Wyniki wyszukiwania - Biblioteka Nauki

1

Property C for ODE and applications to an inverse problem for a heat equation

100%

Ramm A. G.

|

2009

|

tom Vol. 57, no 3-4

243-249

EN

Let lj := -d2 /dx2 + k2qj(x), k = const > 0, j = 1,2, 0 < ess inf qj(x) ≤ ess sup qj(x) < ∞. Suppose that (∗) [integral of, between limits 1 and 0] p(x)u1(x, k)u2(x, k) dx = 0 for all k > 0, where p is an arbitrary fixed bounded piecewise-analytic function on [0, 1], which changes sign finitely many times, and uj solves the problem ljuj = 0, 0 ≤ x ≤ 1, u'j(0, k) = 0, uj(0, k) = 1. It is proved that (∗) implies p = 0. This result is applied to an inverse problem for a heat equation.

2

Identification of macro and micro parameters in solidification model

100%

Mochnacki B. , Majchrzak E.

|

2007

|

tom Vol. 55, nr 1

107-113

EN

In the paper the thermal processes proceeding in the solidifying metal are analyzed. The basic energy equation determining the course of solidification contains the component (source function) controlling the phase change. This component is proportional to the solidi-fication rate afs/at(fs E [0,1], is a temporary and lo cal volumetric fraction of solid state). The value of fs can be found, among others, on the basic of laws determining the nucleation and nuclei growth. This approach leads to the so called micro/macro models (the second generation models). The capacity of internal heat source appearing in the equation concerning the macro scale (solidification and cooling of domain considered) results from the phenomena proceeding in the micro scale (nuclei growth). The function fs can be defined as a product of nuclei density N and single grain volume V (a linear model of crystallization) and this approach is applied in the paper presented. The problem discussed consists in the simultaneous identification of two parameters determining a course of solidification. In particular it is assumed that nuclei density N (micro scale) and volumetric specific heat of metal (macro scale) are unknown. Formulated in this way inverse problem is solved using the least squares criterion and gradient methods. The additional information which allows to identify the unknown parameters results from knowledge of cooling curves at the selected set of points from solidifying metal domain. On the stage of numerical realization the boundary element method is used. In the final part of the paper the examples of computations are presented.

3

Distributed algorithms and hierarchic optimization for solving a parameter inverse problem

100%

Telega H.

|

1998

|

tom z. 8

7-28

EN

In this paper we present some numerical algorithms for the identification of parameters in inverse problems. We are motivated by the problem of identification of physical parameters in the Swartzendruber formula which appears in the mathematical model of the prelinear filtration of ground water. The parameter inverse problem is formulated as an appropriate control one. An application of standard nonlinear programming methods for solving the problem is presented and obstacles of this approach are pointed out. We propose three strategies in order to deal with many local minima and sensitivity of the algorithms on starting points. The first one is to improve local minimum search in large parts of the domain and the third one is to fasten computations using parallel and distributed techniques. Two algorithms that correspond to these strategies are presented: the hierarchic optimization algorithm and the algorithm of simple parallel search with distribution of computations (multiple starting point parallel optimization). Some modifications to these algorithms are also proposed. The results of the application of the described algorithms to a tested problem are presented. The The computational tests are based on real data obtained from an experimental range.

4

Inverse problems in the thermal theory of foundry processes

100%

Mochnacki B. , Majchrzak E. , Szopa R. , Suchy J. S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

|

2006

|

tom Vol. 5, nr 1

154-169

EN

In the paper the applications of inverse problems in the thermal theory of foundry processes are discussed. Both the macro models of solidification (in particular the fixed domain approach) and macro/micro ones are considered. The information necessary in order to determine the unknown parameters of the process results from the knowledge of cooling (heating) curves at the selected set of points from casting and/or mould subdomains. The identified values can correspond to the thermophysical parameters of casting and mould, parameters appearing in boundary conditions and initial temperatures. In the paper the newest results obtained in this scope by the authors are presented. The examples of numerical solutions are also shown.

5

An agent-oriented hierarchic strategy for solving inverse problems

88%

Smołka M. , Schaefer R. , Paszyński M. , Pardo D. , Álvarez-Aramberri J.

International Journal of Applied Mathematics and Computer Science

|

2015

|

tom 25

|

nr 3

483-498

EN

The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically adjusted for each inverse search step. The computational cost is further decreased by the strategy employed for solution inter-processing and fitness deterioration. The HMS efficiency is compared with the results of a standard evolutionary technique, as well as with the multi-start strategy on benchmarks that exhibit typical inverse problems' difficulties. Finally, an HMS application to a real-life engineering problem leading to the identification of oil deposits by inverting magnetotelluric measurements is presented. The HMS applicability to the inversion of magnetotelluric data is also mathematically verified.

6

Metoda analityczno-numeryczna rozwiązywania zagadnienia odwrotnego dla równania przewodnictwa ciepła

75%

Ciałkowski M. , Maćkiewicz A. , Kołodziej J. , Frąckowiak A.

|

2011

|

tom Nr 64

23-39

PL

W artykule rozważano rozwiązanie zagadnienia odwrotnego dla liniowego niestacjonarnego równania przewodnictwa ciepła. Równanie różniczkowe cząstkowe zdyskretyzowano względem zmiennej przestrzennej i otrzymano układ równań różniczkowych zwyczajnych I rzędu, którego rozwiązanie ma postać splotową. Wyniki numeryczne rozwiązania zagadnienia odwrotnego potwierdzają dużą skuteczność zaproponowanej metody.

EN

The solution of the inverse problem for linear transient heat transfer problem is considered in this paper. The partial differential equation was descretized with respect to the space variable and a system of ordinary differential equations of first order was obtained which solution has weave form. The numerical results of the solution of the inverse problem confirm the excellent effectiveness of the proposed method.

7

Numerical estimation of temperature-dependent thermophysical parameters by means of the inverse method - 2D approach

75%

Zmywaczyk J.

|

2006

|

tom Vol. 27, no. 2

37-54

EN

A modified Newton-Raphson method which has been proposed by Ching-yu Yang [3] to determine the temperature-dependent thermal conductivity and heat capacity from temperature measured at boundaries in a medium (ID case) has now been extended to estimate simultaneously the temperature dependent thermal conductivity k[r](T), k[x](T) and specific heat c[p](T) of an orthotropic material. It has been found that inverse solution of the problem was satisfactory if the degree of polynomials used to estimate the unknown parameters was not greater than three. In addition to this, a D-optimality criterion given by Beck [2] was utilised to determine the finał time of experiment t[f].

8

Simultaneous estimation of the emissivity and the temperature-dependent thermal conductivity and specific heat in a semitransparent plane layer by an inverse method

75%

Zmywaczyk J.

|

2006

|

tom Vol. 27, no. 3

39-62

EN

A model of transient ID conduction-radiation heat transfer in absorbing, emitting and isotropically scattering grey medium with boundary conditions of the third kind for temperature has been considered in this paper. It has been assumed that boundaries of the plane layer of thickness L were of diffusive character. To solve the boundary-value problem a finite difference method (FDM) together with a two-flux method (TFM) based on the Schuster-Schwarzschild approximation was used. In the inverse formulation of the problem it has been accepted as the unknown quantities the total panchromatic hemispherical emissivity [epsilon][1] of the sample surface exposed to external incident radiation and the temperature-dependent thermal conductivity k(T) and specific heat c[p](T) of the sample material. The coefficient inverse heat transfer problem (CIHTP) was solved iteratively using the Levenberg-Marquardt algorithm to find a minimum of a mean square functional J involving residuals between the measured and calculated temperatures. It has been found that the final time of measurements t[f] should be correlated with the disturbance magnitude ZAB so as to reduce uncertainty of the estimated parameters.

9

Numerical estimation of the temperature-dependent thermophysical parameters using hybrid method of differential evolution and the Levenberg-Marquardt algorithm

75%

Zmywaczyk J.

|

2007

|

tom Vol. 28, no. 1

89-106

EN

A hybrid method of estimation the temperature-dependent thermophysical parameters is presented. The method of differential evolution (DE) developed by Storn and Price [1] is used at the beginning of calculations to find an initial set of coefficients which represent the unknown temperature depending thermophysical parameters in a priori given base of functions. Then a deterministic method based on a modified Newton-Raphson approach and the Levenberg-Marquardt algorithm is applied to find a minimum of the mean square functional J(u[^T]) involving the measured and the model temperature response of the system. The proposed hybrid method turned out to be very effective and efficient tool for solving the coefficient inverse heat conduction problem (CIHCP) of simultaneous estimation of the temperature-dependent thermal conductivity k[r](T), k[z](T) and the specific heat C[p](T) of an orthotropic material.

10

Continuous relaxation spectrum - its advantages and methods of calculation

75%

Malkin A. Y.

|

2006

|

tom Vol. 11, no 2

235-243

EN

Some advantages in treating experimental data on viscoelastic properties of polymeric materials in terms of a continuous spectrum instead of generally used fitting these data by means of a discrete relaxation times spectrum were demonstrated. The proposed continuous spectrum of a power-like type contains only three adjustable parameters. They can be found from integral characteristics of viscoelastic material, such as instantaneous modules, Newtonian viscosity, areas under shear and normal stress relaxation curves. The proposed continuous spectrum correctly reflects main peculiarities of viscoelastic properties of real polymeric materials in a wide frequency range.

11

An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications

75%

Borodich F. M. , Galanov B. A. , Gorb S. N. , Prostov M. Y. , Prostov Y. I. , Suarez-Alvarez M. M.

Nanoscale Systems: Mathematical Modeling, Theory and Applications

|

2012

|

tom 1

80-92

EN

We show how the values of the effective elastic modulus of contacting solids and the work of adhesion, that are the crucial material parameters for application of theories of adhesive contact to nanomechanics, may be quantified from a single test using a non-direct approach (the Borodich-Galanov (BG) method). Usually these characteristics are not determined from the same test, e.g. often sharp pyramidal indenters are used to determine the elastic modulus from a nanoindentation test, while the work of adhesion is determined from a different test by the direct measurements of pull-off force of a sphere. The latter measurements can be greatly affected by roughness of contacting solids and they are unstable due to instability of the load-displacement diagrams at tension. The BG method is based on an inverse analysis of a stable region of the force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. Various aspects related to solving the inverse problem for adhesive contact and experimental evaluation of material properties for nanomechanics applications are discussed. It is shown that the BG method is simple and robust. Some theoretical aspects of the method are discussed and the BG method is developed by application of statistical approaches to experimental data. The advantages of the BG method are demonstrated by its application to soft polymer (polyvinylsiloxane) samples.

12

Sensitivity analysis in geometrical inverse problems of vibrating systems

75%

Burczyński T. , Nowakowski M.

|

1998

|

tom z. 6

53-58

EN

This paper deals with the application of varialional-matorial derivative approach to sensitivity analysis of an objective function used in geometrical inverse problems bused on knowledge of eigenfrequencies. The relevant direct eigenvalue problem is solved using BEM. The main motivation of this paper is to explore the. possibility of the application of measured eigenfrequencies in detection of internal voids. Numerical results of sensitivity analysis and identification of circular void are presented.

PL

W pracy przedstawiono zastosowanie metody pochodnej materialnej w analizie wrażliwości funkcji celu, umytej do geometrycznego zagadnienia odwrotnego, bazującego na znajomości częstości drgań własnych układu, Bezpośrednie zagadnienie własne rozwiązano przy zastosowaniu MED. Główną motywacją pracy jest zbadanie możliwości zastosowania częstości drgań w wykrywaniu wewnętrznych otworów, Przedstawiono wyniki numeryczne analizy wrażliwości oraz rezultat identyfikacji otworu kołowego.

13

Zastosowanie metody hybrydowej do rozwiązania zagadnienia odwrotnego wykorzystanego w wyznaczaniu kierunkowch właściwości cieplnych ciał ortotropowych - optymalizacja eksperymentu

75%

Kucypera S.

|

2009

|

tom T. 7, nr 38

109-114

PL

Współcześnie produkowane materiały anizotropowe są najczęściej kompozytami wielowarstwowymi o periodycznie powtarzalnej strukturze, która pozwala traktować je jako jednorodne materiały ortotropowe o średnich parametrach termofizycznych. Wartości tych parametrów zależą od wielu czynników, np.: właściwości cieplnych włókien nośnych i lepiszczy użytych do ich połączenia, co uniemożliwia wyznaczanie ich metodami teoretycznymi. Dlatego w pracy do wyznaczania wielu parametrów termofizycznych w trakcie wykonywania jednego eksperymentu zaproponowano rozwiązanie odwrotnego zagadnienia przewodzenia ciepła metodą hybrydową. Przedstawiono wybrane wyniki badań.

EN

Contemporarily produced anisotropic materials are the most often multi-layered composites with a periodical repeatable structure, which permits to treat it as homogeneous orthotropic materials with average thermophysical parameters. The value of those parameters depend on many factors, for example: the property of thermal bearing fibres and the part of adhesives used to their connection. In described situation it is not possible to determine those parameters by theoretical methods. Therefore in the paper for determination many thermophysical parameters during executing one experiment was proposed the solution of inverse heat conduction problem by the hybrid method. The selected results of described analysis have been presented.

14

Modelowanie problemów odwrotnych w zagadnieniach transportu szynowego

75%

Rydygier E. , Strzyżakowski Z.

|

2011

|

tom nr 6

PL

W pracy przedstawiono wyniki badań nad identyfikacją źródeł pola w przypadku stałej funkcji źródłowej w zagadnieniach transportu szynowego. Jako zagadnienie testowe przedstawiono cieplny problem odwrotny polegający na wyznaczeniu stałej funkcji źródłowej w przypadku rezystancyjnego spiekania pręta wolframowego. Następnie zbadano zagadnienie skręcania szyny kolejowej przy wymuszeniach siłowych. Przedstawiono dokładnie sposób opisu zagadnienia odkształcenia przez skręcanie za pomocą równania ekwiwalentnego z użyciem funkcji pomocniczej. Wykazano analogię między odwrotnym problemem cieplnym dla stałej funkcji źródłowej i zagadnieniem wytrzymałościowym.

EN

In this paper there are presented the results of investigations of the field's sources in transport issues in the instance of constant sources' function. The thermal inverse problem of resistance sintering of tungsten bar is presented as a testing issue for an evaluation of a constant sources' function. Next the tension in a rail due its torsion has been investigated. The descripton of this problem is presented by means of equivalent equations with the auxiliary function. The analogy between the thermal inverse problem for constant sources' function and the problem of elasticy of materials is indicated.

15

Inverse problems in electromagnetism

63%

Marinova I.

|

2007

|

tom R. 83, nr 7-8

148-51

EN

In this paper the inverse problems in electromagnetism are considered. An inverse approach is developed using field theory, high visualization technologies, image processing and data manipulation. This approach is applied for defects and cracks detection during nondestructive testing of the objects and structures with reliable applications. The virtual magnetic microscope is design for analysis of field distributions. The developed approach characterizes with effectiveness, simplicity and applicability for solving different inverse problems in electromagnetism.

PL

Artykuł przedstawia problematykę zagadnień odwrotnych w elektromagnetyzmie. Podejście odwrotne rozwijane jest za pomocą teorii pola. technik wizualizacyjnych, przetwarzania obrazu i obróbki danych. Prezentowane podejście stosuje się w detekcji pęknięć i defektów w testowaniu urządzeń pracujących w odpowiedzialnych zastosowaniach. Do analizy rozkładu pola elektromagnetycznego skonstruowano wirtualny mikroskop. Zaprezentowane podejście charakteryzuje się dużą efektywnością, prostotą i możliwością zastosowania w rozwiązywaniu różnych problemów odwrotnych w elektromagnetyzmie.

16

Numeryczno-eksperymentalna metoda wyznaczania lokalnego obciążenia cieplnego ścian komór paleniskowych kotła

63%

Ludowski P.

|

2011

|

tom R. 108, z. 5-M

21-32

PL

Przedstawiono nową metodę identyfikacji lokalnych warunków pracy rur ekranowych kotłów parowych. Obok lokalnego obciążenia cieplnego ściany komory paleniskowej kotła wyznaczany jest współczynnik wnikania ciepła na wewnętrznej powierzchni rury ekranowej oraz temperatura czynnika wewnątrz rury. Miernik stanowi krótki odcinek mimośrodowej rury, w którym od strony paleniska zamontowane są 2 lub 4 termoelementy w pobliżu zewnętrznej i wewnętrznej powierzchni rury. Nieliniowe zagadnienie najmniejszych kwadratów rozwiązane zostało metodą Levenberga-Marquardta. Rozkład temperatury w przekroju poprzecznym miernika wyznaczany jest w każdym kroku iteracyjnym za pomocą oprogramowania ANSYS/CFX.

EN

The tubular type instrument (flux tube) was developed to identify boundary conditions in water wall tubes of steam boilers. The meter is constructed from a short length of eccentric tube containing two or four thermocouples on the fire side below the inner and outer surfaces of the tube. The fifth thermocouple is located at the rear of the tube on the casing side of the water-wall tube. The non-linear least squares problem is solved numerically using the Levenberg-Marquardt method. Temperature distribution in the cross section of the flux tube was calculated at each iteration step using ANSYS/CFX software.

17

Identification of alloy substitute thermal capacity (broken line model)

63%

Mochnacki B. , Szopa R.

|

2011

|

tom Vol. 11, iss. 4

93-96

EN

The theoretical aspects and also the method of inverse problem solution connected with the identification of alloy substitute thermal capacity are discussed. The substitute thermal capacity (STC) appears when the problem of alloys solidification is described by the energy equation corresponding to the one domain method. The course of STC is assumed in the form of broken line and an alloy latent heat and a certain temperature TM from the interval [TS ,TL] (solidus and liquidus border temperatures) determine the form of function describing the parameter discussed. At the stage of inverse problem solution the basic variant of gradient method is used. The example concerns the estimation of cast carbon steel STC. The computations concerning the numerical solution of direct problem and sensitivity one base on the explicit scheme of finite difference method. In the final part of the paper the results of identification process are shown.

18

Identification of boundary heat flux on the continuous casting surface

63%

Majchrzak E. , Mochnacki B. , Dziewoński M. , Jasiński M.

|

2008

|

tom Vol. 8, iss. 4

105-110

EN

In the paper the numerical solution of the inverse problem consisting in the identification of the heat flux on the continuous casting surface is presented. The additional information results from the measured surface or interior temperature histories. In particular the sequential function specification method using future time steps is applied. On the stage of numerical computations the 1st scheme of the boundary element method for parabolic equations is used. Because the problem is strongly non-linear the additional procedure 'linearizing' the task discussed is introduced. This procedure is called the artificial heat source method. In the final part of the paper the examples of computations are shown.

19

Wykorzystanie zmian w charakterystykach dynamicznych do lokalizacji obciążenia wywołującego uplastycznienie belki

63%

Miller B. , Ziemiański L.

|

2010

|

tom R. 107, z. 3-B

143-151

PL

W artykule przedstawiono lokalizację obciążenia wywołującego uplastycznienie w konstrukcji belkowej na podstawie zmian charakterystyk dynamicznych. Porównując charakterystyki dynamiczne konstrukcji wyjściowej z pomierzonymi na konstrukcji obciążonej dodatkowym, znanym obciążeniem kontrolnym, otrzymano informacje pozwalające zlokalizować obciążenie.

EN

The paper presents the localization of the load casing yielding in a beam structure on the basis of changes of dynamic parameters. The comparison of dynamic characteristics of investigated structure and the structure loaded with an additional, known load gives the information necessary to the identification of the load casing yielding.

20

Identyfikacja strumienia ciepła w warstwie płaskiej - rozwiązanie zagadnienia odwrotnego z wykorzystaniem różnych wariantów metody funkcji Trefftza

63%

Maciąg A. , Pawińska A.

|

2011

|

tom Nr 16

119-138

PL

W artykule wykorzystano funkcje Trefftza do rozwiązano jednowymiarowego, prostego i odwrotnego zagadnienia identyfikacji strumienia ciepła. Zaproponowano dobór punktów pomiarowych temperatury względem czasu w węzłach Czebyszewa. Porównano to podejście z wynikami uzyskanymi dla stałego kroku czasowego. W zagadnieniu odwrotnym testowano podejście globalne (cały obszar czasowo - przestrzenny) oraz bezwęzłową metodę elementów skończonych (sub-structuring) z bazowymi funkcjami Trefftza porównując uzyskane wyniki. Również w tych metodach zastosowano dwa sposoby doboru punktów pomiarowych względem czasu. Zbadano wrażliwość metody na losowe zaburzenia wartości pomiarowych.

EN

In this paper a one-dimensional direct and inverse problem was solved. In the direct problem an influence of different temperature measurements locations on the flux estimation error was checked. Two methods of internal responses simulation were presented: for the constant time interval and in Chebyshev nodes. Comparison of substructuring and Trefftz functions for x e (0,1) was done in the inverse problem. In both methods two ways of choosing temperature measurements locations was shown.