A review on machinery diagnostics and prognostics implementing condition-based maintenance

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Information Theory and Reliable Communication

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Statistical Parametric Mapping The Analysis Of Functional Brain Images

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Methods Of Modern Mathematical Physics

This work considers the design of optimal, energy-constrained transmit signals for active sensing for the case when the designer has incomplete or uncertain knowledge of the target and/or environment. The mathematical formulation is that of a multi-objective optimization problem, wherein one can incorporate a plurality of potential targets, interference, or clutter models and in doing so take advantage of the wide range of results in the literature related to modeling each. It is shown, via simulation, that when the objective function of the optimization problem is chosen to maximize the minimum (i.e., maxmin) probability of detection among all possible model combinations, the optimal waveforms obtained are advantageous. The advantage results because the maxmin waveforms judiciously allocate energy to spectral regions where each of the target models respond strongly and each of the environmental models affect minimal detection performance degradation. In particular, improved detection performance is shown compared to linear frequency modulated transmit signals and compared to signals designed with the wrong target spectrum assumed. Additionally, it is shown that the maxmin design yields performance comparable to an optimal design matched to the correct target/environmental model. Finally, it is proven that the maxmin problem formulation is convex.

Model-based waveform design for optimal detection: A multi-objective approach to dealing with incomplete a priori knowledge

We derive the <inline-formula><tex-math notation="LaTeX">$s$</tex-math></inline-formula>- and <inline-formula><tex-math notation="LaTeX">$z$</tex-math></inline-formula>-plane pole regions for continuous-time and discrete-time LTI systems to yield resonance. In this way, resonance can be identified by visual inspection of the pole-zero plot, without the need for calculations.

Identifying Resonant Poles by Visual Inspection of Pole-Zero Plots

We present methods for obtaining basic signal parameters and apply them to the problem of detection, estimation, and enhancement of biological signals. We apply these methods to human speech and whale sounds. In speech, the methods are used to obtain statistical properties of the signal so that the derived features may be used to cluster speakers. For whale sounds we show that the methods may be effectively used not only to obtain signal components and parameters but to also adaptively filter off the noise.

https://www.computer.org/csdl/pds/api/csdl/proceedings/download-article/12OmNqHqSqN/pdf

Time-frequency methods for biological signal estimation

he study of human postural control, which is critical to most activities of everyday life, is an active area of biomedical research, vital to improving our understanding of human balance and the evaluation and rehabilitation of individuals with balance disorders. Deficiencies in balance lead to an increased likelihood of falls, potentially resulting in injury and even death. The costs associated with falls, in terms of lost wages and medical expenses, are in the billions of dollars annually, exceeded only by motor vehicle injuries [36], [40], [47]. The regulation of balance is a complex multisensory feed

The Utility of Time-Frequency Analysis in Studying Human Balance

We present a new approach to the study of the telegraph equation, that is based on analyzing the equation in phase space. We consider the phase space of time and frequency, as well as of position and spatial frequency (or wavenumber).We show that considerable simplification, both conceptual and mathematical, results from this approach. The basic reason why a phase space approach is fruitful is that when there is dispersion, the group velocity is not constant but changes with frequency and therefore the wave changes as it propagates over space and time. Simple but effective and insightful phase space approximations to the solution of the telegraph equation are presented, with examples.

Patrick J. Loughlin

Papers

Model-based waveform design for optimal detection: A multi-objective approach to dealing with incomplete a priori knowledge

Identifying Resonant Poles by Visual Inspection of Pole-Zero Plots

Time-frequency methods for biological signal estimation

The Utility of Time-Frequency Analysis in Studying Human Balance

Phase Space Analysis of the Telegraph Equation