The automotive industry is reliant on accurate finite element simulations for developing new parts or machines and to achieve this, accurate material models are essential. Material cards contain input about the material model, and are significant; however, time-consuming to calibrate with traditional methods. Therefore a newer method involving Machine Learning (ML) and Feed-Forward Neural Networks (FFNN) is studied in the thesis. The direct application of calibration with FFNN has never been applied to calibrate the Swift hardening law and Barlat yield 2000 criteria, which is done in this thesis. All steps for calibration are performed to achieve a high-fidelity database capable of training the FFNN. The outline of the thesis involves four different phases; experiments, simulations, building the high-fidelity database, and building and optimizing the FFNN. The experiment phase involves tensile testing of three different types of specimens in three material directions with Digital Image Correlation (DIC) to capture local strain. The simulation phase is to replicate all the experiments in LS-DYNA and perform finite element simulation. The finite element models are simulated 100 times and, respectively, 1000 times with different material parameters within a specific range. This range has a lower and upper bound that covers the experimental results. The database phase involves extracting the data from a huge amount of simulations and then extracting the key characteristics from the force-displacement curve. The last phase is building the FFNN and optimizing the network to find the best parameters. It’s first optimized based on Root Mean Square Error (RMSE) and then points from the Swift hardening curve and Barlat yield 2000 criteria are compared with experimental points. The result shows that the FFNN with the high-fidelity database can predict material parameters with an accuracy of over 99 % for the hardening law at the points chosen for optimization and the anisotropy parameters are optimized to 97 % accuracy for the yielding points and Lankford coefficients. The thesis concludes that the FFNN can accurately predict the material parameters with real experimental data. The effectiveness of using this method is significantly faster than traditional methods because only one type of test is needed. / Bilindustrin är beroende av trovärdiga och noggranna finita element simuleringar för utveckling av nya komponenter eller maskiner, och för det behövs noggranna materialmodeller. Materialkort innehåller information om materialmodellerna och är av stor betydelse, men är tidskrävande att kalibrera med traditionella metoder. Därför är en ny metod som involverar Maskininlärning (ML) och Feed-Forward Neurala Nätverk (FFNN) undersökt i avhandlingen. Applikationen av att kalibrera med FFNN har aldrig blivit undersökt för ”Swift hardening law” och anisotropi kriteriet ”Barlat yield 2000”. Alla steg för att kalibrera materialet är utförda för att uppnå en högkvalitativ databas som är kapabel att träna ett FFNN. Arbetets översikt involverar fyra faser som är; experiment, simulationer, databasensuppbyggnad och utvecklingen samt optimeringen av FFNN. Experimentfasen involverar dragprov för tre olika geometrier i tre materialriktningar tillsammans med Digital Image Correlation (DIC) för att fånga lokala töjningspunkter. Simulationsfasen går ut på att replikera experimentfasen genom finita element simuleringar i LS-DYNA. Finita element modellerna är simulerade 100 respektive 1000 gånger med olika materialparametrar inom ett specifikt intervall med en övre och undre gräns som ska täcka experimentdatan. Databasfasen handlar om att extrahera data från de massiva antalet simuleringar och extrahera nyckelbeteenden från kraft-förflyttningskurvan. Den sista fasen är att bygga FFNN och optimera för att hitta bästa möjliga parametrar. Det är först optimerat baserat på Root Mean Squared Error (RMSE) och sedan punkter från Swift härdningskurvan och beteenden genererat från Barlat yield 2000 som är jämförda med experimentella värden som Lankfordkoefficienter och sträckgränser för rullningsriktningarna. Resultatet visar att ett FFNN med en högkvalitiativ databas kan estimera materialparametrar med en noggrannhet över 99 % för härdningskurvan för jämförelsepunkterna och med en 97 % noggrannhet för anisotropipunkterna som Lankfordkoefficienter och sträckgränser i rullningsriktningarna. Exjobbet avslutas med att dra slutsatsen att FFNN kan estimera riktiga materialparametrar med en viss noggrannhet. Effektiviteten av att använda metoden är betydligt snabbare än traditionella metoder eftersom det endast tar några sekunder att estimera parametrarna när datan är extraherad och enbart en typ av test behövs.

Land surface models (LSMs) implemented in numerical weather prediction (NWP) models use several parameters to suitably describe the surface and its interaction with the atmosphere, whose determination is often affected by many uncertainties, strongly influencing simulation results. However, the sensitivity of meteorological model results to these parameters has not yet been studied systematically, especially in complex terrain, where uncertainty is expected to be even larger. This work aims at identifying critical LSM parameters influencing the results of NWP models, focusing in particular on the simulation of thermally-driven circulations over complex terrain. While previous sensitivity analyses employed offline LSM simulations to evaluate the sensitivity to surface parameters, this study adopts an online coupled approach, utilizing the Noah-MP LSM within the Weather Research and Forecasting (WRF) model. To overcome computational constraints, a novel tool, Machine Learning-based Automated Multi-method Parameter Sensitivity and Importance analysis Tool (ML-AMPSIT), is developed and tested. This tool allows users to explore the sensitivity of the results to model parameters using supervised machine learning regression algorithms, including Random Forest, CART, XGBoost, SVM, LASSO, Gaussian Process Regression, and Bayesian Ridge Regression. These algorithms serve as fast surrogate models, greatly accelerating sensitivity analyses while maintaining a high level of accuracy. The versatility and effectiveness of ML-AMPSIT enable the fast implementation of advanced sensitivity methods, such as the Sobol method, overcoming the computational limitations encountered in expensive models like WRF. The suitability of this tool to assess model’s sensitivity to the variation of specific parameters is first tested in an idealized sea breeze case study where six surface parameters are varied. Then, the analysis focuses on the evaluation of the sensitivity to surface parameters in the simulation of thermally-driven circulations in a mountain valley. Specifically, an idealized three-dimensional topography consisting of a valley-plain system is adopted, analyzing a complete diurnal cycle of valley and slope winds. The analysis focuses on all the key surface parameters governing the interactions between NoahMP and WRF. The proposed approach, novel in the context of LSM-NWP model coupling, draws from established applications of machine learning in various Earth science disciplines, underscoring its potential to improve the estimation of parameter sensitivities in NWP models.

Code validation and uncertainty quantification are important tasks in nuclear reactor safety analysis. Code users have to deal with large number of uncertain parameters, complex multi-physics, multi-dimensional and multi-scale phenomena. In order to make results of analysis more robust, it is important to develop and employ procedures for guiding user choices in quantification of the uncertainties.   The work aims to further develop approaches and procedures for system analysis code validation and application to practical problems of safety analysis. The work is divided into two parts.   The first part presents validation of two reactor system thermal-hydraulic (STH) codes RELAP5 and TRACE for prediction of two-phase circulation flow instability.   The goals of the first part are to: (a) develop and apply efficient methods for input calibration and STH code validation against unsteady flow experiments with two-phase circulation flow instability, and (b) examine the codes capability to predict instantaneous thermal hydraulic parameters and flow regimes during the transients.   Two approaches have been developed: a non-automated procedure based on separate treatment of uncertain input parameters (UIPs) and an automated method using genetic algorithm. Multiple measured parameters and system response quantities (SRQs) are employed in both calibration of uncertain parameters in the code input deck and validation of RELAP5 and TRACE codes. The effect of improvement in RELAP5 flow regime identification on code prediction of thermal-hydraulic parameters has been studied.   Result of the code validations demonstrates that RELAP5 and TRACE can reproduce qualitative behaviour of two-phase flow instability. However, both codes misidentified instantaneous flow regimes, and it was not possible to predict simultaneously experimental values of oscillation period and maximum inlet flow rate. The outcome suggests importance of simultaneous consideration of multiple SRQs and different test regimes for quantitative code validation.   The second part of this work addresses core degradation and relocation to the lower head of a boiling water reactor (BWR). Properties of the debris in the lower head provide initial conditions for vessel failure, melt release and ex-vessel accident progression.   The goals of the second part are to: (a) obtain a representative database of MELCOR solutions for characteristics of debris in the reactor lower plenum for different accident scenarios, and (b) develop a computationally efficient surrogate model (SM) that can be used in extensive uncertainty analysis for prediction of the debris bed characteristics.   MELCOR code coupled with genetic algorithm, random and grid sampling methods was used to generate a database of the full model solutions and to investigate in-vessel corium debris relocation in a Nordic BWR. Artificial neural networks (ANNs) with classification (grouping) of scenarios have been used for development of the SM in order to address the issue of chaotic response of the full model especially in the transition region.   The core relocation analysis shows that there are two main groups of scenarios: with relatively small (&lt;20 tons) and large (&gt;100 tons) amounts of total relocated debris in the reactor lower plenum. The domains are separated by transition regions, in which small variation of the input can result in large changes in the final mass of debris.  SMs using multiple ANNs with/without weighting between different groups effectively filter out the noise and provide a better prediction of the output cumulative distribution function, but increase the mean squared error compared to a single ANN. / Validering av datorkoder och kvantifiering av osäkerhetsfaktorer är viktiga delar vid säkerhetsanalys av kärnkraftsreaktorer. Datorkodanvändaren måste hantera ett stort antal osäkra parametrar vid beskrivningen av fysikaliska fenomen i flera dimensioner från mikro- till makroskala. För att göra analysresultaten mer robusta, är det viktigt att utveckla och tillämpa rutiner för att vägleda användaren vid kvantifiering av osäkerheter.Detta arbete syftar till att vidareutveckla metoder och förfaranden för validering av systemkoder och deras tillämpning på praktiska problem i säkerhetsanalysen. Arbetet delas in i två delar.Första delen presenterar validering av de termohydrauliska systemkoderna (STH) RELAP5 och TRACE vid analys av tvåfasinstabilitet i cirkulationsflödet.Målen för den första delen är att: (a) utveckla och tillämpa effektiva metoder för kalibrering av indatafiler och validering av STH mot flödesexperiment med tvåfas cirkulationsflödeinstabilitet och (b) granska datorkodernas förmåga att förutsäga momentana termohydrauliska parametrar och flödesregimer under transienta förlopp.Två metoder har utvecklats: en icke-automatisk procedur baserad på separat hantering av osäkra indataparametrar (UIPs) och en automatiserad metod som använder genetisk algoritm. Ett flertal uppmätta parametrar och systemresponser (SRQs) används i både kalibrering av osäkra parametrar i indatafilen och validering av RELAP5 och TRACE. Resultatet av modifikationer i hur RELAP5 identifierar olika flödesregimer, och särskilt hur detta påverkar datorkodens prediktioner av termohydrauliska parametrar, har studerats.Resultatet av valideringen visar att RELAP5 och TRACE kan återge det kvalitativa beteende av två-fas flödets instabilitet. Däremot kan ingen av koderna korrekt identifiera den momentana flödesregimen, det var därför ej möjligt att förutsäga experimentella värden på svängningsperiod och maximal inloppsflödeshastighet samtidigt. Resultatet belyser betydelsen av samtidig behandling av flera SRQs liksom olika experimentella flödesregimer för kvantitativ kodvalidering.Den andra delen av detta arbete behandlar härdnedbrytning och omfördelning till reaktortankens nedre plenumdel i en kokarvatten reaktor (BWR). Egenskaper hos härdrester i nedre plenum ger inledande förutsättningar för reaktortanksgenomsmältning, hur smältan rinner ut ur reaktortanken och händelseförloppet i reaktorinneslutningen.Målen i den andra delen är att: (a) erhålla en representativ databas över koden MELCOR:s analysresultat för egenskaperna hos härdrester i nedre plenum under olika händelseförlopp, och (b) utveckla en beräkningseffektiv surrogatsmodell som kan användas i omfattande osäkerhetsanalyser för att förutsäga partikelbäddsegenskaper.MELCOR, kopplad till en genetisk algoritm med slumpmässigt urval användes för att generera en databas av analysresultat med tillämpning på smältans omfördelning i reaktortanken i en Nordisk BWR.Analysen av hur härden omfördelas visar att det finns två huvudgrupper av scenarier: med relativt liten (&lt;20 ton) och stor (&gt; 100 ton) total mängd omfördelade härdrester i nedre plenum. Dessa domäner är åtskilda av övergångsregioner, där små variationer i indata kan resultera i stora ändringar i den slutliga partikelmassan. Flergrupps artificiella neurala nätverk med klassificering av händelseförloppet har använts för utvecklingen av en surrogatmodell för att hantera problemet med kaotiska resultat av den fullständiga modellen, särskilt i övergångsregionen. / <p>QC 20170309</p>

This dissertation focuses on the introduction and development of an integrated model-based design and optimization platform to solve the optimal design and optimal control, or hardware and software co-design, problem for hybrid electric propulsion systems. Specifically, the hybrid and plug-in hybrid electric powertrain systems with diesel and natural gas (NG) fueled compression ignition (CI) engines and large Li-ion battery energy storage system (ESS) for propelling a hybrid electric marine vessel are investigated. The combined design and control optimization of the hybrid propulsion system is formulated as a bi-level, nested optimization problem. The lower-level optimization applies dynamic programming (DP) to ensure optimal energy management for each feasible powertrain system design, and the upper-level global optimization aims at identifying the optimal sizes of key powertrain components for the powertrain system with optimized control. Recently, Li-ion batteries became a promising ESS technology for electrified transportation applications. However, these costly Li-ion battery ESSs contribute to a large portion of the powertrain electrification and hybridization costs and suffer a much shorter lifetime compared to other key powertrain components. Different battery performance modelling methods are reviewed to identify the appropriate degradation prediction approach. Using this approach and a large set of experimental data, the performance degradation and life prediction model of LiFePO4 type battery has been developed and validated. This model serves as the foundation for determining the optimal size of battery ESS and for optimal energy management in powertrain system control to achieve balanced reduction of fuel consumption and the extension of battery lifetime. In modelling and design of different hybrid electric marine propulsion systems, the life cycle cost (LCC) model of the cleaner, hybrid propulsion systems is introduced, considering the investment, replacement and operational costs of their major contributors. The costs of liquefied NG (LNG), diesel and electricity in the LCC model are collected from various sources, with a focus on present industrial price in British Columbia, Canada. The greenhouse gas (GHG) and criteria air pollutant (CAP) emissions from traditional diesel and cleaner NG-fueled engines with conventional and optimized hybrid electric powertrains are also evaluated. To solve the computational expensive nested optimization problem, a surrogate model-based (or metamodel-based) global optimization method is used. This advanced global optimization search algorithm uses the optimized Latin hypercube sampling (OLHS) to form the Kriging model and uses expected improvement (EI) online sampling criterion to refine the model to guide the search of global optimum through a much-reduced number of sample data points from the computationally intensive objective function. Solutions from the combined hybrid propulsion system design and control optimization are presented and discussed. This research has further improved the methodology of model-based design and optimization of hybrid electric marine propulsion systems to solve complicated co-design problems through more efficient approaches, and demonstrated the feasibility and benefits of the new methods through their applications to tugboat propulsion system design and control developments. The resulting hybrid propulsion system with NG engine and Li-ion battery ESS presents a more economical and environmentally friendly propulsion system design of the tugboat. This research has further improved the methodology of model-based design and optimization of hybrid electric marine propulsion systems to solve complicated co-design problems through more efficient approaches, and demonstrated the feasibility and benefits of the new methods through their applications to tugboat propulsion system design and control developments. Other main contributions include incorporating the battery performance degradation model to the powertrain size optimization and optimal energy management; performing a systematic design and optimization considering LCC of diesel and NG engines in the hybrid electric powertrains; and developing an effective method for the computational intensive powertrain co-design problem. / Graduate

Cette thèse porte sur la construction de modèles de substitution en régimes transitoire et permanent pour la simulation thermique, en présence de peu d'observations et de plusieurs sorties.Nous proposons dans un premier temps une construction robuste de perceptron multicouche bouclé afin d'approcher une dynamique spatio-temporelle. Ce modèle de substitution s'obtient par une moyennisation de réseaux de neurones issus d'une procédure de validation croisée, dont le partitionnement des observations associé permet d'ajuster les paramètres de chacun de ces modèles sur une base de test sans perte d'information. De plus, la construction d'un tel perceptron bouclé peut être distribuée selon ses sorties. Cette construction est appliquée à la modélisation de l'évolution temporelle de la température en différents points d'une armoire aéronautique.Nous proposons dans un deuxième temps une agrégation de modèles par processus gaussien dans un cadre multifidélité où nous disposons d'un modèle d'observation haute-fidélité complété par plusieurs modèles d'observation de fidélités moindres et non comparables. Une attention particulière est portée sur la spécification des tendances et coefficients d'ajustement présents dans ces modèles. Les différents krigeages et co-krigeages sont assemblés selon une partition ou un mélange pondéré en se basant sur une mesure de robustesse aux points du plan d'expériences les plus fiables. Cette approche est employée pour modéliser la température en différents points de l'armoire en régime permanent.Nous proposons dans un dernier temps un critère pénalisé pour le problème de la régression hétéroscédastique. Cet outil est développé dans le cadre des estimateurs par projection et appliqué au cas particulier des ondelettes de Haar. Nous accompagnons ces résultats théoriques de résultats numériques pour un problème tenant compte de différentes spécifications du bruit et de possibles dépendances dans les observations. / This PhD thesis deals with the construction of surrogate models in transient and steady states in the context of thermal simulation, with a few observations and many outputs.First, we design a robust construction of recurrent multilayer perceptron so as to approach a spatio-temporal dynamic. We use an average of neural networks resulting from a cross-validation procedure, whose associated data splitting allows to adjust the parameters of these models thanks to a test set without any information loss. Moreover, the construction of this perceptron can be distributed according to its outputs. This construction is applied to the modelling of the temporal evolution of the temperature at different points of an aeronautical equipment.Then, we proposed a mixture of Gaussian process models in a multifidelity framework where we have a high-fidelity observation model completed by many observation models with lower and no comparable fidelities. A particular attention is paid to the specifications of trends and adjustement coefficients present in these models. Different kriging and co-krigings models are put together according to a partition or a weighted aggregation based on a robustness measure associated to the most reliable design points. This approach is used in order to model the temperature at different points of the equipment in steady state.Finally, we propose a penalized criterion for the problem of heteroscedastic regression. This tool is build in the case of projection estimators and applied with the Haar wavelet. We also give some numerical results for different noise specifications and possible dependencies in the observations.

Cette thèse propose une nouvelle méthode, via les outils de dosimétrie et de statistiques, pour l'évaluation de l'exposition globale d'une population aux champs électromagnétiques (EMFs) radiofréquences en prenant en compte les différentes technologies, usages et environnements... Nous avons analysé pour la première fois l'exposition moyenne d'une population induite par un réseau 3G, tout en considérant à la fois les émissions EMFs montantes et descendantes dans des différents pays, dans des différentes zones géographiques et pour les différents usages des mobiles. Les résultats montrent une forte hétérogénéité de l'exposition dans le temps et dans l'espace. Contrairement à la croyance populaire, l'exposition aux ondes EMFs 3G est dominée par les émissions montantes, résultant de l'usage voix et data. En outre, l'exposition moyenne de la population diffère d'une zone géographique à une autre, ainsi que d'un pays à un autre, en raison des différentes architectures de réseau cellulaire et de la variabilité de l'usage des mobiles. Ensuite, la variabilité et les incertitudes liées à ces facteurs ont été caractérisées. Une analyse de sensibilité basée sur la variance de l'exposition globale a été effectuée dans le but de simplifier son évaluation. Enfin, une méthodologie simplifiée basée sur des outils statistiques avancés a été proposée pour évaluer l'exposition réelle de la population en tenant compte de la variabilité liée à l'environnement de propagation, à l'usage, ainsi qu'aux émissions EMFs provenant des mobiles et des stations de base (BTS). Les résultats ont souligné l'importance de la densité de puissance reçue depuis les BTS pour l'exposition globale induite par un réseau macro LTE. / Wireless communication technologies, since their introduction, have evolved very quickly and people have been brought in 30 years into a much closer world. In parallel radiofrequency (RF) electromagnetic fields (EMF) are more and more used. As a consequence, people's attentions around health risks of exposure to RF EMFs have grown just as much as their usages of wireless communication technologies. Exposure to RF EMFs can be characterized using different exposure metrics (e.g., incident field metrics, absorption metrics...). However, the existing methodologies are well suited to the maximum exposure assessment for the individual under the worst-case condition. Moreover in most cases, when dealing with exposure issues, exposures linked to RF EMF emitted from base stations (BTS) and by wireless devices (e.g, mobile phones and tablets) are generally treated separately. This thesis has been dedicated to construct and validate a new method for assessing the real day-to-day RF EMF exposure to a wireless network as a whole, exploring the people's daily life, including both downlink and uplink exposures and taking into account different technologies, usages, environments, etc. Towards these objectives, we analyzed for the first time the average population exposure linked to third generation network (3G) induced EMFs, from both uplink and downlink radio emissions in different countries, geographical areas, and for different wireless device usages. Results, derived from device usage statistics, show a strong heterogeneity of exposure, both in time and space. We show that, contrary to popular belief, exposure to 3G EMFs is dominated by uplink radio emissions, resulting from voice and data traffic, and average population EMF exposure differs from one geographical area to another, as well as from one country to another, due to the different cellular network architectures and variability of mobile usage. Thus the variability and uncertainties linked to these influencing factors were characterized. And a variance-based sensitivity analysis of the global exposure was performed for the purpose of simplifying its evaluation. Finally, a substitution model was built to evaluate the day-to-day global LTE induced EMFs exposure of a population taking into account the variability linked to propagation environment, usage, as well as EMFs from personal wireless devices and BTS. Results have highlighted the importance of received power density from BTS to the issue of global exposure induced by a macro LTE network. This substitution model can be further used to analyze the evolution of the wireless network in terms of EMF exposure.

La mécanique computationnelle est un outil incontournable pour le monde de l’ingénierie mécanique. Motivé par un désir de réalisme et soumis à un perpétuel gigantisme, les modèles numériques doivent aujourd’hui inclure des phénomènes physiques de plus en plus complexes. Par conséquence, d’importantes capacités calculatoires sont requises afin de traiter des problèmes à la fois non-linéaires mais aussi de grande taille. Pour atteindre cet objectif, il convient de développer les stations de calculs mais aussi les méthodes algorithmiques utilisées afin de résoudre efficacement ces types de problèmes. Récemment, les méthodes de réduction de modèle se révèlent comme d’excellentes options au développement d’algorithmes de résolution performants. Le problème du contact frottant entre solides élastiques est particulièrement bien connu pour sa complexité et dont les temps de calcul peuvent devenir prohibitifs. En effet, les lois qui le régissent sont très hautement non-linéaires (non différentiables). Dans ce mémoire, nous nous proposons d’appliquer différentes méthodes de réduction de modèle (a posteriori et a priori) à ce type de problème afin de développer des méthodes de calculs accélérées dans le cadre de la méthode des éléments finis. Tout d’abord, en se plaçant dans le cadre des petites perturbations en évolution quasistatique, la réductibilité de diverses solutions impliquant du contact frottant est mise en évidence via leur décomposition en valeur singulière. De plus, leur contenu à échelle séparée est exhibé. La méthode non-incrémentale et non-linéaire à large incrément de temps (LATIN) est par la suite présentée. Dans un second temps et à partir des observations faites précédemment, une méthode LATIN accélérée est proposée en s’inspirant des méthodes multigrilles non-linéaires de type “full approximation scheme” (FAS). Cette méthode s’apparente en partie aux méthodes de réduction de modèle de type a posteriori. De plus, une stratégie de calcul de modes à partir d’un modèle de substitution est proposée. Par la suite, la décomposition propre généralisée (PGD) est utilisée afin de développer une méthode de résolution non-linéaire efficace reposant fondamentalement sur une approche de réduction de modèle de type a priori. Enfin, quelques extensions sont proposées telle que la résolution de problème faisant intervenir des études paramétriques, ou encore la prise en charge de non-linéarités supplémentaires telle que la plasticité. / Computational mechanics is an essential tool for mechanical engineering purposes. Nowadays, numerical models have to take into account complex physical phenomenons to be even more realistic and become larger and larger. As a consequence, more and more computing capacities are required in order to tackle not only non-linear problems but also large scale problems. For that purpose, both computers and numerical methods have to be developed in order to solve them efficiently. In the last decades, model reduction methods show great abilities to assign such challenges. The frictional contact problem between elastic solids is particularly well-known for its difficulty. Because its governing laws are highly non-linear (non-smooth), prohibitive computational time can occur. In this dissertation, model reduction methods (both a posteriori and a priori approaches) are deployed in order to implement efficient numerical methods to solve frictional contact problem in the finite element framework. First, small perturbations hypothesis with a quasi-static evolution are assumed. Then, reducibility of some frictional solutions is emphasized and discussed using the singular value decomposition. In addition, a scale separability phenomenon is enlightened. Then, the non-linear large time increment method (LATIN) is introduced. Secondly, an accelerated LATIN method is suggested by drawing an analogy between previous scale separability observations and the non-linear multigrid full approximation scheme (FAS). This accelerated non-linear solver relies essentially on the a posteriori model reduction approach. A precomputation strategy for modes relying on surrogate models is also suggested. Next, the proper generalized decomposition (PGD) is used to implement a non-linear solver relying fundamentally on an a priori model reduction method. Finally, some extensions are given to assign parametric studies and to take into account an additional non-linearity such as elastoplastic constitutive laws.

This thesis titled, “Nature of Local Interactions at cisPro-Aro Peptide Sequences in Proteins: Evidences for van der Waals type Interactions. Design and Synthesis of Novel Covalent Surrogates for the Peptide Hydrogen Bond”, describes two important studies. The first is to gain a thorough understanding of the nature of interactions that govern cisPro stability at Pro-Aro sequences, which described in the first four chapters. The final chapter describes the synthesis of novel 4-carbon covalent surrogates for the peptide H-bonding interaction. Chapter 1: Local Interactions Governing cisPro Stability: Refining the Model Peptides Chapter 1 Section A: Understanding the role of inter-side chain CH•••Aro interaction in cis-trans isomerization at Pro-Aro and Aro-Pro Sequences. This chapter is divided into two sections. In the first section an exhaustive overview of earlier investigations into the nature of local interactions at Xaa-cisPro-Aro and Aro-cisPro-Xaa peptide sequences, by various groups, are discussed. Most studies have found evidence for the close assemblage between side chains of residues flanking cisPro motifs, when at least one of them is an aromatic group. An electronic C-H•••π nature has been proposed for these assemblies and they are proposed to influence the cisPro stability. We highlight those features in these studies that indicate that these interactions are not always electronically tunable, are insensitive to presence of strong chaotropes in the solvent and occur at protein sequences lacking Pro or cisPro; all of which contradict the electronic C-H•••π model for these inter-side chain assemblages and their perceived influence on cisPro stability. Chapter 1 Section B: Investigation of the Nature of H Xaa•••Aro interaction at Xaa-Pro-Pro-Phe-sequences In Section B, we design and synthesize Pro-Aro containing short peptide models to investigate the nature of local C-H•••Aro interactions in them. We synthesize a series of homologous Pro-Pro-Aro containing peptides (modeled based on earlier studies) and investigate the relative populations of its four Xaa-Pro rotamers using extensive 1D and 2D NMR techniques including TOCSY, HSQC and ROESY. We find several drawbacks that make this a relatively deficient model. Firstly, their relative populations of the rotamers (the most important data for current investigation) cannot be determined with high fidelity as they are dependent on the solvent polarity, solute concentration and chemical shift degeneracy of crucial NMR signals for the rotamers. Importantly, the populations of a few rotamers are influenced by strong 13-membered ring backbone H-bonds. Notably, some of the cisPro rotamers do not even contain the inter-side chain assembly, whose nature is under investigation. Design of novel models – unconstrained by H-bonds We design the Acyl-Pro-Pro-Aro-OMe peptides that lack the possibility of forming the 13-membered ring H-bonded structures. Thorough 1D and 2D NMR analyses of these models reveal that strong Type VI β-turn type 10-membered ring H-bonds are formed in the rotamers of these models – hence precluding their applications for current study. Interestingly, the relative rotamer populations are strongly influenced by solvent polarity and are entirely different from those of the corresponding C-terminal amide models. We further discover that the Pro-Pro-Aro motif is not essential to express the inter-side chain interactions – Ala-Pro-Aro are sufficient. Formation of the 10-membered H-bonding interactions, however, are not precluded. Chapter 2: Design and Synthesis of Acyl-Pro-Phe-OMe: Novel models to investigate the role of HαXaa•••Aro interactions on Xaa-cisPro-Aro stability. Chapter 2 Section A: Design, Synthesis and Conformational Analysis of Ibu-Pro-Phe-OMe Chapter 2 is divided into two sections. In Section A, we replace the amino acid at the N-terminal of the putative Pro residue with simple isosteric isobutyryl group, the resulting minimalist dipeptide model shows the exclusive influence of desired inter-side chain interactions in the cisPro rotamer. Solvent polarity and temperature coefficient studies reveal that absence of any intramolecular H-bonding or Oπ* interactions in it. 1D and 2D NMR analyses clearly indicate the close proximity between the side chains of Ibu and Phe exclusively in the cisPro rotamer. The Kc/t value decreases upon mutation of Phe to Ala. All these features favor the Ibu-Pro-Phe-OMe as an ideal minimalistic model for investigating the nature of Ibu•••Ph assemblages in the cisPro rotamer. Chapter 2 Section B: Investigation of CH•••Aro /Alp•••Alp interactions in Ibu-cisPro-Xaa-OMe In Section B, the 1D and 2D NMR analyses of the complete set of the aliphatic and aromatic analogues Ibu-Pro-Xaa-OMe were investigated. DMSO-d6 was found to be the best solvent for mimicking both the folded and the unfolded local environments of these short peptide sequences. The HαIbu•••Aro assemblage is observed in Aro analogues, but cannot be electronically tuned. The aliphatic analogues also surprisingly contain the HαIbu•••Alp interactions! The Kc/t values (cisPro %) increase in the aliphatic analogues too, where the aliphatic side chain is long. Increase in cisPro stability is not due to ring current effects or intramolecular H-bonds or Oπ* interactions. It seems to be due to van der Waals type interactions between the involved side chains, either of which need not be aromatic in nature. Chapter 3: Nature of Inter-Side Chain Interactions at Acyl-cisPro-Aro Sequences: Evidence for van der Waals Interactions Chapter 3 Section A: Investigation of nature of inter-side chain interactions in R-CO-cisPro-Phe-OMe Chapter 3 has two sections. Section A describes the systematic design and synthesis of Acyl-Pro-Phe-OMe homologues where first the steric bulk and hence the surface area of the aliphatic side chain of the acyl group is varied. Interaction of the phenyl ring of Phe seems to occur with the Cα-Cβ σ-bond of the acyl group. Branching at either Cα or Cβ seems to destabilize the cisPro rotamer. Aliphatic•••Aromatic interactions overwhelm the cisPro rotamer population to be greater than that of transPro. In the analogues where the acidity of the acyl Cα-H bond is increased, the Kc/t does not increase correspondingly. The Δδ(trans-cis) ppm shifts of HαAcyl protons are dependent exclusively on its acidity rather than on the Kc/t values. In carbamyl-Pro, which entirely lack the HαAcyl proton, the Kc/t values are significantly high and improve as the aliphatic surface on the alkoxy group increases. Introduction of benzyloxy carbamyl group at Pro renders almost the same Kc/t values as that of ethyloxy carbamate. All these data contradict the C-H•••π interaction model and strongly support a van der Waals type interaction between the Acyl (preceding cisPro) group’s Xα-Yβ σ-bond and the Aro or Alp side chains (succeeding cisPro). Chapter 3 Section B: Evidence for the Van der Waals nature of Inter Side Chain (Acyl•••S.C.Aro/Alp) interactions- Determination of Interactions energies In Section B, a thorough investigation of both aliphatic•••aliphatic and aliphatic•••aromatic interactions on the background of homologous Acyl-Pro-Aro/Alp-OMe peptide models is undertaken. These models uniquely allow the delineation of contribution of the van der Waals interactions and the ring current effects to the cis/trans isomerization in these peptides. We see that the energy of the van der Waals component of these aliphatic•••aliphatic and aliphatic…aromatic interactions increase linearly with increase in Kc/t, in both DMSO-d6 and D2O. On other hand, energy from the ring current effects largely remains invariant. The Acyl•••Aro/Alp interactions are not hydrophobic and are facilitated by conformational effects. Chapter 4: Crystallographic evidence for van der Waals interaction-mediated stabilization of cisPro conformers Chapter 4 Section A: Systematic crystallization and crystal structure analyses of homologous Xaa-cisPro-Alp and Xaa-cisPro-Aro rotamers: Evidence for van der Waals interactions Chapter 4 has two sections, both of which present crystallographic evidence for the van der Waals nature of the Xaa•••Aro interactions at Xaa-cisPro-Aro sequences. Section A describes the unique crystal structures of five of the Acyl-Pro-Alp-OMe analogues that have been synthesized in the current study. All of them remarkably crystallize with two features: 1) the Acyl-Pro peptide bond adopts the cisPro rotamer in all; and 2) the aliphatic side chains of the acyl group and the Alp side chain are involved in van der Waals type interactions. The cisPro rotamers of even the bulkiest motifs, namely Ibu-Pro-Val-OMe, Piv-Pro-Ile-OMe and Piv-Pro-Leu-OMe crystallize, stabilized by van der Waals packing between aliphatic groups of the acyl and the Leu/Ile/Val side chains. Where the side chains are not long enough to make sub-van der Waals contacts with each other, their acyl C′-Cα σ-bond rotations are restricted due to Oσ* interactions involving the charge on the acyl carbonyl O. Where this occurs, the short space between the acyl and Alp side chains are filled in by aliphatic groups from neighbouring molecules at sub van der Waals distances. The Pro, Alp and χ1(Alp) dihedral angles are restricted to narrow range of values, irrespective of the length of Alp side chain, indicating that this backbone conformation is a conformational minimum when i+3i backbone H-bond is removed, with Pro at the i+1st position. This is further substantiated in Piv-Pro-Gly-OMe, which crystallizes in trans-Pro form, but still adopts similar backbone dihedral angles in spite of lacking any Alp side chain for interactions with the acyl group. Three of the Acyl-Pro-Aro-OMe models also crystallize in cisPro rotamer forms – both exhibit van der Waals type contacts between the Acyl group and backbone of Phe, rather than the aromatic ring of Phe. The phenyl ring of Phe may or may not form intramolecular Ph•••Pro inter-side chain contacts – which is not a pre-requisite for cisPro stabilization. No C-H••• interactions are observed anywhere in these peptides – van der Waals type contacts alone predominate in all cases. There are no abnormal distortions in bond angles or lengths even in the most sterically hindered cases, signifying that the conformations of these cisPro rotamers involving aliphatic•••aliphatic type contacts are natural minima. Chapter 4 Section B: Mining the PDB for Statistical Evidence of van der Waals interactions Section B of chapter 4 describes the data mining and statistical analyses of Xaa-cisPro-Phe, Xaa-cisPro-Val and Xaa-cisProLeu sequences in the PDB. The PEARL program was used to mine the PDB data. The overall frequency of 5.3% for appearance of cisPro among all Xaa-Pro peptide bonds, improves when Xaa is Phe or Tyr. However, several anomalies highlight the need for refining the analyses set to only those sequences where the side chains of Xaa and Aro/Alp face each other. In this refined set, clearly, inter side chain Xaa•••Alp/Aro contacts take precedence over even Aro•••Pro interactions at Aro-cisPro sequences (where Xaa is Aro). The Phe and the Leu side chains induce similar conformational effects on the preceding Xaa-Pro backbone. So does Val. Strong aliphatic•••aliphatic inter side chain contacts at van der Waals distances are observed to flank cisPro in several proteins. Substitution at the Cα of Xaa governs the proximity of the approaching side chain of Alp / Aro residue. The Cα-H of Xaa steers away from the Aro side chain at Xaa-Pro-Phe sequences, as the Aro group gets closer to it – implying the absence of ordered C-H••• contacts between them. There is consistent parallel alignment between Cα-Cβ -bond of Xaa and the C -C bond of the approaching side chain of Alp or Aro group – clearly highlighting the presence of van der Waals type interactions between them. All these evidences clearly point towards the van der Waals nature of local interactions at cisPro-Aro/Alp peptide sequences. Chapter 5: A novel 4-carbon covalent surrogate model for peptide H-Bond Chapter 5 describes the design and synthesis of novel 4-carbon covalent surrogates for the peptide H-bond (HBS). These surrogates would allow the unique constraining of two peptide strands in their extended conformations. The covalent HBS contain four orthogonal functional groups for independent extension at all of the four ends – similar to an endogenous inter-strand peptide H-bond. The synthesis of the surrogate is achieved by directly using natural chiral amino acid derivatives, beginning from amino alcohols obtained from reduction of desired amino acids. Suitably N-protected alcohols undergo oxidation to aldehyde followed by Grignard addition of allyl magnesium bromide, TBDMS protection of the homoallylic alcohol and reductive ozonolysis of the olefin to get a primary alcohol which is subject to Fukuyama-Mitsunobu reaction with desire protected peptide. The residue preferences that produce strongest inter-strand H-bonds were explored. The designed 4-carbon covalent HBS was incorporated using this methodology in a Gramicidin-S analogue, its first structural mimic containing only a single turn motif. This HBS model will have wide applications for constraining peptides in a number of secondary structures.

Diploma thesis is focused on advanced reliability analysis of structures solved by non--linear finite element analysis. Specifically, semi--probabilistic methods for determination of design value of resistance, sensitivity analysis and surrogate model created by polynomial chaos expansion are described in the diploma thesis. Described methods are applied on prestressed reinforced concrete roof girder.

Being able to accurately approximate outputs of computationally expensive simulations for arbitrary input parameters, also called missing points estimation, is central in many different areas of research and development with applications ranging from uncertainty propagation to control system design to name a few. This project investigates the potential of kernel transformations and nonlinear autoencoders as methods of improving the accuracy of the proper orthogonal decomposition method combined with regression. The techniques are applied on aerodynamic pressure CFD data around airplane wings in both two- and three-dimensional settings. The novel methods show potential in select situations, but cannot at this stage be generally considered superior. Their performances are similar although the procedure of design and training of a nonlinear autoencoder is less straight forward and more time demanding than using kernel transformations. The results demonstrate the regression bottleneck of the proper orthogonal decomposition method, which partially is improved with the new methods. Future studies should focus on adapting the autoencoder training strategy to the architecture and data as well as improving the regression stage of all methods.