Luise S. Couchman

Multiaspect target identification with wave-based matched pursuits and continuous hidden Markov models

Multiaspect target identification is effected by fusing the features extracted from multiple scattered waveforms; these waveforms are characteristic of viewing the target from a sequence of distinct orientations. Classification is performed in the maximum-likelihood sense, which we show, under reasonable assumptions, can be implemented via a hidden Markov model (HMM). We utilize a continuous-HMM paradigm and compare its performance to its discrete counterpart. The feature parsing is performed via wave-based matched pursuits. Algorithm performance is assessed by considering measured acoustic scattering data from five similar submerged elastic targets.

Genetic algorithm wavelet design for signal classification

Biorthogonal wavelets are applied to parse multiaspect transient scattering data in the context of signal classification. A language-based genetic algorithm is used to design wavelet filters that enhance classification performance. The biorthogonal wavelets are implemented via the lifting procedure and the optimization is carried out using a classification-based cost function. Example results are presented for target classification using measured scattering data.

Dual hidden Markov model for characterizing wavelet coefficients from multi-aspect scattering data

Angle-dependent scattering (electromagnetic or acoustic) is considered from a general target, for which the scattered signal is a non-stationary function of the target-sensor orientation. A statistical model is presented for the wavelet coefficients of such a signal, in which the angular non-stationarity is characterized by an “outer” hidden Markov model (HMMo). The statistics of the wavelet coefficients, within a state of the outer HMM, are characterized by a second, “inner” HMMi, exploiting the tree structure of the wavelet decomposition. This dual-HMM construct is demonstrated by considering multi-aspect target identification using measured acoustic scattering data.

Mid-frequency structural acoustic and vibration analysis in arbitrary, curved three-dimensional domains

Abstract A high-order finite element infrastructure is described for the numerical solution of the vibratory response of fluid–structure systems in the mid-frequency range. Underlying variational forms along with the use of an unstructured, topology-based, variable-degree, polymorphic finite element discretization scheme is described. Accurate numerical solutions to practical problems, including rigid and elastic acoustic scattering and interior acoustics, are presented to demonstrate the accuracy and flexibility of the infrastructure.

Multiaspect identification of submerged elastic targets via wave-based matching pursuits and hidden Markov models

This paper investigates classification of submerged elastic targets using a sequence of backscattered acoustic signals corresponding to measurements at multiple target-sensor orientations. Wavefront and resonant features are extracted from each of the multiaspect signals using the method of matching pursuits, with a wave-based dictionary. A discrete hidden Markov model (HMM) is designed for each of the target classes under consideration, with identification of an unknown target effected by considering which model has the maximum likelihood of producing the observed sequence of feature vectors. HMMs are stochastic models which are well suited to describing piecewise-stationary processes, and are appropriate for multiaspect classification due to the strong aspect dependence of the scattered fields for most realistic targets. After establishing the physical and geometric correspondence between multiaspect sensing and the HMM parameters, performance is assessed through consideration of measured acoustic data ...

Wideband time-reversal imaging of an elastic target in an acoustic waveguide

Time-reversal is addressed for imaging elastic targets situated in an acoustic waveguide. It is assumed that the target-sensor range is large relative to the channel depth. We investigate the theory of wideband time-reversal imaging of an extended elastic target, for which the target dimensions are large relative to the principal wavelengths. When performing time-reversal imaging one requires a forward model for propagation through the channel, and the quality of the resulting image may be used as a measure of the match between the modeled and actual (measured) channel parameters. It is demonstrated that the channel parameters associated with a given measurement may be determined via a genetic-algorithm (GA) search in parameter space, employing a cost function based on the time-reversal image quality. Example GA channel-parameter-inversion results and imagery are presented for measured at-sea data.

Class-based target identification with multiaspect scattering data

In underwater sensing applications, it is often difficult to train a classifier in advance for all targets that may be seen during testing, due to the large number of targets that may be encountered. We therefore partition the training data into target classes, with each class characteristic of multiple targets that share similar scattering physics. In some cases, one may have a priori insight into which targets should constitute a given class, while in other cases this segmentation must be done autonomously based on the scattering data. For the latter case, we constitute the classes using an information-theoretic mapping criterion. Having defined the target classes, the second phase of our identification procedure involves determining those features that enhance the similarity between the targets in a given class. This is achieved by using a genetic algorithm (GA)-based feature-selection algorithm with a Kullback-Leibler (KL) cost function. The classifier employed is appropriate for multiaspect scattering data and is based on a hidden Markov model (HMM). The performance of the class-based classification algorithm is examined using both measured and computed acoustic scattering data from submerged elastic targets.

A hierarchic p‐version boundary‐element method for axisymmetric acoustic scattering and radiation

A rapidly convergent boundary‐element method that has a high‐accuracy capability is developed for the solution of the exterior Neumann problem for the Helmholtz equation. The approach makes use of the boundary‐operator combination idea of Burton and Miller [A. J. Burton and G. F. Miller, Proc. R. Soc. London Ser. A 323, 201–210 (1971)] to avoid the classical irregular frequency difficulties together with p‐version boundary elements to obtain a high rate of convergence. The entire algorithm is designed to be fully hierarchic to minimize the cost of multiple solutions, which are necessary for a posteriori assessment of accuracy. A new hierarchic singular‐kernel quadrature rule is developed for this purpose. Numerical examples demonstrate the accuracy and convergence rate of the method.

A sparse integral equation method for acoustic scattering

Numerical calculations of acoustic scattering may be based on either differential equations or on corresponding integral equations. The differential equations generate a sparse matrix problem involving (possibly implicitly) an M by M matrix. Integral equations generate a matrix of size N by N, where N is much smaller than M. In the past the matrix resulting from an integral equation was necessarily full. A method for greatly reducing the storage required is presented here. The full N by N matrix resulting from the discretization of the Helmholtz integral is transformed into a sparse N by N matrix using the interaction matrix localization (IML) method. IML is a general method for integral equations describing wave phenomena. It produces a sparse matrix by partitioning the scatterer into several regions and using groups of basis functions each of which is nonzero over an entire region. The basis functions for a region are chosen so that each radiates a narrow beam in a different direction. The number of imp...

SCATTERING AND INVERSE SCATTERING OF SOUND-HARD OBSTACLES VIA SHAPE DEFORMATION

Direct and inverse scattering of plane acoustic waves from sound-hard obstacles are discussed. The direct problem is solved via the application of the Pade approximation. It is shown that this involves solving only certain algebraic recursion relations and requires neither Greens functions nor integral representations of the field. The shape of the scatterer is assumed to be a superposition of a deformation (allowed to be finite) over an underlying simple geometry. It is demonstrated that such a decomposition allows the scattered field to be obtained as solutions of classical Neumann problems in domains exterior to the underlying simple shape instead of the actual deformed contour. This introduces simplifications in the implementation of a Gauss - Newton type inversion procedure which was used in this study. Some inversions of two-dimensional scatterers are presented.