11,109 research outputs found
Characterising poroelastic materials in the ultrasonic range - A Bayesian approach
Acoustic fields scattered by poroelastic materials contain key information
about the materials' pore structure and elastic properties. Therefore, such
materials are often characterised with inverse methods that use acoustic
measurements. However, it has been shown that results from many existing
inverse characterisation methods agree poorly. One reason is that inverse
methods are typically sensitive to even small uncertainties in a measurement
setup, but these uncertainties are difficult to model and hence often
neglected. In this paper, we study characterising poroelastic materials in the
Bayesian framework, where measurement uncertainties can be taken into account,
and which allows us to quantify uncertainty in the results. Using the finite
element method, we simulate measurements where ultrasonic waves are incident on
a water-saturated poroelastic material in normal and oblique angles. We
consider uncertainties in the incidence angle and level of measurement noise,
and then explore the solution of the Bayesian inverse problem, the posterior
density, with an adaptive parallel tempering Markov chain Monte Carlo
algorithm. Results show that both the elastic and pore structure parameters can
be feasibly estimated from ultrasonic measurements.Comment: Published in JSV. https://doi.org/10.1016/j.jsv.2019.05.02
Dimension-Independent MCMC Sampling for Inverse Problems with Non-Gaussian Priors
The computational complexity of MCMC methods for the exploration of complex
probability measures is a challenging and important problem. A challenge of
particular importance arises in Bayesian inverse problems where the target
distribution may be supported on an infinite dimensional space. In practice
this involves the approximation of measures defined on sequences of spaces of
increasing dimension. Motivated by an elliptic inverse problem with
non-Gaussian prior, we study the design of proposal chains for the
Metropolis-Hastings algorithm with dimension independent performance.
Dimension-independent bounds on the Monte-Carlo error of MCMC sampling for
Gaussian prior measures have already been established. In this paper we provide
a simple recipe to obtain these bounds for non-Gaussian prior measures. To
illustrate the theory we consider an elliptic inverse problem arising in
groundwater flow. We explicitly construct an efficient Metropolis-Hastings
proposal based on local proposals, and we provide numerical evidence which
supports the theory.Comment: 26 pages, 7 figure
Diffusion models and steady-state approximations for exponentially ergodic Markovian queues
Motivated by queues with many servers, we study Brownian steady-state
approximations for continuous time Markov chains (CTMCs). Our approximations
are based on diffusion models (rather than a diffusion limit) whose
steady-state, we prove, approximates that of the Markov chain with notable
precision. Strong approximations provide such "limitless" approximations for
process dynamics. Our focus here is on steady-state distributions, and the
diffusion model that we propose is tractable relative to strong approximations.
Within an asymptotic framework, in which a scale parameter is taken large,
a uniform (in the scale parameter) Lyapunov condition imposed on the sequence
of diffusion models guarantees that the gap between the steady-state moments of
the diffusion and those of the properly centered and scaled CTMCs shrinks at a
rate of . Our proofs build on gradient estimates for solutions of the
Poisson equations associated with the (sequence of) diffusion models and on
elementary martingale arguments. As a by-product of our analysis, we explore
connections between Lyapunov functions for the fluid model, the diffusion model
and the CTMC.Comment: Published in at http://dx.doi.org/10.1214/13-AAP984 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Estimating Carotid Pulse and Breathing Rate from Near-infrared Video of the Neck
Objective: Non-contact physiological measurement is a growing research area
that allows capturing vital signs such as heart rate (HR) and breathing rate
(BR) comfortably and unobtrusively with remote devices. However, most of the
approaches work only in bright environments in which subtle
photoplethysmographic and ballistocardiographic signals can be easily analyzed
and/or require expensive and custom hardware to perform the measurements.
Approach: This work introduces a low-cost method to measure subtle motions
associated with the carotid pulse and breathing movement from the neck using
near-infrared (NIR) video imaging. A skin reflection model of the neck was
established to provide a theoretical foundation for the method. In particular,
the method relies on template matching for neck detection, Principal Component
Analysis for feature extraction, and Hidden Markov Models for data smoothing.
Main Results: We compared the estimated HR and BR measures with ones provided
by an FDA-cleared device in a 12-participant laboratory study: the estimates
achieved a mean absolute error of 0.36 beats per minute and 0.24 breaths per
minute under both bright and dark lighting.
Significance: This work advances the possibilities of non-contact
physiological measurement in real-life conditions in which environmental
illumination is limited and in which the face of the person is not readily
available or needs to be protected. Due to the increasing availability of NIR
imaging devices, the described methods are readily scalable.Comment: 21 pages, 15 figure
Trans-dimensional inversion of modal dispersion data on the New England Mud Patch
© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Bonnel, J., Dosso, S. E., Eleftherakis, D., & Chapman, N. R. Trans-dimensional inversion of modal dispersion data on the New England Mud Patch. IEEE Journal of Oceanic Engineering, 45(1), (2020): 116-130, doi:10.1109/JOE.2019.2896389.This paper presents single receiver geoacoustic inversion of two independent data sets recorded during the 2017 seabed characterization experiment on the New England Mud Patch. In the experimental area, the water depth is around 70 m, and the seabed is characterized by an upper layer of fine grained sediments with clay (i.e., mud). The first data set considered in this paper is a combustive sound source signal, and the second is a chirp emitted by a J15 source. These two data sets provide differing information on the geoacoustic properties of the seabed, as a result of their differing frequency content, and the dispersion properties of the environment. For both data sets, source/receiver range is about 7 km, and modal time-frequency dispersion curves are estimated using warping. Estimated dispersion curves are then used as input data for a Bayesian trans-dimensional inversion algorithm. Subbottom layering and geoacoustic parameters (sound speed and density) are thus inferred from the data. This paper highlights important properties of the mud, consistent with independent in situ measurements. It also demonstrates how information content differs for two data sets collected on reciprocal tracks, but with different acoustic sources and modal content.10.13039/100000006-Office of Naval Research
10.13039/100007297-Office of Naval Research Globa
A Partially Reflecting Random Walk on Spheres Algorithm for Electrical Impedance Tomography
In this work, we develop a probabilistic estimator for the voltage-to-current
map arising in electrical impedance tomography. This novel so-called partially
reflecting random walk on spheres estimator enables Monte Carlo methods to
compute the voltage-to-current map in an embarrassingly parallel manner, which
is an important issue with regard to the corresponding inverse problem. Our
method uses the well-known random walk on spheres algorithm inside subdomains
where the diffusion coefficient is constant and employs replacement techniques
motivated by finite difference discretization to deal with both mixed boundary
conditions and interface transmission conditions. We analyze the global bias
and the variance of the new estimator both theoretically and experimentally. In
a second step, the variance is considerably reduced via a novel control variate
conditional sampling technique
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