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1

Using Bayesian methods in the task of modeling the patients' pharmacoresistance development

Voronenko Mariia A., Zhunissova Ulzhalgas M., Smailova Saule S., Lytvynenko Luidmila N., Savina Nataliia B., Mulesa Pavlo P., Lytvynenko Volodymyr

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2022

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T. 12, nr 2

77--82

EN

In this paper, we propose a methodology for using static Bayesian networks (BN) in modeling the development of pharmacoresistance in patients with a diagnosis of epilepsy. Methods for constructing the structure of a static BN, their parametric training, validation, sensitivity analysis and “What-if” scenario analysis are considered. The model was designed in collaboration with expert doctors, as well as expert pharmacologists in the selection and quantification of input and output variables.

PL

W niniejszej pracy zaproponowano metodologię wykorzystania statycznych sieci bayesowskich (BN) w modelowaniu rozwoju farmakooporności u pacjentów z rozpoznaniem padaczki. Rozważane są metody konstruowania struktury statycznej BN, jej parametrycznego treningu, walidacji, analizy wrażliwości i analizy scenariuszy "co-jeśli". Model został zaprojektowany we współpracy z ekspertami – lekarzami, a także ekspertami – farmakologami w zakresie doboru i kwantyfikacji zmiennych wejściowych i wyjściowych.

2

Cycles in Bayesian Networks

Shayakhmetova Assem, Litvinenko Natalya, Mamyrbayev Orken, Wójcik Waldemar, Zhamangarin Dusmat

International Journal of Electronics and Telecommunications

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2021

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Vol. 67, No. 2

181--186

EN

The article is devoted to some critical problems of using Bayesian networks for solving practical problems, in which graph models contain directed cycles. The strict requirement of the acyclicity of the directed graph representing the Bayesian network does not allow to efficiently solve most of the problems that contain directed cycles. The modern theory of Bayesian networks prohibits the use of directed cycles. The requirement of acyclicity of the graph can significantly simplify the general theory of Bayesian networks, significantly simplify the development of algorithms and their implementation in program code for calculations in Bayesian networks.

3

Achieving career satisfaction through fostering innovation: lessons from the engineering profession in the Australian public sector

Wipulanusat Warit, Panuwatwanich Kriengsak, Stewart Rodney A., Sunkpho Jirapon, Thamsatitdej Poomporn

Engineering Management in Production and Services

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2021

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Vol. 13, no. 4

7--21

EN

This paper proposes a novel approach that integrates the capability of empirical validation of structural equation modelling (SEM) and the prediction ability of Bayesian networks (BN). The Hybrid SEM–BN approach was used as a decision support framework to examine the interplay between salient organisational constructs and their ability to influence engineers’ career satisfaction in the Australian Public Service (APS). The results emphasise that the ambidextrous culture for innovation was the most important factor that needed to be implemented in their organisation. Managerial implications are recommended for senior managers on how they can implement innovation culture to increase workplace innovation, which could, in turn, help reduce the turnover rate of engineers employed in the APS.

4

Graph models with multiple Bayesian networks

Shayakhmetova Assem

Przegląd Elektrotechniczny

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2020

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R. 96, nr 12

252--255

EN

This paper is devoted to some issues of using multiple Bayesian networks in the various applied problems. Sometimes we deal with applied problems that are difficult to describe with a model that is represented by only one Bayesian network. At the same time, the considered problem may contain blocks with various types of uncertainties that can be well described by multiple Bayesian networks. Even if the problem can be described by only one Bayesian network, the size of this network could be so large that it will be impossible to find the solution with the help of existing software products. In this case, it is better to decompose in some way this large Bayesian network into several smaller ones. However, existing software products are poorly adapted to work with several Bayesian networks simultaneously. In this project, we develop and describe a software product that allows us to work with several Bayesian networks simultaneously.

PL

Artykuł ten jest poświęcony niektórym zagadnieniom związanym z wykorzystaniem szeregu sieci bayesowskich w różnych obszarach zastosowań. Czasami mamy do czynienia z zagadnieniami stosowanymi, które są trudne do opisania za pomocą modelu, który jest reprezentowany przez pojedynczą sieć Bayesa. Jednocześnie, rozważany problem może zawierać bloki z różnymi rodzajami niepewności, które mogą być dobrze opisane przez wiele sieci Bayesa. Nawet jeśli problem może być opisany tylko przez jedną sieć Bayesa, rozmiar tej sieci może być tak duży, że niemożliwe będzie znalezienie rozwiązania przy pomocy istniejącego oprogramowania. W tym przypadku lepiej jest rozłożyć w jakiś sposób tę dużą sieć na kilka mniejszych. Istniejące oprogramowanie jest jednak słabo przystosowane do pracy z kilkoma sieciami jednocześnie. W tym celu opracowaliśmy i opisaliśmy oprogramowanie, które pozwala nam na pracę z kilkoma sieciami Bayesa jednocześnie.

5

Unraveling key drivers for engineer creativity and meaningfulness of work: Bayesian network approach

Wipulanusat Warit, Panuwatwanich Kriengsak, Stewart Rodney A., Parnphumeesup Piya, Sunkpho Jirapon

Management and Production Engineering Review

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2020

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Vol. 11, No. 2

26--37

EN

This study builds on an existing structural model developed to examine the inﬂuence of leadership and organizational culture on innovation and satisfaction of engineers in Australian public sectors (APS). The objective of this study is to increase the understanding of innovation process with a focus on causal relationships among critical factors. To achieve this objective, the study develops an assessment approach to help predict creativity and work meaningfulness of engineers in the APS. Three quantitative analysis methods were sequentially conducted in this study including correlation analysis, path analysis, and Bayesian networks. A correlation analysis was conducted to pinpoint the strong association between key factors studied. Subsequently, path analysis was employed to identify critical pathways which were accordingly used as a structure to develop Bayesian networks. The ﬁndings of the study revealed practical strategies for promoting (1) transformational leadership and (2) innovative culture in public sector organizations since these two factors were found to be key drivers for individual creativity and work meaningfulness of their engineers. This integrated approach may be used as a decision support tool for managing the innovation process for engineers in the public sectors.

6

Application of the Bayesian networks in construction engineering

Leśniak Agnieszka, Janowiec Filip

Civil and Environmental Engineering Reports

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2020

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Vol. 30, no. 2

221--233

EN

Currently, significant development of methods supporting decision making under uncertainty conditions is observed. One of such methods includes Bayesian networks used in many fields of economy and science. The paper presents the use of the Bayesian network method in civil engineering problems with particular emphasis on construction engineering projects. In addition to the existing examples of the use of the method cited, the authors’ method for the risk estimation of additional works is presented.

7

An expert elicitation analysis for vessel allision risk near the offshore wind farm by using fuzzy rule-based bayesian network

Yu Q., Liu K.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2019

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Vol. 13. no. 4

831--837

EN

This paper develops an expert based framework for analysing and synthesising the ship allision risk near the offshore wind farm (OWF) on the basis of a generic Fuzzy Bayesian network and FMEA analysis. This framework is specifically intended to overcome the difficulty of using traditional risk assessment methods in OWF allision. Under the introduced framework, subjective belief degrees are assigned to model the incompleteness encountered in establishing the knowledge base. The fuzzy transformation technology is then used to introduce all judgements results under various situations. Fully, a Bayesian network is established to aggregate all relevant attributes to the conclusion and to prioritise potential allision risk level of each ship categories. A series of case studies of different ship categories are studied to illustrate the application of the proposed framework. Results show that the fishing vessel and the service vessel have a higher allision risk than the merchant vessel due to insufficient risk detection. The collision consequence of the tanker is significantly higher than other types of vessel. The framework facilitates subjective risk assessment when historical failure data is not available in their practice, which provides support to OWF-safeguarding and decision-making.

8

Development and application of a decision making tool for fault diagnosis of turbocompressor based on Bayesian network and fault tree

Lakehal Abdelaziz, Nahal Mourad, Harouz Riad

Management and Production Engineering Review

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2019

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Vol. 10, No. 2

16–-24

EN

Fault Tree is one of the traditional and conventional approaches used in fault diagnosis. By identifying combinations of faults in a logical framework it’s possible to define the structure of the fault tree. The same go with Bayesian networks, but the difference of these probabilistic tools is in their ability to reasoning under uncertainty. Some typical constraints to the fault diagnosis have been eliminated by the conversion to a Bayesian network. This paper shows that information processing has become simple and easy through the use of Bayesian networks. The study presented showed that updating knowledge and exploiting new knowledge does not complicate calculations. The contribution is the structural approach of faults diagnosis of turbo compressor qualitatively and quantitatively, the most likely faults are defined in descending order. The approach presented in this paper has been successfully applied to turbo compressor, which represent vital equipment in petrochemical plant.

9

Reducing pollution levels generated by short sea shipping : use of Bayesian networks to analyse the utilization of liquefied natural gas as an alternative fuel

Molina Serrano Beatriz, González Cancelas Nicoleta, Soler Flores Francisco

Journal of KONES

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2019

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Vol. 26, No. 1

147--158

EN

Pollution adjacent to the continent's shores has increased in the last decades, so it has been necessary to establish an energy policy to improve environmental conditions. One of the proposed solution was the search of alternative fuels to the commonly used in Short Sea Shipping to reduce pollution levels in Europe. Studies and researches show that liquefied natural gas could meet the European Union environmental requirements. Even environmental benefits are important; currently there is not significant number of vessels using it as fuel. Moreover, main target of this article is exposing result of a research in which a methodology to establish the most relevant variables in the decision to implement liquefied natural gas in Short Sea Shipping has been development using data mining. A Bayesian network was constructed because this kind of network allows to get graphically the relationships between variables and to determine posteriori values that quantify their contributions to decision-making. Bayesian model has been done using data from some European countries (European Union, Norway and Iceland) and database was generated by 35 variables classified in 5 categories. Main obtained conclusion in this analysis is that variables of transport and international trade and economy and finance are the most relevant in the decision-making process when implementing liquefied natural gas. Even more, it can be stablish that capacity of liquefied natural gas regasification terminals under construction and modal distribution of water cargo transportation continental as the most decisive variables because they are the root nodes in the obtained network.

10

Vibration testing in buildings and safety of their operation

Jakubczyk-Galczynska A., Siemaszko A.

Scientific Journal of the Military University of Land Forces

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2018

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Vol. 50, No. 3(189)

144-154

EN

The paper presents the issue of vibrations in residential buildings located near roads. It describes the measurement methodology and criteria for assessing the impact of vibrations generated by passing trucks. The article specifies a method to establish the impact on the operation of the examined facilities and it promotes the idea of employing a Bayesian network to determine probabilistically the level of risk to single-family houses.

11

A fuzzy KNN-based model for significant wave height prediction in large lakes

Nikoo M. R., Kerachian R., Alizadeh M. R.

Oceanologia

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2018

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No. 60 (2)

153--168

EN

Some algorithms based on fuzzy set theory (FST) such as fuzzy inference system (FIS) and adaptive-network-based fuzzy inference system (ANFIS) have been successfully applied to significant wave height (SWH) prediction. In this paper, perhaps for the first time, the fuzzy K-nearest neighbor (FKNN) algorithm is utilized to develop a fuzzy wave height prediction model for large lakes, where the fetch length depends on the wind direction. As fetch length (or wind direction) can affect the wave height in lakes, this variable is also considered as one of the inputs of the prediction model. The results of the FKNN model are compared with those of some soft computing techniques such as Bayesian networks (BNs), regression tree induction (named M5P), and support vector regression (SVR). The developed FKNN model is used for SWH prediction in the western part of Lake Superior in North America. The results show that the FKNN and M5P model can outperform the other soft computing techniques.

12

Calculation of the reliability function from actual failures resulting from the operation of one make of farm tractors

Durczak K., Ekielski A., Żelaziński T.

Journal of Research and Applications in Agricultural Engineering

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2018

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Vol. 63, nr 1

18--22

EN

Like all farming machinery, farm tractors should be characterised by high reliability, which guarantees trouble-free operation, especially during intense agrotechnical works. The knowledge of the course of reliability functions, especially the failure intensity function, is of high practical significance. It lets manufacturers lead the right overhaul policy and it lets users make the right purchase choice. Therefore, it is recommended to conduct research comparing the reliability of farming machinery. It is necessary to apply universal methodology and use a vast database providing information about failures of individual working units in various makes, models, types and variants of farming machinery. The method was validated by analysing failures of 29 components of Zetor farm tractors with the engine power ranging from 45 to 90 kW.

PL

Ciągniki rolnicze, tak jak wszystkie maszyny rolnicze, powinny charakteryzować się dużą niezawodnością, która gwarantuje im bezproblemową pracę, zwłaszcza w czasie wzmożonych prac agrotechnicznych. Znajomość przebiegów funkcji niezawodności, a przede wszystkim funkcji intensywności uszkodzeń, ma duże znaczenie praktyczne. Pozwala producentom prowadzić prawidłową politykę przeglądów technicznych, a użytkownikom ułatwić dokonanie prawidłowych wyborów w procesie zakupu. Wskazane są zatem badania pozwalające na porównywanie maszyn rolniczych pod względem ich niezawodności. Do tego celu niezbędna jest uniwersalna metodyka oraz obszerna baza danych o uszkodzeń poszczególnych zespołów roboczych różnych marek, modeli, odmian i wariantów maszyn rolniczych. Walidację metody przeprowadzono na podstawie uszkodzeń 29 podzespołów ciągników rolniczych marki Zetor o mocy silników w zakresie od 45 do 90 kW.

13

Empirical Evaluation of Methods of Filling the Missing Data in Learning Probabilistic Models

Falkowski A. A., Łupińska-Dubicka A.

Advances in Computer Science Research

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2018

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Nr 14

55--67

EN

Missing data is a common problem in statistical analysis and most practical databases contain missing values of some of their attributes. Missing data can appear for many reasons. However, regardless of the reason for the missing values, even a small percent of missing data can cause serious problems with analysis reducing the statistical power of a study and leading to draw wrong conclusions. In this paper the results of handling missing observations in learning probabilistic models were presented. Two data sets taken from UCI Machine Learning Repository were used to learn the quantitative part of the Bayesian networks. To provide the opportunity to compare selected data sets did not contain any missing values. For each model data sets with variety of levels of missing values were artificially generated. The main goal of this paper was to examine whether omitting observations has an influence on model’s reliability. The accuracy was defined as the percentage of correctly classified records and has been compared to the results obtained in the data set not containing missing values.

PL

Brakujące dane są częstym problemem w analizie statystycznej, a większość baz danych zawiera brakujące wartości niektórych z ich atrybutów. Brakujące dane mogą pojawiać się z wielu powodów. Jednak bez względu na przyczynę brakujących wartości nawet ich niewielki procent może spowodować poważne problemy z analizą, zmniejszając siłę statystyczną badania i prowadząc do wyciągnięcia błędnych wniosków. W artykule przedstawiono wyniki uzupełniania danych brakujących w uczeniu modeli probabilistycznych. Dwa zestawy danych pobrane z repozytorium uczenia maszynowego UCI posłużyły do wytrenowania ilościowej części sieci bayesowskich. Aby zapewnić możliwość porównania wybrane zbiory danych nie zawierały żadnych brakujących wartości. Dla każdego modelu zbiory danych z różnymi poziomami brakujących wartości zostały sztucznie wygenerowane. Głównym celem tego artykułu było zbadanie, czy braki w obserwacjach mają wpływ na niezawodność modelu. Dokładność została zdefiniowana jako procent poprawnie zaklasyfikowanych rekordów i została porównana z wynikami uzyskanymi w zbiorze danych niezawierającym brakujących wartości.

14

Empirical Comparison of Methods of Data Discretization in Learning Probabilistic Models

Wójciak M., Łupińska-Dubicka A.

Advances in Computer Science Research

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2018

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Nr 14

177--192

EN

Very often statistical method or machine learning algorithms can handle discrete attributes only. And that is why discretization of numerical data is an important part of the pre–processing. This paper presents the results of the problem of data discretization in learning quantitative part of probabilistic models. Four data sets taken from UCI Machine Learning Repository were used to learn the quantitative part of the Bayesian networks. The continuous variables were discretized using two supervised and two unsupervised discretization methods. The main goal of this paper was to study whether method of data discretization in given data set has an influence on model’s reliability. The accuracy was defined as the percentage of correctly classified records.

XX

Bardzo często algorytmy uczenia maszynowego nie są przystosowane do korzystania ze zmiennych ciągłych. Z tego powodu dyskretyzacja danych jest istotną częścią wstępnego przetwarzania. W artykule przedstawiono wyniki prac nad problemem dyskretyzacji danych w uczeniu modeli probabilistycznych. Cztery zestawy danych pobrane z repozytorium uczenia maszynowego UCI zostały wykorzystane do nauczenia parametrów ilościowej części sieci bayesowskich. Występujące w wybranych zbiorach zmienne ciągłe były dyskretyzowane przy użyciu dwóch metod nadzorowanych i dwóch nienadzorowanych. Głównym celem tego artykułu było zbadanie, czy metoda dyskretyzacji danych w danym zbiorze ma wpływ na niezawodność modelu. Dokładność metod była definiowana jako odsetek poprawnie sklasyfikowanych rekordów.

15

Analysis of economic and agricultural indicators under sustainable agriculture conditions with the use of Bayesian modelling

Grotkiewicz K.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2017

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nr 20(3)

209--225

EN

Searching for relations between the level of production intensity, land efficiency and work performance, comparative analyses were carried out on international scale taking into consideration 45 countries from around the world with the use of the Statistical Yearbook (2013) and International Statistics Yearbook (2015). The research covered basic qualification criteria of sustainable agriculture, i.e. the level of mineral fertilization and stocking density as well as productivity rates, i.e. land efficiency and work performance and factors which shape them. The main aim of the research is the use of Bayesian modelling in order to predict the development of various economical and agricultural indicators and also show relationships between events basing on the theory of probability.

16

Optimization of the logistics function by controlling risks using influence diagram: cases of risks related to road transport

Lakehal A., Tachi F.

Computer Assisted Methods in Engineering and Science

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2017

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Vol. 24, no. 4

239--252

EN

The growth in the number of logistics platforms served by road, rail, waterway, and sea is a logical consequence of the extensive and rapid development of merchandise trade in a globalized economy. Transportand logistics are part of the same activity chain that allowsgoods to be transported to their destination. Dependent on the requirements of their customers and suppliers and subject to strong competition,companies in this sector must manage challenges concerningdeadlines, flexibility, and diversity of goods,while handling other risks associated with transport and logistics. The Bayesian approach, proposed inthis paper, covers all the steps necessary to implement decision support solutions for risk managementand control, starting from the identification of risks and the preparation of intervention to the conductingof various operations in crisis In this work, the predictionand the control of the road risks are conductedusing the influence diagram method, whose final objective is the optimization of the logistics function.After identifying and analyzing the different risks, the Bayesian networks (BNs) are initially used to modelthese risks and to prevent the various challenging situations from taking place in the logistics chain. Asa second step, we use the influence diagram as a tool for the decision-making procedure. Finally, a casestudy is presented to highlight the substantial contribution of this tool to controlling road risks whiletransporting goods.

17

Application of Bayesian networks for forecasting future model of farm

Grotkiewicz K.

Agricultural Engineering

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2017

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Vol. 21, No. 2

69--79

EN

Comparative analyses in the national scale were carried out in 300 individual farms from Małopolskie and Świętokrzyskie Voivodeship in order to search for relations between the production intensity level, work performance and land efficiency and factors which shape them. The analyses concerned the use of Bayesian modelling algorithms for forecasting development of various economic and agricultural indicators which decide on the intensity and competitiveness of agriculture. The paper constitutes the second stage of research, which was preceded with previous preparation of data for modelling with the use of an exploratory overview of available data and TwoStep Cluster Analysis (Grotkiewicz et al., 2016). Based on the analyses, which were carried out, networks were built which present the relations between the analyzed variables, and conditional similarities were verified.

PL

Poszukując zależności między poziomem intensywności produkcji a wydajnością pracy i ziemi oraz czynnikami je kształtującymi, przeprowadzono analizy porównawcze w skali krajowej na tle 300 gospodarstw indywidualnych z województwa małopolskiego i świętokrzyskiego. Analiza dotyczyła zastosowania algorytmów modelowania bayesowskiego do przewidywania rozwoju różnych wskaźników ekonomiczno-rolniczych decydujących o intensywności i konkurencyjności rolnictwa. Praca stanowi drugi etap badań, który poprzedzony był wcześniejszym przygotowaniem danych do modelowania wykorzystując do tego eksploracyjny przegląd dostępnych danych, oraz technikę TwoStep Cluster Analysis (Grotkiewicz i in., 2016). W oparciu o przeprowadzone analizy zbudowano sieci obrazujące związki pomiędzy analizowanymi zmiennymi oraz sprawdzono prawdopodobieństwa warunkowe.

18

A cost benefit analysis approach to identify improvements in merchant navy deck officers’ HELM (Human Element Leadership and Management) training

Saeed F., Bury A., Bonsall S., Riahi R.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2016

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Vol. 10, no. 4

551--560

EN

A review of maritime accidents conducted over the last decade confirms that human error is the main contributing factor in these incidents. Well‐developed Non‐Technical Skills (NTS) can reduce the effects of human error. NTS include both interpersonal and cognitive skills such as situation awareness, teamwork, decision‐making, leadership, managerial skills, communication and language skills. In a crisis situation good NTS allow a deck officer to recognise the problem quickly, take action to manage the situation, and utilise the available team members safely and effectively. This paper identifies the importance of NTS training for merchant navy deck officers. It also highlights room for improvement in the existing HELM training. Research has shown that at present the structure of HELM training is not very effective. The other safety critical domains’ efforts into NTS developments are investigated and examples of best practice are adapted into the maritime domain’s NTS training. Suggestions are given for improvements to the HELM course based on proven successful methods in other safety critical domains (aviation and anaesthesia). A subsequent Cost Benefit Analysis for improving deck officers’ NTS is also carried out through the use of Bayesian Networks and Decision Tree Modelling.

19

How reliable is a measure of model reliability? Bootstrap confidence intervals over validation results

Koźniewski M., Cypko M. A., Drużdżel M. J.

Advances in Computer Science Research

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2016

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Nr 13

27--41

EN

A researcher testing a model will frequently question the reliability of the test results, understanding well the intuition that verification performed on a handful of cases is less reliable than verification based on very large numbers of cases. Because a limited number of verification cases happens pretty often in very specific domains, a question of practical importance is, thus, how reliable is a reported reliability measure. We propose a methodology based on deriving confidence intervals over various measures of accuracy of Bayesian network models by means of bootstrap confidence intervals. We evaluate our approach on ROC and calibration curves derived for a model derived from an UC Irvine Machine Learning Repository data set and a sizeable (over 300 variables) practical model constructed using expert knowledge and evaluated on merely 66 accumulated real patient cases. We show how increasing the number of test cases impacts the width of confidence intervals and how this can aid in estimating a reasonable number of verification cases that will increase the confidence in model reliability.

PL

Przy testowaniu modelu należy zdawać sobie z tego sprawę że weryfikacja modelu przy pomocy małego zbioru danych jest mniej przekonywująca niż weryfikacja bazująca na dużym zbiorze danych. Często napotyka się sytuację, w której do analizy modelu dysponujemy nieznaczną ilością rekordów. Nasuwa się pytanie o wiarygodność oceny modelu. Proponujemy w takiej sytuacji przyjrzeć się bootrstrapowym przedziałom ufności różnych ˙ miar dokładności modelu. W tej pracy określamy bootstrapowe przedziały ufności dla krzywych ROC i krzywych kalibracji modeli uzyskanych z danych z repozytorium UC Irvine. Czynność powtarzamy dla modelu skonstruowanego na podstawie wiedzy ekspertów (ponad 300 zmiennych) i testowanego na 66 zebranych rekordach pacjentów. Pokazujemy jak wzrost liczby rekordów wpływa na szerokość bootstrapowych przedziałów ufności oraz jak taka analiza może pomóc w określeniu liczby rekordów, która może podwyższyć rzetelność weryfikacji modelu.

20

Modelowanie niezawodności farmy wiatrowej z wykorzystaniem sieci bayesowskich i procesów semi-Markowa

Sobolewski R. A.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2015

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Nr 42

183--186

PL

Niezawodność urządzeń technicznych farmy wiatrowej (FW) wpływa między innymi na moc wyjściową farmy. Ilościową miarą tej niezawodności może być rozkład prawdopodobieństwa kombinacji stanów gotowości elektrowni wiatrowych (EW) farmy, tj. stanów oznaczających ich gotowość do produkcji energii elektrycznej i przekazywania jej do sieci elektroenergetycznej. Miarę tę można stosować do np. ilościowej analizy wpływu różnych topologii FW i niezawodności urządzeń farmy na jej niezawodność oraz wyznaczać wartość oczekiwaną mocy farmy z uwzględnieniem niezawodności. W artykule przedstawiono modele probabilistyczne opisujące ilościowo niezawodność FW, wykorzystujące sieci Bayesowskie (BN) i procesy semi-Markowa (PSM). W artykule zaprezentowano przykład obliczeniowy dotyczący analizy niezawodności FW składającej się z 4 EW, potwierdzający użyteczność metody.

EN

Factors that influence wind-farm output power also include the availability of a farm. The availability depends on: arrangements of a wind farm (WF), internal collection grid topology and reliability of electrical equipment included in WF (e.g. generators, transformers, cables, breakers, protective relays, busbars and so on). One of the measures of WF availability can be probability distribution of combinations of availability states of wind turbines generators (WTGs), where availability state means the WTG is able to generate and deliver power to external grid. This measure can be applied in e.g.: (1) study of different internal collection grid topologies and reliability of WF electrical equipment effects on availability of WF and (2) assessment of WF output power considering farm availability. In this work the probabilistic models of WF availability are presented. Because of stochastic nature of electrical equipment failures they rely on two modeling methods, i.e. Bayesian networks and semi-Markov processes. Both approaches allow taking into account the electrical equipment of WF, internal grid topology of WF and reliability characteristics of equipment. The case study of availability modeling is presented as well.