QUADRANT-SEARCHING: A NEW TECHNIQUE TO REDUCE THE SEARCH SPACE OF THE INVERSE PROBLEM OF EIT USING BEM TO THE DIRECT PROBLEM

2011 ◽  
Vol 22 (08) ◽  
pp. 825-839 ◽  
Author(s):  
OLAVO H. MENIN ◽  
VANESSA ROLNIK
Keyword(s):  
Inverse Problem ◽  
Iterative Method ◽  
Direct Problem ◽  
Search Space ◽  
Initial Solution ◽  
New Technique ◽  
Time Interval ◽  
Functional Surface ◽  
Error Functional ◽  
The Error Functional

The image reconstruction using the EIT (Electrical Impedance Tomography) technique is a nonlinear and ill-posed inverse problem which demands a powerful direct or iterative method. A typical approach for solving the problem is to minimize an error functional using an iterative method. In this case, an initial solution close enough to the global minimum is mandatory to ensure the convergence to the correct minimum in an appropriate time interval. The aim of this paper is to present a new, simple and low cost technique (quadrant-searching) to reduce the search space and consequently to obtain an initial solution of the inverse problem of EIT. This technique calculates the error functional for four different contrast distributions placing a large prospective inclusion in the four quadrants of the domain. Comparing the four values of the error functional it is possible to get conclusions about the internal electric contrast. For this purpose, initially we performed tests to assess the accuracy of the BEM (Boundary Element Method) when applied to the direct problem of the EIT and to verify the behavior of error functional surface in the search space. Finally, numerical tests have been performed to verify the new technique.

Asymptotic solution of the inverse problem for restoring the modular type source in Burgers’ equation with modular advection

2020 ◽  
Vol 28 (5) ◽  
pp. 633-639
Author(s):  
Nikolay Nikolaevich Nefedov ◽  
V. T. Volkov
Keyword(s):  
Inverse Problem ◽  
Direct Problem ◽  
Burgers Equation ◽  
Type Equation ◽  
Singularly Perturbed ◽  
Time Interval ◽  
Internal Transition Layer ◽  
Internal Transition ◽  
Time Periodic ◽  
Time Periodic Solution

AbstractFor a singularly perturbed Burgers’ type equation with modular advection that has a time-periodic solution with an internal transition layer, asymptotic analysis is applied to solve the inverse problem for restoring the function of the source using known information about the observed solution of a direct problem at a given time interval (period).

Solution to Inverse Problem of Manufacturing by Surface Modification With Controllable Surface Integrity Correlated to Performance: A Case Study of Thermally Sprayed Coatings for Wear Performance

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
X. P. Zhu ◽  
P. C. Du ◽  
Y. Meng ◽  
M. K. Lei ◽  
D. M. Guo
Keyword(s):  
Inverse Problem ◽  
Surface Modification ◽  
Surface Integrity ◽  
High Performance ◽  
Surface Characteristics ◽  
Spray Angle ◽  
Functional Surface ◽  
Machining Processes ◽  
Wear Performance ◽  
Surface Features

Inverse problem of manufacturing is studied under a framework of high performance manufacturing of components with functional surface layer, where controllable generation of surface integrity is emphasized due to its pivotal role determining final performance. Surface modification techniques capable of controlling surface integrity are utilized to verify such a framework of manufacturing, by which the surface integrity desired for a high performance can be more effectively achieved as reducing the material and geometry constraints of manufacturing otherwise unobtainable during conventional machining processes. Here, thermal spraying of WC–Ni coatings is employed to coat stainless steel components for water-lubricated wear applications, on which a strategy for direct problem from process to performance is implemented with surface integrity adjustable through spray angle and inert N2 shielding. Subsequently, multiple surface integrity parameters can be evaluated to identify the major ones responsible for wear performance by elucidating the wear mechanism, involving surface features (coating porosity and WC phase retention) and surface characteristics (microhardness, elastic modulus, and toughness). The surface features predominantly determine tribological behaviors of coatings in combination with the surface characteristics that are intrinsically associated with the surface features. Consequently, the spray process with improved N2 shielding is designed according to the desired surface integrity parameters for higher wear resistance. It is demonstrated that the correlations from processes to performance could be fully understood and established via controllable surface integrity, facilitating solution to inverse problem of manufacturing, i.e., realization of a material and geometry integrated manufacturing.

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

Improving the Generalization Properties of Radial Basis Function Neural Networks

1991 ◽  
Vol 3 (4) ◽  
pp. 579-588 ◽  
Author(s):  
Chris Bishop
Keyword(s):  
Neural Networks ◽  
Radial Basis Function ◽  
Basis Function ◽  
Learning Algorithm ◽  
Error Functional ◽  
Radial Basis ◽  
The Error Functional ◽  
Network Mapping ◽  
Nonlinear Mappings

An important feature of radial basis function neural networks is the existence of a fast, linear learning algorithm in a network capable of representing complex nonlinear mappings. Satisfactory generalization in these networks requires that the network mapping be sufficiently smooth. We show that a modification to the error functional allows smoothing to be introduced explicitly without significantly affecting the speed of training. A simple example is used to demonstrate the resulting improvement in the generalization properties of the network.

scholarly journals The Problem of Determining of the Source Function and of the Leading Coefficient in the Many-dimensional Semilinear Parabolic Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 497-506
Author(s):  
Svetlana V. Polyntseva ◽  
◽  
Kira I. Spirina
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Source Function ◽  
Time Interval ◽  
Semilinear Parabolic Equation ◽  
Existence And Uniqueness Theorem ◽  
Bounded Functions ◽  
The Many ◽  
Semilinear Parabolic

We consider the problem of determining the source function and the leading coefficient in a multidimensional semilinear parabolic equation with overdetermination conditions given on two different hypersurfaces. The existence and uniqueness theorem for the classical solution of the inverse problem in the class of smooth bounded functions is proved. A condition is found for the dependence of the upper bound of the time interval, in which there is a unique solution to the inverse problem, on the input data

scholarly journals On investigation of the inverse problem for a parabolic integro-differential equation with a variable coefficient of thermal conductivity

2020 ◽  
Vol 30 (4) ◽  
pp. 572-584
Author(s):  
D.K. Durdiev ◽  
J.Z. Nuriddinov
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Variable Coefficient ◽  
Direct Problem ◽  
Local Existence ◽  
Problem Solution ◽  
Volterra Type ◽  
Integral Term ◽  
Local Existence And Uniqueness ◽  
Coefficient Of Thermal Conductivity

The inverse problem of determining a multidimensional kernel of an integral term depending on a time variable $t$ and $ (n-1)$-dimensional spatial variable $x'=\left(x_1,\ldots, x_ {n-1}\right)$ in the $n$-dimensional heat equation with a variable coefficient of thermal conductivity is investigated. The direct problem is the Cauchy problem for this equation. The integral term has the time convolution form of kernel and direct problem solution. As additional information for solving the inverse problem, the solution of the direct problem on the hyperplane $x_n = 0$ is given. At the beginning, the properties of the solution to the direct problem are studied. For this, the problem is reduced to solving an integral equation of the second kind of Volterra-type and the method of successive approximations is applied to it. Further the stated inverse problem is reduced to two auxiliary problems, in the second one of them an unknown kernel is included in an additional condition outside integral. Then the auxiliary problems are replaced by an equivalent closed system of Volterra-type integral equations with respect to unknown functions. Applying the method of contraction mappings to this system in the Hölder class of functions, we prove the main result of the article, which is a local existence and uniqueness theorem of the inverse problem solution.

scholarly journals Another point of view on proportional navigation

1998 ◽  
Vol 4 (3) ◽  
pp. 201-231
Author(s):  
E. Duflos ◽  
P. Penel ◽  
P. Vanbeeghe ◽  
P. Borne
Keyword(s):  
Inverse Problem ◽  
Direct Problem ◽  
Point Of View ◽  
Proportional Navigation ◽  
Guidance Laws ◽  
The Way

Proportional navigation is one of the most popular and one of the most used of the guidance laws. But the way it is studied is always the same: the acceleration needed to reach a known target is derived or analyzed. This way of studying guidance laws is called “the direct problem” by the authors. On the contrary, the problem considered here is to find, from the knowledge of a part of the trajectory of a maneuvering object, the target of this object. The authors call this way of studying guidance laws “the inverse problem”.

Algorithm for Detecting Multiple Partial Blockages in Liquid Pipelines by Using Inverse Transient Analysis

SPE Journal ◽  
2021 ◽  
pp. 1-29
Author(s):  
C. Zhang ◽  
J. J. Zhang ◽  
C. B. Ma ◽  
G. E. Korobkov
Keyword(s):  
Inverse Problem ◽  
Crude Oil ◽  
Direct Problem ◽  
Pressure Response ◽  
Analytical Evaluation ◽  
Long Distance ◽  
Local Flow ◽  
Measuring Point ◽  
Detection Techniques ◽  
Oil Pipelines

Summary Partial blockages form on the inner wall of the crude-oil pipelines as a result of asphaltene precipitation, scale deposition, and so forth. If not controlled and rehabilitated periodically, these partial blockages can have a serious adverse effect on the efficiency, economy, and safety of the operation of the pipeline. Before each rehabilitation operation, the detection of the local flow-condition deterioration (change in diameter) is necessary for efficiency and economy considerations, especially for long-distance subsea crude-oil pipelines. Most conventional detection techniques require the installment of detecting devices along the pipeline. However, they are economically expensive and even technically impossible for pipelines in operation. The present work focuses on an economically efficient technique that can realize remote nonintrusive measurement (i.e., the pressure-wave technique). The purpose of our research is to develop a method for calibrating multiple irregular partial blockages inside the liquid pipe by using the pressure response in the time domain at certain measuring points along the pipe under the transient state. The method involves the direct problem and the inverse problem. The direct problem is the simulation of the transient flow in the liquid pipe with single or multiple partial blockages. A second-order direct problem solver is developed in the framework of the Godunov-typefinite-volume method (FVM). The inverse problem is to determine the partial-blockage distribution by using the pressure response at the measuring point under transient conditions. Our algorithm to solve the inverse problem comprises analytical evaluation and optimization. The analytical evaluation provides a reliable search space for the following optimization procedure, and thus effectively alleviates the local optimum problem. Numerical results demonstrate the efficiency and accuracy of proposed methods for solving the direct and inverse problems.

Analysis and Optimization of Diagnostic Procedures for Aviation Radioelectronic Equipment

2021 ◽  
pp. 948-972
Author(s):  
Maksym Zaliskyi ◽  
Oleksandr Solomentsev ◽  
Ivan Yashanov
Keyword(s):  
Inverse Problem ◽  
Probability Density Function ◽  
Health Monitoring ◽  
Direct Problem ◽  
Diagnostic Procedures ◽  
Operation System ◽  
Equipment Operation ◽  
Efficiency Estimation ◽  
Function Calculation ◽  
Simulation Results

In this chapter, the authors present the questions of aviation radioelectronic equipment operation. The structure of operation system is considered based on processes approach with adaptable control principles usage. Operation system contains processes of diagnostics and health monitoring. The authors consider the direct problem of efficiency estimation for diagnostics process, and main attention is paid to probability density function calculation for diagnostics duration. Simulation results were used for adequacy testing of these calculations. The authors also take into account the possibility of first and second kind errors presence. The inverse problem for diagnostics is defined and solved for mathematical expectation of repair time. In general case, the inverse problem can be solved for seven options of optimization.

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