Analysis of a semigroup approach in the inverse problem of identifying an unknown parameters

2011 ◽  
Vol 218 (3) ◽  
pp. 965-969 ◽  
Author(s):  
Ebru Ozbilge ◽  
Ali Demir
Keyword(s):  
Inverse Problem ◽  
Unknown Parameters ◽  
Semigroup Approach

Computer Simulation for Active Control of Vibration in Beam Structures

1995 ◽  
Author(s):  
Masa. Tanaka ◽  
T. Matsumoto ◽  
L. Huang
Keyword(s):  
Inverse Problem ◽  
Active Control ◽  
Inverse Analysis ◽  
Taylor Series Expansion ◽  
Integral Equation Method ◽  
Unknown Parameters ◽  
Bending Vibration ◽  
Linear System Of Equations ◽  
Elastic Beams ◽  
The Laplace Transform

Abstract This paper is concerned with an inverse problem of the active control of non-steady dynamic vibration in elastic beams. A simulation technique based on the boundary element method and the extended Kalman filter or a new filter theory is successfully applied to the inverse problem. The Laplace-transform integral equation method is used for the solution of dynamic bending vibration in elastic beams. Through a Taylor series expansion, the linear system of equations is derived for modification of the unknown parameters, and it is solved iteratively so that an appropriate norm is minimized. The usefulness of the proposed method of inverse analysis is demonstrated through numerical computation of a few examples.

Lipschitz stability for a semi-linear inverse stochastic transport problem

2020 ◽  
Vol 28 (2) ◽  
pp. 185-193
Author(s):  
Zhongqi Yin
Keyword(s):  
Inverse Problem ◽  
Main Tool ◽  
Terminal State ◽  
Lipschitz Stability ◽  
Unknown Parameters ◽  
Initial Displacement ◽  
Stochastic Transport ◽  
Random Term ◽  
Global Carleman Estimate ◽  
Stochastic Transport Equation

AbstractThis paper is addressed to a semi-linear stochastic transport equation with three unknown parameters. It is proved that the initial displacement, the terminal state and the random term in diffusion are uniquely determined by the state on partial boundary and a Lipschitz stability of the inverse problem is established. The main tool we employ is a global Carleman estimate for stochastic transport equations.

scholarly journals A Nonlinear Solute Transport Model and Data Reconstruction with Parameter Determination in an Undisturbed Soil-Column Experiment

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Gongsheng Li ◽  
De Yao ◽  
Yongzai Wang ◽  
Xianzheng Jia
Keyword(s):  
Inverse Problem ◽  
Solute Transport ◽  
Transport Model ◽  
Soil Column ◽  
Parameter Determination ◽  
Nonlinear Transport ◽  
Inversion Algorithm ◽  
Unknown Parameters ◽  
Undisturbed Soil ◽  
Optimal Perturbation

A real undisturbed soil-column infiltrating experiment in Zibo, Shandong, China, is investigated, and a nonlinear transport model for a solute ion penetrating through the column is put forward by using nonlinear Freundlich's adsorption isotherm. Since Freundlich's exponent and adsorption coefficient and source/sink terms in the model cannot be measured directly, an inverse problem of determining these parameters is encountered based on additional breakthrough data. Furthermore, an optimal perturbation regularization algorithm is introduced to determine the unknown parameters simultaneously. Numerical simulations are carried out and then the inversion algorithm is applied to solve the real inverse problem and reconstruct the measured data successfully. The computational results show that the nonlinear advection-dispersion equation discussed in this paper can be utilized by hydrogeologists to research solute transport behaviors with nonlinear adsorption in porous medium.

scholarly journals Inverse problem of the Holling-Tanner model and its solution

BIOMATH ◽  
2018 ◽  
Vol 7 (2) ◽  
pp. 1812057
Author(s):  
Adejimi Adesola Adeniji ◽  
Igor Fedotov ◽  
Michael Y. Shatalov
Keyword(s):  
Inverse Problem ◽  
Nonlinear System ◽  
Integration Method ◽  
Complete Information ◽  
Time Interval ◽  
Problem Solution ◽  
Finite Time Interval ◽  
Nonlinear System Of Equations ◽  
Unknown Parameters ◽  
The Given

In this paper we undertake to consider the inverse problem of parameter identification of nonlinear system of ordinary differential equations for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval. In this model the equations are nonlinearly dependent on the unknown parameters. By means of the proposed transformation the obtained equations become linearly dependent on new parameters functionally dependent on the original ones. This simplification is achieved by the fact that the new set of parameters becomes dependent and the corresponding constraint between the parameters is nonlinear. If the conventional approach based on introduction of the Lagrange multiplier is used this circumstance will result in a nonlinear system of equations. A novel algorithm of the problem solution is proposed in which only one nonlinear equation instead of the system of six nonlinear equations has to be solved. Differentiation and integration methods of the problem solution are implemented and it is shown that the integration method produces more accurate results and uses less number of points on the given time interval.

Prediction of Microstructure and Mechanical Properties of Weld Metal in Hybrid Laser-Arc Welding

2015 ◽  
Vol 1120-1121 ◽  
pp. 1292-1296 ◽  
Author(s):  
Victor A. Karkhin ◽  
Pavel N. Homich ◽  
Sergei Yu. Ivanov ◽  
Vesselin Michailov ◽  
Oleg V. Panchenko
Keyword(s):  
Mechanical Properties ◽  
Inverse Problem ◽  
Weld Metal ◽  
Arc Welding ◽  
Data Input ◽  
Unknown Parameters ◽  
Hybrid Laser Arc Welding ◽  
Calculation Technique ◽  
Temperature Problem ◽  
Microstructure And Mechanical Properties

Calculation technique in order to reconstruct the 3D temperature field and predict the microstructure and mechanical properties of the weld metal in hybrid laser-arc welding is developed. The technique is based on the solution of the direct 3D temperature problem by a function-analytical method, the numerical solution of the inverse problem for the unknown parameters of a volume heat source, the employment of the known models for prediction of the microstructure and mechanical properties. The proposed calculation technique makes it possible to reduce considerably the total time for data input and solution. It is demonstrated with an example of butt hybrid laser-arc welding.

Determination of uncertain parameters of a two-axis gimbal and motion tracking via Fuzzy logic control approach

2020 ◽  
Vol 39 (5) ◽  
pp. 6565-6577
Author(s):  
Roya Jahanandish ◽  
Amir Khosravifard ◽  
Ramin Vatankhah
Keyword(s):  
Inverse Problem ◽  
Fuzzy Control ◽  
Measurement Errors ◽  
Motion Tracking ◽  
Controller Design ◽  
Uncertain Parameters ◽  
Control Performance ◽  
Unknown Parameters ◽  
Control Approach ◽  
Control Scheme

This paper proposes a new method to improve fuzzy control performance accuracy in the stabilization of the two-axis gimbal system. To this end, due to the fact that the knowledge of the accurate behavior of the system plays a substantial role in fuzzy control performance, all the uncertain parameters of the dynamic model such as friction, mass imbalance and moments of inertia are estimated prior to the controller design and without imposing any computational burden on the control scheme. To estimate the uncertainties and disturbances which exist in the dynamic equations, an identification process formulated as an inverse problem is utilized, and the Gauss– Newton method is adopted for the optimization process. Regarding the severe sensitivity of inverse problems to measurement errors, this undesirable effect is reduced by using a proper smoothing technique. In order to increase the accuracy of the final results, a novel procedure for calculation of the sensitivity coefficients of the inverse problem is proposed. This procedure is based on the direct differentiation of the governing equations with respect to the unknown parameters. At the end, simulation results are presented to confirm the effectiveness of the proposed scheme.

OBJECTIVE FUNCTIONS FOR OCEAN ACOUSTIC INVERSION DERIVED BY LIKELIHOOD METHODS

2000 ◽  
Vol 08 (02) ◽  
pp. 259-270 ◽  
Author(s):  
CHRISTOPH F. MECKLENBRÄUKER ◽  
PETER GERSTOFT
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Likelihood Function ◽  
Point Of View ◽  
Single Frequency ◽  
Posteriori Probability ◽  
A Posteriori ◽  
Objective Functions ◽  
Unknown Parameters ◽  
A Posteriori Probability

Selection of a suitable objective function is an integral part of the inverse problem, and poor selection can have a strong influence on the inverse result. Objective functions are here derived for many practical occasions such as for single frequency and broadband, with and without knowledge of source strength, and with and without the received signal phase. These objective functions are all derived from a unified approach based on maximum likelihood and additive Gaussian noise models. The assumptions for the objective function are thus clear and the resulting estimator has good properties. From a Bayesian point of view, the solution to the inverse problem is the a posteriori probability distribution of the unknown parameters, which can be found from the likelihood function. Thus using objective functions based on likelihood functions facilitates computing the a posteriori distributions.

scholarly journals Solution of the inverse radiation problem for anisotropically scattering medium using the control volume finite element method

2010 ◽  
Vol 14 (2) ◽  
pp. 373-382 ◽  
Author(s):  
Hajer Grissa ◽  
Faouzi Askri ◽  
Fethi Albouchi ◽  
Nasrrallah Ben
Keyword(s):  
Finite Element Method ◽  
Inverse Problem ◽  
Finite Element ◽  
Control Volume ◽  
Measured Temperature ◽  
Scattering Medium ◽  
Unknown Parameters ◽  
Radiation Problem ◽  
Control Volume Finite Element ◽  
Element Method

In this paper, an inverse analysis is performed for the estimation of radiative parameters from the measured temperature profile in an absorbing, emitting, and anisotropically scattering medium. The control volume finite element method is employed to solve the direct problem in a 3-D rectangular furnace. The inverse problem is formulated as an optimization problem between the calculated and the experimental data and the Levenberg-Marquardt method is used for its solution. The sensitivity analysis is made in order to determine whether it is possible to identify the parameters. Also, the effects of angular and spatial grid numbers and the initial guesses on the accuracy of the inverse problem are investigated. This method combination, which is applied for the first time to solve 3-D inverse radiation problem, has been found to accurately predict the unknown parameters.

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