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Sparse Representations and Quadratic Approximations in Path Integral Techniques for Stochastic Response Analysis of Diverse Systems/Structures.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Sparse Representations and Quadratic Approximations in Path Integral Techniques for Stochastic Response Analysis of Diverse Systems/Structures./
作者:	Psaros Andriopoulos, Apostolos.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:	148 p.
附註:	Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Contained By:	Dissertations Abstracts International81-04B.
標題:	Civil engineering. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13901385
ISBN:	9781085678926

Sparse Representations and Quadratic Approximations in Path Integral Techniques for Stochastic Response Analysis of Diverse Systems/Structures.
Psaros Andriopoulos, Apostolos.

Sparse Representations and Quadratic Approximations in Path Integral Techniques for Stochastic Response Analysis of Diverse Systems/Structures. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 148 p.

Source: Dissertations Abstracts International, Volume: 81-04, Section: B.

Thesis (Ph.D.)--Columbia University, 2019.

This item must not be sold to any third party vendors.

Uncertainty propagation in engineering mechanics and dynamics is a highly challenging problem that requires development of analytical/numerical techniques for determining the stochastic response of complex engineering systems. In this regard, although Monte Carlo simulation (MCS) has been the most versatile technique for addressing the above problem, it can become computationally daunting when faced with high-dimensional systems or with computing very low probability events. Thus, there is a demand for pursuing more computationally efficient methodologies.Recently, a Wiener path integral (WPI) technique, whose origins can be found in theoretical physics, has been developed in the field of engineering dynamics for determining the response transition probability density function (PDF) of nonlinear oscillators subject to non-white, non-Gaussian and non-stationary excitation processes. In the present work, the Wiener path integral technique is enhanced, extended and generalized with respect to three main aspects; namely, versatility, computational efficiency and accuracy.Specifically, the need for increasingly sophisticated modeling of excitations has led recently to the utilization of fractional calculus, which can be construed as a generalization of classical calculus. Motivated by the above developments, the WPI technique is extended herein to account for stochastic excitations modeled via fractional-order filters. To this aim, relying on a variational formulation and on the most probable path approximation yields a deterministic fractional boundary value problem to be solved numerically for obtaining the oscillator joint response PDF.Further, appropriate multi-dimensional bases are constructed for approximating, in a computationally efficient manner, the non-stationary joint response PDF. In this regard, two distinct approaches are pursued. The first employs expansions based on Kronecker products of bases (e.g., wavelets), while the second utilizes representations based on positive definite functions. Next, the localization capabilities of the WPI technique are exploited for determining PDF points in the joint space-time domain to be used for evaluating the expansion coefficients at a relatively low computational cost.Subsequently, compressive sampling procedures are employed in conjunction with group sparsity concepts and appropriate optimization algorithms for decreasing even further the associated computational cost. It is shown that the herein developed enhancement renders the technique capable of treating readily relatively high-dimensional stochastic systems. More importantly, it is shown that this enhancement in computational efficiency becomes more prevalent as the number of stochastic dimensions increases; thus, rendering the herein proposed sparse representation approach indispensable, especially for high-dimensional systems.Next, a quadratic approximation of the WPI is developed for enhancing the accuracy degree of the technique. Concisely, following a functional series expansion, higher-order terms are accounted for, which is equivalent to considering not only the most probable path but also fluctuations around it. These fluctuations are incorporated into a state-dependent factor by which the exponential part of each PDF value is multiplied. This localization of the state-dependent factor yields superior accuracy as compared to the standard most probable path WPI approximation where the factor is constant and state-invariant. An additional advantage relates to efficient structural reliability assessment, and in particular, to direct estimation of low probability events (e.g., failure probabilities), without possessing the complete transition PDF.Overall, the developments in this thesis render the WPI technique a potent tool for determining, in a reliable manner and with a minimal computational cost, the stochastic response of nonlinear oscillators subject to an extended range of excitation processes. Several numerical examples, pertaining to both nonlinear dynamical systems subject to external excitations and to a special class of engineering mechanics problems with stochastic media properties, are considered for demonstrating the reliability of the developed techniques. In all cases, the degree of accuracy and the computational efficiency exhibited are assessed by comparisons with pertinent MCS data.

ISBN: 9781085678926Subjects--Topical Terms:

860360
Civil engineering.
Subjects--Index Terms:

Engineering dynamics

Sparse Representations and Quadratic Approximations in Path Integral Techniques for Stochastic Response Analysis of Diverse Systems/Structures.
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100 1 $a Psaros Andriopoulos, Apostolos. $3 3550067
245 1 0 $a Sparse Representations and Quadratic Approximations in Path Integral Techniques for Stochastic Response Analysis of Diverse Systems/Structures.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 148 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
500 $a Advisor: Kougioumtzoglou, Ioannis.
502 $a Thesis (Ph.D.)--Columbia University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a Uncertainty propagation in engineering mechanics and dynamics is a highly challenging problem that requires development of analytical/numerical techniques for determining the stochastic response of complex engineering systems. In this regard, although Monte Carlo simulation (MCS) has been the most versatile technique for addressing the above problem, it can become computationally daunting when faced with high-dimensional systems or with computing very low probability events. Thus, there is a demand for pursuing more computationally efficient methodologies.Recently, a Wiener path integral (WPI) technique, whose origins can be found in theoretical physics, has been developed in the field of engineering dynamics for determining the response transition probability density function (PDF) of nonlinear oscillators subject to non-white, non-Gaussian and non-stationary excitation processes. In the present work, the Wiener path integral technique is enhanced, extended and generalized with respect to three main aspects; namely, versatility, computational efficiency and accuracy.Specifically, the need for increasingly sophisticated modeling of excitations has led recently to the utilization of fractional calculus, which can be construed as a generalization of classical calculus. Motivated by the above developments, the WPI technique is extended herein to account for stochastic excitations modeled via fractional-order filters. To this aim, relying on a variational formulation and on the most probable path approximation yields a deterministic fractional boundary value problem to be solved numerically for obtaining the oscillator joint response PDF.Further, appropriate multi-dimensional bases are constructed for approximating, in a computationally efficient manner, the non-stationary joint response PDF. In this regard, two distinct approaches are pursued. The first employs expansions based on Kronecker products of bases (e.g., wavelets), while the second utilizes representations based on positive definite functions. Next, the localization capabilities of the WPI technique are exploited for determining PDF points in the joint space-time domain to be used for evaluating the expansion coefficients at a relatively low computational cost.Subsequently, compressive sampling procedures are employed in conjunction with group sparsity concepts and appropriate optimization algorithms for decreasing even further the associated computational cost. It is shown that the herein developed enhancement renders the technique capable of treating readily relatively high-dimensional stochastic systems. More importantly, it is shown that this enhancement in computational efficiency becomes more prevalent as the number of stochastic dimensions increases; thus, rendering the herein proposed sparse representation approach indispensable, especially for high-dimensional systems.Next, a quadratic approximation of the WPI is developed for enhancing the accuracy degree of the technique. Concisely, following a functional series expansion, higher-order terms are accounted for, which is equivalent to considering not only the most probable path but also fluctuations around it. These fluctuations are incorporated into a state-dependent factor by which the exponential part of each PDF value is multiplied. This localization of the state-dependent factor yields superior accuracy as compared to the standard most probable path WPI approximation where the factor is constant and state-invariant. An additional advantage relates to efficient structural reliability assessment, and in particular, to direct estimation of low probability events (e.g., failure probabilities), without possessing the complete transition PDF.Overall, the developments in this thesis render the WPI technique a potent tool for determining, in a reliable manner and with a minimal computational cost, the stochastic response of nonlinear oscillators subject to an extended range of excitation processes. Several numerical examples, pertaining to both nonlinear dynamical systems subject to external excitations and to a special class of engineering mechanics problems with stochastic media properties, are considered for demonstrating the reliability of the developed techniques. In all cases, the degree of accuracy and the computational efficiency exhibited are assessed by comparisons with pertinent MCS data.
590 $a School code: 0054.
650 4 $a Civil engineering. $3 860360
650 4 $a Applied mathematics. $3 2122814
653 $a Engineering dynamics
653 $a Fractional calculus
653 $a Nonlinear systems
653 $a Sparse representations
653 $a Stochastic processes
653 $a Wavelets
690 $a 0543
690 $a 0364
710 2 $a Columbia University. $b Civil Engineering and Engineering Mechanics. $3 2093087
773 0 $t Dissertations Abstracts International $g 81-04B.
790 $a 0054
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13901385