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1

Comprehensive approach to addressing oil spills from critical infrastructure accidents

Dąbrowska Ewa

Safety and Reliability of Systems and Processes

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2023

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Summer Safety and Reliability Seminar 2023

33--46

EN

This chapter presents a general approach to analyzing oil spills, which are frequently caused by critical infrastructure accidents. The definitions of critical infrastructure and complex system are given and the main sectors significant to the safety of industry operations are listed. The chapter underlines the importance of properly maintaining and monitoring shipping critical infrastructure to respond to potential accidents and ensuring the security of the people and goods transported. There are also presented different categories of oil spills, which can help responders to understand the scope of the problem and mitigate the effects of environmental damage if the oil discharges reach sensitive ecosystems or accumulate in large quantities. The application of useful mathematical models is described to support decision-making in oil spill response. The main factors affecting oil spill movement are listed, including the effects of hydro-meteorological conditions on predicting oil spill trajectory. Moreover, the development steps of constructing and verifying a proper probabilistic model for oil spill management are given. The chapter concludes by highlighting the need for further research in this area to improve our understanding of the complexity of the oil spill issue at the considered area

2

Modelling oil spill layer thickness and hydro-meteorological conditions impacts on its domain movement at sea area

Dąbrowska Ewa

Safety and Reliability of Systems and Processes

|

2022

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Summer Safety and Reliability Seminar 2022

51--64

EN

The general model of oil spill domain movement forecasting dependent on the thickness of oil spill layer based on a probabilistic approach considering the influence of the hydro-meteorological conditions at sea area is proposed. A semi-Markov model of the process of changing hydro-meteorological conditions is constructed. A two-dimensional stochastic process is used to describe the oil spill domain central point position movement. Parametric equation of oil spill domain central point drift trend curve considering the initial thickness of oil spill layer at the oil spill central point is used. Next, the method of oil spill domain determination dependent on the thickness of oil spill layer for various hydro-meteorological conditions is presented. The generalization of the presented approach assuming that the thickness is changing with time is also proposed. At the end, the research further perspective is given.

3

Deterministic versus stochastic modelling of unsaturated flow in a sandy field soil based on dual tracer breakthrough data

Nützmann Gunnar, Maciejewski Stanisław, Gorczewska-Langner Wioletta

Geological Quarterly

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2022

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Vol. 66, No. 4

art. no. 37

EN

The 216 km2 Neuenhagen Millcreeck catchment can be characterized as a drought-sensitive landscape in NE Germany. It is therefore of fundamental human interest to understand how water that fell as precipitation moves through the unsaturated soils and recharges groundwater. Additionally, a better knowledge of nutrient transport from soil to groundwater is important, especially in landscapes with light sandy soils. For a better understanding of these processes a dual tracer field experiment with bromide (Br-) and deuterium (D2 O) was carried out some years ago. The aim of the present study is to use the results of this experiment to model tracer transport in the unsaturated zone via two different concepts, the classical deterministic advection-dispersion equation and a new stochastic approach. The advantage of the stochastic modelling method proposed here for field-scale tracer application is to produce reliable information about expected total solute fluxes from the unsaturated zone to groundwater and about mean transit times. Moreover, this allows one to evaluate the mass of solute in the soil profile and to determine the range of water velocity fluctuations. Field experiments should be concentrated on estimation of fluctuation of water flow velocity to make stochastic models more accurate. To summarize, this work contributes to new modelling methods for the simulation of water and solute transport in unsaturated sandy soils which are heavily affected by droughts and irregular hydrological processes in the subsurface.

4

Short-term forecasting of accidental oil spill movement in harbours

Dąbrowska Ewa

Safety and Reliability of Systems and Processes

|

2021

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Summer Safety and Reliability Seminar 2021

59--75

EN

The general model of oil spill movement forecasting based on a probabilistic approach is proposed. A semi-Markov model of the process of changing hydro-meteorological conditions is constructed. The method of oil spill domain determination for various hydro-meteorological conditions is recommended. Moreover, Monte Carlo simulation procedure for predicting the oil spill domain movement is proposed. The procedure is practically applied for Gdynia and Karlskrona ports' water areas.

5

Stable distribution in application to fixational eye movement description

Szmigiel Marta, Grzesiek Aleksandra, Wyłomańska Agnieszka, Kasprzak Henryk

Optica Applicata

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2019

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Vol. 49, nr 2

365--377

EN

To give an appropriate description of fixational eye movements is a very challenging problem. Over the years authors tried to describe the movements through different methods. The time series of the movements exhibit very characteristic behavior, which is the visible impulses. This may suggest the heavy-tailed distribution behind the data. In this paper on stochastic description of fixational eye movements, the α-stable distribution as the most important member of heavy-tailed family of distributions is proposed. The fixational eye movements together with head movement of both eyes of eight healthy subjects were measured and recorded by use of own designed optical system. Further analysis of changes in position of the pupil center in two-dimensional plane was performed. It was shown that head movement has very small impact on values of stability parameter α of fixational eye movements. The α-stable based analysis can be useful in better understanding of the character of the eye globe dynamics.

6

Modelling, identification and prediction of oil spill domains at port and sea water areas

Dąbrowska Ewa, Kołowrocki Krzysztof

Journal of Polish Safety and Reliability Association

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2019

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Vol. 10, No. 1

43--58

EN

Methods of oil spill domains determination are reviewed and a new method based on a probabilistic approach to the solution of this problem is recommended. A semi-Markov model of the process of changing hydro-meteorological conditions is constructed. To describe the oil spill domain central point position a two-dimensional stochastic process is used. Parametric equations of oil spill domain central point drift trend curve for different kinds of hydro-meteorological conditions are determined. The general model of oil spill domain determination for various hydro-meteorological conditions is proposed. Moreover, statistical methods of this general model unknown parameters estimation are proposed. These methods are presented in the form of algorithms giving successive steps which should be done to evaluate these unknown model parameters on the base of statistical data coming from experiments performed at the sea. Moreover, approximate expected stochastic prediction and Monte Carlo Simulation in real time prediction of the oil spill domain movement are proposed.

7

A model for random fire induced tree-grass coexistence in savannas

Klimasara P., Tyran-Kamińska M.

Mathematica Applicanda

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2018

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Vol. 46, no. 1

87--96

EN

Tree-grass coexistence in savanna ecosystems depends strongly on environment al disturbances out of which crucial is fire. Most modeling attempts in the literature lack stochastic approach to fire occurrences which is essential to reflect their unpredictability. Existing models that actually include stochasticity of fire are usually analyzed only numerically. We introduce a new minimalistic model of treegrass coexistence where fires occur according to a stochastic process. We use the tools of the linear semigroup theory to provide a more careful mathematical analysis of the model. Essentially we show that there exists a unique stationary distribution of tree and grass biomasses.

PL

Sawanny zajmują ok. 20% lądowej powierzchni Ziemi. W tym ekosystemie korony drzew są na tyle oddzielone od siebie nawzajem, że do podłoża dociera wystarczająco dużo światła, aby utrzymywała się równomierna warstwa traw. Takie długotrwałe współistnienie traw i drzew, czyli brak konwersji do łąki lub lasu, jest możliwe dzięki różnym czynnikom. Uważa się, że najważniejsze z nich to powtarzające się pożary, obfitość pory deszczowej oraz uszczuplanie warstwy roślinnej przez roślinożerców i działalność człowieka. Większość dotychczasowych modeli koegzystencji traw i drzew jest deterministyczna, jeżeli już przyjmuje się stochastyczne występowanie pożarów lub deszczu, to zazwyczaj w bardzo uproszczonej formie, a analiza jest przeprowadzana numerycznie. W tym artykule wprowadzamy uproszczony model, składający się z układu równań różniczkowych, opisujących wzrost traw i drzew w czasie oraz procesu stochastycznego, odpowiadającego za losowe pojawianie się pożarów. Analizujemy ten proces, korzystając z metod teorii półgrup liniowych, co pozwala nam pokazać, że startując z dowolnego rozkładu początkowego biomasy traw i drzew, po odpowiednio długim czasie rozkład tych biomas się stabilizuje. Istnieje jedyny (absolutnie ciągły względem dwuwymiarowej miary Lebesgue’a) taki rozkład stacjonarny. Planujemy rozbudować zaproponowany model o dodatkowe czynniki środowiskowe wymienione wcześniej oraz konkurencje o zasoby pomiędzy trawami a sadzonkami drzew. Ponadto podobne uwzględnienie stochastycznej natury występowania pożarów można uwzględnić w modelowaniu innych zjawisk przyrodniczych jak związek pomiędzy pożarami lasów a populacją żywiących się korą sosen chrząszczy.

8

Accuracy of Precise Point Positioning (PPP) with the use of different International GNSS Service (IGS) products and stochastic modelling

Kiliszek D., Szołucha M., Kroszczyński K.

Geodesy and Cartography

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2018

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Vol. 67, no. 2

207--238

EN

This paper provides analyses of the accuracy and convergence time of the PPP method using GPS systems and different IGS products. The official IGS products: Final, Rapid and Ultra Rapid as well as MGEX products calculated by the CODE analysis centres were used. In addition, calculations with weighting function of the observations were carried out, depending on the elevation angle. The best results were obtained for CODE products, with a 5-minute interval precision ephemeris and precise corrections to satellite clocks with a 30-second interval. For these calculations the accuracy of position determination was at the level of 3 cm with a convergence time of 44 min. Final and Rapid products, which were orbit with a 15-minute interval and clock with a 5 minute interval, gave very similar results. The same level of accuracy was obtained for calculations with CODE products, for which both precise ephemeris and precise corrections to satellite clocks with the interval of 5 minutes. For these calculations, the accuracy was 4 cm with the convergence time of 70 min. The worst accuracy was obtained for calculations with Ultra-rapid products, with an interval of 15 minutes. For these calculations, the accuracy was 10 cm with a convergence time of 120 min. The use of the weighting function improved the accuracy of position determination in each case, except for calculations with Ultra-rapid products. The use of this function slightly increased the convergence time, in addition to the CODE calculation, which was reduced to 9 min.

9

Modelling of the National Power System’s Daily Balancing Conditions in the Long-Term Horizon

Czarnecki B.

Acta Energetica

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2018

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nr 1

34--39

EN

The paper presents a proposal of a stochastic methodology to assess the conditions of the daily balancing of the National Power System (NPS) in a long-term perspective. The simulation consists in multiple generation of time series corresponding to daily variation of individual components of the NPS power balance. The randomly generated time series take into account daily and seasonal variability of the power balance components consisting of power demand, output of non-centrally dispatched generating units (nJWCD), including renewable energy sources (RES), and centrally dispatched generating units (JWCD), which allows one to analyse the coincidence of many changing power balance components. The simulation results are the mean annual values and probability distributions of: 1. use of NPS regulatory resources, e.g. pumped storage power plants (ESP) 2. occurrence of critical events, e.g. power regulation bandwidth deficit or violation of the minimum number of operating JWCD criterion 3. events involving the need to limit RES power due to NPS operational security.

PL

W artykule przedstawiono propozycję metodyki stochastycznej oceny warunków dobowego bilansowania Krajowego Systemu Elektroenergetycznego (KSE) w długim horyzoncie czasu. Symulacja polega na wielokrotnym generowaniu szeregów czasowych odpowiadających dobowym przebiegom poszczególnych składowych bilansu mocy KSE. Generowane losowo przebiegi uwzględ- niają dobową i sezonową zmienność składników bilansu mocy składającego się z zapotrzebowania na moc odbiorców, generacji jednostek wytwórczych niebędących centralnie dysponowanymi (nJWCD), w tym odnawialnych źródeł energii (OZE), oraz jedno- stek wytwórczych centralnie dysponowanych (JWCD), co pozwala na analizę koincydencji wielu zmieniających się składowych bilansu mocy. Wynikiem symulacji są średnie roczne wartości oraz rozkłady prawdopodobieństwa: 1. wykorzystania zasobów regulacyjnych w KSE, np. elektrowni szczytowo-pompowych (ESP) 2. występowania krytycznych zdarzeń, np. deficytu pasma regulacji mocy lub naruszenia kryterium minimalnej wymaganej ilości pracujących JWCD 3. zdarzeń polegających na konieczności ograniczania mocy OZE ze względu na bezpieczeństwo pracy KSE.

10

Stochastic modelling of the repairable system

Andrzejczak K.

Journal of KONBiN

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2015

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No. 3 (35)

5--14

EN

All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

PL

Wszelkie modele niezawodności uwzględniające czynniki z losowym czasem przyjmują postać różnych procesów stochastycznych. W tej publikacji przywołujemy definicje podstawowych procesów stosowanych do modelowania systemów naprawialnych. W szczególności przedstawione są procesy stochastyczne wspomagające podejmowanie decyzji dotyczących utrzymania systemu technicznego. Rozważamy najprostszy jednoelementowy system z zaniedbywalnym czasem naprawy lub wymiany, tj. jednostka jest użytkowana a po uszkodzeniu jest naprawiana lub wymieniana w na tyle krótkim czasie, że można go pominąć. Po naprawie lub wymianie jednostka jest tak dobra jak nowa i dalej jest użytkowana. Stochastyczne modelowanie systemów naprawialnych stanowi doskonałą metodę wspomagania procesów decyzyjnych w ich utrzymaniu i pozwala na bardziej racjonalną ich eksploatację.

11

On the mathematical condition-based maintenance modelling for continuously deteriorating systems

Bérenguer C.

Journal of Polish Safety and Reliability Association

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2008

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Vol. 1

41--52

EN

This paper presents a modelling framework of condition-based maintenance policies for continuously deteriorating systems, based on semi-regenerative stochastic techniques.

12

Stochastic model of cavitation erosion of low-plasticity metallic materials

Gireń B. G.

Transactions of the Institute of Fluid-Flow Machinery

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2006

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nr 118

101-126

EN

Stochastic model of cavitation erosion of low plasticity solids was presented. It is a kinetic type model based on the energy conservation law. Mathematical formulation comprised equations for the energy accumulation and release rates. Micro-cracks were assumed to be the main negative source of energy. In calculations carried out, the random element was omitted and deterministic dependences of energy absorbed and relaxed in the process were found. Conformability of the theoretical and experimental curves was taken in favour of the model. The material fatique effect was expressed by the delay of micro-cracks appearance with respect to the force action time. The model sets a calculation direction of the temporal development of cavitation erosion. An application to practical cases requires the use of proper loading functions, as well as probabilistic distributions of the absorption and relaxation of energy, being the function of material parameters of the destroyed solid.

13

Conditional simulation of spatiotemporal random fields of environmental contamination

Jankowski R., Walukiewicz H.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2006

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Vol. 10, No 1

21-26

EN

The paper considers a method of conditional simulation of spatiotemporal scalar random fields of certain environmental phenomena. The method can be used to predict field values at given space points at specified time, on the basis of field values at other locations and data on second order moment functions in the domain. This approach has been applied to a space-time prognosis of soil contamination fields. The assessment of the spatiotemporal variability of heavy metals' concentrations provides the knowledge needed to monitor and control soil contamination. Empirical data of heavy metal (viz. chromium) concentration in the soil of northern Poland have been used in the study. The acceptance-rejection method has been applied to generate covariance matrices and vectors of discrete field values, taking into account conditional probability distributions. The results of the study show that the considered method can be successfully used to model conditional, spatiotemporal random fields of contamination with relatively small simulation errors.

14

Monitoring and stochastic modelling of tectonic movements in the Simitli Graben, SW Bulgaria

Tsenko T., Dobrev N.

Reports on Geodesy

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2004

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nr 1/68

35--43

EN

Clarifying the mechanism of some risky geodynamical processes could be performed using monitoring on the especially chosen sites. The obtained information is useful for studying and predicting of fault and landslide movements. For this purpose, three extensometers, type TM-71, Czech product, had been installed in 1982 at the southern parts of Simitii graben, SW Bulgaria. In the present paper, we present the results obtained by a long-term in-situ monitoring within the period 1984-2000. A stochastic modeling of the results of measurements to clarify some relationships in the behaviour of tectonic movements is applied. During the modeling, it was proposed some competitive programs - ARIMA and TRAMO/SEATS for models of temporary rows. Tendencies in the development of studied processes are established. Correlations between the tectonic movements and the temperature fluctuations are established, too. The adequateness of the models and the effectiveness of the prognoses were made using diagnostic verification of the statistical tests. The experimental investigations were performed using DEMETRA program.