This thesis is aimed at the optimum design of uncertain mechanical components and systems involving multiple objectives and constraints. There are various mechanical and design problems that are encountered every now and then which require the output that equalize several conflicting objectives. In recent years several methods have been developed to find a solution to multiobjective problems. The most efficient method for obtaining a compromise solution is the game theory method, which is based on the Pareto minimum or optimum solution. A thorough methodology is developed, and subsequently applied to three examples problems. The first problem is to design four helical springs which are further used to support a milling machine. The objective is to minimize the weight of the spring, also to minimize the deflection, and to maximize the natural frequency thus making the problem as a multiobjective problem. Further the subjected constraint is the shear stress constraint. After finding the optimized solution of the deterministic problem, the problem is again solved using Stochastic Nonlinear Programming, and after that it is solved using Interval Analysis. Game theory is used individually in all the three cases. The second problem is to design a gear box where the objectives are defined as the weight of the gear box, stress developed in the shaft 1, and the stress developed in shaft 2. It is subjected to nine constraints which are bending stress in teeth, contact stress of teeth, transverse displacement of shafts 1 and 2, and constraints related to the torque. The third problem is to design a power screw and the objective is to minimize the volume of the screw, and to maximize the critical buckling load and thus making it a multiobjective problem. It is subjected to constraints of being screw to be self locking, then the shear stress in screw thread, and the bearing stress in threads. The results of all the three problems that are achieved using Deterministic, Stochastic Nonlinear Programming, and Interval Analysis Method are tabulated, and the value of each objective achieved using these three methods for each problem at a time are compared to find out the most optimized solution.

Résumé : Le travail réalisé au cours de cette thèse traite de la mise au point de méthodes d’estimation d’état robuste, avec deux domaines d’application en ligne de mire. Le premier concerne le positionnement sécuritaire en transport. L’objectif est de fournir la position et la vitesse du véhicule sous la forme d’intervalles avec un grand degré de confiance. Le second concerne la synthèse de capteurs logiciels pour les bioprocédés, et en particulier la reconstruction des concentrations de composants réactionnels à partir d’un nombre limité de mesures et d’un modèle mathématique interprétant le comportement dynamique de ces composants. L’objectif principal est de concevoir des algorithmes qui puissent fournir des estimations acceptables en dépit des incertitudes provenant de la mauvaise connaissance du système comme les incertitudes sur les paramètres du modèle ou les incertitudes de mesures. Dans ce contexte, plusieurs algorithmes ont été étudiés et mis au point. Ainsi, dans le cadre du positionnement de véhicule, la recherche s’est dirigée vers les méthodes robustes Hinfini et les méthodes par intervalles. Les méthodes Hinfini sont des méthodes linéaires prenant en compte une incertitude dans la modélisation et réalisant une optimisation min-max, c’est-à-dire minimisant une fonction de coût qui représente la pire situation compte tenu des incertitudes paramétriques. La contribution de ce travail concerne l’extension à des modèles faiblement non linéaires et l’utilisation d’une fenêtre glissante pour faire face à des mesures asynchrones. Les méthodes par intervalles développées ont pour but de calculer les couloirs de confiance des variables position et vitesse en se basant sur la combinaison d’intervalles issus des capteurs d’une part et sur l’utilisation conjointe d’un modèle dynamique et cinématique du véhicule d’autre part. Dans le cadre des capteurs logiciels pour bioprocédés, trois familles de méthodes ont été étudiées: le filtrage particulaire, les méthodes par intervalles et le filtrage par horizon glissant. Le filtrage particulaire est basé sur des méthodes de Monte-Carlo pour estimer la densité de probabilité conditionnelle de l’état connaissant les mesures. Un de ses principaux inconvénients est sa sensibilité aux erreurs paramétriques. La méthode développée s’applique aux bioprocédés et profite de la structure particulière des modèles pour proposer une version du filtrage particulaire robuste aux incertitudes des paramètres cinétiques. Des méthodes d’estimation par intervalles sont adaptées à la situation où les mesures sont disponibles à des instants discrets, avec une faible fréquence d’échantillonnage, en développant des prédicteurs appropriés. L’utilisation d’un faisceau de prédicteurs grâce à des transformations d’état et le couplage entre les prédicteurs avec des réinitialisations fréquentes permettent d’améliorer les résultats d’estimation. Enfin, une méthode basée sur le filtre à horizon glissant est étudiée en effectuant une optimisation min-max : la meilleure condition initiale est reconstruite pour le plus mauvais modèle. Des solutions sont aussi proposées pour minimiser la quantité de calculs. Pour conclure, les méthodes et résultats obtenus constituent un ensemble d’améliorations dans le cadre de la mise au point d’algorithmes robustes vis-à-vis des incertitudes. Selon les applications et les objectifs fixés, telle ou telle famille de méthodes sera privilégiée. Cependant, dans un souci de robustesse, il est souvent utile de fournir les estimations sous forme d’intervalles auxquels est associé un niveau de confiance lié aux conditions de l’estimation. C’est pourquoi, une des méthodes les plus adaptées aux objectifs de robustesse est représentée par les méthodes par intervalles de confiance et leur développement constituera un point de recherche futur. __________________________________________ Abstract : This thesis work is about the synthesis of robust state estimation methods applied to two different domains. The first area is dedicated to the safe positioning in transport. The objective is to compute the vehicle position and velocity by intervals with a great confidence level. The second area is devoted to the software sensor design in bioprocess applications. The component concentrations are estimated from a limited number of measurements and a mathematical model describing the dynamical behavior of the system. The main interest is to design algorithms which achieve estimation performance and take uncertainties into account coming from the model parameters and the measurement errors. In this context, several algorithms have been studied and designed. Concerning the vehicle positioning, the research activities have led to robust Hinfinity methods and interval estimation methods. The robust Hinfinity methods use a linear model taking model uncertainty into account and perform a min-max optimization, minimizing a cost function which describes the worst-case configuration. The contribution in this domain is an extension to some systems with a nonlinear model and the use of a receding time window facing with asynchronous data. The developed interval algorithms compute confidence intervals of the vehicle velocity and position. They use interval combinations by union and intersection operations obtained from sensors along with kinematic and dynamic models. In the context of bioprocesses, three families of state estimation methods have been investigated: particle filtering, interval methods and moving-horizon filtering. The particle filtering is based on Monte-Carlo drawings to estimate the posterior probability density function of the state variables knowing the measurements. A major drawback is its sensitivity to model uncertainties. The proposed algorithm is dedicated to bioprocess applications and takes advantage of the characteristic structure of the models to design an alternative version of the particle filter which is robust to uncertainties in the kinetic terms. Moreover, interval observers are designed in the context of bioprocesses. The objective is to extend the existing methods to discrete-time measurements by developing interval predictors. The use of a bundle of interval predictors thanks to state transformations and the use of the predictor coupling with reinitializations improve significantly the estimation performance. Finally, a moving-horizon filter is designed, based on a min-max optimization problem. The best initial conditions are generated from the model using the worst parameter configuration. Furthermore, additional solutions have been provided to reduce the computational cost. To conclude, the developed algorithms and related results can be seen as improvements in the design of estimation methods which are robust to uncertainties. According to the application and the objectives, a family may be favored. However, in order to satisfy some robustness criteria, an interval is preferred along with a measure of the confidence level describing the conditions of the estimation. That is why, the development of confidence interval observers represents an important topic in the future fields of investigation.

This study investigated the reproduction and survival of Formosan macaques (Macaca cyclopis). Data on birth and death of Formosan macaques at Mt. Longevity were collected from 1996 till 2006. The birth of Formosan macaques peaked from April to June (94.4%). The sex ratio of 604 infants at birth was 1:1.2 (female to male), which was not significantly different from 1:1. The death of less than one-month-old infants accounted for 22.2% of all infant death. Infant mortality (less than 1 years old) was very high (35.2%) and no sexual difference was found (p > 0.05). Mortality of males equal or older than 6 years old (16.8-33.3%) were higher than those of females (p < 0.05). In primiparous females, most females (57.6%) gave birth at four years old. The average interbirth intervals of females after infant death within the first 3 months was 0.96 years (¡Ó 0.07, n = 23) which was significantly shorter than that after the successful rearing infants (1.02 years ¡Ó 0.09, n = 185, p < 0.05). Maternal ranks, age, infant sex ratio and troop size had no significant effect on the interbirth intervals (p > 0.05). The average interbirth intervals of high-ranking females (1.03 years) were similar to those from middle- (1.10 years) and low-ranking females (1.01 years). The average interbirth intervals after daughters were slightly longer than those after sons (1.02 and 1.01 years, prospectively). Interbirth intervals among small-sized troops (0.97 years) was slightly shorter than those from large- (1.02 years) and middle-sized troops (1.00 years). The birth rates of high- and middle-ranking females (66.3% and 68.0%, prospectively) were significantly higher than that of low-ranking females (45.6%, p < 0.05). Maternal rank and age had no significant effect on male infant ratio (p > 0.05). However, male infant ratio of high-ranking and young-aged females (76.2%) was 1.3-1.6 times of high-ranking, middle- and old-aged females, 1.5-1.7 times of middle-, low-ranking and young-aged females. Male infant ratio of middle troop size and high-ranking females (66.7%) was 1.2-1.4 times of large- and small-sized troops; 1.4-1.5 times of middle troop size and middle- and low-ranking females.

The strength of time-dependent correlations known as stride interval (SI) dynamics have been proposed as an indicator of neurologically healthy gait. Most recently, it has been hypothesized that these dynamics may be necessary for gait efficiency although the supporting evidence to date is limited. To gain a better understanding of this relationship, this study investigated stride interval dynamics, the energy cost of walking, and physical activity in a pediatric population. The findings indicate that differences in energy cost are not reflected in the stride interval dynamics of able-bodied children. Interestingly, increasing physical activity levels were associated with decreasing variance in stride interval dynamics between subjects, though this finding only approached significance (p=0.054). Lastly, this study found that stride interval dynamics in children as young as nine years were comparable to stride interval dynamics found in healthy young adults.

The strength of time-dependent correlations known as stride interval (SI) dynamics have been proposed as an indicator of neurologically healthy gait. Most recently, it has been hypothesized that these dynamics may be necessary for gait efficiency although the supporting evidence to date is limited. To gain a better understanding of this relationship, this study investigated stride interval dynamics, the energy cost of walking, and physical activity in a pediatric population. The findings indicate that differences in energy cost are not reflected in the stride interval dynamics of able-bodied children. Interestingly, increasing physical activity levels were associated with decreasing variance in stride interval dynamics between subjects, though this finding only approached significance (p=0.054). Lastly, this study found that stride interval dynamics in children as young as nine years were comparable to stride interval dynamics found in healthy young adults.

The receiver operating characteristic, or the ROC curve, is widely utilized to evaluate the diagnostic performance of a test, in other words, the accuracy of a test to discriminate normal cases from diseased cases. In the biomedical studies, we often meet with missing data, which the regular inference procedures cannot be applied to directly. In this thesis, the random hot deck imputation is used to obtain a 'complete' sample. Then empirical likelihood (EL) confidence intervals are constructed for ROC curves. The empirical log-likelihood ratio statistic is derived whose asymptotic distribution isproved to be a weighted chi-square distribution. The results of simulation study show that the EL confidence intervals perform well in terms of the coverage probability and the average length for various sample sizes and response rates.

An <i>Interval Routing Scheme (IRS)</i> represents the routing tables in a network in a space-efficient way by labeling each vertex with an unique integer address and the outgoing edges at each vertex with disjoint subintervals of these addresses. An IRS that has at most <i>k</i> intervals per edge label is called a <i>k-IRS</i>. In this thesis, we propose a new type of interval routing scheme, called an <i>Ordered Interval Routing Scheme (OIRS)</i>, that uses an ordering of the outgoing edges at each vertex and allows nondisjoint intervals in the labels of those edges. Our results on a number of graphs show that using an OIRS instead of an IRS reduces the size of the routing tables in the case of <i>optimal</i> routing, i. e. , routing along shortest paths. We show that optimal routing in any <i>k</i>-tree is possible using an OIRS with at most 2^k-1 intervals per edge label, although the best known result for an IRS is 2^k+1 intervals per edge label. Any torus has an optimal 1-OIRS, although it may not have an optimal 1-IRS. We present similar results for the Petersen graph, <i>k</i>-garland graphs and a few other graphs.

An <i>Interval Routing Scheme (IRS)</i> represents the routing tables in a network in a space-efficient way by labeling each vertex with an unique integer address and the outgoing edges at each vertex with disjoint subintervals of these addresses. An IRS that has at most <i>k</i> intervals per edge label is called a <i>k-IRS</i>. In this thesis, we propose a new type of interval routing scheme, called an <i>Ordered Interval Routing Scheme (OIRS)</i>, that uses an ordering of the outgoing edges at each vertex and allows nondisjoint intervals in the labels of those edges. Our results on a number of graphs show that using an OIRS instead of an IRS reduces the size of the routing tables in the case of <i>optimal</i> routing, i. e. , routing along shortest paths. We show that optimal routing in any <i>k</i>-tree is possible using an OIRS with at most 2^k-1 intervals per edge label, although the best known result for an IRS is 2^k+1 intervals per edge label. Any torus has an optimal 1-OIRS, although it may not have an optimal 1-IRS. We present similar results for the Petersen graph, <i>k</i>-garland graphs and a few other graphs.

A nonparametric test for the interval-censored failure time data is proposed in determining whether p lifetime populations come from the same distribution. For the comparison problem based on interval-censored failure time data, Sun proposed some nonparametric test procedures in recent year. In this paper, we present simulation procedures to verify the test proposed by Sun. The simulation results indicate that the proposed test is not approximately Chisquare distribution with degrees of freedom p-1 but Chisquare distribution with degrees of freedom p-1 times a constant.

The field strength prediction chart is a set of statistical curves obtained through the analysis of huge amount of field strength measurement data of the specific radio band in some area. It reflects the natural or artificial effects such as geography, atmospheric condition and buildings, etc. that affect the radio wave propagation. One advantage is that we can predict the rough relationship between the field strength and distance easily. As a result, we don¡¦t have to perform simulation field measurement in every radio planning. With prediction chart and field strength interference /protection ratio standard, we can suggest a minimum distance separation criterion between co-channel and adjacent channel broadcasting stations. It also provides a reference to authority to examine the broadcasting service application. The FCC develops the F(50,50) charts and minimum separation between radio stations base on data collected in the U.S.. Presently, the regulations concerning the broadcasting applications in Taiwan still follow the FCC¡¦s suggestion. In general, the field strength distribution is affected by two main factors: geography and atmospheric condition, which can be different from those in the U.S.. With the acquisition of digital terrain data of Taiwan, the terrain profile for a given path can be generated. In this thesis, we¡¦ll use Deygout model and the database of existed broadcasting stations to generate field strength distribution database for each station and analyze the database to develop the prediction chart that is suitable for the propagation environment in Taiwan. When combine with the field strength interference /protection ratio standard, we¡¦ll provide a minimum distance separation criterion of co-channel and adjacent channel in the FM band broadcasting stations. Our study can help the authority to achieve the most effective spectrum management in FM band.