Abstract: A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.
Abstract: The noise requirements for naval and research vessels
have seen an increasing demand for quieter ships in order to fulfil
current regulations and to reduce the effects on marine life. Hence,
new methods dedicated to the characterization of propeller noise,
which is the main source of noise in the far-field, are needed. The
study of cavitating propellers in closed-section is interesting for
analyzing hydrodynamic performance but could involve significant
difficulties for hydroacoustic study, especially due to reverberation
and boundary layer noise in the tunnel. The aim of this paper
is to present a numerical methodology for the identification of
hydroacoustic sources on marine propellers using hydrophone arrays
in a large hydrodynamic tunnel. The main difficulties are linked to the
reverberation of the tunnel and the boundary layer noise that strongly
reduce the signal-to-noise ratio. In this paper it is proposed to estimate
the reflection coefficients using an inverse method and some reference
transfer functions measured in the tunnel. This approach allows to
reduce the uncertainties of the propagation model used in the inverse
problem. In order to reduce the boundary layer noise, a cleaning
algorithm taking advantage of the low rank and sparse structure of the
cross-spectrum matrices of the acoustic and the boundary layer noise
is presented. This approach allows to recover the acoustic signal even
well under the boundary layer noise. The improvement brought by
this method is visible on acoustic maps resulting from beamforming
and DAMAS algorithms.
Abstract: In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solutions are analyzed. Several methods for removing the influence of uncontrollable inaccuracy have been suggested.
Abstract: In this study, a comparative analysis of the approaches
associated with the use of neural network algorithms for effective
solution of a complex inverse problem – the problem of identifying
and determining the individual concentrations of inorganic salts in
multicomponent aqueous solutions by the spectra of Raman
scattering of light – is performed. It is shown that application of
artificial neural networks provides the average accuracy of
determination of concentration of each salt no worse than 0.025 M.
The results of comparative analysis of input data compression
methods are presented. It is demonstrated that use of uniform
aggregation of input features allows decreasing the error of
determination of individual concentrations of components by 16-18%
on the average.
Abstract: The overall objective of this paper is to retrieve soil
surfaces parameters namely, roughness and soil moisture related to
the dielectric constant by inverting the radar backscattered signal
from natural soil surfaces.
Because the classical description of roughness using statistical
parameters like the correlation length doesn't lead to satisfactory
results to predict radar backscattering, we used a multi-scale
roughness description using the wavelet transform and the Mallat
algorithm. In this description, the surface is considered as a
superposition of a finite number of one-dimensional Gaussian
processes each having a spatial scale. A second step in this study
consisted in adapting a direct model simulating radar backscattering
namely the small perturbation model to this multi-scale surface
description. We investigated the impact of this description on radar
backscattering through a sensitivity analysis of backscattering
coefficient to the multi-scale roughness parameters.
To perform the inversion of the small perturbation multi-scale
scattering model (MLS SPM) we used a multi-layer neural network
architecture trained by backpropagation learning rule. The inversion
leads to satisfactory results with a relative uncertainty of 8%.
Abstract: In this paper, we establish existence and uniqueness of
solutions for a class of inverse problems of degenerate differential
equations. The main tool is the perturbation theory for linear operators.