Water resources managers are required to develop comprehensive water resource plans based on severely uncertain information of the effects of climate change on local hydrology and future socio-economic changes to localised demand. In England and Wales, current water resource planning methodologies include a headroom estimation process separate from water resources simulation modelling. This process quantifies uncertainty based on only one point of an assumed range of deviations from the expected climate and projected demand 25 years into the future. The research presented herein addresses this problem by developing an integrated the Water Resources Planning Robustness Assessment (WRP-RA) method based on Information-Gap Decision Theory (IGDT) to quantitatively assess the robustness of various supply side and demand side management options over a broad range of plausible futures. Findings show that beyond the uncertainty range explored with the headroom method, a preference reversal can occur, i.e. some management strategies that underperform at lower uncertainties, outperform at higher levels of uncertainty. Also, some management strategies that perform relatively well within the headroom range of uncertainty, fail just beyond this range. Additionally, this thesis demonstrates that when 50% or more of the population adopts demand side management in the form of efficiency related measures and/or innovative options such as rainwater collection and/or greywater reuse, the robustness of a management strategy can be greatly improved as can its ability to recover after a drought episode. The use of Multi-Criteria Decision Analysis shifts the focus away from reservoir expansion options and large-scale river abstractions that perform best in regards to water availability, to strategies that include innovative demand side management actions of rainwater collection and greywater reuse as well efficiency measures along with more traditional supply-side schemes. Therefore, this thesis illustrates how the WRP-RA can offer a comprehensive picture of the relative robustness of management strategies to more extreme supply/demand futures. The knowledge of which options and collections of options perform better in response to higher demands and lower supplies offers insight into more secure long term investment strategies.

Les travaux présentés dans cette thèse visent à apporter des outils d’aide à la décision à partir de modèles prenant en compte une représentation Info-Gap des différentes sources de méconnaissance du système. Il est en effet possible en utilisant des simulations numériques de développer des indicateurs de support à la décision sous un certain niveau d’incertitude aléatoire ou épistémique. Le principe de conception est ici utilisé au sens large, et peut entrer sans le cadre du dimensionnement structural de composants, de la définition de l’amplitude d’excitation maximum d’un essai, ou encore de la mise en place d’une distribution de capteurs. Ces différentes méthodologies sont ici développées puis appliquées sur des systèmes académiques et industriels / The work presented in this PhD thesis aims at propose new decision making tools in order to take into account a Info-Gap modelling of the different sources of lack of knowledge. Indeed, numerical simulation allow to develop useful indicators for decision making under a given level of random or epistemic uncertainty. The design principle is hereby used in its very large sense, and can stand for structural component design, maximum load definition fir vibrating test or sensor placement design. In this manuscript, these different methodologies are developed and applied to academic and industrial structures.

Le comportement dynamique de structures complexes, comme les alternateurs, doit être maîtrisé afin d’en garantir un fonctionnement fiable. Cependant, la modélisation comporte de nombreuses incertitudes rendant délicates la prédiction du comportement vibratoire. Ces travaux de recherche ont pour objectif de fournir des outils d’aide à la décision afin de faciliter la prise de décision rapide suite au redémarrage d’alternateurs. Basé sur la théorie info-gap, un premier outil d’aide à la décision est proposé : il a pour objectif d’évaluer la robustesse de réponses dynamiques vis-à-vis d’un modèle modal incertain. Nous avons également étudié comment de l’information nouvelle peut être intégrée au modèle d’incertitude pour améliorer sa représentativité à la réalité.Une expansion par l’erreur en relation de comportement étendue de modes propres identifiés permet ensuite d’enrichir la représentativité du modèle numérique fournissant ainsi un modèle qualifié d’hybride et permettant d’évaluer les niveaux de réponse. Comme la modélisation comporte de nombreuses méconnaissances, nous avons proposé le procédé d’expansion robuste dont l’objectif est d’obtenir des vecteurs étendus robustes. En présence de méconnaissances sévères, nous montrons enfin qu’il est préférable de calibrer un modèle en maximisant la robustesse vis-à-vis des incertitudes plutôt qu’en maximisant uniquement la fidélité vis-à-vis des données. Couplée à des techniques de réduction de modèle et de construction de méta modèles,nous appliquons cette démarche à une structure de complexité industrielle représentative du contexte industriel. / The complex structural dynamic behavior of alternator must be well understood in order to insuretheir reliable and safe operation. The numerical model is however difficult to construct mainlydue to the presence of a high level of uncertainty. The objective of this work is to providedecision support tools in order to assess the vibratory levels in operation before to restart thealternator. Based on info-gap theory, a first decision support tool is proposed: the objective hereis to assess the robustness of the dynamical response to the uncertain modal model. Based on realdata, the calibration of an info-gap model of uncertainty is also proposed in order to enhance itsfidelity to reality. Then, the extended constitutive relation error is used to expand identified modeshapes which are used to assess the vibratory levels. The robust expansion process is proposed inorder to obtain robust expanded mode shapes to parametric uncertainties. In presence of lack-ofknowledge,the trade-off between fidelity-to-data and robustness-to-uncertainties which expressesthat robustness improves as fidelity deteriorates is emphasized on an industrial structure by usingboth reduced order model and surrogate model techniques.

La maîtrise du calcul prévisionnel du comportement dynamique de structures mécaniques demeure un enjeu majeur pour l'amélioration de la conception en présence de facteurs mal maîtrisés. Dans ce document, nous présentons des méthodologies de conception permettant de prendre en compte dans le processus de décision, les incertitudes sur les paramètres de conception, les incertitudes sur les mesures ou encore l'impact des modifications. Dans la première partie, nous étudions le potentiel d'une méthode de synthèse modale basée sur l'utilisation des modes propres orthogonaux. Une méthodologie de vérification et d'optimisation de super-éléments est également présentée. Enfin, nous montrons qu'un algorithme génétique peut permettre une sélection optimale des coordonnées physiques dans les méthodes de réduction. La deuxième partie concerne l'identification paramétrique des structures mécaniques à partir d'observations incertaines et la quantification de l'information susceptible d'être obtenue grâce à des mesures expérimentales. Nous utilisons dans cette étude une formulation probabiliste des problèmes inverses. Une planification d'essais en vue d'un gain d'information est réalisée avec des plans d'expérience bayésiens. Dans la dernière partie, l'approche non-probabiliste info-gap est appliquée afin d'évaluer la robustesse aux incertitudes de deux méthodes de recalage. Cette méthode permet aussi de vérifier que, dans un environnement incertain et pour un critère de performance donné, il peut être préférable de choisir un modèle " satisfaisant" plutôt qu'un modèle optimal.

Substantial anthropogenic change of the Earth’s climate is modifying patterns of rainfall, river flow, glacial melt and groundwater recharge rates across the planet, undermining many of the stationarity assumptions upon which water resources infrastructure has been historically managed. This hydrological uncertainty is creating a potentially vast range of possible futures that could threaten the dependability of vital regional water supplies. This, combined with increased urbanisation and rapidly growing regional populations, is putting pressures on finite water resources. One of the greatest international challenges facing decision makers in the water industry is the increasing influences of these “deep” climate change and population growth uncertainties affecting the long-term balance of supply and demand and necessitating the need for adaptive action. Water companies and utilities worldwide are now under pressure to modernise their management frameworks and approaches to decision making in order to identify more sustainable and cost-effective water management adaptations that are reliable in the face of uncertainty. The aim of this thesis is to compare and contrast a range of existing Decision Making Methods (DMMs) for possible application to Water Resources Management (WRM) problems, critically analyse on real-life case studies their suitability for handling uncertainties relating to climate change and population growth and then use the knowledge generated this way to develop a new, resilience-based WRM planning methodology. This involves a critical evaluation of the advantages and disadvantages of a range of methods and metrics developed to improve on current engineering practice, to ultimately compile a list of suitable recommendations for a future framework for WRM adaptation planning under deep uncertainty. This thesis contributes to the growing vital research and literature in this area in several distinct ways. Firstly, it qualitatively reviews a range of DMMs for potential application to WRM adaptation problems using a set of developed criteria. Secondly, it quantitatively assesses two promising and contrasting DMMs on two suitable real-world case studies to compare highlighted aspects derived from the qualitative review and evaluate the adaptation outputs on a practical engineering level. Thirdly, it develops and reviews a range of new potential performance metrics that could be used to quantitatively define system resilience to help answer the water industries question of how best to build in more resilience in future water resource adaptation planning. This leads to the creation and testing of a novel resilience driven methodology for optimal water resource planning, combining optimal aspects derived from the quantitative case study work with the optimal metric derived from the resilience metric investigation. Ultimately, based on the results obtained, a list of suitable recommendations is compiled on how to improve the existing methodologies for future WRM planning under deep uncertainty. These recommendations include the incorporation of more complex simulation models into the planning process, utilisation of multi-objective optimisation algorithms, improved uncertainty characterisation and assessments, an explicit robustness examination and the incorporation of additional performance metrics to increase the clarity of the strategy assessment process.

An analytical model of cracked composite beams vibrating in coupled bending-torsion is developed. The beam is made of fiber-reinforced composite with fiber angles in each ply aligned in the same direction. The crack is assumed open. The local flexibility concept is implemented to model the open crack and the associated compliance matrix is derived. The crack introduces additional boundary conditions at the crack location and these effects in conjunction with those of material properties are investigated. Free vibration analysis of the cracked composite beam is presented. The results indicate that variation of natural frequencies in the presence of a crack is affected by the crack ratio and location, as well as the fiber orientation. In particular, the variation pattern is different as the magnitude of bending-torsion coupling changes due to different fiber angles. When bending and torsional modes are essentially decoupled at a certain fiber angle if there is no crack, the crack introduces coupling to the initially uncoupled bending and torsion. Based on the crack model, aeroelastic characteristics of an unswept composite wing with an edge crack are investigated. The cracked composite wing is modeled by a cracked composite cantilever and the inertia coupling terms are included in the model. An approximate solution on critical flutter and divergence speeds is obtained by Galerkin's method in which the fundamental mode shapes of the cracked wing model in free vibration are used. It is shown that the critical divergence/flutter speed is affected by the elastic axis location, the inertia axis location, fiber angles, and the crack ratio and location. Moreover, model-based crack detection (size and location) by changes in natural frequencies is addressed. The Cawley-Adams criterion is implemented and a new strategy in grouping frequencies is proposed to reduce the probability of measurement errors. Finally, sensitivity of natural frequencies to model parameter uncertainties is investigated. Uncertainties are modeled by information-gap theory and represented with a collection of nested sets. Five model parameters that may have larger uncertainties are selected in the analysis, and the frequency sensitivities to uncertainties in the five model parameters are compared in terms of two immunity functions. / Ph. D.

Due to increasing interest in sustainable development, today s engineer is often tasked with designing systems that are environmentally benign over their entire life cycles. Unfortunately, environmental assessments commonly suffer from significant uncertainty due to lack of information, particularly for time-distant life cycle aspects. Under severe uncertainty, traditional uncertainty formalisms require more information than is available. However, a recently devised formalism, information-gap decision theory (IGDT), requires no more information than a nominal estimate; error bounds on that estimate are unknown. The IGDT decision strategy, accordingly, favors the design that is robust to the most estimation error while still guaranteeing no worse than some good enough critical level of performance. In some cases, one can use IGDT to identify a preferable design option without needing more information or more complex uncertainty analysis. In this dissertation, IGDT is investigated and shown to enhance decision support for environmentally benign design and manufacturing (EBDM) problems. First, the applicability of the theory to EBDM problems is characterized. Conditions that warrant an info-gap analysis are reviewed, the insight it can reveal about design robustness is demonstrated, and practical limitations to its use are revealed. Second, a new mathematical technique is presented that expands capabilities for analyzing robustness to multiple info-gap uncertainties simultaneously. The technique elicits scaling factors more rigorously than before and allows one to imprecisely express their beliefs about info-gap scaling. Two examples problems affected by info-gaps are investigated: oil filter selection and remanufacturing process selection. It is shown that limited information about uncertainty can, in some cases, indeed enable one to identify a most preferable design without requiring more information.

Les structures assemblées par points de soudure doivent satisfaire à un grand nombre de critères de performance, portant entre autres sur des aspects statiques, dynamiques, acoustiques, ou crash, qui sont fortement influencés par le nombre et la position des points de soudure. De plus, certains d’entre eux peuvent être défaillants en sortie de ligne d’assemblage ou le devenir au cours de la vie du véhicule, ce qui induit des dispersions des performances. Le challenge est donc de déterminer, dans un temps d’analyse raisonnable, le nombre et la répartition optimale des points de soudure permettant la vérification des objectifs de performance tout en garantissant le meilleur compromis entre le coût de fabrication et la robustesse des performances. Une procédure adaptative est proposée, permettant à chaque itération d’ajouter et de supprimer des points de soudure, afin d’obtenir une conception robuste. Une procédure itérative de robustesse info-gap est également présentée, afin d’analyser l’impact de la perte des points de soudure les plus influents. On définit ainsi une procédure de contrôle qualité, portant sur un petit nombre de points de soudure, permettant de garantir l’homogénéité des performances des structures fabriquées en série. Toutes les méthodologies sont validées sur une caisse en blanc de véhicule industriel.En pratique, la conception doit satisfaire plusieurs critères antagonistes. La procédure adaptative est donc étendue à l’optimisation multi-objectifs, afin d’obtenir le meilleur compromis possible en fonction des critères considérés. Une illustration portant sur l’optimisation dynamique et vibro-acoustique d’une cavité passager est finalement mené / Spot welded structures must satisfy a large variety of performance characteristics including static, noise, vibration and harshness and crash, which are strongly influenced by the numbers and positions of the spot welds. Moreover, some spot welds may be missing when structures leave the assembly line or break during lifetime of vehicle, inducing large variations in the performance characteristics. The challenge is to find the best locations and number of spot welds to achieve the performance goals while taking into account the trade-offs between manufacturing cost and robust to uncertainty in reasonable time frame. An adaptive optimization procedure is proposed, which iteratively adds and removes spot welds to obtain the robust design efficiently. An iterative procedure is also proposed to obtain the info-gap robustness curve, which allows analyzing the impact of the loss of the most influential spot welds on performance. This leads to define a quality control procedure for a small number of spot welds to guarantee the performance of a population of nominally identical structures within acceptable limits. All the methodologies are validated on a full industrial body-in-white of a vehicle.In practice, the design must satisfy several stringent and conflicting objectives simultaneously. Thus, we extend the adaptive procedure to handle multi-objective problems using the weight-sum approach reflecting the importance given to individual spot welds to obtain efficient solutions in the objective space. Finally, we propose a strategy to optimize the vibro-acoustic behavior of the passenger cabin of a vehicle by designing the numbers and positions of the spot welds.

Les travaux de la présente thèse portent sur le recalage de modèles dynamiques d’aubes de turbinecomposites à matrice céramique. Ils s’inscrivent dans le cadre de la quantification d’incertitudes pour la validation de modèles et ont pour objectif de fournir des outils d’aide à la décision pour les ingénieurs desbureaux d’études. En effet, la dispersion importante observée lors des campagnes expérimentales invalidel’utilisation des méthodes de recalage déterministe. Après un état de l’art sur la relation entre les incertitudeset la physique, l’approche de Vérification & Validation a été introduite comme approche permettantd’assurer la crédibilité des modèles numériques. Puis, deux méthodes de recalages stochastiques, permettantde déterminer la distribution statistique des paramètres, ont été comparées sur un cas académique. La priseen compte des incertitudes n’élude pas les potentielles compensations entre paramètres. Par conséquent, desindicateurs ont été développés afin de détecter la présence de ces phénomènes perturbateurs. Ensuite, lathéorie info-gap a été employée en tant que moyen de modéliser ces méconnaissances. Une méthode derecalage stochastique robuste a ainsi été proposée, assurant un compromis entre la fidélité du modèle auxessais et la robustesse aux méconnaissances. Ces outils ont par la suite été appliqués sur un modèle éléments / This work is focused on the stochastic updating of ceramic matrix composite turbine blade model. They arepart of the uncertainty quantification framework for model validation. The aim is to enhance the existing toolused by the industrial decision makers. Indeed, consequent dispersion was measured during the experimentalcampaigns preventing the use of deterministic approaches. The first part of this thesis is dedicated to therelationship between mechanical science and uncertainty. Thus, Verification and Validation was introduced asthe processes by which credibility in numerical models is established. Then two stochastic updatingtechniques, able to handle statistic distribution, were compared through an academic example. Nevertheless,taking into account uncertainties doesn’t remove potential compensating effects between parameters.Therefore, criteria were developed in order to detect these disturbing phenomena. Info-gap theory wasemployed as a mean to model these lack of knowledge. Paired with the stochastic updating method, a robuststochasticapproach has been proposed. Results demonstrate a trade-off relationship between the model’sfidelity and robustness. The developed tools were applied on a ceramic matrix composite turbine blade finiteelement model.

Sensor nodes in a wireless sensor network (WSN) have a small, non-rechargeable power supply. Each message transmission or reception depletes a sensor node’s energy. Many WSN applications are ad-hoc deployments where a sensor node is only aware of its immediate neighbours. The lack of a predefined route path and the need to restrict the amount of communication that occurs within the application area impose constraints on WSNs not prevalent in other types of networks. An area of active research has been how to notify the central sink (or monitoring hub) about an event in real-time by utilising the minimum number of messages to route a message from a source node to the destination sink node. In this thesis, strategies to limit communication within a WSN application area, while ensuring that events are reported on and responded to in real-time, is presented. A solution based on modelling a WSN as a small world network and then transmitting an initialisation message (IM) on network start-up to create multiple route paths from any sensor node to one or more sinks is proposed. The reason for modelling a WSN as a small world network is to reduce the number of nodes required to re-transmit a message from a source sensor node to a sink. The purpose of sending an IM at network start-up is to ensure that communication within the WSN is minimised. When routing a message to a static sink, the nodes closest to the static sink receive a disproportionate number of messages, resulting in their energy being consumed earlier. The use of mobile sinks has been proposed but to our knowledge no studies have been undertaken on the paths these mobile sinks should follow. An algorithm to determine the optimum path for mobile sinks to follow in a WSN application area is described. The purpose of an optimum path is to allow more equitable usage of all nodes to transfer an event message to a mobile sink. The idea of using multiple static sinks placed at specific points in the small world model is broadened to include using multiple mobile sinks called actors to move within a WSN application area and respond to an event in real-time. Current coordination solutions to determine which actor(s) must respond to the event result in excessive message communication and limit the real-time response to an event. An info gap decision theory (IGDT) model to coordinate which actor or set of actors should respond to the event is described. A comparison of the small world routing (SWR) model against routing using flooding and gossiping shows that the SWR model significantly reduces the number of messages transmitted within the network. An analysis of the number of IMs transmitted and received at individual node level shows that prudent selection of the hop count (number of additional nodes required to route a message to sink) to a sink node will result in a reduced number of messages transmitted and received per node within the network. The use of the IGDT model results in a robust decision on the actor(s) chosen to respond to an event even when uncertainty about the location and available energy of other actor(s) exists. / Thesis (PhD(Eng))--University of Pretoria, 2012. / Electrical, Electronic and Computer Engineering / unrestricted