Time-domain radiation from large two-dimensional apertures via narrow-waisted Gaussian beams

This paper deals with the short-pulse radiation of three-dimensional (3-D) vector electromagnetic fields from arbitrarily polarized large two-dimensional (2-D) truncated aperture distributions, which are parameterized in terms of narrow-waisted ray-like pulsed Gaussian basis beams centered on a discretized Gabor lattice in a four-dimensional (4-D) configuration-spectrum phase space. The study extends our previous Gabor-based investigation of time-domain (TD) short-pulse radiation of 2-D fields from 1-D large truncated apertures with nonphased, linearly phased (delayed) and nonlinearly phased focusing aperture field profiles . We begin with, and summarize, a Gabor-based frequency domain (FD) formulation of the 2-D aperture problem which has been presented and tested elsewhere, but we include additional numerical examples for validation and quality assessment. As done by Galdi, Felsen and Castanon (see ibid., vol 49, p. 1322-32, Sept. 2001) we access the time domain by Fourier inversion from the FD, starting from the initial 3-D space-time Kirchhoff formulation (whose numerical integration furnishes reference solutions), and then passing on to Gabor-parameterized field representations in terms of pulsed beam (PB) wavepackets which are launched by linearly and nonlinearly phase-delayed focusing aperture distributions. Example calculations and comparisons with numerically generated reference data serve to calibrate the Gabor-PB algorithms and assess their domains of validity.     

A limit set stabilization by means of the Port Hamiltonian system approach

A solution to the stabilization problem of a compact set by means of the Interconnection and Damping Assignment Passivity‐Based Control methodology, for an affine nonlinear system, was introduced. To this end, we expressed the closed‐loop system as a Port Hamiltonian system, having the property of almost all their trajectories asymptotically converge to a convenient limit set, except for a set of measure zero. It was carried out by solving a partial differential equation (PDE) or single matching condition, which allows the desired energy level or limit set E to be shaped explicitly. The control strategy was tested using the magnetic beam balance system and the pendulum actuated by a direct current motor (DC‐motor), having obtained satisfactory results. Copyright © 2014 John Wiley & Sons, Ltd.     

Short-pulse three-dimensional scattering from moderately rough surfaces: a comparison between narrow-waisted Gaussian beam algorithms and FDTD

In this paper, with reference to short-pulse three-dimensional scattering from moderately rough surfaces, we present a comparison between Gabor-based narrow-waisted Gaussian beam (NW-GB) and finite-difference time-domain (FDTD) algorithms. NW-GB algorithms have recently emerged as an attractive alternative to traditional (ray-optical) high-frequency/short-pulse approximate methods, whereas FDTD algorithms are well-established full-wave tools for electromagnetic wave propagation and scattering. After presentation of relevant background material, results are presented and discussed for realistic parameter configurations, involving dispersive soils and moderately rough surface profiles, of interest in pulsed ground penetrating radar applications. Results indicate a generally satisfying agreement between the two methods, which tends to improve for slightly dispersive soils. Computational aspects are also compared.     

Multifrequency reconstruction of moderately rough interfaces viaquasi-ray Gaussian beams

In this paper, we present a new technique for determining the surface profile of a moderately rough interface between air and a homogeneous dielectric half-space. Based on sparsely sampled step-frequency ground penetrating radar measurements, the proposed inversion scheme uses a quasi-ray Gaussian beam fast forward model, coupled with a low-order parameterization of the surface profile in terms of B-splines. The profile estimation problem is posed as a parameter optimization problem, which is solved using a multiresolution continuation method via frequency hopping. Numerical experiments establish that the algorithm is efficient and yields accurate reconstructions throughout most of the illuminated region even in noisy environments, losing accuracy only in regions with very weak illumination     

On stochastic dynamic stackelberg strategies

Feedback Stackelberg strategies are considered for two-person linear multi-stage games with quadratic performance criteria and noisy measurements. Explicit solutions are given when the information sets are nested; the solutions are closely related to the ‘separation theorem’ of stochastic control.     

Quasi-ray Gaussian beam algorithm for time-harmonic two-dimensionalscattering by moderately rough interfaces

Gabor-based Gaussian beam (GB) algorithms, in conjunction with the complex source point (CSP) method for generating beam-like wave objects, have found application in a variety of high-frequency wave propagation and diffraction scenarios. Of special interest for efficient numerical implementation is the noncollimated narrow-waisted species of GB, which reduces the computationally intensive complex ray tracing for collimated GB propagation and scattering to quasi-real ray tracing, without the failure of strictly real ray field algorithms in caustic and other transition regions. The Gabor-based narrow-waisted CSP-GB method has been applied previously to two-dimensional (2-D) propagation from extended nonfocused and focused aperture distributions through arbitrarily curved 2-D layered environments. In this 2-D study the method is applied to aperture-excited field scattering from, and transmission through, a moderately rough interface between two dielectric media. It is shown that the algorithm produces accurate and computationally efficient solutions for this complex propagation environment, over a range of calibrated combinations of the problem parameters. One of the potential uses of the algorithm is as an efficient forward solver for inverse problems concerned with profile and object reconstruction     

Narrow-waisted Gaussian beam discretization for short-pulseradiation from one-dimensional large apertures

We develop a Gabor-based Gaussian beam (GB) algorithm for representing two-dimensional (2-D) radiation from finite aperture distributions with short-pulse excitation in the time domain (TD). The work extends previous results using 2-D frequency-domain (FD) narrow-waisted Gaussian beams. The FD algorithm evolves from the rigorous Kirchhoff integration over the aperture distribution, which is then parameterized via the discrete Gabor basis and evaluated asymptotically for high frequencies to furnish the GB propagators to the observer. The TD results are obtained by Fourier inversion from the FD and yield pulsed beams (PB). We describe the resulting TD algorithm for several aperture distributions, ranging from simple linearly phased (linear delay) to arbitrary time delay profiles; the latter accommodate the important case of focusing TD aperture fields. For modulated pulses with Gaussian envelopes, we compute accurate closed form analytic solutions, which have been calibrated against numerical reference data. Our results confirm that the previously established utility of the Gabor-based narrow-waisted FD-GB algorithm for radiation from distributed apertures remains intact in the TD     

Further results on the asymptotic agreement problem

The problem of reaching a concensus between two decision-makers provided with different information is considered. The problem in which the decision-makers may have different underlying probability models is studied. Results are developed to characterize the likelihood of an agreement being reached eventually in terms of the nature of the inter-decision-maker communications. The problem in which the decision-makers are aware of the possibility that they may have different models is treated. It is found that in this case a deadlock can be reached where neither decision maker can learn additional information from the concensus process and they cannot reach a concensus decision. This result indicates that incorporating human uncertainty in probability assessment into the asymptotic agreement problem can lead to outcomes not anticipated in the general theory previously developed     

Multilevel classification of milling tool wear with confidence estimation

An important problem during industrial machining operations is the detection and classification of tool wear. Past research in this area has demonstrated the effectiveness of various feature sets and binary classifiers. Here, the goal is to develop a classifier which makes use of the dynamic characteristics of tool wear in a metal milling application and which replaces the standard binary classification result with two outputs: a prediction of the wear level (quantized) and a gradient measure that is the posterior probability (or confidence) that the tool is worn given the observed feature sequence. The classifier tracks the dynamics of sensor data within a single cutting pass as well as the evolution of wear from sharp to dull. Different alternatives to parameter estimation with sparsely-labeled training data are proposed and evaluated. We achieve high accuracy across changing cutting conditions, even with a limited feature set drawn from a single sensor.     

A curve evolution approach to object-based tomographic reconstruction

We develop a new approach to tomographic reconstruction problems based on geometric curve evolution techniques. We use a small set of texture coefficients to represent the object and background inhomogeneities and a contour to represent the boundary of multiple connected or unconnected objects. Instead of reconstructing pixel values on a fixed rectangular grid, we then find a reconstruction by jointly estimating these unknown contours and texture coefficients of the object and background. By designing a new "tomographic flow", the resulting problem is recast into a curve evolution problem and an efficient algorithm based on level set techniques is developed. The performance of the curve evolution method is demonstrated using examples with noisy limited-view Radon transformed data and noisy ground-penetrating radar data. The reconstruction results and computational cost are compared with those of conventional, pixel-based regularization methods. The results indicate that the curve evolution methods achieve improved shape reconstruction and have potential computation and memory advantages over conventional regularized inversion methods.