Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/15737
Title: Optimization by Stochastic Simulation and Variational Methods: Application to Neutronic Systems
Authors: Khan, Hamda
Keywords: Physical Sciences
Mathematics
Issue Date: 2020
Publisher: Riphah International University, Islamabad
Abstract: Research carried out and presented in this thesis is in the general area of optimization based on both stochastic and deterministic methods with applications in neutronic systems formulated by the Boltzmann transport equation. The objective of optimization is to obtain the ‘best possible’ design with the help of well-defined, developed and elaborate mathematical methods and techniques. It draws its attractiveness in engineering design supported by the rapid developments in computational hardware platforms and system software. With diverse applicability, research in optimization is still the subject of considerable importance where researchers’ objectives include development of methods for enhanced computational efficiency to solve larger, complex and realistic problems. In stochastic optimization, this thesis uses Monte Carlo (MC) simulation as applied to the transport of neutrons, photons, and charged particles in a large class of problems covering both ‘fixed-source’ and eigenvalue or ‘multiplying systems’. In this work, the main thrust has been the development of formalisms derived from first principles in the following areas (i) continuous ‘variational’ formulation for obtaining an optimal material distribution, (ii) discrete Pontryagin’s form for ‘optimal control’, (iii) genetic algorithms coupled with fixed-source diffusion model for design optimization, (iv) design optimization of a state-of-the-art detection system for explosives, (v) variational assisted MC perturbation for optimization in both fixed and multiplying source neutronic systems, and (vi) determination of ‘zone’ importances for material placement. In essence, this thesis covers analyses and applications of optimization in a broad spectrum of neutronic systems. Two representative configurations considered for fixed-source and multiplying neutronic systems are (i) an explosives detection system (EDS) based on active radiation interrogation, and (ii) a simplified ‘core’ model of a nuclear power reactor as well as criticality safety aspects. Both configurations inherently contain the mathematics, science and engineering complexity of large realistic systems for which optimization has tangible benefits. While MC gives reliable results, it is known to be ill-suited to optimization methods which often require repeated ‘runs’ in iterative algorithms. One of the outcomes of this research is an insight into a strategy, which provides enhanced computational efficiency. Alternative optimization strategies covered are the coupling of deterministic ‘diffusion’ models with a xxiv heuristic optimization method based on random search with Genetic Algorithms, and classical variational methods based on constrained Lagrangian optimization applied extensively in optimal control. For simulations, the MCNP5 code has been used while for finite-difference numerical solutions of the two-group diffusion equations, GA programming and post-processing of MCNP for graphics, MATLAB® was used. The research efforts and outcomes of this thesis are bound to be useful to applied mathematicians engaged in the development of computationally efficient optimization methods.
Gov't Doc #: 20873
URI: http://prr.hec.gov.pk/jspui/handle/123456789/15737
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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