On the Compression of Translation Operator Tensors in FMM-FFT-Accelerated SIE Simulators via Tensor Decompositions

Tensor decomposition methodologies are proposed to reduce the memory requirement of translation operator tensors arising in the fast multipole method-fast Fourier transform (FMM-FFT)-accelerated surface integral equation (SIE) simulators. These methodologies leverage Tucker, hierarchical Tucker (H-Tucker), and tensor train (TT) decompositions to compress the FFT'ed translation operator tensors stored in three-dimensional (3D) and four-dimensional (4D) array formats. Extensive numerical tests are performed to demonstrate the memory saving achieved by and computational overhead introduced by these methodologies for different simulation parameters. Numerical results show that the H-Tucker-based methodology for 4D array format yields the maximum memory saving while Tucker-based methodology for 3D array format introduces the minimum computational overhead. For many practical scenarios, all methodologies yield a significant reduction in the memory requirement of translation operator tensors while imposing negligible/acceptable computational overhead

Uncertainty Quantification for Electromagnetic Analysis via Efficient Collocation Methods.

Electromagnetic (EM) devices and systems often are fraught by uncertainty in their geometry, configuration, and excitation. These uncertainties (often termed “random variables”) strongly and nonlinearly impact voltages and currents on mission-critical circuits or receivers (often termed “observables”). To ensure the functionality of such circuits or receivers, this dependency should be statistically characterized. In this thesis, efficient collocation methods for uncertainty quantification in EM analysis are presented. First, a Stroud-based stochastic collocation method is introduced to statistically characterize electromagnetic compatibility and interference (EMC/EMI) phenomena on electrically large and complex platforms. Second, a multi-element probabilistic collocation (ME-PC) method suitable for characterizing rapidly varying and/or discontinuous observables is presented. Its applications to the statistical characterization of EMC/EMI phenomena on electrically and complex platforms and transverse magnetic wave propagation in complex mine environments are demonstrated. In addition, the ME-PC method is applied to the statistical characterization of EM wave propagation in complex mine environments with the aid of a novel fast multipole method and fast Fourier transform-accelerated surface integral equation solver -- the first-ever full-wave solver capable of characterizing EM wave propagation in hundreds of wavelengths long mine tunnels. Finally, an iterative high-dimensional model representation technique is proposed to statistically characterize EMC/EMI observables that involve a large number of random variables. The application of this technique to the genetic algorithm based optimization of EM devices is presented as well.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100086/1/acyucel_1.pd

Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.Comment: 25 pages, 10 Figure

A Depth-Adaptive Filtering Method for Effective GPR Tree Roots Detection in Tropical Area

This study presents a technique for processing Stepfrequency continuous wave (SFCW) ground penetrating radar (GPR) data to detect tree roots. SFCW GPR is portable and enables precise control of energy levels, balancing depth and resolution trade-offs. However, the high-frequency components of the transmission band suffers from poor penetrating capability and generates noise that interferes with root detection. The proposed time-frequency filtering technique uses a short-time Fourier transform (STFT) to track changes in frequency spectrum density over time. To obtain the filter window, a weighted linear regression (WLR) method is used. By adopting a conversion method that is a variant of the chirp Z-Transform (CZT), the timefrequency window filters out frequency samples that are not of interest when doing the frequency-to-time domain data conversion. The proposed depth-adaptive filter window can selfadjust to different scenarios, making it independent of soil information and effectively determines subsurface tree roots. The technique is successfully validated using SFCW GPR data from actual sites in a tropical area with different soil moisture levels, and the two-dimensional (2D) radar map of subsurface root systems is highly improved compared to existing methods.Comment: 10 pages, 12 figures, Accepted by IEEE TI

Accurate Tree Roots Positioning and Sizing over Undulated Ground Surfaces by Common Offset GPR Measurements

Tree roots detection is a popular application of the Ground-penetrating radar (GPR). Normally, the ground surface above the tree roots is assumed to be flat, and standard processing methods based on hyperbolic fitting are applied to the hyperbolae reflection patterns of tree roots for detection purposes. When the surface of the land is undulating (not flat), these typical hyperbolic fitting methods becomes inaccurate. This is because, the reflection patterns change with the uneven ground surfaces. When the soil surface is not flat, it is inaccurate to use the peak point of an asymmetric reflection pattern to identify the depth and horizontal position of the underground target. The reflection patterns of the complex shapes due to extreme surface variations results in analysis difficulties. Furthermore, when multiple objects are buried under an undulating ground, it is hard to judge their relative positions based on a B-scan that assumes a flat ground. In this paper, a roots fitting method based on electromagnetic waves (EM) travel time analysis is proposed to take into consideration the realistic undulating ground surface. A wheel-based (WB) GPR and an antenna-height-fixed (AHF) GPR System are presented, and their corresponding fitting models are proposed. The effectiveness of the proposed method is demonstrated and validated through numerical examples and field experiments.Comment: 11 pages, 6 figures, accepted by IEEE TI

DMRF-UNet: A Two-Stage Deep Learning Scheme for GPR Data Inversion under Heterogeneous Soil Conditions

Traditional ground-penetrating radar (GPR) data inversion leverages iterative algorithms which suffer from high computation costs and low accuracy when applied to complex subsurface scenarios. Existing deep learning-based methods focus on the ideal homogeneous subsurface environments and ignore the interference due to clutters and noise in real-world heterogeneous environments. To address these issues, a two-stage deep neural network (DNN), called DMRF-UNet, is proposed to reconstruct the permittivity distributions of subsurface objects from GPR B-scans under heterogeneous soil conditions. In the first stage, a U-shape DNN with multi-receptive-field convolutions (MRF-UNet1) is built to remove the clutters due to inhomogeneity of the heterogeneous soil. Then the denoised B-scan from the MRF-UNet1 is combined with the noisy B-scan to be inputted to the DNN in the second stage (MRF-UNet2). The MRF-UNet2 learns the inverse mapping relationship and reconstructs the permittivity distribution of subsurface objects. To avoid information loss, an end-to-end training method combining the loss functions of two stages is introduced. A wide range of subsurface heterogeneous scenarios and B-scans are generated to evaluate the inversion performance. The test results in the numerical experiment and the real measurement show that the proposed network reconstructs the permittivities, shapes, sizes, and locations of subsurface objects with high accuracy. The comparison with existing methods demonstrates the superiority of the proposed methodology for the inversion under heterogeneous soil conditions

3DInvNet: A Deep Learning-Based 3D Ground-Penetrating Radar Data Inversion

The reconstruction of the 3D permittivity map from ground-penetrating radar (GPR) data is of great importance for mapping subsurface environments and inspecting underground structural integrity. Traditional iterative 3D reconstruction algorithms suffer from strong non-linearity, ill-posedness, and high computational cost. To tackle these issues, a 3D deep learning scheme, called 3DInvNet, is proposed to reconstruct 3D permittivity maps from GPR C-scans. The proposed scheme leverages a prior 3D convolutional neural network with a feature attention mechanism to suppress the noise in the C-scans due to subsurface heterogeneous soil environments. Then a 3D U-shaped encoder-decoder network with multi-scale feature aggregation modules is designed to establish the optimal inverse mapping from the denoised C-scans to 3D permittivity maps. Furthermore, a three-step separate learning strategy is employed to pre-train and fine-tune the networks. The proposed scheme is applied to numerical simulation as well as real measurement data. The quantitative and qualitative results show the network capability, generalizability, and robustness in denoising GPR C-scans and reconstructing 3D permittivity maps of subsurface objects