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ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN COMPLEX SYSTEMS

Yang, Chao
http://orcid.org/0000-0001-8272-3576
http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Mechanical Engineering.
This dissertation aims to study three crucial problems related to Monte Carlo based particle methods for solving uncertainty quantification problems in complex systems. The first problem concerns the existence of a "benchmark" sampling method that i.) can generate an ensemble directly drawn from the unknown, propagated state pdf, and ii.) guarantee the quality of the aforementioned ensemble with respect to the true evolved state uncertainty at all future times. In this context, a new particle uncertainty forecasting framework is proposed that combines Markov chain Monte Carlo (MCMC) sampling with the method of characteristics (MOC). The resulting MCMC-MOC ensemble is by construction, directly sampled from the true (and unknown) propagated state probability density function, and thereby equivalent in measure to the truth. Inspired by the new MCMC-MOC approach, a second problem on the transient effectiveness of MCS is posed in the context of Markov chain Monte Carlo theory. The propagated ensemble is viewed as the realization of a Markov chain at each time instant, generated by an associated instantaneous transition kernel. An equation governing the time evolution of the transition kernel is developed. It is shown that for a special class of nonlinear systems that have zero divergence, the propagated kernel is in detailed balance with the true state probability density function. This guarantees statistical consistency of the MCS ensemble with the truth at all times for such systems. The third and final problem addressed in this dissertation is the following: "is it possible to develop adaptation rules for MCS such that it may perform within prescribed bounds of accuracy using the "minimum" possible number of simulations at all future times?" In the context of this problem, a new adaptive MCS framework is developed. This approach is designed to control its transient performance as well as the associated computational load on-the-fly. When the transient performance of MCS fails to meet the user-defined lower bound on its accuracy, "optimally" selected particles are sequentially introduced at the initial time, and then forward propagated to join the current ensemble until it reaches the required level of accuracy. This is done by following a two-layer approach targeted at improving its rate of convergence by satisfying both non-collapsing and space-filling properties. On the other hand, when MCS exceeds the prescribed accuracy level, particles are removed from the current ensemble in the interest of reducing computational load. Particle removal is based on their relative weightage evaluated via the associated stochastic Liouville equation. Finally, numerical simulations are given to illustrate the benefits of the developed tools for solving uncertainty forecasting problems, including applications in space situational awareness and wind forecasting.
Mrinal Kumar (Advisor)
Andrea Serrani (Committee Member)
Junmin Wang (Committee Member)
222 p.
Mechanical Engineering
Markov chain Monte Carlo theory; Mechanical Engineering

Recommended Citations

Citations

  • Yang, C. (2017). ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN COMPLEX SYSTEMS [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962

    APA Style (7th edition)

  • Yang, Chao. ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN COMPLEX SYSTEMS. 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962.

    MLA Style (8th edition)

  • Yang, Chao. "ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN COMPLEX SYSTEMS." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962

    Chicago Manual of Style (17th edition)

osu1511967797285962
629
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This open access ETD is published by The Ohio State University and OhioLINK.