contains a parameter, called regularization. A great density of solving effort is focused on this point and the opening of research is still on demand. The regularizationmethod compromises between the system error norm (precision) and the solution norm (viability, stability). In the case of non linear systems of equations, regularization takes the form of an adapted iterative method.
A brief description has been made of the applicative level and of the theoretical apparatus on which this level is based, in the field of inverse electromagnetic problems. Up to the present moment, applications such as the ones given as examples above are approached from the perspective of following the modeling structure in the mentioned synthesis stages. Special attention is given to the mathematic process of actual regularization, of solving equation systems in a optimum technical direction. However, the meeting of the uniqueness conditions in the stage of the construction of the phenomenological model, or the adequate choice and the computationally efficient implementation of the mathematic model processing method, are far from being neglected. In these directions alternatives of action still allow continuous research. Identifying new applications in the field of electric circuits synthesis or quadripole synthesis appears again to be an open gate to creative study.
In the context where a large bibliographical spectrum comprising over 80 I.E.E.E, COMPEL, S.I.A.M., Inverse Problems articles, and several reference books that treat the solving of ill-defined inverse problems in an oriented manner has already been approached, a first assumed contribution will be the writing of a theoretical monography that would comprise, in an original way, essential aspects of the mathematic apparatus or ill-defined inverse electromagnetic problems. An attempt will be made to devise it as a unitary construction, which would serve as guide in the theoretical course of solving the problems in the field.
While working to achieve the precedent goal, an introduction of regularizing elements in the stage of mathematic modelling is envisaged, when this modelling comes down to first class Fredholm integral equations. Thus, a series of classical numeric methods appear as direct alternatives of continuing to solve the problem, without having to resort to the numeric processing methods mentioned in the first chapter, which have a high computational cost.
In the actual regularization stage of the linear equation systems an extension of the Tikhonov filter application will be recommended. The idea comes from accepting as valid the combination of decomposition methods according to proper values and the classical Tikhonov regularization. For testing, several applications will be chosen out of those mentioned in the first chapter.
Another envisaged theme is that of consolidating the link between the regularizing functional expressed by a matrix and the one recently put forward as being its statistic equivalent [B13]. A re-evalution of the inventory of possible useful numeric methods will be made, both following the matrix way and that of statistic calculation, on basis of the finding that less attention has been given to this issue.
The contribution foreseen as being the most important will be centred on devising an expert system, comprising the actual methods of choosing the regularization parameter (the discrepancy principle, the quasi-optimality criterion, the cross validation, the L curve criterion and the connected variants, the Miller functional, the binomial coefficients method), principles of method selection experimentally verified, according to the numeric processing model, according to the application class, and to the computational effort. An attempt will be made to demonstrate the possibility of combining some of the methods of choosing the regularization parameter. Also, the advantage of this parameter’s existence as a control factor will be demonstrated, both by resorting to the wide range of mentioned calculation alternatives of the regularization parameter, and via the ideatic approach, as a flexible means of optimum solving of ill-defined inverse electromagnetic problems.
Furthermore, in the field of non linear problems, the regularizing filter problem will be approached from the perspective of successive solving of linear problems, aspect that has yet been less debated upon.
It is noted that a large part of the potentially assumed contributions lie within a theoretical limit. Nonetheless, it would be a mistake to assume that the project course will lack applicative testings, concrete incursions in problems that have a practical aim. In accordance to the real material basis and to previsions of its improvement, problems of crack detecting, of the identification of thunderbolt effects over electric wires, of synthesizing field devices and adapted projection of quadripoles from reactive energy symmetrization and compensation equipment installation devices will be approached.
The results of the research undertaken during this project must prove useful, serving aims embodied by practical applications of ill-defined inverse electromagnetic problems. As shown by the objectives and activities put forward for the development of the project, the theoretical characteristic of the research tries to approach the concrete solving necessities by soft implementations. This inclination towards a theoretical approach belongs to the author of the project, but it is highly justified in the open and still inconsistently established perspectives provided by the inverse electromagnetic problem theory.
As previously stated, the documenting process for understanding and appropriating the current stage if knowledge in the field has had in view a bibliographical spectrum of high level, and the course of the approach has been permanently accompanied by alternative attempts and treatment of the studied material – aspects materialized in collegial debates, in papers recommended to students for symposiums addressed to them, in three articles sent to prestigious conferences and, perhaps the most important issue, in making contacts with personalities of reference in the field.
It is intended to keep the same spirit of action. To continue with, Chair discussions will make up the prime form of debating ideas in progress, the propulsion means for publishing scientific papers, and the support in the implementation of the nominated practical activities. That any completion of a mentioned objective will be accompanied by a technical report over its content and approach method is considered to be implicit. Collaboration and guiding interested students will not be given up upon, this activity generating great satisfaction and having a high formative potential.
The successful accomplishment of the propositions made in this project will stimulate the promotion of the objects of study, in the academic environment by reports and notifications, and in the potentially interested by oriented demonstrations. Attempts will be made to fasten the bond with reference researchers in the field and to initiate further collaborations. The project and its results must increase the prestige of the institution to which the author belongs.
The effort of completing a doctoral thesis will be well supported by the activity undertaken to accomplish the present project, but under no circumstances will it end once this thesis is handed in. The involvement in the field of inverse problem solving can and is desired to be continued on a long term.
As before, the research results will be incorporated in scientific papers that target local conferences with wider thematic, but the main targets will be those field specific conferences, those specialist publications where the evaluation of the works would be fairly expressed and for the preparation of which the experience of previous researches and articles would be necessary (IEEE Transaction on Magnetics, Inverse Problems, COMPEL, Revue Roumaine des sciences techniques, Analele Universitatii din Oradea, Acta Electrotehnica Cluj-Napoca).
Minimum sums of money have been taken into consideration for the retribution of research work, in favor of expenses for turning the results into account, article publishing, and the editing of informative brochures that would promote the results in the potentially interested industrial environment. Likewise, a substantial part of the cost was allocate for the acquisition of the materials that will constitute the object of testing of the nominated algorithms, as well as for the software advisers for the application of the expert system of regularizing parameter selection.
The affiliated institution, the Technical University in Cluj-Napoca, the Electrotehnics Departament, holds a material basis sufficiently equipped with auxiliary means and personel so that further aquisitions in the field would not become necessary. Possible financiary outcomes of the objects of this project will furthermore have in view acquisitions for the subsequent endowment of laboratories. A list of existing equipment in the electrotehnica laboratories of the mentioned institution, to which doctorands have a limited access, is given.
The involvement of the colleagues from the Chair staff, and from the other staffs as well will reside in periodical debate cercles, in collaborations in the writing of articles where the fields of competence intersect and can actively and usefully interact.
The present project proposition has set as objectives the accomplishment of three products. The first immaterial but quantifiable object would be the creation of a theoretical calculation structure, by which, using the Fredholm integral equation model, a direct regularization process could be applied, without resorting to a regularizing functional as an intermediate stage. This would be an implementable module of alternative solving of inverse electromagnetic problems that are reduced to Fredholm integral equations.
The second object, this time a material one, would be the soft and theoretical devise of an expert selection system of the regularizing parameter, under multicriterial conditions, based on the previous experience of applying parameter selection methods. Within the same objective an attempt will be made to synthesize the magnetic field of a device from the magnetic resonance systems in Imagistic. This device will be a palpable object resulted from the research, that would function as a prototype promoting first of all the expert system solving method; it will be a guarantee of the success of the expert system.
Scientific research must have as final, more or less immediate goal, the practical application of the results. In the field of Electrotechnics the materialization of theories obtained through scientific research is achieved through the designing activity. The designer of electrotechnical devices must have at hand well determined and safe algorithms for any situation. At the present level of computer technology the designing activity is closely related to the electromagnetic field synthesis, in that a lot of designing problems are formulated in terms specific to the electromagnetic field synthesis.
The work environment will be characterized by an extremely cooperant and cordial atmosphere, which will have a positive influence over the results.
All researched sources will be adequately referred to in bibliographies, without claming a single element that has not been discovered in the course of the designated research.
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