In this thesis the oxidation of monoterpenes by O3 and NO2 and factors that influenced the oxidation were studied. In the environment both ozone (O3) and nitrogen dioxide (NO2) are present as oxidising gases, which causes sampling artefacts when using Tenax TA as an adsorbent to sample organic compounds in the air. A scrubber was developed to remove O3 and NO2 prior to the sampling tube, and artefacts during sampling were minimised when using the scrubber. The main organic compounds sampled in this thesis were two monoterpenes, alfa-pinene and delta-3-carene, due to their presence in both indoor and outdoor air. The recovery of the monoterpenes through the scrubber varied between 75-97% at relative humidities of 15-75%. The reactions of alfa-pinene and delta-3-carene with O 3, NO2 and nitric oxide (NO) at different relative humidities (RHs) and reaction times were studied in a dark reaction chamber. The experiments were planned and performed according to an experimental design were the factors influencing the reaction (O3, NO2, NO, RH and reaction times) were varied between high and low levels. In the experiments up to 13% of the monoterpenes reacted when O3, NO2, and reaction time were at high levels, and NO, and RH were at low levels. In the evaluation eight and seven factors (including both single and interaction factors) were found to influence the amount of alfa-pinene and delta-3-carene reacted, respectively. The three most influencing factors for both of the monoterpenes were the O 3 level, the reaction time, and the RH. Increased O3 level and reaction time increased the amount of monoterpene reacted, and increased RH decreased the amount reacted. A theoretical model of the reactions occurring in the reaction chamber was created. The amount of monoterpene reacted at different initial settings of O3, NO2, and NO were calculated, as well as the influence of different reaction pathways, and the concentrations of O3 and NO2, and NO at specific reaction times. The results of the theoretical model were that the reactivity of the gas mixture towards alfa-pinene and delta-3-carene was underestimated. But, the calculated concentrations of O3, NO2, and NO in the theoretical model were found to correspond to a high degree with experimental results performed under similar conditions. The possible associations between organic compounds in indoor air, building variables and the presence of sick building syndrome were studied using principal component analysis. The most complex model was able to separate 71% of the “sick” buildings from the “healthy” buildings. The most important variables that separated the “sick” buildings from the “healthy” buildings were a more frequent occurrence or a higher concentration of compounds with shorter retention times in the “sick” buildings. The outcome of this thesis could be summarised as follows; - - - -

L’objectif de cette thèse était d’appliquer des méthodes d’analyse multivariées au traitement des données provenant de la spectroscopie de plasma induit par laser (LIBS) et de la spectroscopie térahertz (THz) dans le but d’accroître les performances analytiques de ces techniques.Les spectres LIBS provenaient de campagnes de mesures directes sur différents sites géologiques. Une approche univariée n’a pas été envisageable à cause d’importants effets de matrices et c’est pour cela qu’on a analysé les données provenant des spectres LIBS par réseaux de neurones artificiels (ANN). Cela a permis de quantifier plusieurs éléments mineurs et majeurs dans les échantillons de sol avec un écart relatif de prédiction inférieur à 20% par rapport aux valeurs de référence, jugé acceptable pour des analyses sur site. Dans certains cas, il a cependant été nécessaire de prendre en compte plusieurs modèles ANN, d’une part pour classer les échantillons de sol en fonction d’un seuil de concentration et de la nature de leur matrice, et d’autre part pour prédire la concentration d’un analyte. Cette approche globale a été démontrée avec succès dans le cas particulier de l’analyse du plomb pour un échantillon de sol inconnu. Enfin, le développement d’un outil de traitement par ANN a fait l’objet d’un transfert industriel.Dans un second temps, nous avons traité des spectres d’absorbance terahertz. Ce spectres provenaient de mesures d’absorbance sur des mélanges ternaires de Fructose-Lactose-acide citrique liés par du polyéthylène et préparés sous forme de pastilles. Une analyse semi-quantitative a été réalisée avec succès par analyse en composantes principales (ACP). Puis les méthodes quantitatives de régression par moindres carrés partiels (PLS) et de réseaux de neurons artificiels (ANN) ont permis de prédire les concentrations de chaque constituant de l’échantillon avec une valeur d’erreur quadratique moyenne inférieure à 0.95 %. Pour chaque méthode de traitement, le choix des données d’entrée et la validation de la méthode ont été discutés en détail. / The aim of this work was the application of multivariate methods to analyze spectral data from laser-induced breakdown spectroscopy (LIBS) and terahertz (THz) spectroscopy to improve the analytical ability of these techniques.In this work, the LIBS data were derived from on-site measurements of soil samples. The common univariate approach was not efficient enough for accurate quantitative analysis and consequently artificial neural networks (ANN) were applied. This allowed quantifying several major and minor elements into soil samples with relative error of prediction lower than 20% compared to reference values. In specific cases, a single ANN model didn’t allow to successfully achieving the quantitative analysis and it was necessary to exploit a series of ANN models, either for classification purpose against a concentration threshold or a matrix type, or for quantification. This complete approach based on a series of ANN models was efficiently applied to the quantitative analysis of unknown soil samples. Based on this work, a module of data treatment by ANN was included into the software Analibs of the IVEA company. The second part of this work was focused on the data treatment of absorbance spectra in the terahertz range. The samples were pressed pellets of mixtures of three products, namely fructose, lactose and citric acid with polyethylene as binder. A very efficient semi-quantitative analysis was conducted by using principal component analysis (PCA). Then, quantitative analyses based on partial least squares regression (PLS) and ANN allowed quantifying the concentrations of each product with a root mean square error (RMSE) lower than 0.95 %. All along this work on data processing, both the selection of input data and the evaluation of each model have been studied in details.

Ce travail a porté sur les remaniements corticaux précoces des circuits moteurs et extramoteurs dans la SLA grâce à l’étude des activations IRMf issues de tâches motrices et cognitives. La première partie de nos travaux nous a permis de montrer grâce des tâches simples d’activation motrice en IRMf (1) qu’alors que les patients SLA présentaient un déficit moteur discret, une augmentation des activations corticales est apparue dans les aires sensorimotrices bilatérales du cerveau. (2) Ces modifications précoces de l’activité neuronale étaient corrélées à la latéralisation du déficit moteur du membre ou la prédominance manuelle et surtout, (3) au taux de progression de la maladie à un an et à la survie, suggérant que ce remaniement de l’activité qui correspond probablement à de la plasticité cérébrale a des implications fonctionnelles. Enfin, (4) ce phénomène apparaissait actif puisqu’il s’est poursuivi pendant au moins onze mois. Dans la deuxième partie, nous avons montré lors d’une tâche de fluence verbale silencieuse que (1) les SLA présentaient une suractivation initiale des aires dévolues au processus sémantique avec un renforcement de la connectivité fonctionnelle entre les réseaux (CFR). (2) Au bout de onze mois et alors que l’atteinte des fluences était stable, ce phénomène de compensation s’épuisait avec une diminution conjointe de l’activation des réseaux et de la CFR. La tâche de 2-Back, réalisée alors que les patients ne présentaient pas d’atteinte de la mémoire de travail lors des tests psychométriques, nous a permis de montrer en outre que certains circuits non-moteurs se réorganisaient très précocement chez les patients, alors même qu’ils étaient asymptomatiques / In this work we used motor and cognitive tasks in an fMRI study to explore the early cortical reorganizations of the motor and extra-motor circuits in ALS patients. In a first part, using a simple motor task, we demonstrated (1) that increased cortical BOLD signal changes occurred in specific regions of the brain of ALS patients when their motor deficit was still moderate, and that this early signal changes correlated with (2) the lateralisation of the motor deficit or hand predominance and, more importantly, (3) with the rate of disease progression at one year and survival time, suggesting that modulations of cerebral activity in ALS may have functional implications. Furthermore, (4) this brain plasticity was maintained with time and disease progression during at least eleven months. In a second part, we demonstrated during a silent verbal fluency task (1) that ALS patients presented initially an increased cortical activation of areas devolved to the semantic process with an intensification of the functional network connectivity (FNC). (2) After eleven months and while their performance in tests of verbal fluency was stable, this cerebral compensation ran out with a decrease of the previous cerebral activations and the FNC. A N-back working memory paradigm, realized while the patients did not present any deficit of their working memory, allowed us to show that certain non-motor circuits were reorganized prematurely while patients were still asymptomatic

[pt] Um dos principais desafios no mercado financeiro é simular preços mantendo a estrutura de correlação entre os inúmeros ativos de um portfólio. Análise de Componentes Principais emerge como uma solução para este último problema. Além disso, dada a incerteza presente nos mercados de commodities de derivados de petróleo, o investidor quer proteger seus ativos de perdas potenciais. Como uma alternativa a esse problema, a otimização de várias medidas de risco, como Value-at-risk, Conditional Value-at-risk e medida Ômega, são ferramentas financeiras importantes. Além disso, o backtest é amplamente utilizado para validar e analisar o desempenho do método proposto. Nesta dissertação, trabalharemos com um portfólio de commodities de petróleo. Vamos unir diferentes técnicas e propor uma nova metodologia que consiste na diminuição da dimensão do portfólio proposto. O passo seguinte é simular os preços dos ativos na carteira e, em seguida, otimizar a alocação do portfólio de commodities de derivados do petróleo. Finalmente, vamos usar técnicas de backtest, a fim de validar nosso método. / [en] One of the main challenges in the financial market is to simulate prices keeping the correlation structure among numerous assets. Principal Component Analysis emerges as solution to the latter problem. Also, given the uncertainty present in commodities markets, an investor wants to protect his/her assets from potential losses, so as an alternative, the optimization of various risk measures, such as Value-at-risk, Conditional Value-at-risk and Omega Ratio, are important financial tools. Additionally, the backtest is widely used to validate and analyze the performance of the proposed methodology. In this dissertation, we will work with a portfolio of oil commodities. We will put together different techniques and propose a new methodology that consists in the (potentially) decrease the dimension of the proposed portfolio. The following step is to simulate the prices of the assets in the portfolio and then optimize the allocation of the portfolio of oil commodities. Finally, we will use backtest techniques in order to validate our method.

O uso de dados biométricos da face para verificação automática de identidade é um dos maiores desafios em sistemas de controle de acesso seguro. O processo é extremamente complexo e influenciado por muitos fatores relacionados à forma, posição, iluminação, rotação, translação, disfarce e oclusão de características faciais. Hoje existem muitas técnicas para se reconhecer uma face. Esse trabalho apresenta uma investigação buscando identificar uma face no banco de dados ORL com diferentes grupos de treinamento. É proposto um algoritmo para o reconhecimento de faces baseado na técnica de subespaço LDA (PCA + LDA) utilizando uma rede neural SOM para representar cada classe (face) na etapa de classificação/identificação. Aplicando o método do subespaço LDA busca-se extrair as características mais importantes na identificação das faces previamente conhecidas e presentes no banco de dados, criando um espaço dimensional menor e discriminante com relação ao espaço original. As redes SOM são responsáveis pela memorização das características de cada classe. O algoritmo oferece maior desempenho (taxas de reconhecimento entre 97% e 98%) com relação às adversidades e fontes de erros que prejudicam os métodos de reconhecimento de faces tradicionais. / The use of biometric technique for automatic personal identification is one of the biggest challenges in the security field. The process is complex because it is influenced by many factors related to the form, position, illumination, rotation, translation, disguise and occlusion of face characteristics. Now a days, there are many face recognition techniques. This work presents a methodology for searching a face in the ORL database with some different training sets. The algorithm for face recognition was based on sub-space LDA (PCA + LDA) technique using a SOM neural net to represent each class (face) in the stage of classification/identification. By applying the sub-space LDA method, we extract the most important characteristics in the identification of previously known faces that belong to the database, creating a reduced and more discriminated dimensional space than the original space. The SOM nets are responsible for the memorization of each class characteristic. The algorithm offers great performance (recognition rates between 97% and 98%) considering the adversities and sources of errors inherent to the traditional methods of face recognition.

Esta tese foi dedicada à duas alternativas para tratamento dos lixiviados de aterros sanitários. A primeira delas, o tratamento consorciado do lixiviado com esgoto sanitário em sistemas aeróbios, teve como objetivo principal verificar se a remoção da matéria orgânica do lixiviado seria devida à biodegradação ou à simples diluição no esgoto sanitário. Para responder esse questionamento, propôs-se o método tentativo \"equivalente em ácido húmico\" (Eq.AH). Em ensaios com reatores de lodos ativados (10 L) operados em batelada, avaliaram-se as remoções de matéria orgânica e nitrogênio para diferentes misturas de lixiviado e esgoto sanitários brutos e pré-tratados, com proporções volumétricas de lixiviado de 0, 0,2, 2 e 5%. O tratamento foi mais eficiente para a mistura esgoto bruto e lixiviado pré-tratado por air stripping (para remoção da amônia) na proporção volumétrica de 2%. Essa condição foi avaliada em reatores piloto de lodos ativados (95 L) e biofiltro aerado submerso (178 L), alimentados continuamente com tempo de detenção hidráulica (TDH) de 24 h. O reator piloto de lodos ativados removeu 59% do COD e a eficiência de nitrificação foi de 60%; enquanto que o biofiltro removeu 83% do COD e eficiência de nitrificação foi de 77%. Com o método tentativo Eq.AH, verificou-se que a remoção da matéria orgânica do lixiviado pré-tratado se deu por biodegradação parcial com o esgoto sanitário, resultado confirmado por espectroscopia de infravermelho por transformada de Fourier. As remoções do COD Eq.AH nos reatores piloto de lodos ativados e biofiltro aerado submerso foram de, respectivamente, 47 e 71%. Adicionalmente, o monitoramento da remoção da matéria orgânica pôde ser realizado com eficácia pelo teste de coloração com nanquim, utilizando o método de classificação de tonalidades proposto nesta Tese. A segunda alternativa proposta nesta Tese consistiu no tratamento dos lixiviados bruto e pré-tratado com cal em reatores de lodos ativados. Os resultados, todavia, foram insatisfatórios: indicaram que essa alternativa se mostrou inviável: após 20 dias de aeração nos reatores de bancada alimentados em batelada, a remoção da matéria orgânica foi inferior a 40% e a remoção do nitrogênio foi devida à volatilização da amônia. / This thesis was dedicated to two alternatives for landfill leachate treatment. The first one, the aerobic co-treatment of leachate and domestic wastewater in aerobic systems, aimed to verify if the organic matter of leachate was removed by biodegradation or dilution with domestic wastewater. To answer this questioning, it was proposed the tentative method \"equivalent in humic acid\" (Eq.HA). In the experiments with bench-scale activated sludge reactors (10 L) operated in batch mode, it was evaluated the organic matter and nitrogen removal from mixtures containing raw and pre-treated leachate and domestic wastewater, at the volumetric ratios of 0, 0.2, 2 and 5%. The treatment was mostly efficient when it was used the mixture domestic wastewater and leachate pre-treated by air stripping (for ammonia removal), at a volumetric ratio of 2%. This condition was also evaluated in a pilot-scale activated sludge reactor (95 L) and a submerged aerobic biofilter (178 L), operated under continuous-flow regime with a 24-h hydraulic retention time. The pilot-scale activated sludge reactor removed 59% of DOC and nitrification efficiency was 60%; whereas the submerged aerobic biofilter removed 83% of DOC and nitrification efficiency was 77%. Using the Eq.HA approach, it was determined that pre-treated leachate organic matter removal was due to partial biodegradation with domestic wastewater, which was confirmed by Fourier transform infrared spectroscopy. The removals of COD Eq.HA were 47% for the pilot-scale activated sludge reactor and 71% for the submerged aerobic biofilter. Aditionally, organic matter could be assessed with the India ink reverse stain test, using the proposed method for tonalities classification. The second alternative proposed by this Thesis consisted in the treatment of raw and pre-treated leachate by lime addition, using activated sludge reactors. The results did not indicate the feasibility of this alternative: after 20 days of aeration, the organic matter removal was lesser than 40%, and nitrogen was mostly removed by ammonia volatilization.

No description available.

Esta tese foi dedicada à duas alternativas para tratamento dos lixiviados de aterros sanitários. A primeira delas, o tratamento consorciado do lixiviado com esgoto sanitário em sistemas aeróbios, teve como objetivo principal verificar se a remoção da matéria orgânica do lixiviado seria devida à biodegradação ou à simples diluição no esgoto sanitário. Para responder esse questionamento, propôs-se o método tentativo \"equivalente em ácido húmico\" (Eq.AH). Em ensaios com reatores de lodos ativados (10 L) operados em batelada, avaliaram-se as remoções de matéria orgânica e nitrogênio para diferentes misturas de lixiviado e esgoto sanitários brutos e pré-tratados, com proporções volumétricas de lixiviado de 0, 0,2, 2 e 5%. O tratamento foi mais eficiente para a mistura esgoto bruto e lixiviado pré-tratado por air stripping (para remoção da amônia) na proporção volumétrica de 2%. Essa condição foi avaliada em reatores piloto de lodos ativados (95 L) e biofiltro aerado submerso (178 L), alimentados continuamente com tempo de detenção hidráulica (TDH) de 24 h. O reator piloto de lodos ativados removeu 59% do COD e a eficiência de nitrificação foi de 60%; enquanto que o biofiltro removeu 83% do COD e eficiência de nitrificação foi de 77%. Com o método tentativo Eq.AH, verificou-se que a remoção da matéria orgânica do lixiviado pré-tratado se deu por biodegradação parcial com o esgoto sanitário, resultado confirmado por espectroscopia de infravermelho por transformada de Fourier. As remoções do COD Eq.AH nos reatores piloto de lodos ativados e biofiltro aerado submerso foram de, respectivamente, 47 e 71%. Adicionalmente, o monitoramento da remoção da matéria orgânica pôde ser realizado com eficácia pelo teste de coloração com nanquim, utilizando o método de classificação de tonalidades proposto nesta Tese. A segunda alternativa proposta nesta Tese consistiu no tratamento dos lixiviados bruto e pré-tratado com cal em reatores de lodos ativados. Os resultados, todavia, foram insatisfatórios: indicaram que essa alternativa se mostrou inviável: após 20 dias de aeração nos reatores de bancada alimentados em batelada, a remoção da matéria orgânica foi inferior a 40% e a remoção do nitrogênio foi devida à volatilização da amônia. / This thesis was dedicated to two alternatives for landfill leachate treatment. The first one, the aerobic co-treatment of leachate and domestic wastewater in aerobic systems, aimed to verify if the organic matter of leachate was removed by biodegradation or dilution with domestic wastewater. To answer this questioning, it was proposed the tentative method \"equivalent in humic acid\" (Eq.HA). In the experiments with bench-scale activated sludge reactors (10 L) operated in batch mode, it was evaluated the organic matter and nitrogen removal from mixtures containing raw and pre-treated leachate and domestic wastewater, at the volumetric ratios of 0, 0.2, 2 and 5%. The treatment was mostly efficient when it was used the mixture domestic wastewater and leachate pre-treated by air stripping (for ammonia removal), at a volumetric ratio of 2%. This condition was also evaluated in a pilot-scale activated sludge reactor (95 L) and a submerged aerobic biofilter (178 L), operated under continuous-flow regime with a 24-h hydraulic retention time. The pilot-scale activated sludge reactor removed 59% of DOC and nitrification efficiency was 60%; whereas the submerged aerobic biofilter removed 83% of DOC and nitrification efficiency was 77%. Using the Eq.HA approach, it was determined that pre-treated leachate organic matter removal was due to partial biodegradation with domestic wastewater, which was confirmed by Fourier transform infrared spectroscopy. The removals of COD Eq.HA were 47% for the pilot-scale activated sludge reactor and 71% for the submerged aerobic biofilter. Aditionally, organic matter could be assessed with the India ink reverse stain test, using the proposed method for tonalities classification. The second alternative proposed by this Thesis consisted in the treatment of raw and pre-treated leachate by lime addition, using activated sludge reactors. The results did not indicate the feasibility of this alternative: after 20 days of aeration, the organic matter removal was lesser than 40%, and nitrogen was mostly removed by ammonia volatilization.

Orientador: Alexandre César Rodrigues da Silva / Resumo: O reconhecimento de atividades humanas abrange diversas técnicas de classificação que permitem identificar padrões específicos do comportamento humano no momento da ocorrência. A identificação é realizada analisando dados gerados por diversos sensores corporais, entre os quais destaca-se o acelerômetro, pois responde tanto à frequência como à intensidade dos movimentos. A identificação de atividades é uma área bastante explorada. Porém, existem desafios que necessitam ser superados, podendo-se mencionar a necessidade de sistemas leves, de fácil uso e aceitação por parte dos usuários e que cumpram com requerimentos de consumo de energia e de processamento de grandes quantidades de dados. Neste trabalho apresenta-se o desenvolvimento do Sistema de Reconhecimento de atividades Humanas e Avaliação do Equilíbrio Postural, denominado SIRAH. O sistema está baseado no uso de um acelerômetro localizado na cintura do usuário. As duas fases do reconhecimento de atividades são apresentadas, fase Offline e fase Online. A fase Offline trata do treinamento de uma rede neural artificial do tipo perceptron de três camadas. No treinamento foram avaliados três estudos de caso com conjuntos de atributos diferentes, visando medir o desempenho do classificador na diferenciação de 3 posturas e 4 atividades. No primeiro caso o treinamento foi realizado com 15 atributos, gerados no domínio do tempo, com os que a rede neural artificial alcançou uma precisão de 94,40%. No segundo caso foram gerados 34 ... (Resumo completo, clicar acesso eletrônico abaixo) / Doutor

La thèse se concentre sur une recherche méthodologique sur l'optimisation structurelle catégorielle au moyen d'un apprentissage multiple. Dans cette thèse, les variables catégorielles non ordinales sont traitées comme des variables discrètes multidimensionnelles. Afin de réduire la dimensionnalité, les nombreuses techniques d'apprentissage sont introduites pour trouver la dimensionnalité intrinsèque et mapper l'espace de conception d'origine sur un espace d'ordre réduit. Les mécanismes des techniques d'apprentissage à la fois linéaires et non linéaires sont d'abord étudiés. Ensuite, des exemples numériques sont testés pour comparer les performances de nombreuses techniques d’apprentissage. Sur la base de la représentation d'ordre réduit obtenue par Isomap, les opérateurs de mutation et de croisement évolutifs basés sur les graphes sont proposés pour traiter des problèmes d'optimisation structurelle catégoriels, notamment la conception du dôme, du cadre rigide de six étages et des structures en forme de dame. Ensuite, la méthode de recherche continue consistant à déplacer des asymptotes est exécutée et fournit une solution compétitive, mais inadmissible, en quelques rares itérations. Ensuite, lors de la deuxième étape, une stratégie de recherche discrète est proposée pour rechercher de meilleures solutions basées sur la recherche de voisins. Afin de traiter le cas dans lequel les instances de conception catégorielles sont réparties sur plusieurs variétés, nous proposons une méthode d'apprentissage des variétés k-variétés basée sur l'analyse en composantes principales pondérées. / The thesis concentrates on a methodological research on categorical structural optimizationby means of manifold learning. The main difficulty of handling the categorical optimization problems lies in the description of the categorical variables: they are presented in a category and do not have any orders. Thus the treatment of the design space is a key issue. In this thesis, the non-ordinal categorical variables are treated as multi-dimensional discrete variables, thus the dimensionality of corresponding design space becomes high. In order to reduce the dimensionality, the manifold learning techniques are introduced to find the intrinsic dimensionality and map the original design space to a reduced-order space. The mechanisms of both linear and non-linear manifold learning techniques are firstly studied. Then numerical examples are tested to compare the performance of manifold learning techniques mentioned above. It is found that the PCA and MDS can only deal with linear or globally approximately linear cases. Isomap preserves the geodesic distances for non-linear manifold however, its time consuming is the most. LLE preserves the neighbour weights and can yield good results in a short time. KPCA works like a non-linear classifier and we proves why it cannot preserve distances or angles in some cases. Based on the reduced-order representation obtained by Isomap, the graph-based evolutionary crossover and mutation operators are proposed to deal with categorical structural optimization problems, including the design of dome, six-story rigid frame and dame-like structures. The results show that the proposed graph-based evolutionary approach constructed on the reduced-order space performs more efficiently than traditional methods including simplex approach or evolutionary approach without reduced-order space. In chapter 5, the LLE is applied to reduce the data dimensionality and a polynomial interpolation helps to construct the responding surface from lower dimensional representation to original data. Then the continuous search method of moving asymptotes is executed and yields a competitively good but inadmissible solution within only a few of iteration numbers. Then in the second stage, a discrete search strategy is proposed to find out better solutions based on a neighbour search. The ten-bar truss and dome structural design problems are tested to show the validity of the method. In the end, this method is compared to the Simulated Annealing algorithm and Covariance Matrix Adaptation Evolutionary Strategy, showing its better optimization efficiency. In chapter 6, in order to deal with the case in which the categorical design instances are distributed on several manifolds, we propose a k-manifolds learning method based on the Weighted Principal Component Analysis. And the obtained manifolds are integrated in the lower dimensional design space. Then the method introduced in chapter 4 is applied to solve the ten-bar truss, the dome and the dame-like structural design problems.