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Author : Michael Schick
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (775 download)
Download or read book Uncertainty Quantification for Stochastic Dynamical Systems written by Michael Schick and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jian Deng
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Uncertainty Quantification of Dynamical Systems and Stochastic Symplectic Schemes written by Jian Deng and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Parikshit Dutta
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (817 download)
Download or read book New Algorithms for Uncertainty Quantification and Nonlinear Estimation of Stochastic Dynamical Systems written by Parikshit Dutta and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been growing interest to characterize and reduce uncertainty in stochastic dynamical systems. This drive arises out of need to manage uncertainty in complex, high dimensional physical systems. Traditional techniques of uncertainty quantification (UQ) use local linearization of dynamics and assumes Gaussian probability evolution. But several difficulties arise when these UQ models are applied to real world problems, which, generally are nonlinear in nature. Hence, to improve performance, robust algorithms, which can work efficiently in a nonlinear non-Gaussian setting are desired. The main focus of this dissertation is to develop UQ algorithms for nonlinear systems, where uncertainty evolves in a non-Gaussian manner. The algorithms developed are then applied to state estimation of real-world systems. The first part of the dissertation focuses on using polynomial chaos (PC) for uncertainty propagation, and then achieving the estimation task by the use of higher order moment updates and Bayes rule. The second part mainly deals with Frobenius-Perron (FP) operator theory, how it can be used to propagate uncertainty in dynamical systems, and then using it to estimate states by the use of Bayesian update. Finally, a method to represent the process noise in a stochastic dynamical system using a nite term Karhunen-Loeve (KL) expansion is proposed. The uncertainty in the resulting approximated system is propagated using FP operator. The performance of the PC based estimation algorithms were compared with extended Kalman filter (EKF) and unscented Kalman filter (UKF), and the FP operator based techniques were compared with particle filters, when applied to a duffing oscillator system and hypersonic reentry of a vehicle in the atmosphere of Mars. It was found that the accuracy of the PC based estimators is higher than EKF or UKF and the FP operator based estimators were computationally superior to the particle filtering algorithms.
Author : Mircea Grigoriu
Publisher : Springer Science & Business Media
ISBN 13 : 1447123271
Total Pages : 534 pages
Book Rating : 4.4/5 (471 download)
Download or read book Stochastic Systems written by Mircea Grigoriu and published by Springer Science & Business Media. This book was released on 2012-05-15 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis Probabilistic models for random variables and functions needed to formulate stochastic equations describing realistic problems in engineering and applied sciences Practical methods for quantifying the uncertain parameters in the definition of stochastic equations, solving approximately these equations, and assessing the accuracy of approximate solutions Stochastic Systems provides key information for researchers, graduate students, and engineers who are interested in the formulation and solution of stochastic problems encountered in a broad range of disciplines. Numerous examples are used to clarify and illustrate theoretical concepts and methods for solving stochastic equations. The extensive bibliography and index at the end of the book constitute an ideal resource for both theoreticians and practitioners.
Author : Nan Chen
Publisher : Springer Nature
ISBN 13 : 3031222490
Total Pages : 208 pages
Book Rating : 4.0/5 (312 download)
Download or read book Stochastic Methods for Modeling and Predicting Complex Dynamical Systems written by Nan Chen and published by Springer Nature. This book was released on 2023-03-13 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book enables readers to understand, model, and predict complex dynamical systems using new methods with stochastic tools. The author presents a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. An emphasis is placed on the balance between computational efficiency and modeling accuracy, providing readers with ideas to build useful models in practice. Successful modeling of complex systems requires a comprehensive use of qualitative and quantitative modeling approaches, novel efficient computational methods, physical intuitions and thinking, as well as rigorous mathematical theories. As such, mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools are presented. Both theoretical and numerical approaches are included, allowing readers to choose suitable methods in different practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational science, and data science. In addition, the author discusses how to choose and apply suitable mathematical tools to several disciplines including pure and applied mathematics, physics, engineering, neural science, material science, climate and atmosphere, ocean science, and many others. Readers will not only learn detailed techniques for stochastic modeling and prediction, but will develop their intuition as well. Important topics in modeling and prediction including extreme events, high-dimensional systems, and multiscale features are discussed.
Author : José Eduardo Souza De Cursi
Publisher : Springer Nature
ISBN 13 : 3030536696
Total Pages : 472 pages
Book Rating : 4.0/5 (35 download)
Download or read book Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling written by José Eduardo Souza De Cursi and published by Springer Nature. This book was released on 2020-08-19 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings book discusses state-of-the-art research on uncertainty quantification in mechanical engineering, including statistical data concerning the entries and parameters of a system to produce statistical data on the outputs of the system. It is based on papers presented at Uncertainties 2020, a workshop organized on behalf of the Scientific Committee on Uncertainty in Mechanics (Mécanique et Incertain) of the AFM (French Society of Mechanical Sciences), the Scientific Committee on Stochastic Modeling and Uncertainty Quantification of the ABCM (Brazilian Society of Mechanical Sciences) and the SBMAC (Brazilian Society of Applied Mathematics).
Author : Eduardo Souza de Cursi
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (133 download)
Download or read book Uncertainty Quantification and Stochastic Modeling with Matlab written by Eduardo Souza de Cursi and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones. This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlab illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study
Author : Eduardo Souza de Cursi
Publisher : Elsevier
ISBN 13 : 0081004710
Total Pages : 457 pages
Book Rating : 4.0/5 (81 download)
Download or read book Uncertainty Quantification and Stochastic Modeling with Matlab written by Eduardo Souza de Cursi and published by Elsevier. This book was released on 2015-04-09 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones. This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlab® illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study. Discusses the main ideas of Stochastic Modeling and Uncertainty Quantification using Functional Analysis Details listings of Matlab® programs implementing the main methods which complete the methodological presentation by a practical implementation Construct your own implementations from provided worked examples
Author : Akash Phadnis
Publisher :
ISBN 13 :
Total Pages : 197 pages
Book Rating : 4.:/5 (87 download)
Download or read book Uncertainty Quantification and Prediction for Non-autonomous Linear and Nonlinear Systems written by Akash Phadnis and published by . This book was released on 2013 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: The science of uncertainty quantification has gained a lot of attention over recent years. This is because models of real processes always contain some elements of uncertainty, and also because real systems can be better described using stochastic components. Stochastic models can therefore be utilized to provide a most informative prediction of possible future states of the system. In light of the multiple scales, nonlinearities and uncertainties in ocean dynamics, stochastic models can be most useful to describe ocean systems. Uncertainty quantification schemes developed in recent years include order reduction methods (e.g. proper orthogonal decomposition (POD)), error subspace statistical estimation (ESSE), polynomial chaos (PC) schemes and dynamically orthogonal (DO) field equations. In this thesis, we focus our attention on DO and various PC schemes for quantifying and predicting uncertainty in systems with external stochastic forcing. We develop and implement these schemes in a generic stochastic solver for a class of non-autonomous linear and nonlinear dynamical systems. This class of systems encapsulates most systems encountered in classic nonlinear dynamics and ocean modeling, including flows modeled by Navier-Stokes equations. We first study systems with uncertainty in input parameters (e.g. stochastic decay models and Kraichnan-Orszag system) and then with external stochastic forcing (autonomous and non-autonomous self-engineered nonlinear systems). For time-integration of system dynamics, stochastic numerical schemes of varied order are employed and compared. Using our generic stochastic solver, the Monte Carlo, DO and polynomial chaos schemes are inter-compared in terms of accuracy of solution and computational cost. To allow accurate time-integration of uncertainty due to external stochastic forcing, we also derive two novel PC schemes, namely, the reduced space KLgPC scheme and the modified TDgPC (MTDgPC) scheme. We utilize a set of numerical examples to show that the two new PC schemes and the DO scheme can integrate both additive and multiplicative stochastic forcing over significant time intervals. For the final example, we consider shallow water ocean surface waves and the modeling of these waves by deterministic dynamics and stochastic forcing components. Specifically, we time-integrate the Korteweg-de Vries (KdV) equation with external stochastic forcing, comparing the performance of the DO and Monte Carlo schemes. We find that the DO scheme is computationally efficient to integrate uncertainty in such systems with external stochastic forcing.
Author : Manolis Papadrakakis
Publisher : Springer Science & Business Media
ISBN 13 : 9400751346
Total Pages : 362 pages
Book Rating : 4.4/5 (7 download)
Download or read book Computational Methods in Stochastic Dynamics written by Manolis Papadrakakis and published by Springer Science & Business Media. This book was released on 2012-10-03 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and its influence on the reliability of the computational models are continuously gaining in significance. In particular, the problems of dynamic response analysis and reliability assessment of structures with uncertain system and excitation parameters have been the subject of continuous research over the last two decades as a result of the increasing availability of powerful computing resources and technology. This book is a follow up of a previous book with the same subject (ISBN 978-90-481-9986-0) and focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The selected chapters are authored by some of the most active scholars in their respective areas and represent some of the most recent developments in this field. The book consists of 21 chapters which can be grouped into several thematic topics including dynamic analysis of stochastic systems, reliability-based design, structural control and health monitoring, model updating, system identification, wave propagation in random media, seismic fragility analysis and damage assessment. This edited book is primarily intended for researchers and post-graduate students who are familiar with the fundamentals and wish to study or to advance the state of the art on a particular topic in the field of computational stochastic structural dynamics. Nevertheless, practicing engineers could benefit as well from it as most code provisions tend to incorporate probabilistic concepts in the analysis and design of structures.
Author : Christian Soize
Publisher : Springer
ISBN 13 : 3319543393
Total Pages : 344 pages
Book Rating : 4.3/5 (195 download)
Download or read book Uncertainty Quantification written by Christian Soize and published by Springer. This book was released on 2017-04-24 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials. Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available. This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.
Author : Sunetra Sarkar
Publisher : World Scientific
ISBN 13 : 9814730599
Total Pages : 197 pages
Book Rating : 4.8/5 (147 download)
Download or read book Uncertainty Quantification In Computational Science: Theory And Application In Fluids And Structural Mechanics written by Sunetra Sarkar and published by World Scientific. This book was released on 2016-08-18 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decade, research in Uncertainty Quantification (UC) has received a tremendous boost, in fluid engineering and coupled structural-fluids systems. New algorithms and adaptive variants have also emerged.This timely compendium overviews in detail the current state of the art of the field, including advances in structural engineering, along with the recent focus on fluids and coupled systems. Such a strong compilation of these vibrant research areas will certainly be an inspirational reference material for the scientific community.
Author : Khanh D. Pham
Publisher : Springer
ISBN 13 : 3319087053
Total Pages : 222 pages
Book Rating : 4.3/5 (19 download)
Download or read book Resilient Controls for Ordering Uncertain Prospects written by Khanh D. Pham and published by Springer. This book was released on 2014-09-05 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with a detailed examination of resilient controls in risk-averse decision, this monograph is aimed toward researchers and graduate students in applied mathematics and electrical engineering with a systems-theoretic concentration. This work contains a timely and responsive evaluation of reforms on the use of asymmetry or skewness pertaining to the restrictive family of quadratic costs that have been appeared in various scholarly forums. Additionally, the book includes a discussion of the current and ongoing efforts in the usage of risk, dynamic game decision optimization and disturbance mitigation techniques with output feedback measurements tailored toward the worst-case scenarios. This work encompasses some of the current changes across uncertainty quantification, stochastic control communities, and the creative efforts that are being made to increase the understanding of resilient controls. Specific considerations are made in this book for the application of decision theory to resilient controls of the linear-quadratic class of stochastic dynamical systems. Each of these topics are examined explicitly in several chapters. This monograph also puts forward initiatives to reform both control decisions with risk consequences and correct-by-design paradigms for performance reliability associated with the class of stochastic linear dynamical systems with integral quadratic costs and subject to network delays, control and communication constraints.
Author : Olivier Le Maitre
Publisher : Springer
ISBN 13 : 9789048135196
Total Pages : 536 pages
Book Rating : 4.1/5 (351 download)
Download or read book Spectral Methods for Uncertainty Quantification written by Olivier Le Maitre and published by Springer. This book was released on 2010-04-08 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.
Author : Isaac Elishakoff
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111354237
Total Pages : 384 pages
Book Rating : 4.1/5 (113 download)
Download or read book Multifaceted Uncertainty Quantification written by Isaac Elishakoff and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-23 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book exposes three alternative and competing approaches to uncertainty analysis in engineering. It is composed of some essays on various sub-topics like random vibrations, probabilistic reliability, fuzzy-sets-based analysis, unknown-but-bounded variables, stochastic linearization, possible difficulties with stochastic analysis of structures.
Author : Ramin Jahanbin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Novel Uncertainty Quantification Methods for Stochastic Isogeometric Analysis written by Ramin Jahanbin and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this study is to develop novel computational methods for general high-dimensional uncertainty quantification (UQ) with a focus on stochastic isogeometric analysis. The objective is pursued by: (1) development of an isogeometric collocation method for random field discretization, (2) generalization of isogeometric methods for random field discretization on arbitrary multipatch domains, (3) establishment of a spline dimensional decomposition for high-dimensional UQ, (4) stochastic isogeometric analysis in linear elasticity, (5) stochastic isogeometric analysis on arbitrary multipatch domains, and (6) UQ in linear dynamical systems.
Author : Matthew Scott Bonney
Publisher :
ISBN 13 :
Total Pages : 308 pages
Book Rating : 4.:/5 (12 download)
Download or read book Uncertainty Quantification in Dynamical System Design Using Reduced Order Models written by Matthew Scott Bonney and published by . This book was released on 2017 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mechanical design process undergoes large variability from dramatic design changes, particularly geometric changes, and machining tolerance build-up. These changes are particularly caused through topology optimization or model calibration and typically produce small nominal values. Machining tolerance build-up becomes very important for precision geometric values, such as those generated from the topology optimization that allows only small tolerances to aid in the optimization algorithm. Through the use of hyper-dual numbers, a response surface surrogate model that uses numerically exact sensitivity information for enrichment of a sparse design space, called the hyper-dual meta-model, is evaluated and compared to similar surrogate models. When utilizing surrogate models, the choice of models can produce epistemic uncertainty via model form error. One method to quantify this uncertainty is the use of stochastic modeling, called the non-parametric maximum entropy approach. This modeling and calibration process is presented and applied to engineering systems. This is presented in order to characterize uncertainty due to model reduction and in uncertain properties of the system. The work presented in this dissertation shows novel research, expansion of previous theory, and implementation of current state-of-the-art research.
