Mathematical Imbalance Determination From Vibrational Measurements and Industrial Applications

2008 ◽  
Author(s):  
Jenny Niebsch ◽  
Ronny Ramlau
Keyword(s):  
Inverse Problem ◽  
Direct Problem ◽  
Industrial Applications ◽  
Rotating Machinery ◽  
Regularization Techniques ◽  
Ill Posed ◽  
Linear And Nonlinear ◽  
Nonlinear Nature

The paper focuses on the identification of imbalances from vibrational measurements in rotating machinery and its application to industrial problems. Since it is an ill-posed inverse problem the reconstruction is based on regularization techniques. To handle the direct problem, a model of the rotor under consideration has to be provided. We have employed the imbalance reconstruction principle to several industrial applications of linear and nonlinear nature.

scholarly journals Bayesian Reconstruction through Adaptive Image Notion

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 21
Author(s):  
Fabrizia Guglielmetti ◽  
Eric Villard ◽  
Ed Fomalont
Keyword(s):  
Inverse Problem ◽  
Image Plane ◽  
Source Distribution ◽  
Bayesian Probability ◽  
Model Parameters ◽  
Uncertain Information ◽  
Source Detection ◽  
Component Mixture ◽  
Ill Posed ◽  
Image Planes

A stable and unique solution to the ill-posed inverse problem in radio synthesis image analysis is sought employing Bayesian probability theory combined with a probabilistic two-component mixture model. The solution of the ill-posed inverse problem is given by inferring the values of model parameters defined to describe completely the physical system arised by the data. The analysed data are calibrated visibilities, Fourier transformed from the ( u , v ) to image planes. Adaptive splines are explored to model the cumbersome background model corrupted by the largely varying dirty beam in the image plane. The de-convolution process of the dirty image from the dirty beam is tackled in probability space. Probability maps in source detection at several resolution values quantify the acquired knowledge on the celestial source distribution from a given state of information. The information available are data constrains, prior knowledge and uncertain information. The novel algorithm has the aim to provide an alternative imaging task for the use of the Atacama Large Millimeter/Submillimeter Array (ALMA) in support of the widely used Common Astronomy Software Applications (CASA) enhancing the capabilities in source detection.

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.

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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