A Full Wave Electromagnetic Framework for Optimization and Uncertainty Quantification of Communication Systems in Underground Mine Environments

Abstract

Wireless communication, sensing, and tracking systems in mine environments are essential for protecting miners’ safety and daily operations. The design, deployment, and post-event reconfiguration of such systems greatly benefits from electromagnetic (EM) frameworks that can statistically analyze and optimize the wireless systems in realistic mine environments. This thesis proposes such a framework by developing two fast and efficient full-wave EM simulators and coupling them with a modern optimization algorithm and an efficient uncertainty quantification (UQ) method to synthesize system configurations and produce statistical insights. The first simulator is a fast multipole method – fast Fourier transform (FMM-FFT) accelerated surface integral equation (SIE) simulator. It relies on Muller and combined fields SIEs to account for scattering from mine walls and conductors, respectively. During the iterative solution of the SIE system, the computational and memory costs are reduced by using the FMM-FFT scheme. The memory costs are further reduced by compressing large data structures via singular value and Tucker decomposition. The second simulator is a domain decomposition (DD)-based SIE simulator. It first divides the physical domain of a mine tunnel or gallery into subdomains and then characterizes EM wave propagation in each subdomain separately. Finally, the DD-based SIE simulator assembles the solutions of subdomains and solves an inter-domain system using an efficient subdomain-combining scheme. While the DD-based SIE simulator is faster and more memory-efficient than the FMM-FFT accelerated SIE simulator when characterizing EM wave propagation in electrically large mine environments, it does not apply to certain scenarios that the FMM-FFT accelerated SIE simulators can handle. The optimization algorithm and UQ method that are coupled with the EM simulators are the dividing rectangles (DIRECT) algorithm and the high dimensional model representation (HDMR)-enhanced multi-element probabilistic collocation (ME-PC) method, respectively. The DIRECT algorithm is a Lipschitzian optimization method but does not require the knowledge of the Lipschitz constant. It performs a series of moves that explore the behavior of the objective function at a set of points in the carefully picked sub-regions of the search space. The HDMR-enhanced ME-PC method permits the accurate and efficient construction of surrogate models for EM observables in high dimensions. The HDMR expansion expresses the observable as finite sums of component functions that represent independent and combined contributions of random variables to the observable and hence reduces the complexity of UQ by including only the most significant component functions to minimize the computational cost of building the surrogate model. This research numerically validated and verified the two EM simulators and demonstrated the efficiency and applicability of the EM framework via its application to optimization and UQ problems in large and realistic mine environments.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146028/1/wtsheng_1.pd