**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2597

# Search results for: inverse problems

##### 2597 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.

##### 2596 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

##### 2595 On a New Inverse Polynomial Numerical Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations

**Authors:**
R. B. Ogunrinde

**Abstract:**

**Keywords:**
Differential equations,
Numerical,
Initial value
problem,
Polynomials.

##### 2594 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.

##### 2593 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.

##### 2592 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.

##### 2591 Inverse Heat Conduction Analysis of Cooling on Run Out Tables

**Authors:**
M. S. Gadala,
Khaled Ahmed,
Elasadig Mahdi

**Abstract:**

In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems.

**Keywords:**
Inverse Analysis,
Function Specification,
Neural Net
Works,
Particle Swarm,
Run Out Table.

##### 2590 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.

##### 2589 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.

##### 2588 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.

##### 2587 Approximate Method of Calculation of Inviscid Hypersonic Flow

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

**Abstract:**

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

##### 2586 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.

##### 2585 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.

##### 2584 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.

##### 2583 MRI Reconstruction Using Discrete Fourier Transform: A tutorial

**Authors:**
Abiodun M. Aibinu,
Momoh J. E. Salami,
Amir A. Shafie,
Athaur Rahman Najeeb

**Abstract:**

The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing Magnetic Resonance Imaging (MRI) from uniformly sampled K-space data. In this tutorial, three of the major problems associated with the use of IFFT in MRI reconstruction are highlighted. The tutorial also gives brief introduction to MRI physics; MRI system from instrumentation point of view; K-space signal and the process of IDFT and IFFT for One and two dimensional (1D and 2D) data.

**Keywords:**
Discrete Fourier Transform (DFT),
K-space Data,
Magnetic Resonance (MR),
Spin,
Windows.

##### 2582 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.

##### 2581 An Iterative Algorithm for Inverse Kinematics of 5-DOF Manipulator with Offset Wrist

**Authors:**
Juyi Park,
Jung-Min Kim,
Hee-Hwan Park,
Jin-Wook Kim,
Gye-Hyung Kang,
Soo-Ho Kim

**Abstract:**

**Keywords:**
5-DOF manipulator,
Inverse kinematics,
Iterative
algorithm,
Wrist offset.

##### 2580 Further Thoughtson a Sequential Life Testing Approach Using an Inverse Weibull Model

**Authors:**
D. I. De Souza,
G. P. Azevedo,
D. R. Fonseca

**Abstract:**

In this paper we will develop further the sequential life test approach presented in a previous article by [1] using an underlying two parameter Inverse Weibull sampling distribution. The location parameter or minimum life will be considered equal to zero. Once again we will provide rules for making one of the three possible decisions as each observation becomes available; that is: accept the null hypothesis H0; reject the null hypothesis H0; or obtain additional information by making another observation. The product being analyzed is a new electronic component. There is little information available about the possible values the parameters of the corresponding Inverse Weibull underlying sampling distribution could have.To estimate the shape and the scale parameters of the underlying Inverse Weibull model we will use a maximum likelihood approach for censored failure data. A new example will further develop the proposed sequential life testing approach.

**Keywords:**
Sequential Life Testing,
Inverse Weibull Model,
Maximum Likelihood Approach,
Hypothesis Testing.

##### 2579 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.

##### 2578 Optimization of Inverse Kinematics of a 3R Robotic Manipulator using Genetic Algorithms

**Authors:**
J. Ramírez A.,
A. Rubiano F.

**Abstract:**

**Keywords:**
Direct Kinematic,
Genetic Algorithm,
InverseKinematic,
Optimization,
Robot Manipulator

##### 2577 Neural Adaptive Switching Control of Robotic Systems

**Authors:**
A. Denker,
U. Akıncıoğlu

**Abstract:**

**Keywords:**
Neural networks,
robotics,
direct inverse control,
predictive control.

##### 2576 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.

##### 2575 Artificial Neural Network with Steepest Descent Backpropagation Training Algorithm for Modeling Inverse Kinematics of Manipulator

**Authors:**
Thiang,
Handry Khoswanto,
Rendy Pangaldus

**Abstract:**

Inverse kinematics analysis plays an important role in developing a robot manipulator. But it is not too easy to derive the inverse kinematic equation of a robot manipulator especially robot manipulator which has numerous degree of freedom. This paper describes an application of Artificial Neural Network for modeling the inverse kinematics equation of a robot manipulator. In this case, the robot has three degree of freedoms and the robot was implemented for drilling a printed circuit board. The artificial neural network architecture used for modeling is a multilayer perceptron networks with steepest descent backpropagation training algorithm. The designed artificial neural network has 2 inputs, 2 outputs and varies in number of hidden layer. Experiments were done in variation of number of hidden layer and learning rate. Experimental results show that the best architecture of artificial neural network used for modeling inverse kinematics of is multilayer perceptron with 1 hidden layer and 38 neurons per hidden layer. This network resulted a RMSE value of 0.01474.

**Keywords:**
Artificial neural network,
back propagation,
inverse kinematics,
manipulator,
robot.

##### 2574 Genetic-Fuzzy Inverse Controller for a Robot Arm Suitable for On Line Applications

**Authors:**
Abduladheem A. Ali,
Easa A. Abd

**Abstract:**

**Keywords:**
Fuzzy network,
genetic algorithm,
robot control,
online genetic control,
parameter identification.

##### 2573 Prediction of the Thermal Parameters of a High-Temperature Metallurgical Reactor Using Inverse Heat Transfer

**Authors:**
Mohamed Hafid,
Marcel Lacroix

**Abstract:**

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

**Keywords:**
Inverse heat transfer,
phase change,
metallurgical reactor,
Levenberg–Marquardt method,
Broyden method,
bank thickness.

##### 2572 Design of a 4-DOF Robot Manipulator with Optimized Algorithm for Inverse Kinematics

**Authors:**
S. Gómez,
G. Sánchez,
J. Zarama,
M. Castañeda Ramos,
J. Escoto Alcántar,
J. Torres,
A. Núñez,
S. Santana,
F. Nájera,
J. A. Lopez

**Abstract:**

**Keywords:**
Kinematics,
degree of freedom,
optimization,
robot
manipulator.

##### 2571 A Note on Toeplitz Matrices

**Authors:**
Hsuan-Chu Li

**Abstract:**

**Keywords:**
Toeplitz matrices,
LU factorization,
inverse of amatrix.

##### 2570 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.

##### 2569 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.

##### 2568 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.