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Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis. / Abhishek Kundu

Swansea University Author: Abhishek Kundu

Abstract

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...

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Published: 2014
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42292
first_indexed 2018-08-02T18:54:21Z
last_indexed 2018-08-03T10:09:45Z
id cronfa42292
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spelling 2018-08-02T16:24:28.7137853 v2 42292 2018-08-02 Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis. e5437ca50cc8062c0143cc2394a6c400 NULL Abhishek Kundu Abhishek Kundu true true 2018-08-02 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. E-Thesis Computer science.;Systems science. 31 12 2014 2014-12-31 COLLEGE NANME Engineering COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:28.7137853 2018-08-02T16:24:28.7137853 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Abhishek Kundu NULL 1 0042292-02082018162442.pdf 10798000.pdf 2018-08-02T16:24:42.9730000 Output 22091084 application/pdf E-Thesis true 2018-08-02T16:24:42.9730000 false
title Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis.
spellingShingle Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis.
Abhishek Kundu
title_short Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis.
title_full Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis.
title_fullStr Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis.
title_full_unstemmed Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis.
title_sort Efficient uncertainty propagation schemes for dynamical systems with stochastic finite element analysis.
author_id_str_mv e5437ca50cc8062c0143cc2394a6c400
author_id_fullname_str_mv e5437ca50cc8062c0143cc2394a6c400_***_Abhishek Kundu
author Abhishek Kundu
author2 Abhishek Kundu
format E-Thesis
publishDate 2014
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description 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.
published_date 2014-12-31T05:28:50Z
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score 11.08895

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