**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3746

# Search results for: Inverse problem

##### 3746 Uncontrollable Inaccuracy in Inverse Problems

**Authors:**
Yu. Menshikov

**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.

**Keywords:**
Inverse problems,
uncontrollable inaccuracy,
filtration.

##### 3745 Iterative Methods for An Inverse Problem

**Authors:**
Minghui Wang,
Shanrui Hu

**Abstract:**

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

**Keywords:**
doubly center matrix,
electric network theory,
iterative methods,
least-square problem.

##### 3744 Approximate Method of Calculation of Inviscid Hypersonic Flow

**Authors:**
F. Sokhanvar,
A. B. Khoshnevis

**Abstract:**

**Keywords:**
Hypersonic flow,
Inverse problem method

##### 3743 Recovering the Boundary Data in the Two Dimensional Inverse Heat Conduction Problem Using the Ritz-Galerkin Method

**Authors:**
Saeed Sarabadan,
Kamal Rashedi

**Abstract:**

**Keywords:**
Inverse problem,
parabolic equations,
heat equation,
Ritz-Galerkin method,
Landweber iterations.

##### 3742 A New Algorithm for Determining the Leading Coefficient of in the Parabolic Equation

**Authors:**
Shiping Zhou,
Minggen Cui

**Abstract:**

**Keywords:**
parabolic equations,
coefficient inverse problem,
reproducing
kernel.

##### 3741 Loudspeaker Parameters Inverse Problem for Improving Sound Frequency Response Simulation

**Authors:**
Y. T. Tsai,
Jin H. Huang

**Abstract:**

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.

**Keywords:**
Inverse problem,
cone effective area,
loudspeaker,
nonlinear conjugate gradient method.

##### 3740 The Inverse Eigenvalue Problem via Orthogonal Matrices

**Authors:**
A. M. Nazari,
B. Sepehrian,
M. Jabari

**Abstract:**

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

**Keywords:**
Householder matrix,
nonnegative matrix,
Inverse eigenvalue problem.

##### 3739 Inverse Matrix in the Theory of Dynamic Systems

**Authors:**
R. Masarova,
M. Juhas,
B. Juhasova,
Z. Sutova

**Abstract:**

**Keywords:**
Dynamic system,
transfer matrix,
inverse matrix,
modeling.

##### 3738 Topological Sensitivity Analysis for Reconstruction of the Inverse Source Problem from Boundary Measurement

**Authors:**
Maatoug Hassine,
Mourad Hrizi

**Abstract:**

**Keywords:**
Geometric inverse source problem,
heat equation,
topological sensitivity,
topological optimization,
Kohn-Vogelius
formulation.

##### 3737 Vibration Base Identification of Impact Force Using Genetic Algorithm

**Authors:**
R. Hashemi,
M.H.Kargarnovin

**Abstract:**

**Keywords:**
Genetic Algorithm,
Inverse problem,
Optimization,
Vibration.

##### 3736 Inverse Heat Transfer Analysis of a Melting Furnace Using Levenberg-Marquardt Method

**Authors:**
Mohamed Hafid,
Marcel Lacroix

**Abstract:**

**Keywords:**
Melting furnace,
inverse heat transfer,
enthalpy method,
Levenberg–Marquardt Method.

##### 3735 On a Class of Inverse Problems for Degenerate Differential Equations

**Authors:**
Fadi Awawdeh,
H.M. Jaradat

**Abstract:**

**Keywords:**
Inverse Problem,
Degenerate Differential Equations,
Perturbation Theory for Linear Operators

##### 3734 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

**Authors:**
Xingping Sheng

**Abstract:**

**Keywords:**
Generalized inverse A(2)
T,
S,
Restricted inner product,
Iterative method,
Orthogonal projection.

##### 3733 Inverse Problem Methodology for the Measurement of the Electromagnetic Parameters Using MLP Neural Network

**Authors:**
T. Hacib,
M. R. Mekideche,
N. Ferkha

**Abstract:**

**Keywords:**
Inverse problem,
MLP neural network,
parametersidentification,
FEM.

##### 3732 The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation

**Authors:**
Yongxin Yuan,
Hao Liu

**Abstract:**

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

**Keywords:**
Inverse problem,
Least-squares solution,
model updating,
Singular value decomposition (SVD),
Optimal approximation.

##### 3731 A Reproduction of Boundary Conditions in Three-Dimensional Continuous Casting Problem

**Authors:**
Iwona Nowak,
Jacek Smolka,
Andrzej J. Nowak

**Abstract:**

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.

**Keywords:**
Boundary inverse problem,
sensitivity analysis,
continuous casting,
numerical simulation.

##### 3730 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

**Authors:**
Ioannis N. Koukoulis,
Clio G. Vossou,
Christopher G. Provatidis

**Abstract:**

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.

**Keywords:**
Elastostatic,
inverse problem,
optimization.

##### 3729 Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network

**Authors:**
Won Sup Kim,
Xue-Mei Cui,
Seung Kee Han

**Abstract:**

We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.

**Keywords:**
Chaotic oscillator,
complex network,
inverse coherence matrix,
network estimation.

##### 3728 Software Development for the Kinematic Analysis of a Lynx 6 Robot Arm

**Authors:**
Baki Koyuncu,
Mehmet Güzel

**Abstract:**

The kinematics of manipulators is a central problem in the automatic control of robot manipulators. Theoretical background for the analysis of the 5 Dof Lynx-6 educational Robot Arm kinematics is presented in this paper. The kinematics problem is defined as the transformation from the Cartesian space to the joint space and vice versa. The Denavit-Harbenterg (D-H) model of representation is used to model robot links and joints in this study. Both forward and inverse kinematics solutions for this educational manipulator are presented, An effective method is suggested to decrease multiple solutions in inverse kinematics. A visual software package, named MSG, is also developed for testing Motional Characteristics of the Lynx-6 Robot arm. The kinematics solutions of the software package were found to be identical with the robot arm-s physical motional behaviors.

**Keywords:**
Lynx 6,
robot arm,
forward kinematics,
inverse
kinematics,
software,
DH parameters,
5 DOF ,
SSC-32 ,
simulator.

##### 3727 An Inverse Heat Transfer Algorithm for Predicting the Thermal Properties of Tumors during Cryosurgery

**Authors:**
Mohamed Hafid,
Marcel Lacroix

**Abstract:**

This study aimed at developing an inverse heat transfer approach for predicting the time-varying freezing front and the temperature distribution of tumors during cryosurgery. Using a temperature probe pressed against the layer of tumor, the inverse approach is able to predict simultaneously the metabolic heat generation and the blood perfusion rate of the tumor. Once these parameters are predicted, the temperature-field and time-varying freezing fronts are determined with the direct model. The direct model rests on one-dimensional *Pennes* bioheat equation. The phase change problem is handled with the enthalpy method. The *Levenberg-Marquardt* Method (LMM) combined to the *Broyden* Method (BM) is used to solve the inverse model. The effect (a) of the thermal properties of the diseased tissues; (b) of the initial guesses for the unknown thermal properties; (c) of the data capture frequency; and (d) of the noise on the recorded temperatures is examined. It is shown that the proposed inverse approach remains accurate for all the cases investigated.

**Keywords:**
Cryosurgery,
inverse heat transfer,
Levenberg-Marquardt method,
thermal properties,
Pennes model,
enthalpy method.

##### 3726 Determination of Moisture Diffusivity of AACin Drying Phase using Genetic Algorithm

**Authors:**
Jan Kočí,
Jiří Maděra,
Miloš Jerman,
Robert Černý

**Abstract:**

The current practice of determination of moisture diffusivity of building materials under laboratory conditions is predominantly aimed at the absorption phase. The main reason is the simplicity of the inverse analysis of measured moisture profiles. However, the liquid moisture transport may exhibit significant hysteresis. Thus, the moisture diffusivity should be different in the absorption (wetting) and desorption (drying) phase. In order to bring computer simulations of hygrothermal performance of building materials closer to the reality, it is then necessary to find new methods for inverse analysis which could be used in the desorption phase as well. In this paper we present genetic algorithm as a possible method of solution of the inverse problem of moisture transport in desorption phase. Its application is demonstrated for AAC as a typical building material.

**Keywords:**
autoclaved aerated concrete,
desorption,
genetic
algorithm,
inverse analysis

##### 3725 A Multigrid Approach for Three-Dimensional Inverse Heat Conduction Problems

**Authors:**
Jianhua Zhou,
Yuwen Zhang

**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.

**Keywords:**
Conduction,
inverse problems,
conjugated gradient method,
laser.

##### 3724 Base Change for Fisher Metrics: Case of the q−Gaussian Inverse Distribution

**Authors:**
Gabriel I. Loaiza O.,
Carlos A. Cadavid M.,
Juan C. Arango P.

**Abstract:**

It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ = −1/2 , as does the family of usual Gaussian distributions. In the present paper, firstly we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ1, θ2; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the Inverse q−Gaussian distribution family (q < 3), as the family obtained by replacing the usual exponential function by the Tsallis q−exponential function in the expression for the Inverse Gaussian distribution, and observe that it supports two possible geometries, the Fisher and the q−Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q−Fisher geometry of the Inverse q−Gaussian distribution family, similar to the ones obtained in the case of the Inverse Gaussian distribution family.

**Keywords:**
Base of Changes,
Information Geometry,
Inverse
Gaussian distribution,
Inverse q-Gaussian distribution,
Statistical
Manifolds.

##### 3723 On Method of Fundamental Solution for Nondestructive Testing

**Abstract:**

**Keywords:**
ill-posed,
TSVD,
Laplace's equation,
inverse problem,
L-curve,
Generalized Cross Validation.

##### 3722 Numerical Inverse Laplace Transform Using Chebyshev Polynomial

**Authors:**
Vinod Mishra,
Dimple Rani

**Abstract:**

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.

**Keywords:**
Chebyshev polynomial,
Numerical inverse Laplace transform,
Odd cosine series.

##### 3721 An Extension of the Kratzel Function and Associated Inverse Gaussian Probability Distribution Occurring in Reliability Theory

**Authors:**
R. K. Saxena,
Ravi Saxena

**Abstract:**

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

**Keywords:**
Fox-Wright function,
Inverse Gaussian distribution,
Krtzel function & Bessel function of the third kind.

##### 3720 Comparison of Three Versions of Conjugate Gradient Method in Predicting an Unknown Irregular Boundary Profile

**Authors:**
V. Ghadamyari,
F. Samadi,
F. Kowsary

**Abstract:**

**Keywords:**
Boundary elements,
Conjugate Gradient Method,
Inverse Geometry Problem,
Sensitivity equation.

##### 3719 The Design of Axisymmetric Ducts for Incompressible Flow with a Parabolic Axial Velocity Inlet Profile

**Authors:**
V.Pavlika

**Abstract:**

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.

**Keywords:**
Inverse problem,
irrotational incompressible flow,
Boundary value problem.

##### 3718 Confidence Interval for the Inverse of a Normal Mean with a Known Coefficient of Variation

**Authors:**
Arunee Wongkha,
Suparat Niwitpong,
Sa-aat Niwitpong

**Abstract:**

In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

**Keywords:**
The inverse of a normal mean,
confidence interval,
generalized confidence intervals,
known coefficient of variation.

##### 3717 Multiparametric Optimization of Water Treatment Process for Thermal Power Plants

**Authors:**
B. Mukanova,
N. Glazyrina,
S. Glazyrin

**Abstract:**

The formulated problem of optimization of the technological process of water treatment for thermal power plants is considered in this article. The problem is of multiparametric nature. To optimize the process, namely, reduce the amount of waste water, a new technology was developed to reuse such water. A mathematical model of the technology of wastewater reuse was developed. Optimization parameters were determined. The model consists of a material balance equation, an equation describing the kinetics of ion exchange for the non-equilibrium case and an equation for the ion exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion exchange. A direct problem of calculating the impurity concentration at the outlet of the water treatment plant was numerically solved. The direct problem was approximated by an implicit point-to-point computation difference scheme. The inverse problem was formulated as relates to determination of the parameters of the mathematical model of the water treatment plant operating in non-equilibrium conditions. The formulated inverse problem was solved. Following the results of calculation the time of start of the filter regeneration process was determined, as well as the period of regeneration process and the amount of regeneration and wash water. Multi-parameter optimization of water treatment process for thermal power plants allowed decreasing the amount of wastewater by 15%.

**Keywords:**
Direct problem,
multiparametric optimization,
optimization parameters,
water treatment.