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1
Content available remote Physical Ergodicity and Exact Response Relations for Low-dimensional Maps
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EN
Recently, novel ergodic notions have been introduced in order to find physically relevant formulations and derivations of fluctuation relations. These notions have been subsequently used in the development of a general theory of response, for time continuous deterministic dynamics. The key ingredient of this theory is the Dissipation Function , that in nonequilibrium systems of physical interest can be identified with the energy dissipation rate, and that is used to determine exactly the evolution of ensembles in phase space. This constitutes an advance compared to the standard solution of the (generalized) Liouville Equation, that is based on the physically elusive phase space variation rate. The response theory arising in this framework focuses on observables, rather than on details of the dynamics and of the stationary probability distributions on phase space. In particular, this theory does not rest on metric transitivity, which amounts to standard ergodicity. It rests on the properties of the initial equilibrium, in which a system is found before being perturbed away from that state. This theory is exact, not restricted to linear response, and it applies to all dynamical systems. Moreover, it yields necessary and sufficient conditions for relaxation of ensembles (as in usual response theory), as well as for relaxation of single systems. We extend the continuous time theory to time discrete systems, we illustrate our results with simple maps and we compare them with other recent theories.
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EN
The paper presents possibilities and limitations associated with technical state predicting procedure of devices, as well as it indicates the necessity of improving the present scheduling methods of preventive maintenance operations of ship power plant devices. It has been also showed that by making transformation of the wear rate distributions of device elements into the distributions of time of their correct- to-limit-state operation it is possible to predict their technical state and to suitably schedule their maintenance operations.
EN
The paper is concerned with a class of knowledge-based pattern recognition systems with logical representation. In this case the knowledge representation has the form of the facts - the logical formulae and for the generation of the solution we can use the logic-algebraic method. The purpose is to present a formulation and solution algorithms of the multi-level knowledge-based pattern recognition problem for the system as a whole and for the subsystems. Both approaches are compared. A simple example illustrating the general method is presented. In practice, this method is implemented in MESS software.
EN
The paper is concerned with recognition problems based on relational knowledge representations with two kinds of unknown parameters: uncertain parameters characterized by certainty distributions given by an expert and random parameters described by probability distributions. After a short presentation of uncertain variables and their application to the knowledge-based recognition under uncertainty, the different versions in two formulations of the recognition problem are discussed. In the first formulation two unknown parameters (uncertain and random) in the relation describing the set of object to be recognized are considered. The second formulation concerns the case with one unknown parameter in the knowledge representation, described by a certainty distribution with a random parameter or by a probability distribution with an uncertain parameter. Simple examples illustrate the presented approach. The application of so called C-uncertain variables and the description of the recognition system with three-level uncertainty are included.
PL
Przedstawiono metody obliczania niepewności pomiaru w oparciu o rozkład płasko-normalny. Rozkład ten jest splotem rozkładu prostokątnego z normalnym. Metody opracowano w dwóch postaciach: analitycznej i numerycznej. Można je wykorzystać do obliczania niepewności pomiaru, gdy model pomiaru jest liniowy lub linearyzowany oraz gdy wielkościom wejściowym można przypisać rozkład Studenta, normalny, prostokątny lub trójkątny. Przedstawiono ocenę dokładności proponowanych metod i zilustrowano je praktycznym przykładem obliczeniowym.
EN
The paper presents methods using the Flatten-Gaussian distribution for calculating the measurement uncertainty. The Flatten-Gaussian distribution is a convolution of rectangular and normal distributions. The methods were worked out in the analytical and the numerical form. They can be used when the measurand model is a linear or linearized mathematical function, and the model input quantities are characterized by Student's, normal, rectangular, triangular and trapezoidal distributions. The proposed methods enable calculation of the measurement uncertainty with the accuracy close to that of the Monte Carlo method recommended in [2]. The analytical method is based on formula (6) including the quantile of the Flatten-Gaussian distribution, whereas the numerical method is based on sampling from this distribution as a random number generator given by formula (8). This random number generator can be created from two random number generators based on drawing from the rectangular and normal distribution. It immediately provides the set of possible values for the measurand. The methods can be easily implemented in common computational tools, such as a spreadsheet. They do not require the specialized software. The paper presents an example of a practical use of the proposed methods.
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Content available A logical device for processing nautical data
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EN
Nautical measurements are randomly and systematically corrupted. There is a rich scope of knowledge regarding the randomness shown by results of observations. The distribution of stochastic distortions remains an estimate and is imprecise with respect to their parameters. Uncertainties can also occur through the subjective assessment of each piece of available data. The ability to model and process all of the aforementioned items through traditional approaches is rather limited. Moreover, the results of observations, the final outcome of a quality evaluation, can be estimated prior to measurements being taken. This a posteriori analysis is impaired and it is outside the scope of traditional, inaccurate data handling methods. To propose new solutions, one should start with an alternative approach towards modelling doubtfulness. The following article focusses on belief assignments that may benefit from the inclusion of uncertainty. It starts with a basic interval uncertainty model. Then, assignments engaging fuzzy locations around nautical indications are discussed. This fragment includes transformation from density functions to probability distributions of random errors. Diagrams of the obtained conversions are included. The presentation concludes with a short description of a computer application that implements the presented ideas.
PL
W artykule przedstawiono wyniki eksploatacyjnych badań niezawodności pomp w pompowniach I i Ii-go stopnia oraz układu zasilania energetycznego tych pompowni. Obiekty badawcze funkcjonują w systemie zaopatrzenia w wodę miasta liczącego ok. 15 tysięcy mieszkańców. Do oceny niezawodności obiektów zastosowano model dwustanowy z odnową niezerową dobrze sprawdzający się w odniesieniu do obiektów wodociągowych. Prezentowany artykuł zawiera wartości podstawowych wskaźników niezawodności jak: średni czas pracy między uszkodzeniami (średni czas pracy), średni czas odnowy, parametr strumienia uszkodzeń, intensywność odnowy, wskaźnik gotowości i wskaźnik postoju oraz prawdopodobieństwo pracy pomp.
EN
The paper presents the results of field reliability tests of pumps in pumping stations of the 1st and the 2nd degree and their energy supply system. The investigated objects exist in water supply system of 15 thousand habitants city. The two-stages model with non-zero renewal to reliability assessment of investigated objects has been used. Presented paper contains the values of basing reliability estimators and probability distributions of work time of investigated objects.
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Content available remote Rozkłady prawdopodobieństwa ciągu zależnych czasów pomiędzy odnowami.
63%
PL
Praca dotyczy modelu odnowy, gdy czas naprawy jest pomijalny, a czasy pomiędzy odnowami są zależne. Taki opis rozkładu prawdopodobieństwa, ciągu czasów pomiędzy odnowami, pozwala lepiej uwzględnić rzeczywiste warunki występujące w procesie eksploatacji urządzeń. Uzyskane wyniki zilustrowano przykładem liczbowym.
EN
The paper concerns the reconditioning model when the repair time negligible and periods between renewals are dependent. Such description of probability distribution of the series of periods between reconditioning allows for regard to teal conditions that occur in the maintenance process of devices. Results are illustrated by the numerical example.
PL
W artykule rozważono możliwość zastosowania rozkładu uogólnionego gamma jako narzędzia pomocnego w szacowaniu niezawodności nienaprawialnych obiektów technicznych. Omówiono związki występujące pomiędzy rozkładem uogólnionym gamma a rozkładami: wykładniczym, Weibulla, gamma i normalnym, powszechnie wykorzystywanymi przy ocenie niezawodności. Wyniki obliczeń, dla zaproponowanej metody i przy użyciu opracowanego programu komputerowego, potwierdzają możliwości wykorzystania rozkładu trójparametrowego w analizach niezawodności.
EN
The possibility of using generalised gamma distribution as a tool useful for estimating the reliability of technical objects was discussed in the paper. The connections between generalised gamma distribution and exponential, Weibull, gamma and normal distributions, used in the reliability estimation, were presented. The results obtained for the proposed method and with the use of the developed computer program give the reasons for using generalised gamma distribution for reliability analysis.
EN
As a step toward probabilistic seismic hazard assessment in the Ibero–Maghreb region, this study focuses on the estimation and the analysis of main seismic hazard parameters, namely the magnitude of completeness mc, the occurrence rate λ, the Gutenberg–Richter b value, and the maximum expected magnitude Mmax. The most recent earthquake catalog database has been compiled using different earthquake sources, including historical and instrumental earthquake records covering the time period 1045−2019. International Seismological Centre catalog database has been used to get the preliminary instrumental catalog covering the study region. Then, a magnitude inter-scale conversion analysis has been carried out to obtain magnitude conversion empirical laws. These later have been used to compile a homogenized catalog with all magnitudes unified to the moment magnitude Mw scale, which is quite reliably linked to fault physical parameters. The completeness magnitude has been estimated for different time periods using the maximum curvature and the entire magnitude range methods. Subsequently, the spatio-temporal variation of the completeness magnitude has been studied to better appreciate regional data quality. This analysis resulted in three complete sub-catalogs corresponding to different magnitude of completeness, namely mc=3.5, 4.5, and 5.5, starting from 1997, 1967 and 1959. The remaining seismic hazard parameters (λ, b and Mmax) were analyzed taking into account former magnitudes of completeness. Indeed, the use of incomplete data may add significant bias to seismic hazard parameters estimates. Main results are presented as spatial maps showing variation of seismic hazard parameters for different mc values. In particular, for the first time, a combined maximum magnitude–intensity map is elaborated and analyzed. The region corresponding to the largest maximum possible magnitude Mmax has been delimited as including Chelif basin and its surrounding areas west of the capital city Algiers. Mmax hotspots with values exceeding 7 have been delimitated close to Lakhdaria and Boumerdes cities east of the capital Algiers. The corresponding hotspots include the epicenter of the 1910 Mw7 and the 2003 Mw6.8 Aumale and Zemmouri earthquakes, respectively. The magnitude of completeness mc has been found to decrease significantly during the last two decades, especially in the western part. The results obtained in this study can serve as a road map for future seismic hazard studies performed on the Ibero–Maghreb region.
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