Relevant bibliographies by topics / Uncertainty propagation in a dynamical context

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Academic literature on the topic 'Uncertainty propagation in a dynamical context'

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Published: 1 March 2025

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Journal articles on the topic "Uncertainty propagation in a dynamical context"

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Raïssi, Tarek, and Denis Efimov. "Some recent results on the design and implementation of interval observers for uncertain systems." at - Automatisierungstechnik 66, no. 3 (March 26, 2018): 213–24. http://dx.doi.org/10.1515/auto-2017-0081.

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Abstract Based on the theory of positive systems, the goal of interval observers is to compute sets of admissible values of the state vector at each instant of time for systems subject to bounded uncertainties (noises, disturbances and parameters). The size of the estimated sets, which should be minimised, has to be proportional to the model uncertainties. An interval estimation can be seen as a conventional point estimation (the centre of the interval) with an estimation error given by the interval radius. The reliable uncertainties propagation performed in this context can be useful in several fields such as robust control, diagnosis and fault-tolerant control. This paper presents some recent results on interval observers for several dynamical systems classes such as continuous-time and switched systems.
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Martins, L. L., J. P. Gomes, and A. S. Ribeiro. "Metrological quality of the excitation force in forced vibration test of concrete dams." Journal of Physics: Conference Series 2647, no. 21 (June 1, 2024): 212001. http://dx.doi.org/10.1088/1742-6596/2647/21/212001.

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Abstract This paper describes the study of the metrological quality of the excitation force in the context of force vibration test of concrete dams. For this purpose, a measurement uncertainty evaluation was performed, based on available probabilistic information about the input quantities – rotation frequency, mass, radial position, dimension, diameter and density of the generator’s rod – which support the determination of the excitation force in an eccentric masses vibration generator, used by LNEC in concrete dam’s field observation. The uncertainty propagation from the input quantities to the output quantity was performed by a Monte Carlo method, considering the mathematical model used for the determination of the excitation force. Two experimental cases were studied: (A) the use of five weights in the generator in the frequency range of 1 Hz up to 6 Hz; and (B) the use of a single weight in the generator in the frequency interval comprised between 5 Hz and 15 Hz. In the first case, the excitation force estimates and expanded measurement uncertainties (considering a 95 % confidence interval) varied between 3.55 kN ± 0.14 kN and 127.68 kN ± 0.91 kN, being rotation frequency the major contribution for the obtained dispersion of force values. In the second case, the excitation force estimates and expanded measurement uncertainties varied between 16.71 kN ± 0.25 kN and 150.4 kN ± 1.8 kN, being the generator’s rod diameter the main contribution for the output measurement uncertainty. The obtained knowledge is essential to assure confidence and rigorous knowledge about the applied excitation force, namely, in extreme situations near dynamical structural safety limits of the observed concrete dam and of the testing equipment.
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Mezić, Igor, and Thordur Runolfsson. "Uncertainty propagation in dynamical systems." Automatica 44, no. 12 (December 2008): 3003–13. http://dx.doi.org/10.1016/j.automatica.2008.04.020.

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Banks, H. T., and Shuhua Hu. "Propagation of Uncertainty in Dynamical Systems." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2012 (May 5, 2012): 134–39. http://dx.doi.org/10.5687/sss.2012.134.

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Piqueira, José R. C., and Felipe Barbosa Cesar. "Dynamical Models for Computer Viruses Propagation." Mathematical Problems in Engineering 2008 (2008): 1–11. http://dx.doi.org/10.1155/2008/940526.

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Nowadays, digital computer systems and networks are the main engineering tools, being used in planning, design, operation, and control of all sizes of building, transportation, machinery, business, and life maintaining devices. Consequently, computer viruses became one of the most important sources of uncertainty, contributing to decrease the reliability of vital activities. A lot of antivirus programs have been developed, but they are limited to detecting and removing infections, based on previous knowledge of the virus code. In spite of having good adaptation capability, these programs work just as vaccines against diseases and are not able to prevent new infections based on the network state. Here, a trial on modeling computer viruses propagation dynamics relates it to other notable events occurring in the network permitting to establish preventive policies in the network management. Data from three different viruses are collected in the Internet and two different identification techniques, autoregressive and Fourier analyses, are applied showing that it is possible to forecast the dynamics of a new virus propagation by using the data collected from other viruses that formerly infected the network.
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DeMars, Kyle J., Robert H. Bishop, and Moriba K. Jah. "Entropy-Based Approach for Uncertainty Propagation of Nonlinear Dynamical Systems." Journal of Guidance, Control, and Dynamics 36, no. 4 (July 2013): 1047–57. http://dx.doi.org/10.2514/1.58987.

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Park, Inkwan, Kohei Fujimoto, and Daniel J. Scheeres. "Effect of Dynamical Accuracy for Uncertainty Propagation of Perturbed Keplerian Motion." Journal of Guidance, Control, and Dynamics 38, no. 12 (December 2015): 2287–300. http://dx.doi.org/10.2514/1.g000956.

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Xu, Tianlai, Zhe Zhang, and Hongwei Han. "Adaptive Gaussian Mixture Model for Uncertainty Propagation Using Virtual Sample Generation." Applied Sciences 13, no. 5 (February 27, 2023): 3069. http://dx.doi.org/10.3390/app13053069.

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Orbit uncertainty propagation plays an important role in the analysis of a space mission. The accuracy and computation expense are two critical essences of uncertainty propagation. Repeated evaluations of the objective model are required to improve the preciseness of prediction, especially for long-term propagation. To balance the computational complexity and accuracy, an adaptive Gaussian mixture model using virtual sample generation (AGMM-VSG) is proposed. First, an unscented transformation and Cubature rule (UT-CR) based splitting method is employed to adaptive update the weights of Gaussian components for nonlinear dynamics. The Gaussian mixture model (GMM) approximation is applied to better approximate the original probability density function. Second, instead of the pure expensive evaluations by conventional GMM methods, virtual samples are generated using a new active-sampling-based Kriging (AS-KRG) method to improve the propagation efficiency. Three cases of uncertain orbital dynamical systems are used to verify the accuracy and efficiency of the proposed manuscript. The likelihood agreement measure (LAM) criterion and the number of expense evaluations prove the performance.
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Baili, H., and G. A. Fleury. "Indirect Measurement Within Dynamical Context: Probabilistic Approach to Deal With Uncertainty." IEEE Transactions on Instrumentation and Measurement 53, no. 6 (December 2004): 1449–54. http://dx.doi.org/10.1109/tim.2004.831138.

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Kuehn, Christian. "Uncertainty transformation via Hopf bifurcation in fast–slow systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2200 (April 2017): 20160346. http://dx.doi.org/10.1098/rspa.2016.0346.

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Propagation of uncertainty in dynamical systems is a significant challenge. Here we focus on random multiscale ordinary differential equation models. In particular, we study Hopf bifurcation in the fast subsystem for random initial conditions. We show that a random initial condition distribution can be transformed during the passage near a delayed/dynamic Hopf bifurcation: (i) to certain classes of symmetric copies, (ii) to an almost deterministic output, (iii) to a mixture distribution with differing moments and (iv) to a very restricted class of general distributions. We prove under which conditions the cases (i)–(iv) occur in certain classes vector fields.
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Dissertations / Theses on the topic "Uncertainty propagation in a dynamical context"

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Hernandez-Sabio, Sylvain. "Contribution à la métrologie des faibles forces : traçabilité des mesures dynamiques par inversion ensembliste." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2024. http://www.theses.fr/2024UBFCD058.

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Cette thèse est une contribution à la métrologie des faibles forces qui s'inscrit dans la continuité des activités de recherche menées au département AS2M de l'institut FEMTO-ST. Ce manuscrit présente la conception et la mise en œuvre expérimentale d'un accéléromètre pendulaire triaxial qui mesure les composantes non filtrées du régime sismique, puisque ces dernières sont susceptibles de perturber le fonctionnement d'une balance de micro-nanoforce électromagnétique actuellement en développement. Une méthodologie alternative de calcul est également proposée dans ce manuscrit afin d'estimer spécifiquement la valeur et l'incertitude associée à une ou plusieurs grandeurs d'intérêt inconnues, par l'intermédiaire d'un système dynamique SISO dont le comportement est incertain et perturbé. Cette approche repose sur la représentation exacte de ce système grâce à une entrée correctrice virtuelle qui contient les grandeurs d'intérêt. Cette entrée est estimée puis mise en forme afin de déterminer l'incertitude associée à ces grandeurs d'intérêt, en utilisant les outils de l'analyse par intervalles. La méthodologie proposée est validée à partir de simulations de l'accéléromètre en modes actif et passif, puis illustrée sur le dispositif expérimental. Une étude en simulation du fonctionnement couplé de la future balance de micro-nanoforce électromagnétique avec l'accéléromètre triaxial est également réalisée. L'approche proposée est mise en œuvre lors d'un essai simulé visant à caractériser la raideur mécanique d'un levier élastique
This PhD thesis is a contribution to small force metrology, in line with the research activities carried out in the AS2M department of the FEMTO-ST institute. This manuscript presents the design and experimental implementation of a triaxial pendulous accelerometer, which measures the unfiltered seismic activity, since the latter is likely to interfere with the operation of an electromagnetic micro-nanoforce balance currently under development. An alternative methodology is also proposed in this manuscript to specifically estimate the value and uncertainty associated with one or more unknown quantities of interest, using a dynamical SISO system whose behavior is uncertain and disturbed. This approach is based on the exact representation of this system by means of a virtual corrective input containing the quantities of interest. This input is estimated and then shaped to determine the uncertainty associated with these quantities of interest, using the tools of interval analysis. The proposed methodology is validated on the basis of simulated accelerometer responses in active and passive modes, then illustrated on the experimental setup. A simulation study of the coupled operation of the future electromagnetic micro-nanoforce balance with the triaxial accelerometer is also carried out. The proposed approach is implemented in a simulated test aiming at characterizing the mechanical stiffness of an elastic cantilever
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Kundu, Abhishek. "Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis." Thesis, Swansea University, 2014. https://cronfa.swan.ac.uk/Record/cronfa42292.

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Efficient uncertainty propagation schemes for dynamical systems are investigated here within the framework of stochastic finite element analysis. Uncertainty in the mathematical models arises from the incomplete knowledge or inherent variability of the various parametric and geometric properties of the physical system. These input uncertainties necessitate the use of stochastic mathematical models to accurately capture their behavior. The resolution of such stochastic models is computationally quite expensive. This work is concerned with development of model order reduction techniques for obtaining the dynamical response statistics of stochastic finite element systems. Efficient numerical methods have been proposed to propagate the input uncertainty of dynamical systems to the response variables. Response statistics of randomly parametrized structural dynamic systems have been investigated with a reduced spectral function approach. The frequency domain response and the transient evolution of the response of randomly parametrized structural dynamic systems have been studied with this approach. An efficient discrete representation of the input random field in a finite dimensional stochastic space is proposed here which has been integrated into the generic framework of the stochastic finite element weak formulation. This framework has been utilized to study the problem of random perturbation of the boundary surface of physical domains. Truncated reduced order representation of the complex mathematical quantities which are associated with the stochastic isoparametric mapping of the random domain to a deterministic master domain within the stochastic Galerkin framework have been provided. Lastly, an a-priori model reduction scheme for the resolution of the response statistics of stochastic dynamical systems has also been studied here which is based on the concept of balanced truncation. The performance and numerical accuracy of the methods proposed in this work have been exemplified with numerical simulations of stochastic dynamical systems and the convergence behavior of various error indicators.
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Perrin, Guillaume. "Random fields and associated statistical inverse problems for uncertainty quantification : application to railway track geometries for high-speed trains dynamical responses and risk assessment." Phd thesis, Université Paris-Est, 2013. http://pastel.archives-ouvertes.fr/pastel-01001045.

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Les nouvelles attentes vis-à-vis des nouveaux trains à grande vitesse sont nombreuses: on les voudrait plus rapides, plus confortables, plus stables, tout en étant moins consommateur d'énergie, moins agressif vis-à-vis des voies, moins bruyants... Afin d'optimiser la conception de ces trains du futur, il est alors nécessaire de pouvoir se baser sur une connaissance précise de l'ensemble des conditions de circulations qu'ils sont susceptibles de rencontrer au cours de leur cycle de vie. Afin de relever ces défis, la simulation a un très grand rôle à jouer. Pour que la simulation puisse être utilisée dans des perspectives de conception, de certification et d'optimisation de la maintenance, elle doit alors être tout à fait représentative de l'ensemble des comportements physiques mis en jeu. Le modèle du train, du contact entre les roues et le rail, doivent ainsi être validés avec attention, et les simulations doivent être lancées sur des ensembles d'excitations qui sont réalistes et représentatifs de ces défauts de géométrie. En ce qui concerne la dynamique, la géométrie de la voie, et plus particulièrement les défauts de géométrie, représentent une des principales sources d'excitation du train, qui est un système mécanique fortement non linéaire. A partir de mesures de la géométrie d'un réseau ferroviaire, un paramétrage complet de la géométrie de la voie et de sa variabilité semblent alors nécessaires, afin d'analyser au mieux le lien entre la réponse dynamique du train et les propriétés physiques et statistiques de la géométrie de la voie. Dans ce contexte, une approche pertinente pour modéliser cette géométrie de la voie, est de la considérer comme un champ aléatoire multivarié, dont les propriétés sont a priori inconnues. En raison des interactions spécifiques entre le train et la voie, il s'avère que ce champ aléatoire n'est ni Gaussien ni stationnaire. Ce travail de thèse s'est alors particulièrement concentré sur le développement de méthodes numériques permettant l'identification en inverse, à partir de mesures expérimentales, de champs aléatoires non Gaussiens et non stationnaires. Le comportement du train étant très non linéaire, ainsi que très sensible vis-à-vis de la géométrie de la voie, la caractérisation du champ aléatoire correspondant aux défauts de géométrie doit être extrêmement fine, tant du point de vue fréquentiel que statistique. La dimension des espaces statistiques considérés est alors très importante. De ce fait, une attention toute particulière a été portée dans ces travaux aux méthodes de réduction statistique, ainsi qu'aux méthodes pouvant être généralisées à la très grande dimension. Une fois la variabilité de la géométrie de la voie caractérisée à partir de données expérimentales, elle doit ensuite être propagée au sein du modèle numérique ferroviaire. A cette fin, les propriétés mécaniques d'un modèle numérique de train à grande vitesse ont été identifiées à partir de mesures expérimentales. La réponse dynamique stochastique de ce train, soumis à un très grand nombre de conditions de circulation réalistes et représentatives générées à partir du modèle stochastique de la voie ferrée, a été ainsi évaluée. Enfin, afin d'illustrer les possibilités apportées par un tel couplage entre la variabilité de la géométrie de la voie et la réponse dynamique du train, ce travail de thèse aborde trois applications
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Audinot, Timothée. "Développement d’un modèle de dynamique forestière à grande échelle pour simuler les forêts françaises dans un contexte non-stationnaire." Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0179.

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Contexte. Depuis la révolution industrielle, les forêts européennes connaissent une dynamique d’expansion de leur surface et de leur stock de bois. Cette expansion, conjuguée au changement climatique, entraîne des modifications des processus de dynamique forestière. L’émergence de la bioéconomie européenne augure dans ce contexte d’évolutions des stratégies de gestion forestière à l’échelle européenne et nationale. La simulation des ressources forestières futures et de leur pilotage par des modèles à grande échelle spatiale est donc indispensable pour fournir des outils de planification stratégique. En France, les ressources forestières se caractérisent par une diversité marquée par rapport à d’autres pays européens. Le modèle de dynamique forestière MARGOT (MAtrix model of forest Resource Growth and dynamics On the Territory scale), a été mis en place par l’inventaire forestier national (IFN) en 1993 pour simuler les ressources forestières françaises à partir des données de cet inventaire, mais n’a été l’objet que de travaux de recherche restreints depuis son origine. Ses simulations restent limitées à un horizon temporel de moyen terme (inférieur à 30 ans), sous des scénarios de gestion de type business as usual, et ne tenant pas compte des contextes forestiers et environnementaux non-stationnaires.Objectifs. Cette thèse a pour ambition générale de consacrer un effort de recherche de rupture sur le modèle MARGOT, afin d’aborder les enjeux forestiers actuels. Les objectifs précis sont : i) de déterminer la capacité du modèle MARGOT à restituer l’expansion forestière française sur une période rétrospective longue (1971-2016), ii) de prendre en compte de façon synthétique de l’hétérogénéité des forêts à grande échelle, iii) de prendre en compte le phénomène de densification des forêts dans la dynamique démographique, iv) d’inclure les forçages climatiques externes dans la dynamique de croissance des forêts, v) dans un contexte devenu très incertain, de pouvoir mesurer le niveau d’incertitude des simulations résultant de l’erreur d’échantillonnage de l’inventaire forestier au regard des évolutions tendancielles considérées. Le développement de scénarios de gestion forestière reste hors du champ de ce travail. Principaux résultats. Une méthode générique de partition des forêts selon leur hétérogénéité géographique et compositionnelle a été mise en place, avec une vocation applicative à d’autres contextes forestiers européens. Une méthode de propagation de l’incertitude d’échantillonnage aux paramètres du modèle, puis aux simulations, a été développée à partir d’approches de ré-échantillonnage de données et de modélisation d’erreurs. Une approche originale d’intégration des phénomènes de densité-dépendance démographique, fondée sur une métrique de densité et la réintroduction d’un concept de « peuplement forestier » adapté à ce modèle, a été développée. Une stratégie d’intégration des forçages climatiques des paramètres démographiques du modèle a été développée à partir d’une approche d’hybridation entrées-sorties avec le modèle fonctionnel CASTANEA pour un sous-ensemble de la forêt française incluant les espèces de chênes, de hêtre, d’épicéa commun, et de pin sylvestre. L’ensemble de ces développements a permis de réduire très notablement le biais de prédiction du modèle initial. Conclusions. Les développements consentis font du modèle MARGOT un outil d’exploration et de planification plus fiable des ressources forestières, et reposant sur une approche de modélisation originale et unique en Europe. L’utilisation de statistiques forestières anciennes permettra d’évaluer le modèle et de simuler le stock de carbone de la forêt française sur un horizon temporel plus importante (de plus de 100 ans). Une évaluation approfondie des performances de ce nouveau modèle par des simulations intensives doit être conduite
Context. Since the industrial revolution, European forests have shown expansion of their area and growing stock. This expansion, together with climate change, drive changes in the processes of forest dynamic. The emergence of a European bioeconomy strategy suggests new developments of forest management strategies at European and national levels. Simulating future forest resources and their management with large-scale models is therefore essential to provide strategic planning support tools. In France, forest resources show high diversity as compared with other European countries' forests. The MARGOT forest dynamic model (MAtrix model of forest Resource Growth and dynamics On the Territory scale), was developed by the national forest inventory (IFN) in 1993 to simulate French forest resources from data of this inventory, but has been the subject of restricted developments, and simulations remain limited to a time horizon shorter than 30 years, under “business as usual” management scenarios, and not taking into account non-stationary forest and environmental contexts.Aims. The general ambition of this thesis was to consent a significant development effort on MARGOT model, in order to tackle current forestry issues. The specific objectives were: i) to assess the capacity of MARGOT to describe French forest expansion over a long retrospective period (1971-2016), ii) to take into account the heterogeneity of forests at large-scale in a holistic way, iii) to account for the impacts of forest densification in demographic dynamic processes, iv) to encompass external climatic forcing in forest growth, v) in a very uncertain context, to be able to quantify NFI sampling uncertainty in model parameters and simulations with respect to the magnitude of other trends considered. The development of forest management scenarios remained outside the scope of this work.Main results. A generic method for forest partitioning according to their geographic and compositional heterogeneity has been implemented. This method is intended to be applied to other European forest contexts. A method of propagating sampling uncertainty to model parameters and simulations has been developed from data resampling and error modelling approaches. An original approach to integrating density-dependence in demographic processes has been developed, based on a density metric and the reintroduction of forest stand entities adapted to the model. A strategy for integrating climate forcing of model demographic parameters was developed based on an input-output coupling approach with the process-based model CASTANEA, for a subset of French forests including oak, beech, Norway spruce, and Scots pine forests. All of these developments significantly reduced the prediction bias of the initial model.Conclusions. These developments make MARGOT a much more reliable forest resource assessment tool, and are based on an original modeling approach that is unique in Europe. The use of ancient forest statistics will make it possible to evaluate the model and simulate the carbon stock of French forests over a longer time horizon (over 100 years). Intensive simulations to assess the performance of this new model must be done
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Books on the topic "Uncertainty propagation in a dynamical context"

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Louchet, Francois. Snow Avalanches. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198866930.001.0001.

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This work is a critical update of the most recent and innovative developments of the avalanche science. It aims at re-founding it on clear scientific bases, from field observations and experiments up to strong mathematical and physical analysis and modeling. It points out snow peculiarities, regarding both static mechanical properties and flow dynamics, that may strongly differ from those of compact solids for the former, and of Newtonian fluids for the latter. It analyzes the general processes involved in avalanche release, in terms of brittle fracture and ductile plasticity, specific friction laws, flow of healable granular materials, percolation concepts, cellular automata, scale invariance, criticality, theory of dynamical systems, bifurcations, etc. As a result, slab triggering (including remote triggering) can be summarized by the “slab avalanche release in 4 steps” concept, based on weak layer local collapse and subsequent propagation driven by slab weight. The frequent abortion of many incipient avalanches is easily explained in terms of snow grain dynamical healing. Sluffs and full-depth avalanches are also analyzed. Such advances pave the way for significant progress in risk evaluation procedures. In the present context of a speeding-up climate warming, possible evolutions of snow cover extent and stability are also tentatively discussed. We show how, in mountainous areas, the present analysis can be extended to other gravitational failures (rock-falls, landslides) that are likely to take over from avalanches in such circumstances. The text is supported by on-line links to field experiments and lectures on triggering mechanisms, risk management, and decision making.
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Book chapters on the topic "Uncertainty propagation in a dynamical context"

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Chelle-Michou, Cyril, and Urs Schaltegger. "U–Pb Dating of Mineral Deposits: From Age Constraints to Ore-Forming Processes." In Isotopes in Economic Geology, Metallogenesis and Exploration, 37–87. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27897-6_3.

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AbstractThe timing and duration of ore-forming processes are amongst the key parameters required in the study of mineral systems. After more than a century of technical developments, innovations and investigation, the U–Pb system arguably is the most mature radioisotopic system in our possession to conduct absolute dating of a wide range of minerals across geological environments and metallogenic processes. Here, we review the basics of U–Pb geochronology, the key historic developments of the method, and the most commonly used analytical techniques (including data reduction, Pb-correction, uncertainty propagation and data presentation) and minerals while pointing out their respective advantages, weaknesses and potential pitfalls. We also highlight critical aspects that need to be considered when interpreting a date into the age of a geological process (including field and petrographic constraints, open-system behavior, handling and interpretation of uncertainties). While U–Pb geochronology is strongly biased toward zircon dating, we strive to highlight the great diversity of minerals amenable to U–Pb dating (more than 16 mineral species) in the context of mineral systems, and the variety of geological events they can potentially date (magmatism, hydrothermal activity, ore-formation, cooling, etc.). Finally, through two case studies we show (1) how multi-mineral geochronological studies have been used to bracket and decipher the age of multiple geological events associated with the world-class Witwatersrand gold province, and (2) how rather than the absolute age, the duration and rate of the mineralizing event at porphyry copper deposits opens new avenues to understand ore-forming processes and the main controls on the size of such deposits. The improving precision, accuracy and spatial resolution of analyses in tandem with high-quality field and petrographic observations, numerical modelling and geochemical data, will continue to challenge paradigms of ore-forming processes and contribute significant breakthroughs in ore deposit research and potentially to the development of new exploration tools.
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"Propagation of Uncertainty in a Continuous Time Dynamical System." In Modeling and Inverse Problems in the Presence of Uncertainty, 223–322. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b16760-9.

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Hans Alexander and Udluft Steffen. "Uncertainty Propagation for Efficient Exploration in Reinforcement Learning." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2010. https://doi.org/10.3233/978-1-60750-606-5-361.

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Reinforcement learning aims to derive an optimal policy for an often initially unknown environment. In the case of an unknown environment, exploration is used to acquire knowledge about it. In that context the well-known exploration-exploitation dilemma arises—when should one stop to explore and instead exploit the knowledge already gathered? In this paper we propose an uncertainty-based exploration method. We use uncertainty propagation to obtain the Q-function's uncertainty and then use the uncertainty in combination with the Q-values to guide the exploration to promising states that so far have been insufficiently explored. The uncertainty's weight during action selection can be influenced by a parameter. We evaluate one variant of the algorithm using full covariance matrices and two variants using an approximation and demonstrate their functionality on two benchmark problems.
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West, Mike. "Some Statistical Issues in Palæoclimatology¹." In Bayesian Statistics 5, 461–84. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198523567.003.0024.

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Abstract This paper discusses some issues arising in the study of patterns of historical climate change based on geochemical measurements in deep lake sediment cores. The specific climatological focus is on patterns of variability, and possible cycles, in climatic indicators during the past two or three millenia. The statistical issues raised relate to various aspects of statistical calibration of raw data records, data quality and uncertainty propagation through data processing stages, and problems of time series analysis to assess patterns of variation in the geological records over time. Novel time series methods are introduced to address the questions of cyclicality in the data records and to allow for various sources of uncertainty in dating of the records. Dynamic models with cyclical auto-regressive components, and various aspects of their simulation based analyses, are discussed, and some exploratory analyses of currently available palreoclimatologicaldata are summarised. Other issues discussed include radiocarbon calibration, uncertainties in data timing, missing data, model combination, and the future prospects in the current and related palreoclimatological contexts.
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Chadwick, P., and N. H. Scott. "Linear dynamical stability in constrained thermoelasticity I. Deformation-temperature constraints." In Nonlinear Elasticity and Theoretical Mechanics, 125–34. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198534860.003.0011.

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Abstract Equations are derived governing an infinitesimal disturbance of a uniform equilibrium state Be of an unbounded body composed of a heat-conducting elastic material subject to a constraint linking the deformation and the temperature. No restriction is placed on the symmetry of the material and the freedom of choice of Be allows the presence of an arbitrary homogeneous prestrain. The stability of Be, in the context of linearized dynamics, is examined by studying the nature of plane-harmonic-wave solutions of the governing equations. It is found that, under very mild restrictions on the relevant material constants in Be, at least one of the four modes of wave propagation is always unstable, a conclusion which seriously undermines the legitimacy of the assumed type of constraint. The particular case of incompressibility at uniform temperature has been discussed by previous authors and is recapitulated here. Finally, an explanation of the inherent instability is provided by treating the constraint as a limit.
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Chakraverty, S., and Smita Tapaswini. "Numerical Solution of Fuzzy Differential Equations and its Applications." In Advances in Computational Intelligence and Robotics, 127–49. IGI Global, 2014. http://dx.doi.org/10.4018/978-1-4666-4991-0.ch007.

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Theory of fuzzy differential equations is the important new developments to model various science and engineering problems of uncertain nature because this theory represents a natural way to model dynamical systems under uncertainty. Since, it is too difficult to obtain the exact solution of fuzzy differential equations so one may need reliable and efficient numerical techniques for the solution of fuzzy differential equations. In this chapter we have presented various numerical techniques viz. Euler and improved Euler type methods and Homotopy Perturbation Method (HPM) to solve fuzzy differential equations. Also application problems such as fuzzy continuum reaction diffusion model to analyse the dynamical behaviour of the fire with fuzzy initial condition is investigated. To analyse the fire propagation, the complex fuzzy arithmetic and computation are used to solve hyperbolic reaction diffusion equation. This analysis finds the rate of burning number of trees in bounds where wave variable/ time are defined in terms of fuzzy. Obtained results are compared with the existing solution to show the efficiency of the applied methods.
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Bullough, R. K., and R. Hynne. "Ewald’s optical extinction theorem." In P. P. Ewald and his Dynamical Theory of X-ray Diffraction, 98–110. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198553793.003.0012.

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Abstract In his commentary on Ewald’s fundamental papers (1916a,b, 1917, 1937) in Chapter 11, Hellmut Juretschke draws attention to the elegant way in which P.P. Ewald solved the boundary problem for the propagation of electromagnetic (e.m.) waves in a crystal. He describes how by using a half-space (with a boundary) Ewald was able to show that the incident e.m. field (the field incident upon the crystal from outside) was extinguished inside the crystal and replaced by another e.m. field with different wave number. Similar considerations were independently developed more macroscopically by C.W. Oseen (1915) and the extinction process gained the name of the ‘extinction theorem’ (or the ‘optical extinction theorem’ in the sense of ‘optics’) of Ewald-Oseen. This chapter reanalyses the action of this ‘extinction theorem’ in an amorphous optical dielectric rather than a crystal and traces some of the subsequent history of the extinction theorem and its various applications in this context.
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Antolin, William P., Aurélien Costes, Mélanie C. Rochoux, and Patrick Le Moigne. "Accounting for the canopy drag effects on wildland fire spread in coupled atmosphere/fire simulations." In Advances in Forest Fire Research 2022, 959–64. Imprensa da Universidade de Coimbra, 2022. http://dx.doi.org/10.14195/978-989-26-2298-9_145.

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While near-surface wind is the main influential parameter governing the fire rate of spread (ROS), its characterization remains key to simulate wildland fire behavior. The correct repre- sentation of the intensity and variability of the near-surface wind under complex terrain and vegetation remains an open problem but is essential to make a coupled atmosphere-fire model applicable to actual wildfires. In this work, we study the impact of canopy drag effects on the near-surface flow and the fire behavior simulated by the coupled Meso-NH/BLAZE model in the context of the FireFlux I experimental grass fire for which trees were located upstream and on the flanks. Drag effects can be activated in Meso-NH running in large-eddy simulation mode following work by Aumond et al. (2013). The drag approach formulation consists of adding drag terms to the momentum equation and subgrid turbulent kinetic energy dissipation as a function of the foliage density. This approach is compared to the standard roughness approach and to the homogeneous case considered in Costes et al. (2021) where homogeneous grass was considered over the whole computational domain. Results show the dynamical influence of the surrounding vegetation. Results also indicate that the choice of parameterization, due to the difference in the represented physics, induces differences on the fire front propagation. This encourages us to explore different options to accurately represent the surface boundary layer in presence of complex vegetation for coupled atmosphere-fire modeling in future work.
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Conference papers on the topic "Uncertainty propagation in a dynamical context"

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Zanoni, Andrea, Michele Zilletti, Gianni Cassoni, Carmen Talamo, Davide Marchesoli, Pierangelo Masarati, and Francesca Colombo. "An Uncertainty Propagation Approach to Collective Bounce Rotorcraft-Pilot Couplings Analysis." In Vertical Flight Society 80th Annual Forum & Technology Display, 1–12. The Vertical Flight Society, 2024. http://dx.doi.org/10.4050/f-0080-2024-1321.

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In the context of Rotorcraft Pilot Couplings, the biomechanics of the pilot body play a fundamental role in determining the stability of the pilot-vehicle closed loop system. The response of the pilot body is, in turn, inherently stochastic, being a function of pilot biometrics and muscular activation. Coupling the statistical distribution of pilot biomechanical behavior determined in specialized experimental campaign with linear models of the helicopter heave dynamics, an uncertainty propagation procedure is developed, with the aim of estimating the statistical distribution of the stability margins of the closed loop pilot-vehicle system. Results obtained varying the collective lever characteristics, as well as the helicopter model parameters, align well with results obtained previously in deterministic settings. However, the new scheme allows to define quantitative robustness indices.
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Kumar, Alok, and Atul Kelkar. "Uncertainty Propagation in Dynamical Systems Using Koopman Eigenfunctions." In 2023 8th International Conference on Automation, Control and Robotics Engineering (CACRE). IEEE, 2023. http://dx.doi.org/10.1109/cacre58689.2023.10209022.

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Mezic, I. "Coupled nonlinear dynamical systems: asymptotic behavior and uncertainty propagation." In 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). IEEE, 2004. http://dx.doi.org/10.1109/cdc.2004.1430303.

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Terejanu, Gabriel, Puneet Singla, Tarunraj Singh, and Peter Scott. "Uncertainty Propagation for Nonlinear Dynamical Systems Using Gaussian Mixture Models." In AIAA Guidance, Navigation and Control Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-7472.

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Diez, Matteo, Zhaoyuan Wang, Sungtek Park, Christian Milano, Frederick Stern, Hironori Yasukawa, Andrew Gunderson, and John Scherer. "Multi-Fidelity MMG-Model for Digital Design of High-Speed Small Craft." In SNAME Power Boat Symposium. SNAME, 2024. http://dx.doi.org/10.5957/cpbs-2024-008.

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This paper introduces advanced methods for ship maneuvering predictions in the context of digital design of high-speed craft. While these methods are not yet commonly used by naval architects, it is believed that the present paper provides guidance to naval architects as to the way forward for advanced tools in ship design. Specifically, the paper presents the integration of the ship Maneuvering Modeling Group (MMG) model with multi-fidelity (MF) computational fluid dynamics (CFD) input data, particularly tailored for the analysis of high-speed small craft within the digital design paradigm. An uncertainty propagation approach via Monte Carlo sampling is introduced and discussed, covering from CFD computations to final MF-MMG predictions, passing trough the MF surrogate model. The investigation focuses on the straight-ahead self-propulsion of a standardized hull form, namely a 40 ft Generic Prismatic Planing Hull (GPPH), offering the opportunity to test both the MMG and the MF approaches against a challenging real world application. The study demonstrates how multi-fidelity methods could effectively reduce computational costs while maintaining predictive accuracy. Results show how a deterministic MMG model trained by MF-CFD simulations predicts a speed at maximum engine power above the required threshold, whereas the stochastic model (i.e., MF-MMG with uncertainty prediction) indicates a 95% confidence of achieving only a speed below the threshold at maximum power. Similarly, the speed that the boat can achieve at maximum shaft speed is larger than the threshold if evaluated by the deterministic model, whereas falls below the threshold if we consider the 95% confidence band provided by the stochastic model.
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De, Saibal, Reese Jones, and Hemanth Kolla. "Uncertainty Propagation in Dynamical Systems via Stochastic Collocation on Model Dynamics." In Proposed for presentation at the USACM Thematic Conference on Uncertainty Quantification for Machine Learning Integrated Physics Modeling (UQ-MLIP) held August 18-19, 2022 in Crystal City, Arlington, Virginia. US DOE, 2022. http://dx.doi.org/10.2172/2004300.

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De, Saibal, Reese Jones, and Hemanth Kolla. "Uncertainty Propagation in Dynamical Systems via Stochastic Collocation on Model Dynamics." In Proposed for presentation at the USACM Thematic Conference on Uncertainty Quantification for Machine Learning Integrated Physics Modeling (UQ-MLIP) held August 18-19, 2022 in Crystal City, Arlington, Virginia. US DOE, 2022. http://dx.doi.org/10.2172/2004282.

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Schäfer, Felicitas, Shuai Guo, and Wolfgang Polifke. "The Impact of Exceptional Points on the Reliability of Thermoacoustic Stability Analysis." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-15496.

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Abstract Exceptional points can be found for specific sets of parameters in thermoacoustic systems. At an exceptional point, two eigenvalues and their corresponding eigenfunctions coalesce. Given that the sensitivity of these eigenvalues to parameter changes becomes infinite at the exceptional point, their occurrence may greatly affect the outcome and reliability of numerical stability analysis. We propose a new method to identify exceptional points in thermoacoustic systems. By iteratively updating the system parameters, two initially selected eigenvalues are shifted towards each other, ultimately colliding and generating the exceptional point. Using this algorithm, we were able to identify for the first time a physically meaningful exceptional point with positive growth rate in a thermoacoustic model. Furthermore, our analysis goes beyond previous studies inasmuch as we employ a more realistic flame transfer function to model flame dynamics. Building on these results, we analyze the effect of exceptional points on the reliability of thermoacoustic stability analysis. In the context of uncertainty quantification, we show that surrogate modeling is not reliable in the vicinity of an exceptional point, even when large sets of training samples are provided. The impact of exceptional points on the propagation of input uncertainties is demonstrated via Monte Carlo computations. The increased sensitivity associated with the exceptional point results in large variances for eigenvalue predictions, which needs to be taken into account for reliable stability analysis.
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Varigonda, S., T. Kalmar-Nagy, B. LaBarre, and I. Mezic. "Graph decomposition methods for uncertainty propagation in complex, nonlinear interconnected dynamical systems." In 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). IEEE, 2004. http://dx.doi.org/10.1109/cdc.2004.1430306.

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Ramapuram Matavalam, Amarsagar Reddy, Umesh Vaidya, and Venkataramana Ajjarapu. "Data-Driven Approach for Uncertainty Propagation and Reachability Analysis in Dynamical Systems." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147295.

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Reports on the topic "Uncertainty propagation in a dynamical context"

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Banks, H. T., and Shuhua Hu. Propagation of Uncertainty in Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, October 2011. http://dx.doi.org/10.21236/ada556937.

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Parsons, Donald. A Tutorial for Generating Correlated Random Samples in the Context of Replica Cross Section Data Used in the Propagation of Uncertainty (Second Edition). Office of Scientific and Technical Information (OSTI), November 2023. http://dx.doi.org/10.2172/2228641.

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