A Multigrid Approach for Three-Dimensional Inverse Heat Conduction Problems
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.
Numerical Simulations of Acoustic Imaging in Hydrodynamic Tunnel with Model Adaptation and Boundary Layer Noise Reduction
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.
Recovering the Boundary Data in the Two Dimensional Inverse Heat Conduction Problem Using the Ritz-Galerkin Method
This article presents a numerical method to find the
heat flux in an inhomogeneous inverse heat conduction problem with
linear boundary conditions and an extra specification at the terminal.
The method is based upon applying the satisfier function along with
the Ritz-Galerkin technique to reduce the approximate solution of the
inverse problem to the solution of a system of algebraic equations.
The instability of the problem is resolved by taking advantage of
the Landweber’s iterations as an admissible regularization strategy.
In computations, we find the stable and low-cost results which
demonstrate the efficiency of the technique.
Uncontrollable Inaccuracy in Inverse Problems
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.
Parameters Optimization of the Laminated Composite Plate for Sound Transmission Problem
In this paper, the specific sound Transmission Loss
(TL) of the Laminated Composite Plate (LCP) with different material
properties in each layer is investigated. The numerical method to
obtain the TL of the LCP is proposed by using elastic plate theory. The
transfer matrix approach is novelty presented for computational
efficiency in solving the numerous layers of dynamic stiffness matrix
(D-matrix) of the LCP. Besides the numerical simulations for
calculating the TL of the LCP, the material properties inverse method
is presented for the design of a laminated composite plate analogous to
a metallic plate with a specified TL. As a result, it demonstrates that
the proposed computational algorithm exhibits high efficiency with a
small number of iterations for achieving the goal. This method can be
effectively employed to design and develop tailor-made materials for
Application of Adaptive Neural Network Algorithms for Determination of Salt Composition of Waters Using Laser Spectroscopy
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.
Loudspeaker Parameters Inverse Problem for Improving Sound Frequency Response Simulation
The sound pressure level (SPL) of the moving-coil
loudspeaker (MCL) is often simulated and analyzed using the lumped
parameter model. However, the SPL of a MCL cannot be simulated
precisely in the high frequency region, because the value of cone
effective area is changed due to the geometry variation in different
mode shapes, it is also related to affect the acoustic radiation mass and
resistance. Herein, the paper presents the inverse method which has a
high ability to measure the value of cone effective area in various
frequency points, also can estimate the MCL electroacoustic
parameters simultaneously. The proposed inverse method comprises
the direct problem, adjoint problem, and sensitivity problem in
collaboration with nonlinear conjugate gradient method. Estimated
values from the inverse method are validated experimentally which
compared with the measured SPL curve result. Results presented in
this paper not only improve the accuracy of lumped parameter model
but also provide the valuable information on loudspeaker cone design.
On Method of Fundamental Solution for Nondestructive Testing
Nondestructive testing in engineering is an inverse
Cauchy problem for Laplace equation. In this paper the problem
of nondestructive testing is expressed by a Laplace-s equation with
third-kind boundary conditions. In order to find unknown values on
the boundary, the method of fundamental solution is introduced and
realized. Because of the ill-posedness of studied problems, the TSVD
regularization technique in combination with L-curve criteria and
Generalized Cross Validation criteria is employed. Numerical results
are shown that the TSVD method combined with L-curve criteria is
more efficient than the TSVD method combined with GCV criteria.
The abstract goes here.
On a Class of Inverse Problems for Degenerate Differential Equations
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.
The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation
In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw
Generalized Inverse Eigenvalue Problems for Symmetric Arrow-head Matrices
In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.
Approximate Method of Calculation of Inviscid Hypersonic Flow
In the present work steady inviscid hypersonic flows
are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic
shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the
surface distribution of pressure is obtained.
A New Algorithm for Determining the Leading Coefficient of in the Parabolic Equation
This paper investigates the inverse problem of determining
the unknown time-dependent leading coefficient in the parabolic
equation using the usual conditions of the direct problem and an additional
condition. An algorithm is developed for solving numerically
the inverse problem using the technique of space decomposition in a
reproducing kernel space. The leading coefficients can be solved by a
lower triangular linear system. Numerical experiments are presented
to show the efficiency of the proposed methods.
The Design of Axisymmetric Ducts for Incompressible Flow with a Parabolic Axial Velocity Inlet Profile
In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.
A Reproduction of Boundary Conditions in Three-Dimensional Continuous Casting Problem
The paper discusses a 3D numerical solution of the inverse boundary problem for a continuous casting process of alloy. The main goal of the analysis presented within the paper was to estimate heat fluxes along the external surface of the ingot. The verified information on these fluxes was crucial for a good design of a mould, effective cooling system and generally the whole caster. In the study an enthalpy-porosity technique implemented in Fluent package was used for modeling the solidification process. In this method, the phase change interface was determined on the basis of the liquid fraction approach. In inverse procedure the sensitivity analysis was applied for retrieving boundary conditions. A comparison of the measured and retrieved values showed a high accuracy of the computations. Additionally, the influence of the accuracy of measurements on the estimated heat fluxes was also investigated.
Development of a Neural Network based Algorithm for Multi-Scale Roughness Parameters and Soil Moisture Retrieval
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%.
Inverse Problem Methodology for the Measurement of the Electromagnetic Parameters Using MLP Neural Network
This paper presents an approach which is based on the
use of supervised feed forward neural network, namely multilayer
perceptron (MLP) neural network and finite element method (FEM)
to solve the inverse problem of parameters identification. The
approach is used to identify unknown parameters of ferromagnetic
materials. The methodology used in this study consists in the
simulation of a large number of parameters in a material under test,
using the finite element method (FEM). Both variations in relative
magnetic permeability and electrical conductivity of the material
under test are considered. Then, the obtained results are used to
generate a set of vectors for the training of MLP neural network.
Finally, the obtained neural network is used to evaluate a group of
new materials, simulated by the FEM, but not belonging to the
original dataset. Noisy data, added to the probe measurements is used
to enhance the robustness of the method. The reached results
demonstrate the efficiency of the proposed approach, and encourage
future works on this subject.
Vibration Base Identification of Impact Force Using Genetic Algorithm
This paper presents the identification of the impact
force acting on a simply supported beam. The force identification is
an inverse problem in which the measured response of the structure is
used to determine the applied force. The identification problem is
formulated as an optimization problem and the genetic algorithm is
utilized to solve the optimization problem. The objective function is
calculated on the difference between analytical and measured
responses and the decision variables are the location and magnitude
of the applied force. The results from simulation show the
effectiveness of the approach and its robustness vs. the measurement
noise and sensor location.
A Parametric Study of an Inverse Electrostatics Problem (IESP) Using Simulated Annealing, Hooke & Jeeves and Sequential Quadratic Programming in Conjunction with Finite Element and Boundary Element Methods
The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.