Wyniki wyszukiwania - BazTech

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Efektywne wyznaczanie naprężeń za pomocą metody PURC z wykorzystaniem uogólnionej strategii aproksymacji pochodnych

Bołtuć A., Zieniuk E.

Modelowanie Inżynierskie

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2013

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T. 16, nr 47

41--47

PL

W pracy dokonano uogólnienia strategii aproksymacji pochodnych rozwiązań uzyskiwanych za pomocą metody PURC. Opracowano i przebadano różne warianty strategii w celu uzyskania algorytmu stabilnego oraz pozwalającego na efektywne wyznaczanie naprężeń. Jego wiarygodność i dokładność została przetestowana na przykładzie z rozwiązaniem analitycznym.

EN

The paper presents the generalization of the approximation strategy for derivatives of solutions obtained by PIES. Authors have developed and tested various options of the mentioned strategy to achieve a stable algorithm which allows for an efficient determination of stresses. Its reliability and accuracy has been tested on the example with the analytical solution.

2

Correlation between diagonal ratio and condition number of the generalized inertia matrix of a serial-chain

Shah S. V., Saha S. K.

Archive of Mechanical Engineering

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2013

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Vol. LX, nr 1

147--156

EN

The condition number of the Generalized Inertia Matrix (GIM) of a serial chain can be used to measure its ill-conditioning. However, computation of the condition number is computationally very expensive. Therefore, this paper investigates alternative means to estimate the condition number, in particular, for a very long serial-chain. For this, the diagonal elements of the GIM are examined. It is found that the ratio of the largest and smallest diagonal elements of the GIM, when scaled using an initial estimate of the condition number, closely resembles the condition number. This significantly simplifies the process of detecting ill-conditioning of the GIM, which may help to decide on stability of the system at hand.

PL

Wskaźnik uwarunkowania jest wykorzystywany jako miara złego uwarunkowania macierzy, np. dla uogólnionej macierzy bezwładności (GIM) łańcucha szeregowego. Niemniej, wyznaczenie tego współczynnika wymaga znacznego nakładu mocy obliczeniowej. Tak więc, w artykule zaproponowano sposoby alternatywne, pozwalające estymować współczynnik uwarunkowania, w szczególności dla bardzo długiego łańcucha szeregowego. W tym celu bada się elementy diagonalne uogólnionej macierzy bezwładności. Wykazano, że stosunek diagonalny (stosunek największego do najmniejszego elementu na głównej przekątnej macierzy bezwładności), przeskalowany przy użyciu estymatora początkowej wartości wskaźnika uwarunkowania, ma wartość bardzo zbliżoną do rzeczywistego wskaźnika uwarunkowania. Jego zastosowanie upraszcza w znaczący sposób ocenę złego uwarunkowania macierzy, dzięki czemu można od razu zdecydować czy układ jest stabilny.

3

Inverse problems formulated in terms of first-kind Fredholm integral equations in indirect measurements

Mroczka J., Szczuczyński D.

Metrology and Measurement Systems

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2009

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Vol. 16, nr 3

333-357

EN

Direct measurements of many properties of real-world systems are not possible. Information on these properties can only be inferred from the result of measurements of other quantities which may be measured directly. The process comprising direct measurements of certain characteristics of the object followed by inference on its sought-for properties from the directly measured characteristics based on a mathematical relation between unknown properties and measured characteristics is called indirect measurement, whereas inference is referred to as an inverse problem in indirect measurement. In general an inverse problem consists either in determining the characteristics of a system under study, driven by controlled or known exciting signals, or in reconstructing exciting signals acting on a system whose internal characteristics are known. In both cases, it is formulated in terms of a mathematical model relating unknown and measured characteristics and signals. One can distinguish continuous and discrete inverse problems, depending on whether the measured and sought-for quantities are represented by functions or by vectors (tuples), respectively. Very many nontrivial inverse problems in indirect measurements are ill-posed which means that they have no solution or the solution exists but is non-unique or unstable, i.e. very small disturbances in the measurement data result in large disturbances in the result of inference. High error amplification is referred to as ill-conditioning. Ill-posedness and ill-conditioning result from the lack of information on sought-for quantities, carried by the measurement data. Therefore, a priori knowledge about the space of admissible solutions has to be employed for solving such inverse problems. The theory of inverse problems and - in particular - effective numerical methods for solving them are of great importance for measurement science and technology; they are crucial for the development of many measurement, imaging and diagnostic techniques. Indirect measurements may be formulated using various mathematical models of the measurement object followed by a measuring system. A broad class of inverse problems, being of importance for indirect measurements, is formulated in terms of Fredholm integral equations of the first kind. These problems are ill-posed and strongly ill-conditioned after discretization. Therefore, sophisticated inverse procedures, utilizing various kinds of a priori knowledge, are applied for solving them. In this paper, theoretical and numerical aspects of inverse problem in indirect measurements are reviewed. In particular the concept of generalized solution (pseudosolution) and the notion of well-posedness is presented and analysed. The review is focused on inverse problems formulated in terms of Fredholm integral equations of the first kind: a general presentation of such problems, at the level of functional analysis, is followed by an overview of numerical aspects of their discretized versions. A concise presentation of selected groups of numerical methods, called inverse methods, for solving inverse problems is also provided.

4

Some Algorithmic Aspects of Subspace Identification With Inputs

Chiuso A., Picci G.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

55-75

EN

It has been experimentally verified that most commonly used subspace methods for identification of linear state-space systems with exogenous inputs may, in certain experimental conditions, run into ill-conditioning and lead to ambiguous results. An analysis of the critical situations has lead us to propose a new algorithmic structure which could be used either to test difficult cases and/or to implement a suitable combination of new and old algorithms presented in the literature to help fixing the problem.