Dejan Brkić's personal collection : Scipedia

Sampling the Darcy friction factor using Halton, Hammersley, Sobol, and Korobov sequences: Data points from the Colebrook relation
D. Brkić, M. Milošević

Dejan Brkić's personal collection (2025). 8

Abstract
When the Colebrook equation is used in its original implicit form, the unknown pipe flow friction factor can only be obtained through time-consuming and computationally demanding iterative calculations. The empirical Colebrook equation relates the unknown Darcy friction factor to a known Reynolds number and a known relative roughness of a pipe’s inner surface. It is widely used in engineering. To simplify computations, a variety of explicit approximations have been developed, the accuracy of which must be carefully evaluated. For this purpose, this Data Descriptor gives a sufficient number of pipe flow friction factor values that are computed using a highly accurate iterative algorithm to solve the implicit Colebrook equation. These values serve as reference data, spanning the range relevant to engineering applications, and provide benchmarks for evaluating the accuracy of the approximations. The sampling points within the datasets are distributed in a way that minimizes gaps in the data. In this study, a Python Version v1 script was used to generate quasi-random samples, including Halton, Hammersley, Sobol, and deterministic lattice-based Korobov samples, which produce smaller gaps than purely random samples generated for comparison purposes. Using these sequences, a total of 220= 1,048,576 data points were generated, and the corresponding datasets are provided in in the zenodo repository. When a smaller subset of points is needed, the required number of initial points from these sequences can be used directly. Dataset:https://doi.org/10.5281/zenodo.17280142
Abstract
When the Colebrook equation is used in its original implicit form, the unknown pipe flow friction factor can only be obtained through time-consuming and computationally demanding [...]
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Reducing the number of input variables through symbolic regression
D. Brkić, P. Praks, M. Marek, U. Ilić, Z. Stajić

Electronic Research Archive (2025). 2. Brkić, D., Praks, P., Marek, M., Ilić, U., Stajić, Z. (2025). Reducing the number of input variables through symbolic regression. Electronic Research Archive, Vol. 33, No. 9, paper No. 5158-5178.

Abstract
Symbolic regression, a type of machine learning technique, can efficiently disregard variables that are not significant to the final output, even if they were initially preselected as inputs. Various input parameters are tested in the three examples presented here, where the outputs are modeled using symbolic regression: estimating the middle plasma torch temperature used for waste gasification, the active energy of a solar power plant, and the diameter of a pipe with a known flow and pressure drop through it. Final highly accurate formulas are produced after numerous attempts with lower performances. The process for rejecting the parameters without or with limited influence is automatic and can be performed without human intervention and supervision. The results obtained using symbolic regression are easily interpretable by human experts. This approach shows how to use machine learning-based modeling as an additional tool for sensitivity analysis.
Abstract
Symbolic regression, a type of machine learning technique, can efficiently disregard variables that are not significant to the final output, even if they were initially preselected [...]
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Maintenance optimization for unavailability enhancement of representative interconnected infrastructure based on minimum cost
P. Praks, R. Fujdiak, D. Brkić

Science Progress (2025). Briš, R., Praks, P., Fujdiak, R., Vrtal, M. and Brkić, D., 2025. Maintenance optimization for unavailability enhancement of representative interconnected infrastructure based on minimum cost. Science Progress, 108(3), p.00368504251366357.

Abstract
This paper explores the feasibility of solving a maintenance optimization problem in an interconnected smart grid system, comprising a power grid and a communication network, to reduce system unavailability. The unavailability, which must be in practice under the control of a system operator, is particularly sensitive to critical components in the power grid that must be under preventive maintenance (PM). The main goal is to find an optimal setup of PM within the specified mission time, minimizing system operation costs and reducing time-dependent unavailability. The method for unavailability quantification was remade to include different stochastic models for the unavailability calculation of system components working in different maintenance modes. A cost model is suggested to estimate the cost of various maintenance configurations. By applying these methodological tools designed to benefit users of any complex system, an optimal PM policy was developed for the selected smart grid. This policy reduces grid unavailability by approximately 20% and lowers costs by about 8.5% compared to a configuration without maintenance.
Abstract
This paper explores the feasibility of solving a maintenance optimization problem in an interconnected smart grid system, comprising a power grid and a communication network, [...]
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Natural Gas Heating in Serbian and Czech Towns: The Role of Urban Topologies and Building Typologies
D. Brkić, Z. Stajić

Urban Science (2025). Brkić, D.; Stajić, Z.; Temeljkovski Novaković, D. Natural Gas Heating in Serbian and Czech Towns: The Role of Urban Topologies and Building Typologies. Urban Sci. 2025, 9, 284. https://doi.org/10.3390/urbansci9070284

Abstract
This article presents an analysis on natural gas heating in residential areas, focusing on two primary systems: (1) local heating, where piped gas is delivered directly to individual dwellings equipped with autonomous gas boilers, and (2) district heating, where gas or an alternative fuel powers a central heating plant, and the generated heat is distributed to buildings via a thermal network. The choice between these systems should first consider safety and environmental factors, followed by the urban characteristics of the settlement. In particular, building typology—such as size, function, and spatial configuration—and urban topology, referring to the relative positioning of buildings, play a crucial role. For example, very tall buildings often exclude the use of piped gas due to safety concerns, whereas in other cases, economic efficiency becomes the determining factor. To support decisionmaking, a comparative cost analysis is conducted, assessing the required infrastructure for both systems, including pipelines, boilers, and associated components. The study identifies representative residential building types in selected urban areas of Serbia and Czechia that are suitable for either heating approach. Additionally, the article examines the broader energy context in both countries, with emphasis on recent developments in the natural gas sector and their implications for urban heating strategies.
Abstract
This article presents an analysis on natural gas heating in residential areas, focusing on two primary systems: (1) local heating, where piped gas is delivered directly to [...]
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European Efficiency Schemes for Domestic Gas Boilers: Estimation of Savings in Heating of Settlements
D. Brkić

Algorithms (2025). Brkić, D. European Efficiency Schemes for Domestic Gas Boilers: Estimation of Savings in Heating of Settlements. Algorithms 2025, 18, 416. https://doi.org/10.3390/a18070416

Abstract
This article aims to evaluate the seasonal efficiency of natural gas boilers used in European households, highlighting the cost effectiveness, environmental benefits, and user comfort associated with higher-efficiency models, particularly those based on condensing technology. The study applies a standardized algorithm used in European energy labeling schemes to calculate the seasonal efficiency of household gas boilers. It further includes a comparative analysis of selected boiler models available on the Serbian market and outlines a step-by-step method for estimating gas savings when replacing older, less efficient boilers with modern units. Condensing boilers demonstrate significantly higher seasonal efficiency than standard models by recovering additional heat from exhaust gases. These improved boilers produce lower greenhouse gas emissions and offer annual fuel savings of approximately 10% to 30%, depending on the boiler’s age, system design, and usage patterns. The results also confirm the direct correlation between seasonal efficiency and annual fuel consumption, validating the use of efficiency-based cost comparisons. The analysis focuses on residential gas boilers available in the Serbian market, although the models examined are commonly distributed across Europe. The findings highlight the important role of energy efficiency labels—based on a standardized algorithm—in guiding boiler selection, helping consumers and policymakers make informed decisions that promote energy savings and reduce environmental impact. This article contributes to the theoretical and practical understanding of gas boiler efficiency by integrating algorithm-based evaluation with market data and user-centered considerations. It offers actionable insights for consumers, energy advisors, and policymakers in the context of Europe’s energy transition. Verifying the efficiency calculations of gas boilers requires a careful combination of theoretical methods, measured data, and adherence to standards.
Abstract
This article aims to evaluate the seasonal efficiency of natural gas boilers used in European households, highlighting the cost effectiveness, environmental benefits, and [...]
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Experimental Analysis of Magnetic Focusing of the Plasma Arc of a Cutting Torch
M. Marek, D. Brkić, P. Praks, T. Kozubek, J. Frantík

Materials (2025). Marek, M.; Brkić, D.; Praks, P.; Kozubek, T.; Frantík, J. Experimental Analysis of Magnetic Focusing of the Plasma Arc of a Cutting Torch. Materials 2025, 18, 1811. https://doi.org/10.3390/ma18081811

Abstract
This study aimed to verify the possibility of stabilizing and focusing a plasma column generated by a plasma cutter. The simulation performed by the COMSOL Multiphysics software is based on the actual configuration and geometry of the burner. This article presented a universal computational method based on FEM simulations, focusing on the deflection of the current of electrically charged particles in a magnetic field within the context of a plasma cutting torch. The simulations estimate the optimal shape and positioning of a focused electron beam for various magnetic lens positions and plasma stream energies, revealing that higher initial electron energies lead to a more even beam focus. Among the configurations tested, positioning the cathode 3 mm above the ring-shaped permanent magnet proved most effective, maintaining beam linearity and minimizing electron scattering, making it suitable for practical implementations.
Abstract
This study aimed to verify the possibility of stabilizing and focusing a plasma column generated by a plasma cutter. The simulation performed by the COMSOL Multiphysics software [...]
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Fire Hazards Caused by Equipment Used in Offshore Oil and Gas Operations: Prescriptive vs. Goal-Oriented Legislation
D. Brkić

Fire (2025). https://www.mdpi.com/2571-6255/8/1/29

Abstract
Тhis article offers a concise overview of the best practices for safety in offshore oil and gas operations, focusing on the risks associated with various types of equipment, particularly on the risk of fire. It identifies specific machinery and systems that could pose hazards, assesses their potential impact on safety, and explores conditions that may lead to accidents. Some of the largest accidents were analyzed for their associations with fire hazards and specific equipment. Two primary regulatory approaches to offshore safety are examined: the prescriptive approach in the United States (US) and the goal-oriented approach in Europe. The prescriptive approach mandates strict compliance with specific regulations, while in the goal-oriented approach a failure to adhere to recognized best practices can result in legal accountability for negligence, especially concerning human life and environmental protection. This article also reviews achievements in safety through the efforts of regulatory authorities, industry collaborations, technical standards, and risk assessments, with particular attention given to the status of Mobile Offshore Drilling Units (MODUs). Contrary to common belief, the most frequent types of accidents are not those involving a fire/explosion caused by the failure of the Blowout Preventer (BOP) after a well problem has already started. Following analysis, it can be concluded that the most frequent type of accident typically occurs without fire and is due to material fatigue. This can result in the collapse of the facility, capsizing of the platform, and loss of buoyancy of mobile units, particularly in bad weather or during towing operations. It cannot be concluded that accidents can be more efficiently prevented under a specific type of safety regime, whether prescriptive or goal-oriented.
Abstract
Тhis article offers a concise overview of the best practices for safety in offshore oil and gas operations, focusing on the risks associated with various types of equipment, [...]
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Serbian energy sector in the global political landscape amid the Russia‑Ukraine war: a focus on perspectives of integration into the European Union
D. Brkić

Discover Energy (2024). https://link.springer.com/article/10.1007/s43937-024-00056-2

Abstract
This article consists of two main parts, both in relation to Serbia’s accession to the European Union EU in relation to its energy sector: (1) Political and policy issues, and (2) Energy production, consumption and pricing. Each is heavily influenced by the Russia-Ukraine War. Political issues are primarily related to Kosovo, which unilaterally declared independence from Serbia. Regarding supply, Serbia’s energy sector is affected unevenly: while electricity production remains self-sufficient, shortages in oil and gas necessitate imports. Natural gas imports, primarily from Russia, now bypass Ukraine, aided by the new Turk Stream pipeline via Black Sea and also new EU-funded interconnector with Bulgaria. Newly introduced EU sanctions restrict Russian crude oil imports especially via maritime routes, but Russian influence still dominates domestic refineries and hydrocarbon extraction. Serbia’s heavy reliance on environmentally unfriendly lignite conflicts with EU renewable goals, but on the other hand protests against small hydropower projects for capturing rivers in pipes are frequent nowadays. Recent issues in the largest thermal power plant led to costly temporary imports. Despite challenges, Serbia navigates a complex energy landscape, balancing geopolitical realities with domestic and EU objectives while addressing environmental concerns, energy security and its national interest.
Abstract
This article consists of two main parts, both in relation to Serbia’s accession to the European Union EU in relation to its energy sector: (1) Political and policy issues, [...]
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Two iterative methods for sizing pipe diameters in gas distribution networks with loops
D. Brkić

Computation (2024). Brkić D. Two Iterative Methods for Sizing Pipe Diameters in Gas Distribution Networks with Loops. Computation. 2024; 12(2):25.

Abstract
Closed-loop pipe systems allow the possibility of the flow of gas from both directions across each route, ensuring supply continuity in the event of a failure at one point, but their main shortcoming is in the necessity to model them using iterative methods. Two iterative methods of determining the optimal pipe diameter in a gas distribution network with closed loops are described in this paper, offering the advantage of maintaining the gas velocity within specified technical limits, even during peak demand. They are based on the following: (1) a modified Hardy Cross method with the correction of the diameter in each iteration and (2) the node-loop method, which provides a new diameter directly in each iteration. The calculation of the optimal pipe diameter in such gas distribution networks relies on ensuring mass continuity at nodes, following the first Kirchhoff law, and concluding when the pressure drops in all the closed paths are algebraically balanced, adhering to the second Kirchhoff law for energy equilibrium. The presented optimisation is based on principles developed by Hardy Cross in the 1930s for the moment distribution analysis of statically indeterminate structures. The results are for steady-state conditions and for the highest possible estimated demand of gas, while the distributed gas is treated as a noncompressible fluid due to the relatively small drop in pressure in a typical network of pipes. There is no unique solution; instead, an infinite number of potential outcomes exist, alongside infinite combinations of pipe diameters for a given fixed flow pattern that can satisfy the first and second Kirchhoff laws in the given topology of the particular network at hand.
Abstract
Closed-loop pipe systems allow the possibility of the flow of gas from both directions across each route, ensuring supply continuity in the event of a failure at one point, [...]
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Serbian Energy Sector in a Gap Between East and West
D. Brkić

Serbian energy sector in a gap between east and west (2024). 1. Brkić, D. (2024). Serbian energy sector in a gap between east and west. Energy Exploration & Exploitation, Vol. 42, No. 1, 330-340., https://doi.org/10.1177/01445987231215445, eISSN 2048-4054 (online version) - ISSN 0144-5987 (printed version)

Abstract
Serbia’s energy sector is heavily reliant on Russian inﬂuence. On the other hand, Serbia’s status as a candidate country for joining the European Union (EU) membership requires active working toward diversifying energy sources of supply. In the past decade, Serbia has secured a reduced price for natural gas through a bilateral agreement with Russia, addressing the shortfall in its domestic production. The former agreement priced Russian gas at US$270 per thousand cubic meters and expired in 2021. The new deal links gas prices to crude oil and ranges between US $310 and US$408, maintaining its competitive position as one of Europe’s lowest import prices. Furthermore, alongside the new gas pipeline for Russian gas exports, the EU is funding the construction of a new interconnector, both with entry points from Bulgaria. Serbia also faces signiﬁcant dependence on crude oil, and this reliance is compounded by the inability to import it from Russia any longer. Opposite, Serbia is usually self-sufﬁcient in electricity production which still remains under state ownership. The domestic exploration and processing of oil and gas, as well as the sole underground gas storage facility in Serbia, have partial ownership by Russian Gazprom while the transportation of gas is under the full control of the Serbian government. This Communication about the energy situation in the Republic of Serbia put particular emphasis on the evolving political dynamics in the global energy market with a speciﬁc focus on the Russia– Ukraine war. The topic is also linked to the contentious status of the southern Serbian autonomous province, recognized as an independent state by the majority of Western nations but not by Serbia. It is feared that Serbia’s energy dependence on Russia could have signiﬁcant ramiﬁcations for its EU candidacy.
Abstract
Serbia’s energy sector is heavily reliant on Russian inﬂuence. On the other hand, Serbia’s status as a candidate country for joining the European Union (EU) [...]
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Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter
D. Brkić, P. Praks, R. Praksová, T. Kozubek

Axioms (2023). Brkić, D.; Praks, P.; Praksová, R.; Kozubek, T. Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter. Axioms 2023, 12, 850. https://doi.org/10.3390/axioms12090850

Abstract
This study provides novel and accurate symbolic regression-based solutions for the calculation of pipe diameter when flow rate and pressure drop (head loss) are known, together with the length of the pipe, absolute inner roughness of the pipe, and kinematic viscosity of the fluid. PySR and Eureqa, free and open-source symbolic regression tools, are used for discovering simple and accurate approximate formulas. Three approaches are used: (1) brute force of computing power, which provides results based on raw input data; (2) an improved method where input parameters are transformed through the Lambert W-function; (3) a method where the results are based on inputs and the Colebrook equation transformed through new suitable dimensionless groups. The discovered models were simplified by the WolframAlpha simplify tool and/or the equivalent Matlab Symbolic toolbox. Novel models make iterative calculus redundant; they are simple for computer coding while the relative error remains lower compared with the solution through nomograms. The symbolic-regression solutions discovered by brute force computing power discard the kinematic viscosity of the fluid as an input parameter, implying that it has the least influence.
Abstract
This study provides novel and accurate symbolic regression-based solutions for the calculation of pipe diameter when flow rate and pressure drop (head loss) are known, together [...]
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Serbian Natural Gas Sector in a Gap Between East and West: ChatGPT Decision Support
D. Brkić

Dejan Brkić's personal collection (2023). 2

Abstract
This article should examine ideas of how a chatbot can support decision making processes by collecting general opinion about the certain topics. The ChatGPT is tested in this article in respect of natural gas security of supply of the Republic of Serbia in the context of the current political situation in the world. The author first describes its own stance on the topic and then the ChatGPT is asked for its opinion (which most probably collects and compiles phrases from English speaking sources to build a text in a smart way). The topic is ort only about security of gas supply of Serbia but also political and highly sensitive, so it is examined if the ChatGPT can be useful tool to reach a balance between less on more favorable options in the process of policy making.
Abstract
This article should examine ideas of how a chatbot can support decision making processes by collecting general opinion about the certain topics. The ChatGPT is tested in this [...]
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Discussion of “Explicit Solution for Pipe Diameter Problem Using Lambert W-Function”
D. Brkić, P. Praks

Journal of Irrigation and Drainage Engineering (2023). Brkić, D. and Praks, P., 2023. Discussion of “Explicit Solution for Pipe Diameter Problem Using Lambert W-Function”. Journal of Irrigation and Drainage Engineering, 149(7), p.07023016. https://doi.org/10.1061/JIDEDH.IRENG-10071
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Selection of Appropriate Symbolic Regression Models Using Statistical and Dynamic System Criteria: Example of Waste Gasification
P. Praks, D. Brkić

Axioms (2022). Praks, P.; Lampart, M.; Praksová, R.; Brkić, D.; Kozubek, T.; Najser, J. Selection of Appropriate Symbolic Regression Models Using Statistical and Dynamic System Criteria: Example of Waste Gasification. Axioms 2022, 11, 463.

Abstract
In this paper, we analyze the interpretable models from real gasification datasets of the project “Centre for Energy and Environmental Technologies” (CEET) discovered by symbolic regression. To evaluate CEET models based on input data, two different statistical metrics to quantify their accuracy are usually used: Mean Square Error (MSE) and the Pearson Correlation Coefficient (PCC). However, if the testing points and the points used to construct the models are not chosen randomly from the continuum of the input variable, but instead from the limited number of discrete input points, the behavior of the model between such points very possibly will not fit well the physical essence of the modelled phenomenon. For example, the developed model can have unexpected oscillatory tendencies between the used points, while the usually used statistical metrics cannot detect these anomalies. However, using dynamic system criteria in addition to statistical metrics, such suspicious models that do fit well-expected behavior can be automatically detected and abandoned. This communication will show the universal method based on dynamic system criteria which can detect suitable models among all those which have good properties following statistical metrics. The dynamic system criteria measure the complexity of the candidate models using approximate and sample entropy. The examples are given for waste gasification where the output data (percentage of each particular gas in the produced mixture) is given only for six values of the input data (temperature in the chamber in which the process takes place). In such cases instead, to produce expected simple spline-like curves, artificial intelligence tools can produce inappropriate oscillatory curves with sharp picks due to the known tendency of symbolic regression to produce overfitted and relatively more complex models if the nature of the physical model is simple.
Abstract
In this paper, we analyze the interpretable models from real gasification datasets of the project “Centre for Energy and Environmental Technologies” (CEET) discovered [...]
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Reliability-Based Criterion for Evaluating Explicit Approximations of Colebrook Equation
S. Easa, A. Lamri, D. Brkić

Journal of Marine Science and Engineering (2022). Easa SM, Lamri AA, Brkić D. Reliability-Based Criterion for Evaluating Explicit Approximations of Colebrook Equation. Journal of Marine Science and Engineering. 2022; 10(6):803. https://doi.org/10.3390/jmse10060803

Abstract
Numerous explicit approximations of the Colebrook equation have been developed and evaluated based on two criteria: prediction accuracy and computational efficiency. This paper introduces a new evaluation criterion based on the reliability of each equation. The reliability is defined by the coefficient of variation (CV) of the explicit friction factor that is a function of the variabilities of component random variables (roughness height of the internal pipe surface and kinematic viscosity of the fluid). The coefficient of variation of the friction factor depends on its first derivative for roughness height of the inner pipe surface and kinematic viscosity of the fluid and their correlation. Seven explicit approximations were evaluated using the new reliability-based criterion. The results show that all explicit approximations are very reliable, but variations exist regarding the reliability level. The reliabilities of the seven approximations is very close for the rough-flow regime and when the CV of the viscosity is minimal. However, for the smooth-flow regime, and when the CV of the roughness is minimal, various approximations showed substantially different reliabilities. The novelty of the proposed criterion is that it addresses an evaluation dimension that complements the accuracy and efficiency criteria.
Abstract
Numerous explicit approximations of the Colebrook equation have been developed and evaluated based on two criteria: prediction accuracy and computational efficiency. This [...]
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Hydraulic Losses in Systems of Conduits with Flow from Laminar to Fully Turbulent: A New Symbolic Regression Formulation
M. Milošević, D. Brkić, P. Praks, D. Litričin, Z. Stajić

Axioms (2022). Milošević, Marko, Dejan Brkić, Pavel Praks, Dragan Litričin, and Zoran Stajić. 2022. "Hydraulic Losses in Systems of Conduits with Flow from Laminar to Fully Turbulent: A New Symbolic Regression Formulation" Axioms 11, no. 5: 198. https://doi.org/10.3390/axioms11050198

Abstract
Separate flow friction formulations for laminar and turbulent regimes of flow through pipes are in common use in engineering practice. However, variation of different parameters in a system of conduits during conveying of fluids can cause changes in flow pattern from laminar to fully turbulent and vice versa. Because of that, it is useful to unify formulations for laminar and turbulent hydraulic regimes in one single coherent equation. In addition to a physical interpretation of hydraulic friction, this communication gives a short overview of already available Darcy’s flow friction formulations for both laminar and turbulent flow and additionally includes two simple completely new approximations based on symbolic regression.
Abstract
Separate flow friction formulations for laminar and turbulent regimes of flow through pipes are in common use in engineering practice. However, variation of different parameters [...]
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Steady-State Analysis of Electrical Networks in Pandapower Software: Computational Performances of Newton–Raphson, Newton–Raphson with Iwamoto Multiplier, and Gauss– Seidel Methods
J. Vysocký, L. Foltyn, D. Brkić, R. Praksová, P. Praks

Sustainability (2022). Vysocký, J.; Foltyn, L.; Brkić, D.; Praksová, R.; Praks, P. Steady-State Analysis of Electrical Networks in Pandapower Software: Computational Performances of Newton–Raphson, Newton–Raphson with Iwamoto Multiplier, and Gauss–Seidel Methods. Sustainability 2022, 14, 2002. https://doi.org/10.3390/su14042002

Abstract
At the core of every system for the efficient control of the network steady-state operation is the AC-power-flow problem solver. For local distribution networks to continue to operate effectively, it is necessary to use the most powerful and numerically stable AC-power-flow problem solvers within the software that controls the power flows in these networks. This communication presents the results of analyses of the computational performance and stability of three methods for solving the AC-power-flow problem. Specifically, this communication compares the robustness and speed of execution of the Gauss–Seidel (G–S), Newton–Raphson (N–R), and Newton–Raphson method with Iwamoto multipliers (N–R–I), which were tested in open-source pandapower software using a meshed electrical network model of various topologies. The test results show that the pandapower implementations of the N–R method and the N–R–I method are significantly more robust and faster than the G–S method, regardless of the network topology. In addition, a generalized Python interface between the pandapower and the SciPy package was implemented and tested, and results show that the hybrid Powell, Levenberg–Marquardt, and Krylov methods, a quasilinearization algorithm, and the continuous Newton method can sometimes achieve better results than the classical N–R method.
Abstract
At the core of every system for the efficient control of the network steady-state operation is the AC-power-flow problem solver. For local distribution networks to continue [...]
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Approximate flow friction factor: Estimation of the accuracy using Sobol’s Quasi-Random sampling
P. Praks, D. Brkić

Axioms (2022). Praks, P.; Brkić, D. Approximate Flow Friction Factor: Estimation of the Accuracy Using Sobol’s Quasi-Random Sampling. Axioms 2022, 11, 36. https://doi.org/10.3390/axioms11020036

Abstract
The unknown friction factor from the implicit Colebrook equation cannot be expressed explicitly in an analytical way, and therefore to simplify the calculation, many explicit approximations can be used instead. The accuracy of such approximations should be evaluated only throughout the domain of interest in engineering practice where the number of test points can be chosen in many different ways, using uniform, quasi-uniform, random, and quasi-random patterns. To avoid picking points with undetected errors, a sufficient minimal number of such points should be chosen, and they should be distributed using proper patterns. A properly chosen pattern can minimize the required number of testing points that are sufficient to detect maximums of the error. The ability of the Sobol quasi-random vs. random distribution of testing points to capture the maximal relative error using a sufficiently small number of samples is evaluated. Sobol testing points that are quasi-randomly distributed can cover the domain of interest more evenly, avoiding large gaps. Sobol sequences are quasi-random and are always the same, which allows the exact repetition of scientific results.
Abstract
The unknown friction factor from the implicit Colebrook equation cannot be expressed explicitly in an analytical way, and therefore to simplify the calculation, many explicit [...]
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Probability Analysis and Prevention of Offshore Oil and Gas Accidents: Fire as a Cause and a Consequence
D. Brkić, P. Praks

Fire (2021). Brkić, Dejan, and Pavel Praks. 2021. "Probability Analysis and Prevention of Offshore Oil and Gas Accidents: Fire as a Cause and a Consequence" Fire 4, no. 4: 71. https://doi.org/10.3390/fire4040071

Abstract
ailures during the drilling and exploitation of hydrocarbons that result in catastrophic offshore oil and gas accidents are relatively rare but if they occur the consequences can be catastrophic in terms of loss of life and environmental damage. Therefore, to gain insight into their prevention, the largest major offshore oil and gas accidents, those with more than 10 fatalities or with a large environmental impact, are analyzed in this article. Special attention is placed on fire as a cause and a consequence. Relevant technological and legislative changes and updates regarding safety that have followed such accidents and that can prevent potential future similar misfortunes are evaluated. Two main approaches to safety are compared: (1) the American prescriptive vs. (2) the European goal-oriented approach. The main causes of accidents are tested statistically in respect of failure probability, where the exact confidence limits for the estimated probabilities are computed. The results of the statistical test based on exact confidence intervals show that there is no significant difference between the analysed factors, which describe the main causes of offshore oil and gas accidents. Based on the small but carefully chosen group of 24 of the largest accidents, it can be concluded that there is no evidence of a difference between the categories of the main causes of accidents.
Abstract
ailures during the drilling and exploitation of hydrocarbons that result in catastrophic offshore oil and gas accidents are relatively rare but if they occur the consequences [...]
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Excel VBA-based user defined functions for highly precise Colebrook’s pipe flow friction approximations: A comparative overview
D. Brkić, Z. Stajić

Facta Universitatis, series: Mechanical Engineering (FU Mech Eng) (2021). Brkić, D. and Stajić, Z., 2021. Excel VBA-Based User Defined Functions for Highly Precise Colebrook’s Pipe Flow Friction Approximations: A Comparative Overview. Facta Universitatis, Series: Mechanical Engineering 9(2):7267. Available from: http://casopisi.junis.ni.ac.rs/index.php/FUMechEng/article/view/7267

Abstract
This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User Defined Functions – UDFs written in Visual Basic for Applications – VBA, a common programming language for MS Excel spreadsheet solver. Accuracy of the friction factor computed using nine to date the most accurate explicit approximations is compared with the sufficiently accurate solution obtained through an iterative scheme which gives satisfying results after sufficient number of iterations. The codes are given for the presented approximations, for the used iterative scheme and for the Colebrook equation expressed through the Lambert W-function (including its cognate Wright ωfunction). The developed code for the principal branch of the Lambert W-function has additional and more general application for solving different problems from variety branches of engineering and physics. The approach from this review paper automates computational processes and speeds up manual tasks.
Abstract
This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User [...]
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Sampling the Darcy friction factor using Halton, Hammersley, Sobol, and Korobov sequences: Data points from the Colebrook relation

Reducing the number of input variables through symbolic regression

Maintenance optimization for unavailability enhancement of representative interconnected infrastructure based on minimum cost

Natural Gas Heating in Serbian and Czech Towns: The Role of Urban Topologies and Building Typologies

European Efficiency Schemes for Domestic Gas Boilers: Estimation of Savings in Heating of Settlements

Experimental Analysis of Magnetic Focusing of the Plasma Arc of a Cutting Torch

Fire Hazards Caused by Equipment Used in Offshore Oil and Gas Operations: Prescriptive vs. Goal-Oriented Legislation

Serbian energy sector in the global political landscape amid the Russia‑Ukraine war: a focus on perspectives of integration into the European Union

Two iterative methods for sizing pipe diameters in gas distribution networks with loops

Serbian Energy Sector in a Gap Between East and West

Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter

Serbian Natural Gas Sector in a Gap Between East and West: ChatGPT Decision Support

Discussion of “Explicit Solution for Pipe Diameter Problem Using Lambert W-Function”

Selection of Appropriate Symbolic Regression Models Using Statistical and Dynamic System Criteria: Example of Waste Gasification

Reliability-Based Criterion for Evaluating Explicit Approximations of Colebrook Equation

Hydraulic Losses in Systems of Conduits with Flow from Laminar to Fully Turbulent: A New Symbolic Regression Formulation

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Brkić, Dejan 17566

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