Wyniki wyszukiwania - BazTech

1

An efficient method for calculating system non-probabilistic reliability index

Liu Hui, Xiao Ning-Cong

Eksploatacja i Niezawodność

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2021

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Vol. 23, no. 3

498--504

EN

Collecting enough samples is difficult in real applications. Several interval-based non-probabilistic reliability methods have been reported. The key of these methods is to estimate system non-probabilistic reliability index. In this paper, a new method is proposed to calculate system non-probabilistic reliability index. Kriging model is used to replace time-consuming simulations, and the efficient global optimization is used to determine the new training samples. A refinement learning function is proposed to determine the best component (or performance function) during the iterative process. The proposed refinement learning function has considered two important factors: (1) the contributions of components to system nonprobabilistic reliability index, and (2) the accuracy of the Kriging model at current iteration. Two stopping criteria are given to terminate the algorithm. The system non-probabilistic index is finally calculated based on the Kriging model and Monte Carlo simulation. Two numerical examples are given to show the applicability of the proposed method.

2

On the domain of implicit functions in a projective limit setting without additional norm estimates

Magnot Jean-Pierre

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

112--120

EN

We examine how implicit functions on ILB-Fréchet spaces can be obtained without metric or norm estimates which are classically assumed. We obtain implicit functions defined on a domain D which is not necessarily open, but which contains the unit open ball of a Banach space. The corresponding inverse function theorem is obtained, and we finish with an open question on the adequate (generalized) notion of differentiation, needed for the corresponding version of the Fröbenius theorem.

3

Spadki podciśnienia w długim przewodzie mlecznym aparatu udojowego obliczane na podstawie uproszczonego równania Bernoulliego

Majkowska M.

Problemy Inżynierii Rolniczej

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2007

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R. 15, nr 2

77-86

PL

W pracach A. Kupczyka został przedstawiony model matematyczny spadku podciśnienia w długim przewodzie mlecznym [Kupczyk 1999; Iwaszko i in. 1996]. Spadek podciśnienia jest opisany równaniem Bernoulliego na wysokość straconą. Model ten jest nieliniowy, w postaci funkcji uwikłanej. Okazuje się, że ciśnienie w zakresie wartości występujących w aparatach udojowych, w długim przewodzie mlecznym praktycznie nie wpływa na prędkość wznoszenia pęcherza w długim przewodzie mlecznym. Równanie Bernoulliego może być uproszczone do wielomianu czwartego stopnia względem spadku podciśnienia. Przedstawiono model spadków podciśnienia w długim przewodzie mlecznym w postaci uproszczonej, wyniki weryfikacji modelu uproszczonego oraz przykładowe symulacje spadków podciśnienia przeprowadzone zgodnie z modelem uproszczonym.

EN

The mathematical model of vacuum pressure drop in a long milk pipeline was presented by Kupczyk [1; 2]. The pressure drop was described by Bernoulli equation at the lost height. This model is non-linear, in form of implicit function. It was proved that the pressure, within the range of values occurring in long pipeline of milking machines, practically does not affect the velocity of bubble ascending within long milk pipeline. The Bernoulli equation may be simplified to quadric polynomial in relation to the vacuum pressure drop. Paper presented the model of pressure drops in a long milk pipeline in simplified form, the results of simplified model verification and some exemplary simulations of vacuum pressure drops based on the simplified model.

4

Inversion of multifunctions and differential inclusions

Nachi K., Penot J.-P.

Control and Cybernetics

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2005

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Vol. 34, no 3

871-901

EN

We present a new inverse mapping theorem for correspondences. It uses a notion of differentiability for multifunctions which seems to be new. We compare it with previous versions. We provide an application to differential inclusions.

5

Robinson's implicit function theorem

Dontchev A. L.

Control and Cybernetics

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2003

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Vol. 32, no 3

529-541

EN

Robinson's implicit function theorem has played a mayor role in the analysis of stability of optimization problems in the last two decades. In this paper we take a new look at this theorem, and with an updated terminology go back to the roots and present some extensions.