Bridge redundancy can be described as the capacity that a bridge has to continue carrying loads after suffering the failure of one or more main structural components without undergoing significant deformations. In the current AASHTO LRFD Bridge Design Specification, two-girder bridges are classified as fracture critical, which implies that these bridges are not inherently redundant. Therefore, two-girder bridges require more frequent and detailed inspections than other types of bridges, resulting in greater costs for their operation. Despite the fracture-critical classification of two-girder bridges, several historical events involving the failure of main load-carrying members in two-girder bridges constructed of steel plate girders have demonstrated their ability to have significant reserve load carrying capacity. Relative to the steel plate girder bridges, steel box-girder bridges have higher torsional stiffness and more structural elements that might contribute to load redistribution in the event of a fracture of one or more bridge main members. These observations initiated questions on the inherent redundancy that twin box-girder bridges might possess. Given the high costs associated with the maintenance and the inspection of these bridges, there is interest in accurately characterizing the redundancy of bridge systems. In this study, twin steel box-girder bridges, which have become popular in recent years due to their aesthetics and high torsional resistance, were investigated to characterize and to define redundancy sources that could exist in this type of bridge. For this purpose, detailed finite element bridge models were developed with various modeling techniques to capture critical aspects of response of bridges suffering severe levels of damage. The finite element models included inelastic material behavior and nonlinear geometry, and they also accounted for the complex interaction of the shear studs with the concrete deck under progressing levels of damage. In conjunction with the computational analysis approach, three full-scale bridge fracture tests were carried out during this research project, and data collected from these tests were utilized to validate the results obtained from the finite element models. / text

Land-use change is the single most important global driver of changes in biodiversity. Such changes in biodiversity, in turn, are expected to influence the functioning of ecosystems and their resilience to environmental perturbations and disturbances. It is widely recognised that the use of functional traits and functional diversity is best for understanding the causes and functional consequences of changes in biodiversity, but conceptual development has outpaced empirical applications. This thesis explores these ideas in grazing systems, which are expected to undergo rapid intensification of fertiliser use and grazing pressure to meet the growing global demand for livestock products. First, a flexible framework for measuring different facets of functional diversity is described, and a new multidimensional functional diversity index, called functional dispersion (FDis), is presented. Second, two vegetation sampling methods are compared with regard to their ability to detect changes in vegetation composition. Third, shifts in plant trait distributions following land-use changes are quantified and compared to null models, and a maximum entropy approach is used to quantify the direction and strength of selection on each trait. Fourth, it is shown that these shifts in trait distributions have cascading effects on primary production, litter decomposition, soil respiration, and ultimately soil carbon sequestration. Finally, data from 18 land-use intensity gradients are used to show that land-use intensification reduces functional redundancy and response diversity, two components of biodiversity that are thought to influence ecosystem resilience to future disturbances. This study illustrates (i) the importance of considering species functional differences to understand how plant communities react to changes in soil resource availability and grazing pressure, and (ii) how such changes directly, indirectly, and interactively control ecosystem functioning, as well as (iii) increasing the vulnerability of ecosystems to future disturbances.

L’utilisation de robots collaboratifs dans l’industrie de production est en plein essor. Ces robots, dont la puissance est limitée, sont dotés de capteurs leur permettant de détecter la présence d’obstacles, afin de garantir la sécurité des humains se trouvant aux alentours. On s’intéresse dans cette thèse à l’utilisation de systèmes redondants, collaboratifs et mobiles (bras articulés montés sur plateformes mobiles), dans un environnement de production aéronautique peuplé d’humains, pour la réalisation d’opérations d’assemblage. Du point de vue des process, l’utilisation de ces systèmes, souvent beaucoup moins imposants et rigides que leurs homologues non collaboratifs, est jalonnée de défis. La grande souplesse mécanique et les faibles couples qui les caractérisent peuvent induire des imprécisions de positionnement et une incapacité à soutenir l’intensité d’une interaction physique. Ce contexte induit également un besoin d’autonomie de ces systèmes, qui sont amenés à travailler dans des environnements en perpétuelle évolution. Dans cette thèse, une formulation de la redondance cinématique est d’abord présentée. Le formalisme associé permet de simplifier l’exploitation de la liberté que ces systèmes possèdent sur le choix des postures à utiliser pour réaliser des tâches de placement statique de l’effecteur. Ce formalisme est ensuite exploité pour améliorer et caractériser le comportement en déformation et la capacité d’application d’efforts des systèmes redondants sériels. Enfin, le sujet de la planification des mouvements de systèmes robotisés dans un environnement dynamique et encombré est considéré. La solution présentée adapte l’algorithme bien connu des Probabilistic RoadMaps pour y inclure une anticipation des trajectoires des obstacles dynamiques. Cette solution permet de planifier des mouvements sécuritaires, peu intrusifs et efficaces, jusqu’à la destination. / Industrial applications involving collaborative robots are regarded with a growing interest. These power-limited systems are embedded with additional sensing capabilities, which allow them to safely work around humans and conquer new industrial grounds. The subject of managing redundant, collaborative and mobile systems, for assembly operations within a human-populated aircraft production environment, is addressed in this thesis. From a process perspective, the use of these smaller and less stiff counterparts of the non-collaborative robots comes with new challenges. Their high mechanical flexibility and weak actuation can cause shortcomings in positioning accuracy or for interaction force sustainment. The ever-changing nature of human-populated environments also requires highly autonomous solutions. In this thesis, a formulation of positional redundancy is presented. It aims at simplifying the exploitation of the freedom redundant manipulators have on static-task-fulfilling postures. The associated formalism is then exploited to characterise and improve the deformational behaviour and the force capacity of redundant serial systems. Finally, the subject of planning motions within cluttered and dynamic environments is addressed. An adaptation of the well-known Probabilistic RoadMaps method is presented – to which obstacles trajectories anticipation has been included. This solution allows to plan safe, efficient and non-intrusive motions to a given destination.

Les travaux présentés dans cette thèse portent sur la commande en couple de manipulateurs redondants.Nous nous intéressons dans ce cadre à deux problématiques. En premier lieu, nous considérons le cas d’imposition d’une contrainte cinématique de point de passage, dite contrainte du RCM, de l’organe terminal (OT) du robot. Nous proposons alors deux approches pour la gestion de cette contrainte. Dans la première approche, la contrainte est garantie dans l’espace nul d’une tâche principale définie en coordonnées de position de l’OT. Cette méthode exploite une définition explicite de la dynamique de l’espace nul et confère un niveau de priorité secondaire à la contrainte. La seconde approche permet de définir la contrainte du RCM comme tâche principale, en lui assignant le niveau de priorité supérieur ou un niveau de priorité défini par le besoin de l’application. Nous proposons pour cela une nouvelle définition de la cinématique du RCM.En second lieu, nous traitons la question des contacts entre le corps du robot et son environnement (ex. l’humain)pendant que l’OT exécute sa tâche « globale ». Nous proposons pour cela une stratégie de compliance appliquée dans l’espace nul du robot afin de préserver la tâche globale lors des contacts. Cette stratégie estdéfinie pour des bras anthropomorphes à 7-DDL, et est formulée en coordonnées de l’angle de bras, paramètre représentant le degré de redondance du robot. Cela permet de définir un intervalle admissible de mouvement de l’angle de bras. Lorsque les limites de cet intervalle sont atteintes, une loi de compliance de type ressort amortisseur oblige le robot à rester dans l’intervalle, malgré les forces externes exercées.Nous évoquons, tout au long de cette thèse, l’application de chirurgie mini-invasive assistée par robot pour illustrer l’utilité de nos contributions. / The work developped in this PhD thesis concerns the control of redundant torque-controlled robots,dealing with two main issues. Firstly, we study the presence of a RCM constraint imposed to the end-effector. We propose two control approaches to guarantee this kinematic constraint. In the first one, the constraint is performed in the null-space of a main task defined in cartesian coordinates(position). An explicit definition of the null-space dynamics is applied on this control approach, and provides a secondary priority order to the RCM constraint. The second approach allows to define the constraint as the main task, obtaining the highest priority level, or in any desired priority level,according to the needs of the application. Therefore, we propose a new kinematic formulation of the RCM constraint.Secondly, we study the physical interaction between the robot’s body and its environment (e.g. human) during the cartesian global task execution. A null-space compliance control strategy is then proposed in order to preserve the global task when the contacts occur. This strategy, defined for anthropomorphic 7-DOF robots, is formulated in swivel angle coordinates, which is a direct representation of the robot’s null-space. A desired feasible range for the swivel angle values is defined by the user, and a spring-damping compliance law is used to constraint the robot to remain within the feasible angle values range, despite the external forces applied to the robot’s body. Robot-assisted minimally invasive surgery has been used throughout this thesis as an example of application, allowing to demonstrate the usefulness of our contributions.

L’objectif de ce mémoire de thèse est de valider les mesures débimétriques issues des réseaux d’assainissement. Des défaillances techniques dans les capteurs de mesure ou l’existence des phénomènes perturbateurs produisent des anomalies sur ces mesures. Notre travail consiste à proposer une procédure de diagnostic hors ligne capable de détecter et de localiser les défauts de mesures. Cette procédure est à base de modèles analytiques. Nous avons établi dans un premier temps, un ensemble de modèles linéaires pour générer des résidus. Ces derniers ont permis d’établir la matrice des signatures des défauts expérimentales. Ensuite, une première technique de diagnostic a été considérée. Elle consiste à combiner le test de Page pour la détection des défauts et le calcul de distance Euclidienne entre les signatures des défauts théoriques et la signature expérimentale de chaque défaut pour la localisation des capteurs en défauts. Puis, deux autres techniques ont été proposées. Elles sont basées sur l’analyse conjointe des résidus générés et des symptômes des défauts. L’une est appelée DMP (Model Diagnostic Processor) et l’autre est à base de concepts de la logique floue. A la fin, les performances de ces techniques ont été calculées pour pouvoir les comparer. Nous avons amélioré les performances de la dernière technique en proposant un nouvel opérateur d’agrégation et en considérant la persistance des défauts. / The objective of this thesis is to validate flow rate measurements collected from the sewer networks. Technical failures in the sensors or the existence of the disturbing phenomena produce anomalies to these measures. Our work consists in proposing a procedure of diagnosis off line able to detect and isolate the defects of measurements. This procedure is based on analytical models. We first established, a set of linear models used to generate faults indicators called residuals. These last ones allowed us to establish the experimental faults signatures matrix. Then, a first technique of diagnosis was considered. It consists in combining the test of Page for faults detection and on the calculation of Euclidean distance between the theoretical faults signatures and the experimental fault signature of each defect for the isolation of the faulty sensor. Two other techniques suggested, are based on the joint analysis of the generated residuals and the symptoms of the defects. One is called DMP (Model Diagnostic Processor) and the other is based on the fuzzy logic concepts. In the end, the performances of these techniques were calculated to be able to compare them. We improved the performances of the last considered technique by proposing a new operator of aggregation and by considering the persistence of the defects.

La popularité des robots parallèles s’est considérablement accrue lors des dernières décennies. Cette popularité a été stimulée par les nombreux avantages qu’offrent les robots parallèles par rapport à leurs homologues traditionnels sériels concernant certaines applications industrielles nécessitant de fortes accélérations et une bonne précision. Toutefois, afin d'exploiter pleinement leur potentiel et de tirer le meilleur de leurs capacités, un long chemin reste encore à parcourir. En plus de la conception mécanique, l'étalonnage et l'optimisation de la structure, le développement d’une commande efficace joue un rôle primordial dans l’amélioration de la performance globale des robots parallèles. Cependant, ces derniers sont connus par leur dynamique fortement non linéaire qui s’accroît considérablement lorsque de fortes accélérations sont sollicitées conduisant à des vibrations mécaniques. En outre, les incertitudes sont abondantes dans ces systèmes en raison des hypothèses simplificatrices de modélisation, l'usure des composants du robot et les variations de l'environnement. De plus, leur dynamique couplée et la redondance d'actionnement dans certains mécanismes donnent lieu à des problèmes de commande complexes et difficiles à gérer. Par conséquent, les stratégies de commande développées pour les robots parallèles devraient tenir compte de tous les enjeux et défis mentionnées précédemment. L'objectif principal de cette thèse réside dans la proposition de nouvelles stratégies de commande adaptatives pour les robots parallèles tenant compte de leurs caractéristiques et particularités afin d'améliorer leurs performances de suivi de trajectoires. En outre, les stratégies de commande développées devraient être validées d'abord en simulation, puis à travers des expérimentations temps-réel sur les robots parallèles à notre disposition. Dans ce contexte, trois contributions majeures sont proposées dans le cadre de cette thèse. Tout d'abord, une nouvelle classe de contrôleurs adaptatifs avec des gains de retour non linéaires temps-variant est proposée. La deuxième contribution réside dans le développement d’une version adaptative de la commande robuste RISE. Pour la troisième contribution, la stratégie de commande adaptative L1, récemment développée, est appliquée pour la première fois sur un robot parallèle, suivie de deux nouvelles extensions basées-modèle. Des simulations numériques ainsi que des expérimentations temps-réel sur différents prototypes de robots parallèles sont présentées et discutées. Tous les contrôleurs proposés sont validés pour différents scénarios permettant ainsi de montrer leur pertinence et efficacité. / Parallel Kinematic Manipulators (PKMs) have gained an increased popularity in the last few decades. This interest has been stimulated by the significant advantages of PKMs compared to their traditional serial counterparts, with respect to some specific industrial tasks requiring high accelerations and accuracy. However, to fully exploit their potential and to get the most of their capabilities, a long path is still to be covered. In addition to mechanical design, calibration and optimization of the structure, efficient control development plays an essential role in improving the overall performance of PKMs. However, PKMs are known for their highly nonlinear dynamics which increases considerably when operating at high accelerations leading to mechanical vibrations. Moreover, uncertainties are abundant in such systems due to model simplifications, the wear of the components of the robot and the variations of the environment. Furthermore, their coupled dynamics and actuation redundancy in some mechanisms give rise to complex and challenging control issues. Consequently, the developed control schemes should take into account all the previously mentioned issues and challenges. The main goal of this thesis lies in the proposal of new adaptive control schemes for PKMs while considering their characteristics and particularities in order to improve their tracking capabilities. Moreover, the developed control strategies should be first validated through numerical simulations, then through real-time experiments on available PKMs. Within this context, three main contributions are proposed in this thesis. First, a new class of adaptive controllers with nonlinear time-varying feedback gains is proposed. The second contribution lies in an adaptive-based extended version of RISE robust feedback control strategy. For the third contribution, the recently developed L1 adaptive control strategy is applied for the first time on a PKM, followed by two novel model-based extensions. Numerical simulations as well as real-time experiments on various PKMs prototypes are provided and discussed. All the proposed controllers are validated for different operating conditions in order to show their relevance and efficiency.

Tang Wai Sum. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 68-70). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Redundant Manipulators --- p.1 / Chapter 1.2 --- Inverse Kinematics of Robotic Manipulators --- p.2 / Chapter 1.3 --- Inverse Dynamics of Robotic Manipulators --- p.4 / Chapter 1.4 --- Redundancy Resolutions of Manipulators --- p.5 / Chapter 1.5 --- Motivation of Using Neural Networks for these Applications --- p.9 / Chapter 1.6 --- Previous Work for Redundant Manipulator Inverse Kinematics and Inverse Dynamics Computation by Neural Networks --- p.9 / Chapter 1.7 --- Advantages of the Proposed Recurrent Neural Networks --- p.11 / Chapter 1.8 --- Contribution of this work --- p.11 / Chapter 1.9 --- Organization of this thesis --- p.12 / Chapter 2 --- Problem Formulations --- p.14 / Chapter 2.1 --- Constrained Optimization Problems for Inverse Kinematics Com- putation of Redundant Manipulators --- p.14 / Chapter 2.1.1 --- Primal and Dual Quadratic Programs for Bounded Joint Velocity Minimization --- p.14 / Chapter 2.1.2 --- Primal and Dual Linear Programs for Infinity-norm Joint Velocity Minimization --- p.15 / Chapter 2.2 --- Constrained Optimization Problems for Inverse Dynamics Com- putation of Redundant Manipulators --- p.17 / Chapter 2.2.1 --- Quadratic Program for Unbounded Joint Torque Mini- mization --- p.17 / Chapter 2.2.2 --- Primal and Dual Quadratic Programs for Bounded Joint Torque Minimization --- p.18 / Chapter 2.2.3 --- Primal and Dual Linear Programs for Infinity-norm Joint Torque Minimization --- p.19 / Chapter 3 --- Proposed Recurrent Neural Networks --- p.20 / Chapter 3.1 --- The Lagrangian Network --- p.21 / Chapter 3.1.1 --- Optimality Conditions for Unbounded Joint Torque Min- imization --- p.21 / Chapter 3.1.2 --- Dynamical Equations and Architecture --- p.22 / Chapter 3.2 --- The Primal-Dual Network 1 --- p.24 / Chapter 3.2.1 --- Optimality Conditions for Bounded Joint Velocity Min- imization --- p.24 / Chapter 3.2.2 --- Dynamical Equations and Architecture for Bounded Joint Velocity Minimization --- p.26 / Chapter 3.2.3 --- Optimality Conditions for Bounded Joint Torque Mini- mization --- p.27 / Chapter 3.2.4 --- Dynamical Equations and Architecture for Bounded Joint Torque Minimization --- p.28 / Chapter 3.3 --- The Primal-Dual Network 2 --- p.29 / Chapter 3.3.1 --- Energy Function for Infinity-norm Joint Velocity Mini- mization Problem --- p.29 / Chapter 3.3.2 --- Dynamical Equations for Infinity-norm Joint Velocity Minimization --- p.30 / Chapter 3.3.3 --- Energy Functions for Infinity-norm Joint Torque Mini- mization Problem --- p.32 / Chapter 3.3.4 --- Dynamical Equations for Infinity-norm Joint Torque Min- imization --- p.32 / Chapter 3.4 --- Selection of the Positive Scaling Constant --- p.33 / Chapter 4 --- Stability Analysis of Neural Networks --- p.36 / Chapter 4.1 --- The Lagrangian Network --- p.36 / Chapter 4.2 --- The Primal-Dual Network 1 --- p.38 / Chapter 4.3 --- The Primal-Dual Network 2 --- p.41 / Chapter 5 --- Simulation Results and Network Complexity --- p.45 / Chapter 5.1 --- Simulation Results of Inverse Kinematics Computation in Re- dundant Manipulators --- p.45 / Chapter 5.1.1 --- Bounded Least Squares Joint Velocities Computation Using the Primal-Dual Network 1 --- p.46 / Chapter 5.1.2 --- Minimum Infinity-norm Joint Velocities Computation Us- ing the Primal-Dual Network 2 --- p.49 / Chapter 5.2 --- Simulation Results of Inverse Dynamics Computation in Redun- dant Manipulators --- p.51 / Chapter 5.2.1 --- Minimum Unbounded Joint Torques Computation Using the Lagrangian Network --- p.54 / Chapter 5.2.2 --- Minimum Bounded Joint Torques Computation Using the Primal-Dual Network 1 --- p.57 / Chapter 5.2.3 --- Minimum Infinity-norm Joint Torques Computation Us- ing the Primal-Dual Network 2 --- p.59 / Chapter 5.3 --- Network Complexity Analysis --- p.60 / Chapter 6 --- Concluding Remarks and Future Work --- p.64 / Publications Resulted from the Study --- p.66 / Bibliography --- p.68

Nas indústrias química e petroquímica o uso de sistemas redundantes é comum. Exceto pelos programas de lubrificação, a estratégia de manutenção adotada para estes sistemas é, principalmente, a manutenção corretiva. Os objetivos desta dissertação são, a partir do registro do histórico de falhas dos equipamentos de uma unidade fabril petroquímica e conceitos de confiabilidade, estimar o tempo limite que estes sistemas podem operar sem intervenções de manutenção, mantendo a disponibilidade do sistema em níveis adequados. Esse tempo limite foi usado para desenvolver um indicador a ser utilizado no processo de priorização das atividades de manutenção. Para atingir os objetivos foram desenvolvidas as seguintes etapas: a) revisão dos dados de confiabilidade; b) elaboração de modelagem de sistemas de bombeamento. Inicialmente foi realizada uma revisão dos dados de confiabilidade coletados pela empresa em estudo, a partir da qual se obteve análise dos problemas encontrados com os dados, sumário de procedimentos a serem adotados para cada tipo de problema e sugestões para evitar sua reincidência. Por meio dos resultados iniciais, foi elaborada a modelagem de sistemas de bombeamento, utilizando o método de Monte Carlo. Obtevese, como resultado, curvas de disponibilidade do sistema versus tempos para reparo. O método proposto é simples de ser utilizado em campo e, definida a disponibilidade desejada para o sistema redundante, permite o cálculo do máximo tempo para reparo do equipamento em falha. / In chemical and petrochemical industries redundant systems are usual. Except by lubrication programs, the maintenance strategy adopted for these systems is mainly corrective maintenance. Considering the historical failure records of the equipment of a factory and the use of reliability concepts, the goal of this work is to estimate the maximum time that these systems can operate without maintenance interference, while keeping the system availability on adequate levels. This maximum time was used to develop an indicator to be used in the process of prioritization of maintenance activities. To achieve these goals, the following steps have been developed: a) reliability data review; b) elaboration of a pumping system model. Initially, a review of the reliability data collect at the studied company was performed, from which an analysis of the problems encountered at these data, a summary of procedures to be adopted for each type of problem, and suggestions to avoid its recurrence were established. As a consequence of first results, a model for each pumping system using the Monte Carlo method was developed and availability curves of the system versus time to repair were obtained. The proposed method is simple to use in the field and, considering the desired availability for the redundant system, it allows the calculation of the maximum time to repair equipment failures.

L’objectif de ce travail est de montrer — à partir d’un corpus d’entretiens télévisés filmés à deux périodes différentes, 1967-1972 et 2007-2012 — comment se manifestent, en français parlé, les phénomènes de redondance prédicative, c’est-à-dire de reprise du sens d’une prédication (l’énoncé-source) par une autre prédication (l’énoncé reformulé). Le cadre théorique choisi pour mener à bien cette recherche est celui du Lexique-Grammaire élaboré par Maurice Gross et son équipe du LADL, ainsi que la théorie de la reformulation élaborée par Claire Martinot à partir de 1994. Cette reprise, qui suppose la préservation du sens d’origine, peut être strictement littérale (répétition), porter sur des processus uniquement syntaxiques(transformation), consister en une clarification du sens de l’énoncé-source (paraphrase définitoire) ou instaurer une équivalence de sens sans fondement syntaxique (paraphrases sémantiques sensibles ou non à l’influence du contexte). L’hypothèse de départ de ce travail est que mettre en relation milieux sociaux, époques d’enregistrement et types de reformulation doit révéler quels paramètres expliquent le mieux l’usage préférentiel de tel ou tel type de redondance par telle ou telle catégorie de locuteurs. / The purpose of this research project is to show, from a corpus of televised interviews shot in two different periods, 1967-1972 and 2007-2012, how predicative redundancy phenomena occur in spoken French, that is, how a source phrase can be taken over by another phrase. The theoretical frame adopted to lead this research is the Lexicon-Grammar developed by Maurice Gross and his LADL team, as well as the reformulation theory Claire Martinot has been developing since 1994. This rewording, which assumes the preservation of the semantic data of the original phrase, may be strictly literal (repetition), concern only syntactic processes (transformation), consist of a clarification of the meaning of the source phrase (in that case, a form of definition) or institute a semantic equivalence between the phrases without any syntactic corollation, this last type of redundancy proving to be either context-free or context-sensitive. The initial hypothesis of this research project is that making connections between social environments, dates of recording, and types of rewording must be possible and must reveal explanations about the preferential use of specific types of redundancy by specific categories of speakers.

Semiconductor manufacturing defects adversely affect yield and reliability. Manufacturers expend vast resources to reduce defects within their processes. As the minimum feature size get smaller, defects become increasingly difficult to prevent. Defects can change the behavior of a logic circuit resulting in a fault. Manufacturers and designers may improve yield, reliability, and profitability by using design techniques that make products robust even in the presence of faults. Triple modular redundancy (TMR) is a fault tolerant technique commonly used to mask faults using voting outcomes from three processing elements (PE). TMR is effective at masking errors as long as no more than a single processing element is faulty. Time distributed voting (TDV) is proposed as an active fault tolerant technique. TDV addresses the shortcomings of triple modular redundancy (TMR) in the presence of multiple faulty processing elements. A faulty PE may not be incorrect 100% of the time. When a faulty element generates correct results, a majority is formed with the healthy PE. TDV observes voting outcomes over time to make a statistical decision whether a PE is healthy or faulty. In simulation, fault coverage is extended to 98.6% of multiple faulty PE cases. As an active fault tolerant technique, TDV identifies faulty PE's so that actions may be taken to replace or disable them in the system. TDV may provide a positive impact to semiconductor manufacturers by improving yield and reliability even as fault frequency increases.