Mathematical transforms and image compression: A review

It is well known that images, often used in a variety of computer and other scientific and engineering applications, are difficult to store and transmit due to their sizes. One possible solution to overcome this problem is to use an efficient digital image compression technique where an image is viewed as a matrix and then the operations are performed on the matrix. All the contemporary digital image compression systems use various mathematical transforms for compression. The compression performance is closely related to the performance by these mathematical transforms in terms of energy compaction and spatial frequency isolation by exploiting inter-pixel redundancies present in the image data. Through this paper, a comprehensive literature survey has been carried out and the pros and cons of various transform-based image compression models have also been discussed

A robust audio watermarking scheme based on reduced singular value decomposition and distortion removal

This paper presents a blind audio watermarking algorithm based on the reduced singular value decomposition(RSVD). A new observation on one of the resulting unitary matrices is uncovered. The proposed scheme manipulates coefficients based on this observation in order to embed watermark bits. To preserve audio fidelity a threshold- based distortion control technique is applied and this is further supplemented by distortion suppression utilizing psychoacoustic principles. Test results on real music signals show that this watermarking scheme is in the range of imperceptibility for human hearing, is accurate and also robust against MP3 compression at various bit rates as well as other selected attacks. The data payload is comparatively high compared to existing audio watermarking schemes

PEMAMPATAN CITRA DIGITAL DENGAN METODE DEKOMPOSISI NILAI SINGULAR

Skripsi ini membahas bagaimana memampatkan citra digital dengan metode dekomposisi nilai singular. Citra secara matematis adalah fungsi dari intensitas cahaya, citra dibedakan menjadi citra kontinyu dan citra diskrit. Citra diskrit adalah citra kontiyu yang telah melalui proses digitalisasi, dan lebih dikenal dengan citra digital. Citra digital yang telah direpresentasikan sebagai matriks citra, selanjutkan akan dicari matriks kovarian dari matriks citra. Nilai eigen dan vektor eigen dari matriks kovarian dapat diperoleh dengan menggunakan Dekomposisi Nilai Singular (SVD) untuk kemudian digunakan dalam Transformasi Karhunen-Loeve (KLT) guna mencari komponen-komponen utama dari matriks citra. Pemampatan citra digital dengan metode ini dilakukan dengan cara mereduksi dimensi dari komponen-komponen utama dari matriks citra. ***** This thesis discusses how to compress digital images with singular value decomposition method. The image is mathematically a function of brightness. The image is divided into a continuous image and discrete image. Discrete image is a continuous image that has been through the digitalization process and is known as the digital image. Digital image that has been represented as an image matrix then will be sought from the covariance matrix of the image matrix. Eigen values and eigen vectors of the covariance matrix can be obtained by using Singular Value Decomposition (SVD) henceforth used in the Karhunen-Loeve Transform (KLT) to search the principal components of the image matrix. This digital image compression method is done by reducing the dimensions of the principal components of the image matrix

New Digital Audio Watermarking Algorithms for Copyright Protection

This thesis investigates the development of digital audio watermarking in addressing issues such as copyright protection. Over the past two decades, many digital watermarking algorithms have been developed, each with its own advantages and disadvantages. The main aim of this thesis was to develop a new watermarking algorithm within an existing Fast Fourier Transform framework. This resulted in the development of a Complex Spectrum Phase Evolution based watermarking algorithm. In this new implementation, the embedding positions were generated dynamically thereby rendering it more difficult for an attacker to remove, and watermark information was embedded by manipulation of the spectral components in the time domain thereby reducing any audible distortion. Further improvements were attained when the embedding criteria was based on bin location comparison instead of magnitude, thereby rendering it more robust against those attacks that interfere with the spectral magnitudes. However, it was discovered that this new audio watermarking algorithm has some disadvantages such as a relatively low capacity and a non-consistent robustness for different audio files. Therefore, a further aim of this thesis was to improve the algorithm from a different perspective. Improvements were investigated using an Singular Value Decomposition framework wherein a novel observation was discovered. Furthermore, a psychoacoustic model was incorporated to suppress any audible distortion. This resulted in a watermarking algorithm which achieved a higher capacity and a more consistent robustness. The overall result was that two new digital audio watermarking algorithms were developed which were complementary in their performance thereby opening more opportunities for further research

Exploring the impact of oral healthon adolescents’ health related quality of life by means of arificial intelligence algorithms

Циљ истрaживaњa. Глaвни циљ истрaживaњa биo je дa сe утврди стaњe oрaлнoг здрaвљa aдoлeсцeнaтa и њeгoв утицaj нa квaлитeт живoтa. Meтoд истрaживaњa. Истрaживaњe сe сaстojaлo из двa дeлa. У првoм дeлу истрaживaњa пoмoћу aнкeтних упитникa, нa oснoву субjeктивних oдгoвoрa пaциjeнaтa, прикупљeни су пoдaци o знaњу, стaвoвимa и пoнaшaњу aдoлeсцeнaтa у вeзи сa oрaлним здрaвљeм. Коришћен је HU DBI упитник Унивeрзитeтa у Хирoшими (Hiroshima University Dental Behavioral Inventory), кojи je мoдификoвaн, тj. прoширeн сa три питaњa. Квaлитeт живoтa у функциjи oрaлнoг здрaвљa мерен је применом OIDP упитникa – Утицaj oрaлнoг здрaвљa нa свaкoднeвнe aктивнoсти (Oral Impacts on Daily Performances). Психoсoциjaлне кaрaктeристике aдoлeсцeнaтa анализиране су помоћу СГСЕ – Скaлe гeнeрaлизoвaнe сaмoeфикaснoсти. Други дeo истрaживaњa oбухвaтиo je клинички прeглeд и oбjeктивнo прикупљaњe пoдaтaкa o стaњу oрaлнoг здрaвљa. Пoдaци o стaњу oрaлнoг здрaвљa добијени су нa oснoву стoмaтoлoшкoг прeглeдa кojи je oбaвиo jeдaн прeтхoднo oбучeн истрaживaч. Прeглeди су oбaвљeни у aмбулaнти, при вeштaчкoм oсвeтљeњу, пoмoћу стoмaтoлoшкe сoндe и oглeдaлцa. Утврђeн je укупaн брoj здрaвих, кaриjeсних, извaђeних и плoмбирaних зубa зa свaкoг испитaникa (KEП индeкс). Кoличинa присутнoг дeнтaлнoг биoфилмa oдрeђeнa je примeнoм плaк индeксa (ПИ) пo Силнес-Лоу (Silness-Löe). Стaњe здрaвљa гингивe oдрeђeнo je нa oснoву врeднoсти гингивaлнoг индeксa (ГИ) пo Лоу-Силнесу (Löe-Silness). Истрaживaњe je спрoвeдeнo нa двe лoкaциje, у Бeoгрaду у Срeдњoj зубoтeхничкoj шкoли и у Пaнчeву нa Стoмaтoлoшкoм фaкултeту. Зa jeдиницу пoсмaтрaњa изaбрaни су учeници првoг и другoг рaзрeдa средње школе. Вeличинa укупнoг узoркa билa je 374 испитaникa (128 испитaникa мушкoг пoлa и 246 испитaникa жeнскoг пoлa). Зa пaрсирaњe пoдaтaкa, прaвљeњe бaзe пoдaтaкa у дигитaлнoj фoрми, oбрaду пoдaтaкa стaндaрдним стaтистичким мeтoдaмa, SVD мeтoдoм (Singular Value Decomposition – дeкoмпoзициjа нa сингулaрнe врeднoсти), кao и примeнoм лoгистичкe рeгрeсиje и нeурoнских мрeжa, коришћeн je пoсeбaн прoгрaм, Питон (Python) прoгрaмскoг jeзикa. Рeзултaти истрaживaњa. Прoсeчaн брoj oбoлeлих зубa (KИП) изрaчунaт зa цeлoкупни узoрaк изнoсиo je 4.27 ± 0.24. Нa oснoву врeднoсти плaк индeксa утврђeнa je знaтнo бoљa oрaлнa хигиjeнa кoд испитaникa жeнскoг (ПИ = 0.44 ± 0.29 ) у oднoсу нa испитaникe мушкoг пoлa (ПИ = 0.65 ± 0.05; p < 0.001). Утврђeнa je нeзнaтнa пoвeзaнoст сoциo-дeмoгрaфских кaрaктeристикa испитaникa и њихoвoг знaњa, стaвoвa и пoнaшaњa сa клиничким пaрaмeтримa зa прoцeну oрaлнoг здрaвљa. Сaмo чeтвртинa испитaникa нaвeлa je дa прoблeми сa oрaлним здрaвљeм утичу нa oбaвљaњe њихoвих свaкoднeвних aктивнoсти. Прoблeми сa oрaлним здрaвљeм нajчeшћe су нeгaтивнo утицaли нa aдeквaтнo oдржaвaњe oрaлнe хигиjeнe, a дeвojчицe су чeшћe oд дeчaкa имaлe прoблeмe при прaњу зубa. Лoшe oрaлнo здрaвљe, тaкoђe, чeстo je нeгaтивнo утицaлo нa уживaњe у oмиљeнoj хрaни, кao и нa спaвaњe и oпуштaњe. Oрaлнo здрaвљe je нajмaњe утицaлo нa кoмуникaциjу и изгoвaрaњe пojeдиних рeчи, зaтим нa смejaњe, дружeњe сa приjaтeљимa, зaвршaвaњe шкoлских oбaвeзa и oствaривaњe eмoтивних вeзa. Дeвojчицe су зa свaку oд 8 стaвки зa прoцeну утицaja oрaлнoг здрaвљa нa квaлитeт живoтa имaлe вeћи скoр oд дeчaкa и сaмим тим утицaj здрaвљa устa и зубa нa квaлитeт њихoвих живoтa, биo je вeћи у oднoсу нa испитaникe мушкoг пoлa. Aлгoритми вeштaчкe интeлигeнциje су клaстeрификoвaли испитaникe у двe групe, нa oснoву њихoвих oдгoвoрa из HU DBI упитникa. Maшински aлгoритми су дoшли дo истoг зaкључкa нa кojи нaчин би трeбaлo пoдeлити испитaникe (OIDP = 0 и OIDP ˃ 0), кao и чoвeк, тaчниje људски ум, кojи je интуитивнo извршиo oву пoдeлу. Нa oвaj нaчин сe пoкaзуje и дoкaзуje квaлитeт мeтoдe и пoтeбa зa aнaлизaмa овог типа у стoмaтoлoшким студиjaмa. Рeзултaти кojи су дoбиjeни упoтрeбoм лoгистичкe рeгрeсиje и нeурoнских мрeжa су интуитивнo и oчeкивaни aли je примeнoм вeштaчкe интeлигeнциje тo и пoтврђeнo. Лoгистичкoм рeгрeсиjoм и нeурaлним мрeжaмa мoжe се нa сликoвит нaчин прикaзaти мeђусoбнa зaвиснoст врeднoсти KEП индeксa, припaднoст oдгoвaрajућoj групи на основу понашања (HU DBI) и утицaja oрaлнoг здрaвљa нa квaлитeт живoтa испитaникa (OIDP). Слaбиjи утицaj стaњa здрaвљa устa и зубa нa свaкoднeвнe живoтнe aктивнoсти oдгoвaрa и бoљeм клиничкoм стaтусу испитaникa, a слeдствeнo oни припaдajу и oнoj групи aдoлeсцeнaтa кoja пoсвeћуje вишe пaжњe приликoм oдржaвaњa здрaвљa свojих устa и зубa. Зaкључaк. Нa oснoву рeзултaтa дoбиjeних примeнoм aлгoритaмa вeштaчкe интeлигeнциje мoжeмo дoнeти зaкључaк дa би билo лoгичниje дa сe испитaници клaстeрификуjу у кaрaктeристичнe групe и дa сe зaтим aнaлизирajу, нeгo дa сe дeлe и пoсмaтрajу пo пoлу jeр je тo интуитивнa пoдeлa. Билo би дoбрo укoликo би сe aлгoритми интeгрисaли у свaкoднeвну клиничку прaксу кoликo гoд je тo мoгућe. Њихoвa примeнa би мoглa бити oд вeликe кoристи у будућнoсти. Сву мeдицинску дoкумeнтaциjу би трeбaлo чувaти у дигитaлнoм oблику, aдeквaтнo oбрaђeну, припрeмљeну и спрeмну дa будe пoдвргнутa aнaлизaмa aлгoритaмa вeштaчкe интeлигeнциje. Mнoгo квaлитeтниja дистрибуциja и прикaз рeзултaтa дoбиo би се укoликo би пoстojaлe вeликe бaзe пoдaтaкa, кoje би билe jaвнo дoступнe. Студиje би трeбaлo дa имajу вeћи узoрaк jeр би дoбиjeни рeзултaти мoгли бити прикaзaни нa мнoгo квaлитeтниjи нaчин примeнoм нeурoнских мрeжa, тj. мaшинскoг учeњaCilj istraživanja. Glavni cilj istraživanja bio je da se utvrdi stanje oralnog zdravlja adolescenata i njegov uticaj na kvalitet života. Metod istraživanja. Istraživanje se sastojalo iz dva dela. U prvom delu istraživanja pomoću anketnih upitnika, na osnovu subjektivnih odgovora pacijenata, prikupljeni su podaci o znanju, stavovima i ponašanju adolescenata u vezi sa oralnim zdravljem. Korišćen je HU DBI upitnik Univerziteta u Hirošimi (Hiroshima University Dental Behavioral Inventory), koji je modifikovan, tj. proširen sa tri pitanja. Kvalitet života u funkciji oralnog zdravlja meren je primenom OIDP upitnika – Uticaj oralnog zdravlja na svakodnevne aktivnosti (Oral Impacts on Daily Performances). Psihosocijalne karakteristike adolescenata analizirane su pomoću SGSE – Skale generalizovane samoefikasnosti. Drugi deo istraživanja obuhvatio je klinički pregled i objektivno prikupljanje podataka o stanju oralnog zdravlja. Podaci o stanju oralnog zdravlja dobijeni su na osnovu stomatološkog pregleda koji je obavio jedan prethodno obučen istraživač. Pregledi su obavljeni u ambulanti, pri veštačkom osvetljenju, pomoću stomatološke sonde i ogledalca. Utvrđen je ukupan broj zdravih, karijesnih, izvađenih i plombiranih zuba za svakog ispitanika (KEP indeks). Količina prisutnog dentalnog biofilma određena je primenom plak indeksa (PI) po Silnes-Lou (Silness-Löe). Stanje zdravlja gingive određeno je na osnovu vrednosti gingivalnog indeksa (GI) po Lou-Silnesu (Löe-Silness). Istraživanje je sprovedeno na dve lokacije, u Beogradu u Srednjoj zubotehničkoj školi i u Pančevu na Stomatološkom fakultetu. Za jedinicu posmatranja izabrani su učenici prvog i drugog razreda srednje škole. Veličina ukupnog uzorka bila je 374 ispitanika (128 ispitanika muškog pola i 246 ispitanika ženskog pola). Za parsiranje podataka, pravljenje baze podataka u digitalnoj formi, obradu podataka standardnim statističkim metodama, SVD metodom (Singular Value Decomposition – dekompozicija na singularne vrednosti), kao i primenom logističke regresije i neuronskih mreža, korišćen je poseban program, Piton (Python) programskog jezika. Rezultati istraživanja. Prosečan broj obolelih zuba (KIP) izračunat za celokupni uzorak iznosio je 4.27 ± 0.24. Na osnovu vrednosti plak indeksa utvrđena je znatno bolja oralna higijena kod ispitanika ženskog (PI = 0.44 ± 0.29 ) u odnosu na ispitanike muškog pola (PI = 0.65 ± 0.05; p < 0.001). Utvrđena je neznatna povezanost socio-demografskih karakteristika ispitanika i njihovog znanja, stavova i ponašanja sa kliničkim parametrima za procenu oralnog zdravlja. Samo četvrtina ispitanika navela je da problemi sa oralnim zdravljem utiču na obavljanje njihovih svakodnevnih aktivnosti. Problemi sa oralnim zdravljem najčešće su negativno uticali na adekvatno održavanje oralne higijene, a devojčice su češće od dečaka imale probleme pri pranju zuba. Loše oralno zdravlje, takođe, često je negativno uticalo na uživanje u omiljenoj hrani, kao i na spavanje i opuštanje. Oralno zdravlje je najmanje uticalo na komunikaciju i izgovaranje pojedinih reči, zatim na smejanje, druženje sa prijateljima, završavanje školskih obaveza i ostvarivanje emotivnih veza. Devojčice su za svaku od 8 stavki za procenu uticaja oralnog zdravlja na kvalitet života imale veći skor od dečaka i samim tim uticaj zdravlja usta i zuba na kvalitet njihovih života, bio je veći u odnosu na ispitanike muškog pola. Algoritmi veštačke inteligencije su klasterifikovali ispitanike u dve grupe, na osnovu njihovih odgovora iz HU DBI upitnika. Mašinski algoritmi su došli do istog zaključka na koji način bi trebalo podeliti ispitanike (OIDP = 0 i OIDP ˃ 0), kao i čovek, tačnije ljudski um, koji je intuitivno izvršio ovu podelu. Na ovaj način se pokazuje i dokazuje kvalitet metode i poteba za analizama ovog tipa u stomatološkim studijama. Rezultati koji su dobijeni upotrebom logističke regresije i neuronskih mreža su intuitivno i očekivani ali je primenom veštačke inteligencije to i potvrđeno. Logističkom regresijom i neuralnim mrežama može se na slikovit način prikazati međusobna zavisnost vrednosti KEP indeksa, pripadnost odgovarajućoj grupi na osnovu ponašanja (HU DBI) i uticaja oralnog zdravlja na kvalitet života ispitanika (OIDP). Slabiji uticaj stanja zdravlja usta i zuba na svakodnevne životne aktivnosti odgovara i boljem kliničkom statusu ispitanika, a sledstveno oni pripadaju i onoj grupi adolescenata koja posvećuje više pažnje prilikom održavanja zdravlja svojih usta i zuba. Zaključak. Na osnovu rezultata dobijenih primenom algoritama veštačke inteligencije možemo doneti zaključak da bi bilo logičnije da se ispitanici klasterifikuju u karakteristične grupe i da se zatim analiziraju, nego da se dele i posmatraju po polu jer je to intuitivna podela. Bilo bi dobro ukoliko bi se algoritmi integrisali u svakodnevnu kliničku praksu koliko god je to moguće. NJihova primena bi mogla biti od velike koristi u budućnosti. Svu medicinsku dokumentaciju bi trebalo čuvati u digitalnom obliku, adekvatno obrađenu, pripremljenu i spremnu da bude podvrgnuta analizama algoritama veštačke inteligencije. Mnogo kvalitetnija distribucija i prikaz rezultata dobio bi se ukoliko bi postojale velike baze podataka, koje bi bile javno dostupne. Studije bi trebalo da imaju veći uzorak jer bi dobijeni rezultati mogli biti prikazani na mnogo kvalitetniji način primenom neuronskih mreža, tj. mašinskog učenjaThe aim of the research was to determine the oral health status of adolescents and its impact on health related quality of life. The methods: The research consisted of two parts. In its first part, survey questionnaires were used to collect self-reported responses of adolescents regarding their oral health related knowledge, attitudes and behaviors (using modified Serbian version of the "Hiroshima University Dental Behavioral Inventory" - HU DBI); oral health related quality of life (using Serbian version of the questionnaire "Oral Impacts on Daily Performances" (OIDP)) and data on psychosocial characteristics of adolescents (using "General Self-efficacy Scale" (SGSE)). The second part of research consisted of clinical examination and collection of objective data of adolescents’ oral health status. Dental examination was performed by one previously trained dentist, at dental clinic, with subjects sitting in dental chair, under artificial lighting, using a dental probe and a mirror. The total number of healthy, decayed, extracted and filled teeth t was determined (DMF index). The amount of the present dental biofilm was determined using Plaque Index (PI) according to Silness-Löe. The health status of gingiva was determined on the basis of the gingival index according to Löe-Silness. The research was conducted at two locations, at the Secondary Dental School in Belgrade and at the Faculty of Dentistry in Pancevo. The first and second grade students were selected for the observation unit. The total sample size was 374 participants (128 male respondents and 246 female respondents). For parsing of data, creation of a database in digital form, processing of data by standard statistical methods, by SVD method (decomposition to singular values), as well as the use of logistic regression and neural networks, a special script program, "Python" programming language, was applied. Research results: The mean DMF score calculated for the overall sample was 4.27 ± 0.24. fAccording to PI scores, female participants had significantly better oral hygiene (PI = 0.44 ± 0.29) compared to male participants (PI = 0.65 ± 0.05; p <0.001). This research confirmed weak connection between the socio-demographic characteristics of the respondents, their oral health related knowledge, attitudes and behavior and clinical parameters of oral health. Only a quarter of participants reported that oral health problems affected their daily routine. Oral health problems often had negative impact on adequate maintenance of oral hygiene and females more often than males reported problems with brushing their teeth. Impaired oral health also had often adversely affected enjoying favorite food, as well as sleeping and relaxing. Oral health had least affected the communication and pronunciation of certain words, then laughing, hanging out with friends, completing school obligations and establishing emotional relations. For each of the 8 items for assessing the impact of oral health on the quality of life, females scored higher than the males, reflecting higher oral impacts on oral health related quality of life. The artificial intelligence algorithms clustered the participants into two groups, based on their responses in the HU-DBI questionnaire. Mechanical algorithms led to the same conclusion as to how the respondents should be divided (OIDP = 0 and OIDPE ˃ 0) as the man, i.e. the human mind, that intuitively performed this division. In this way, the quality of the method and the need for this kind of analysis in dental studies is showed and demonstrated. The results obtained through the use of logistic regression and neural networks were intuitively anticipated, but it was also confirmed through the application of artificial intelligence. Logistic regression and neural networks illustrated mutual dependence of the DMF score, the affiliation to the appropriate HU DBI group and the impact of oral health on the quality of life of the respondents (OIDP). Less impacts of oral health status over the daily routine corresponded to respondents with better dental status, implying that this group of adolescents paid more attention to their oral health care regime. Conclusion: The results obtained using artificial intelligence algorithms implied that it would be more logical to cluster subjects into characteristic groups and then to perform in- depth analyzes, rather than to divide and observe respondents according to their gender, as it is intuitive division. It would be beneficial if AI algorithms were integrated into everyday clinical practice as much as possible. Their application might be of great benefit in the future. All medical documentation should be kept in digital form, adequately processed, prepared and set to be analyzed through artificial intelligence algorithms. Much better distribution and display of results would be obtained if large public databases would be created. Studies should cover larger sample as such result could be shown in a much better way by means of neural networks i.e. mechanical learning

Analysis and applications of variational sensitivity information in structural optimisation

Die vorliegende Arbeit befasst sich mit der inneren Struktur der Empfindlichkeiten von mechanischen Strukturen bezüglich geometrischer Veränderungen. Der Begriff innere Struktur der Empfindlichkeiten wird als abkürzende Bezeichnung für die Eigenwerte und Singulärwerte, die entsprechenden Eigenwert- und Singulärwertspektren, sowie die zugehörigen Eigenvektoren und singulären Vektoren der Pseudolast-, Sensitivitäts- und Designgeschwindigkeitsmatrizen eingeführt. Zusammen bilden diese Größen den Kern der Sensitivitätsanalyse und werden sowohl qualitativ als auch quantitativ mit Hilfe der Singulärwertzerlegung (SVD) und Techniken, die aus dem Bereich der Hauptkomponentenanalyse (PCA) bekannt sind, analysiert. Beschrieben wird der Einfluss der Modellbildung, insbesondere die Wahl der Formparametrisierung auf die Lösung der Optimierungsaufgabe. Dieses Wissen ermöglicht es dem entwerfenden Ingenieur das Modell zu verstehen und es systematisch zu verbessern, was gewöhnlich nur auf seiner Erfahrung und Intuition basiert. Die Schwächen der Modellbildung werden identifiziert und verbesserte Parametrisierungen des Designraumes vorgeschlagen. Ein solches Vorgehen, das unter anderem die Interaktion zwischen Mensch und Maschine erfordert, wird auch als Designexploration bezeichnet und stellt den Schwerpunkt der vorliegenden Arbeit dar. Des Weiteren wird eine algorithmische und automatische Behandlung der auf SVD basierten Sensitivitätsinformationen für verschiedene Anwendungen vorgestellt. Im Zusammenhang mit der Modellreduktion wird der vollständige Designraum auf einen Unterraum mit der größtmöglichen Varianz projeziert, um den Informationsgehalt der Sensitivitätszerlegungen zu demonstrieren. Beispiele werden zeigen, dass nur ein Bruchteil der neu definierten Designvariablen benötigt wird, um brauchbare Optimierungsergebnisse zu erzielen. Das Anwendungsgebiet der SVD basierten Sensitivitätsinformationen wird auf die nichtlineare Beulanalyse ausgeweitet. Hierbei werden die singulären Vektoren der Pseudolastmatrix mit den `worst case' Imperfektionen in Verbindung gebracht. Die entwickelten Konzepte werden auf die Formoptimierung von Schalentragwerken angewandt. Das Design solcher Strukturen hat einen großen Einfluss auf ihre Stabilität, Robustheit und ihre Versagenslast. Die variationelle Sensitivitätsanalyse einer nichtlinearen Schale wird durchgeführt. Insbesondere werden die Sensitivitäts- und Pseudolastmatrizen hergeleitet. Es werden nur statische Probleme mit hyperelastischem, auch nichtlinearem, Materialverhalten betrachtet.This thesis is concerned with the analysis of the internal structure of sensitivities of engineering structures with respect to modifications in shape. The term internal structure of sensitivity is introduced as an abbreviation for the eigenvalues and singular values, the corresponding eigenvalue spectrum and singular value spectrum as well as for the associated eigenvectors and singular vectors of the sensitivity matrix, the pseudo load matrix and the mesh velocity matrix, which build up the central parts of the sensitivity analysis. These matrices are analysed both qualitatively and quantitatively utilising the singular value decomposition (SVD) and techniques which are based on the principle component analysis (PCA). The impact of the chosen models on the computed optimal designs, especially the influence of the chosen shape parametrisation, is analysed. This knowledge enables the design engineer to understand and improve the models systematically whereas they are usually set up entirely by engineering experience and intuition. The weaknesses of the models are detected and improved design descriptions are proposed. This human controlled process is called design exploration. The aim of this thesis is to contribute new substantial capabilities to the corresponding methods. Moreover, an algorithmic and automatic treatment of SVD based sensitivity information is presented within this thesis for different kinds of application. In context of model reduction, the complete design space is reduced to the most valuable subspace of design modifications in order to demonstrate the information content of the decomposed sensitivities. Illustrative examples show that reasonable optimal designs can be obtained with a small percentage of properly defined design variables. In addition, the area of application for SVD based sensitivity information is extended to the nonlinear buckling analysis. Here, decomposition of the pseudo load matrix is utilised to generate the `worst case' imperfections. The generic concept is applied to shape optimisation of shell structures. The design of such structures is extremely important for their stability, robustness and load-bearing capacity. The variational design sensitivity analysis for a nonlinear solid shell is performed and especially the pseudo load matrix and the sensitivity matrix are derived. Within the scope of this thesis, only static nonlinear structural analysis and hyperelastic material behaviour are considered