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1

Influence of random variable correlation on the reliability of steel structures

Dudzik Agnieszka

Structure and Environment

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2025

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Vol. 17, no. 3

103--112

EN

The study investigated the influence of correlations between random variables on the reliability index of selected structural systems. The structural design parameters were defined as deterministic quantities and random variables, and the correlation between them was modeled using four correlation-matrix variants. The ultimate limit state was adopted as the safety criterion, and appropriate limit state functions were formulated to identify structural failure. A sensitivity analysis of the reliability index with respect to the random variables was carried out using the Hasofer-Lind reliability index as the performance measure. The First-Order Reliability Method served as the primary computational approach, with Monte Carlo simulation as the reference method. All calculations were performed using the NUMPRESS Explore. The analyses demonstrated that increasing the correlation coefficient leads to higher values of the reliability index. The results confirm that the correlation coefficient significantly affects the reliability assessment and should not be neglected in structural safety evaluations.

PL

W pracy analizowano wpływ korelacji zmiennych losowych na wartość wskaźnika niezawodności wybranych układów konstrukcyjnych. Parametry projektowe konstrukcji zdefiniowano jako wielkości deterministyczne oraz zmienne losowe. W analizie uwzględniono korelację zmiennych losowych poprzez zastosowanie czterech wariantów macierzy korelacji. Stan graniczny nośności przyjęto jako kryterium oceny bezpieczeństwa konstrukcji, a do identyfikacji stanu awarii zastosowano odpowiednie funkcje graniczne. Przeprowadzono analizę wrażliwości wskaźnika niezawodności względem zmiennych losowych, przyjmując wskaźnik Hasofera-Linda jako miarę niezawodności. Podstawową metodą obliczeniową była metoda niezawodności pierwszego rzędu (FORM), natomiast metodę Monte Carlo wykorzystano jako metodę referencyjną. Obliczenia przeprowadzono z wykorzystaniem oprogramowania NUMPRESS Explore. Na podstawie przeprowadzonych analiz zaobserwowano, że wzrost wartości współczynnika korelacji prowadzi do zwiększenia wartości wskaźnika niezawodności. Uzyskane wyniki potwierdziły, że współczynnik korelacji wywiera istotny wpływ na wartość wskaźnika niezawodności, wobec czego nie powinien być pomijany w ocenie bezpieczeństwa konstrukcji.

2

Analiza niepewności lokalizacji odometrycznej z wykorzystaniem systemu przechwytywania ruchu i symulacji Monte Carlo

Dudzik Sebastian, Szeląg Piotr

Pomiary Automatyka Robotyka

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2025

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R. 29, nr 1

31--39

PL

W ostatnich latach obserwuje się bardzo dynamiczny rozwój technologii związanych z robotami mobilnymi, zwłaszcza robotami autonomicznymi. Jedną z podstawowych kompetencji robotów mobilnych jest nawigacja i związana z nią lokalizacja. W artykule przedstawiono wyniki badań mających na celu oszacowanie niepewności lokalizacji z wykorzystaniem modelu kinematyki napędu różnicowego. Wykonano badania eksperymentalne i symulacyjne robota mobilnego QBot 2e. W ramach badań eksperymentalnych przeprowadzono symulacje sprzętowe ruchu robota wzdłuż zadanych tras z jednoczesnym pomiarem prędkości. Wyniki pomiarów posłużyły do przeprowadzania symulacji Monte Carlo mającej na celu oszacowanie niepewności wyznaczania położenia robota. Na podstawie wyników badań stwierdzono, że niepewność lokalizacji rośnie wraz z czasem a gęstości prawdopodobieństwa zmiennych losowych reprezentujących położenie robota, mogą być z dużą dokładnością aproksymowane rozkładem normalnym.

EN

In recent years, there has been a very dynamic development of technologies related to mobile robots, especially autonomous robots. One of the basic competences of mobile robots is navigation and related localization. The article presents the results of research aimed at estimating the accuracy of localization using the differential drive kinematics model. Experimental and simulation studies of the QBot 2e mobile robot were performed. As part of the experimental studies, hardware-in-the-loop simulations of the robot’s movement along the given paths were carried out with simultaneous speed measurements. The measurement results were used to conduct Monte Carlo simulations aimed at estimating the uncertainty of determining the robot’s position. Based on the research results, it was found that the uncertainty of localization increases with time and the probability densities of random variables representing the robot’s position can be approximated with high accuracy by the Gaussian distribution.

3

The importance of measurement uncertainty during gauge block calibration in determining compliance with specifications

Stępień Krzysztof, Świderski Jacek, Makieła Włodzimierz

Metrology and Measurement Systems

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2025

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Vol. 32, nr 2

1--15

EN

This article deals with selected problems related to the calibration of gauge blocks. It describes basic terms and definitions concerning principles of determining the conformity of calibration results with specifications, such as measurement uncertainty and measurement traceability. The requirements for laboratories accredited according to ISO/IEC 17025:2017 were discussed that are related to the declaration of compliance with the specification. Guidelines are given on decision rules and compliance principles based on ILAC-G8:09/2019 and JCGM 106:2012 in terms of the guard bands used and the associated risks of making an erroneous decision and the application of two decision rules: binary and nonbinary. The presented problems were supported by an analysis regarding calibration of the gauge blocks by the interferometric and comparative methods with regard to measurement uncertainty and deviations of the length in relation to the nominal length for individual grades in accordance with ISO 3650:1998. As the theoretical analysis has shown, there are no sources in the literature that would allow one to assess the risk of making the wrong decision during the calibration of gauge blocks. Therefore, the authors believe that the results presented in this paper will be of interest both to researchers dealing with the problem of estimating measurement uncertainty and to the staff of measurement laboratories.

4

An algorithm for fast uncertainty evaluation in RMS voltage measurement

Sienkowski Sergiusz, Krajewski Mariusz, Lal-Jadziak Jadwiga

Metrology and Measurement Systems

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2025

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Vol. 32, nr 2

1--20

EN

This paper presents a new algorithm for fast uncertainty evaluation of root mean square (RMS) voltage measurement. It enables the evaluation of the expanded measurement uncertainty and partial uncertainties, which are useful in metrological analysis of the measurement. It can be used for any measurement system in which the RMS value is determined based on voltage samples. Various sources of uncertainty have been considered for this measurement system. The proposed algorithm is easier to implement than the commonly used uncertainty propagation method. Its operating principle is based on the Monte Carlo method. However, it allows the computation of the RMS measurement uncertainty within a significantly shorter time compared to the classical Monte Carlo method. The simulation and experimental results presented in this paper confirm the correct operation of the new algorithm and the acceleration of uncertainty computations up to 200 times in RMS measurement based on 1000 voltage samples.

5

Reliability of water pipelines and operating costs

Studziński Andrzej, Dawidowicz Jacek, Pytlowany Tomasz, Oleniacz Grzegorz, Topolski Krzysztof

Materiały Budowlane

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2025

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nr 7

158--166

EN

In order to determine the impact of the reliability class of water pipes on the operating costs of water supply networks, probabilistic calculations were carried out using Monte Carlo simulations. The model was based on the assumption that repair costs are subject to a log-normal distribution. Three reliability classes were assumed, differentiating the level of acceptable risk depending on the rank and function of a given network section. The analysis performed clearly showed that the pipe reliability class and the assumed variability of operating parameters have a significant impact on the forecasted repair costs in water supply systems. The use of the Monte Carlo method and the log-normal distribution allowed for taking into account asymmetry and determining the occurrence of extreme costs.

PL

W celu określenia wpływu klasy niezawodności przewodów wodociągowych na koszty eksploatacyjne sieci wodociągowych, przeprowadzono obliczenia probabilistyczne z zastosowaniem symulacji Monte Carlo. Model bazuje na założeniu, że koszty naprawy podlegają rozkładowi log-normalnemu. Przyjęto trzy klasy niezawodności, różnicujące poziom ryzyka dopuszczalnego w zależności od rangi i funkcji danego odcinka sieci. Przeprowadzona analiza jednoznacznie wykazała, że klasa niezawodności rur oraz przyjęta zmienność parametrów eksploatacyjnych mają istotny wpływ na prognozowane koszty naprawy w systemach wodociągowych. Wykorzystanie metody Monte Carlo i rozkładu log-normalnego pozwoliło na uwzględnienie asymetrii i określenia wystąpienia kosztów ekstremalnych.

6

Method of Analysis and Assessment of the Impact of Variable Demand from Hard Coal Consumers on the Degree of Utilization of Mine Production Capacities

Fuksa Dariusz

Inżynieria Mineralna

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2025

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Vol. 1, no. 1

15--22

EN

The article presents the author's analysis of the utilization of the usable capacity of mines, which form part of a multi-plant mining enterprise, in conditions of variable demand for coal. The above analysis is based on Monte Carlo tools and is one of the elements developed by the author to rationalize production decisions for the management of a coal company. The presented forecast analysis variants include: • assuming the expected value and dispersion according to retrospective data; • the most probable forecast solution with a predictive formula; • the application of correlated required changes. These results are based on the proposed forms of histograms, inferences about the size of adjusted production capacities, which are taken into account on the market, both in terms of quantity and quality of coal, and forecasting and the probability of applying these changes.

PL

W artykule zaprezentowano opracowaną przez autora metodę analizy stopnia wykorzystania zdolności produkcyjnych rzeczywistych kopalń, wchodzących w skład wielozakładowego przedsiębiorstwa górniczego, w warunkach zmiennego zapotrzebowania na węgiel. Analiza powyższa oparta jest na symulacji Monte Carlo i stanowi jeden z elementów opracowanej przez autora metody racjonalizacji decyzji produkcyjnych dla potrzeb zarządzania spółką węglową. Przedstawione warianty analizy prognoz uwzględniają: • przyjęcie wartości oczekiwanej i dyspersji według danych retrospektywnych; • przyjęcie najbardziej prawdopodobnego błędu prognozy wynikającego z formuł predykcyjnych; • uwzględnienie skorelowanych zmian zapotrzebowania. Uzyskane wyniki, w oparciu o proponowaną metodę w postaci histogramów, pozwalają wnioskować o stopniu dopasowania zdolności produkcyjnej kopalń do wymagań rynkowych, zarówno pod względem ilości, jak i jakości węgla, oraz przewidywać kierunki i praw- dopodobieństwo występowania tych zmian.

7

Monte Carlo validation of the pairwise comparisons method accuracy improvement for 3D objects

Koczkodaj Waldemar W., Kułakowski Konrad, Lau Meng Cheng, Pedrycz Witold, Pigazzini Alexander, Song Yingli, Strzałka Dominik, Żądło Tomasz

Advances in Science and Technology. Research Journal

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2025

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Vol. 19, no. 6

194--202

EN

A Monte Carlo study of the pairwise comparisons method has been designed to validate the accuracy improvement by the pairwise comparisons method for 3D objects. For this, not-so-irregular objects were randomly selected. It is important to emphasize that this study focuses on testing the accuracy of the method rather than the users’ skills. The users’ inability to assess the volume of unrestricted random objects (e.g., a porcupine) would only deviate the results. As a side product, semi-randomly generated 3D objects can also be useful in many other research areas, such as software validation and verification, microeconomics (consumer preferences for products), computer entertainment, and even agriculture (selecting of fruits and vegetables). Further generalizations incorporating additional dimensions, as a comparison of different investment opportunities, can be useful, for example in enhancing financial decision-making processes.

8

The analysis of the metrological properties of contact temperature measurement with the use of selected statistical methods

Michalski Dariusz, Maciejewska Beata, Piasecka Magdalena, Dadas Norbert, Piasecki Artur

International Journal of Electronics and Telecommunications

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2024

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Vol. 70, No. 3

627-634

EN

In this study, the uncertainty of measurement paths was estimated using selected statistical methods. Specifically, temperature measurements obtained from contact temperature sensors used in a heat transfer test section were investigated. The experiments utilized a dry-well temperature calibrator, thermoelements (types K, J, N, and T), and a data acquisition station. Additionally, a certified Pt-100 resistance sensor connected to the temperature meter was considered during measurements. The temperature range for the selected measurement points was 0.3 to 100 °C, covering both increasing and decreasing temperatures. To calculate the expanded uncertainty, both the uncertainty propagation method and the Monte Carlo method were employed. The results were analyzed and found to be similar.

9

The application of predictive stochastic model based on Monte Carlo method in building energy saving renovation

Xiao Juxian

Archives of Civil Engineering

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2024

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Vol. 70, nr 4

43--56

EN

This research has established an energy consumption prediction model based on the Monte Carlo method to resolve the energy-saving transformation problem. First, simplify the building to construct the proposed model. Second, through the principle of building energy balance and Monte Carlo method, the cooling and heat demand model of regional buildings and the energy consumption prediction model of regional buildings are built. Finally, the energy consumption simulation and energy consumption prediction of the regional building complex after energy-saving renovation are carried out. The experiment shows that the building energy consumption in July and August was relatively high, reaching 2.36E+14 and 2.4E+14, respectively. The energy consumption in April and November was relatively low, reaching 1.2E+14 and 1.4E+14, respectively. The highest prediction error was in November, reaching 12%. The lowest prediction error was in January and February, only about 2%. The error of monthly energy consumption predicted by Monte Carlo method is less than 12%, the Root-mean-square deviation is 5%, and the error between predicted and actual annual total energy consumption is only about 2%. By comparing the predicted energy consumption after energy-saving renovation with before, the energy-saving rate reached about 20%. The research results indicate that the proposed Monte Carlo based predictive stochastic model exhibits good predictive performance in building energy-saving renovation, providing theoretical guidance and reference for feasibility studies, planning, prediction, decision-making, and optimization of building energy-saving renovation.

10

New prediction of cracks propagation in repaired steel plate with bonded composite patch at cyclic loading

Maachou Sofiane, Mechab Belaïd, Bouiadjra Bel Abbes Bachir, Salem Mokadem

Acta Mechanica et Automatica

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2024

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Vol. 18, no. 4

579--584

EN

This study presents a numerical prediction of the fatigue life of steel panels repaired by a composite patch. The effect of length cracks, the stress ratio R and properties of the patch is presented. The obtained results show that the bonded composite repair significantly reduces the stress intensity factors at the tip of repaired cracks. The results are in a good agreement with those in the literature. The Monte Carlo method is used to predict the distribution function governing crack propagation in fatigue analysis. In computing the failure probability of the structure, we consider the statistical uncertainty associated with key variables, along with the previously discussed model uncertainty. The results obtained highlight the considerable impact of variations in crack length and stress ratio on the distribution function. Notably, uncertainty in these parameters significantly amplifies the probability of structural failure in plates, thereby diminishing overall structural durability.

11

Power system flexibility assessment for future flexibility needs: high-level screening method of the Macedonian power system

Malcheski Stojan, Kuzarevski Sime, Vuletic Jovica, Angelov Jordanco, Todorovski Mirko

Przegląd Elektrotechniczny

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2023

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R. 99, nr 6

138--141

EN

With the European aim to reduce the carbon footprint of the European energy sector by 2030 North Macedonia strategic framework set an ambitious goal to decommission its coal-fired power plants and replace them with renewable energy sources. The future flexibility and inertia states of the power system are assessed using a Monte Carlo market model calculation and multiple scenarios. On a mid-term planning horizon, this paper employs various metrics to derive a comprehensive estimation of the system's inertia and flexibility requirements for the Macedonian power system.

PL

Realizując europejski cel zmniejszenia śladu węglowego europejskiego sektora energetycznego do 2030 r., w ramach strategicznych Macedonii Północnej wyznaczono ambitny cel likwidacji elektrowni węglowych I zastąpienia ich odnawialnymi źródłami energii. Przyszłe stany elastyczności i bezwładności 138 ystemu elektroenergetycznego są oceniane za pomocą obliczeń modelu rynkowego Monte Carlo i wielu scenariuszy. W horyzoncie planowania średniookresowego niniejszy138ystem138tt wykorzystuje różne wskaźniki w celu uzyskania kompleksowego oszacowania wymagań dotyczących bezwładności i elastyczności 138 ystemu dla macedońskiego 138 ystemu elektroenergetycznego.

12

Monte Carlo simulation of polarization of light back-scattered from randomly rough surfaces

Jiang Yuxiang, Li Zhenhua

Optica Applicata

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2023

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Vol. 53, nr 1

65--85

EN

Laser detection devices obtain target information from back-scattered light, such as lidar. The recognition rate can be improved by analyzing intensity and polarization of echo signal. In this paper, Monte Carlo method is used to generate a large number of randomly rough surfaces to simulate targets. Every rough surface is discretized into a large number of micro-surface elements. Stokes parameters of back-scattered light are calculated by numerical integration. Incident light is p-, s-, 45° linearly polarized light and right-hand circularly polarized light, respectively. Numerical results show that when s- and p-linearly polarized light incident on a metal rough surface, back-scattered light appears circularly polarized component. Metal rough surface resembles a wave plate with phase difference, with the fast axis parallel or perpendicular to the 45° direction. When linearly polarized light is incident on dielectric rough surface, back-scattered light has no circularly polarized component. Experimental data are consistent with the numerical results. The above research provides a new basis for laser detection device to identify metal targets from the environmental background.

13

Co nieco o algorytmach szachowych

Słanina Piotr

MINUT Matematyka i Informatyka na Uczelniach Technicznych

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2023

|

Nr 5

195-210

PL

Algorytmy szachowe i ich implementacja od wielu lat są istotną częścią szachowego świata. Artykuł przybliża historię i działanie podstawowych algorytmów, wykorzystywanych w silnikach szachowych.

14

Determination of measurement uncertainty by a Monte Carlo method for an RF power sensor calibration system using a VNA

Jaworski Marek, Szatkowski Jarosław, Kossek Tomasz

Metrology and Measurement Systems

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2023

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Vol. 30, nr 4

703--720

EN

This work proposes a systematic assessment of measuring type A uncertainty (caused by random errors) used in RF power sensor calibration. To reduce A type uncertainty, several successive measurements are repeated. The uncertainty arises from repeatability errors in connectors caused by changes in their electrical properties during repeated mating. The suitability of the METAS UncLib software was analysed and we concluded that software should be developed to take into account the shape of probability density function (PDF) using a Monte Carlo method (MCM), which was lacking in METAS UncLib. The self-developed software was then tested on an example taken from the literature and the superiority of the MCM over the analytical method (GUM) was confirmed. During the calibration of the RF sensor using a vector network analyzer (VNA), a series of repeated measurements were performed and, after applying our MCM software, it was found that the measurement uncertainties calculated by the MCM method were several times larger than those by the GUM. The reason for this was that the correlation between the measured input quantities was not taken into account. When this was done using a covariance matrix and assuming a normal PDF of the input quantities, the results obtained with the GUM and the MCM converged. Our main objective was to investigate the influence of the PDF shape of the input measurement samples on the measurement uncertainty. Taking more than a dozen measurements is too costly, on the other hand, the small sample size prevents a reliable determination of the PDF shape. Finally, to overcome this inconvenience, we have developed a special method that uses the histograms of standardized input data taken at all measurement frequencies under fixed conditions without disconnecting the connectors, to increasing the total number of results which were needed to create the PDF histograms of input quantities.

15

The Method for Assessing the Impact of Variable Coal Demand on the Efficiency of Mine Operations

Fuksa Dariusz

Inżynieria Mineralna

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2023

|

no. 1

267--273

EN

The method presented in the article is based on Monte Carlo simulation and involves studying the impact of random demand fluctuations on the efficiency of mines and mine groups (companies). For random demand fluctuations, a normal distribution is assumed, and the analysis variants present-ed include: • Adopting the mean and variance values based on retrospective data, • Considering the most probable forecast error resulting from predictive formulas, • Taking into account correlated changes in demand. The results obtained are presented in the form of histograms of the degree of operational lever-age. These histograms allow for predicting how the degree of operational leverage of mines will develop, as well as estimating the direction and probability of these changes. The developed and veri-fied sensitivity analysis using real examples constitutes a useful element in rationalizing decision-making processes.

PL

Zaprezentowana w artykule metoda oparta jest na symulacji Monte Carlo i obejmuje badanie wpływu wahań losowych zapotrzebowania na efektywność kopalń oraz ich grup (spółek). Dla losowych wahań zapotrzebowania przyjęto rozkład normalny, a przedstawione warianty analizy uwzględniają: • przyjęcie wartości oczekiwanej i dyspersji według danych retrospektywnych; • przyjęcie najbardziej prawdopodobnego błędu prognozy wynikającego z formuł predykcyjnych; • uwzględnienie skorelowanych zmian zapotrzebowania. Uzyskane wyniki przedstawiono w postaci histogramów stopnia dźwigni operacyjnej. Pozwalają one przewidywać, jak będzie kształtował się stopień dźwigni operacyjnej kopalń, jak również umożliwia oszacować, w którym kierunku zmiany te będą postępować i z jakim prawdopodobieństwem. Opracowana i zweryfikowana na realnych przykładach analiza wrażliwości stanowi przydatny element racjonalizacji procesów decyzyjnych.

16

Investigation of exhaust emissions from the gasoline engine of a light duty vehicle in the Real Driving Emissions test

Andrych-Zalewska Monika, Chlopek Zdzislaw, Pielecha Jacek, Merkisz Jerzy

Eksploatacja i Niezawodność

|

2023

|

Vol. 25, no. 2

art. no. 165880

EN

The article contains the research results and analysis of the processes that take place as part of a gasoline engine light duty vehicle Real Driving Emissions test. Dimensionless characteristics of exhaust emission and fuel mass consumption in the RDE test were also determined: emission intensity, particle number emission intensity, fuel mass consumption intensity. An algorithm for determining the characteristics specific distance pollutant emission, specific distance particle number and specific distance fuel mass consumption in the vehicle speed domain in the RDE test was presented using the Monte Carlo method. The determined characteristics were approximated by polynomial functions in the form of sets of points. These relationships were characterized by a large dispersion of values, which was primarily due to the fact that the random values of the averaging limits contain very different engine operating conditions.

17

The f.c.c. Crystals of Hard Spheres with an Array of [001]-Nanochannel Inclusions Filled by the Simplest Hard Sphere Molecules

Narojczyk Jakub W.

Computational Methods in Science and Technology

|

2023

|

Vol. 29, No. 1-4

37--44

EN

In this work the systems composed of particles interacting with hard potential are investigated. These systems feature certain modifications to the crystal structure – selected particles are replaced with ones that differ slightly in their diameters. Such modifications, which can be thought of as “inclusions”, concern particles located in cylindrical nanochannels, oriented in [001] direction. In this study, for the first time, additional constrains have been imposed on the particles forming the inclusions. Namely, the replaced spheres have been randomly grouped into neighbouring pairs which were connected to form simple, di-atomic molecules. The results have been compared with previously investigated systems with similar inclusions but without the connections, i.e. filled only by spheres. The comparison of elastic properties between these systems is presented. It is shown that inclusions filled with dimers have different impact on the values of elastic compliances. It has been demonstrated that by introducing a small number of molecules made of spheres whose diameters differ from the rest of the particles forming the crystal, one is able to modify the hardness and shear resistance of the f.c.c. crystal without changing the Poisson’s ratio (with respect to the analogous system without additional constrains imposed on the inclusion particles).

18

Subdiffusive Behavior in Crowded Environments: Impact of Obstacle Mobility and Spatial Restrictions

Polanowski Piotr, Sikorski Andrzej

Computational Methods in Science and Technology

|

2023

|

Vol. 29, No. 1-4

27--35

EN

Biological systems are generally dense reaction-diffusion systems. Therefore, determining the mechanism of motion in such systems is of crucial importance in understanding their dynamics. Subdiffusive behavior is very common in biological systems but its origin usually does not have a clear explanation. One attempt to explain this behavior is the presence of randomly placed stationary obstacles in a medium filled with molecules of a certain medium. With an appropriate concentration of obstacles, the molecules of the medium cease to perform classic Brownian motions and motion becomes subdiffusive. This mechanism seems to be well documented in both simulations and experiments. The question arises whether a similar effect can be obtained in systems where obstacles are not stationary, but their mobility is drastically reduced comparing to medium molecules, or the reduction in mobility is combined with a limitation in movement (the movement of obstacles resembles, for example, the Orestein-Ulhenbeck movement). Is it possible to observe subdiffusion behavior in such a situation? We try to answer this question on the basis of Monte Carlo simulations based on the Dynamic Lattice Liquid (DLL) model. Based on the concept of cooperative movements, this model has a unique feature that allows one to take into account the correlation of movements between the elements that make up the examined system, which is important in the case of high densities due to the strict correlation of movements between the moving elements. The tests concern systems where obstacles were single beads whose mobility was changed with additional restrictions imposed on the displacement. It was shown that no entrapment of medium molecules was observed and a slight deviation from normal diffusion was also shown.

19

Risk assessment in railway rolling stock planning

Gołębiowski Piotr, Góra Ignacy, Bolzhelarskyi Yaroslav

Archives of Transport

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2023

|

Vol. 65, iss. 1

137--154

EN

Rolling stock planning is one of the steps in the traffic planning process considered from the railway undertaking's point of view. It is directly related to the efficiency of rolling stock utilisation, which should be ensured at the highest possible level in the case of rail transport. The planning work stage is subject to certain risks (threats and opportunities), which, if they materialise, will impact it. It, therefore, makes sense to carry out analyses that can anticipate specific events in good time and introduce appropriate countermeasures in advance. This article aims to conduct a risk assessment process concerning rolling stock planning. It was assumed that the considerations were carried out based on the M_o_R (Management of Risk) methodology. Based on this methodology, risk identification and risk analysis (estimation of risk impact) were carried out. Risk assessment was carried out using the Monte Carlo simulation method. The work identified sixteen risks that represent threats. The principle of risk description was used to identify risks. It requires indicating for each risk the reason for its occurrence and the effect it may have. As a part of risk estimation, variables were selected to assess each risk's impact on the objectives of the stage. Publicly available statistical data were used to define the variables. The variables were expressed in monetary units. The work identified five variables describing impact, which were assigned to the individual risks. As a triangular probability distribution was used for the variability of impact description, the variable's minimum, most likely, and maximum value was identified. A risk assessment was carried out for only two impact description variables (for those variables used to describe the impact of the most significant number of risks). For each variable, statistical parameters were indicated and analysed. The resulting value of the variable describing the impact was then read out for each percentile, and the expected value of the risk was calculated. A detailed risk assessment was made for the lower, middle and upper quartiles. A histogram of the incidence of each variable value was presented, and an assessment was made.

20

Determination of exhaust emission characteristics in the RDE test using the Monte Carlo method

Andrych-Zalewska Monika, Chłopek Zdzisław, Merkisz Jerzy, Pielecha Jacek

Archives of Transport

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2023

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Vol. 66, iss. 2

45--60

EN

The article presents a method of determining the characteristics of exhaust emissions and fuel mass consumption in real driving conditions based on a single test using the Monte Carlo method. The exhaust emission characteristics used are the relations between the emissions and the average vehicle speed, and the characteristic of the fuel mass consumption is the dependence of the fuel mass consumption at the average vehicle speed. The results of empirical research of a passenger car with a spark-ignition engine in the RDE test were used. The use of the Monte Carlo method made it possible to select the initial and final moments of averaging the process values, thanks to which it was possible to determine the discrete values of the characteristics for various values of average vehicle speeds. The determined discrete characteristics of the particulate mass and number emissions and fuel mass consumption relative to the average vehicle speed were approximated by polynomial functions of the second and third degree. The determined discrete characteristics, presented as sets of points, were characterized by a relatively small dispersion in relation to their polynomial approximations. The average relative deviation of the points of discrete characteristics from the value of the polynomial was in most cases small – less than 4%, only in the case of the number of particles emitted deviated from this, as the average relative deviation of the measured points from the determined polynomial was nearly 14%. Combined with the results of RDE empirical studies, the Monte Carlo method proved to be an effective method for determining the characteristics of exhaust emissions, measured in real vehicle operating conditions. The main advantage of the proposed method was a significant reduction in the actual workload necessary to carry out the empirical research – where it became possible to determine the characteristics in a large range of vehicle average speed values with just one drive test. Using standard methods of measuring this type of data, it would be necessary to conduct multiple tests, driving at different average vehicle speeds.