Scipedia: Dejan Brkić's personal collection

A data-driven model of waste gasi pyrolysis: One tailored approach for an experimental facility from the Czech Republic

Dejan Brkić — Fri, 30 Jan 2026 23:05:13 +0100

The increasing demand for sustainable energy production necessitates the development of innovative technologies for converting municipal waste into valuable energy offering a viable alternative to fossil fuels. This study presents aﬂexible, portable, and expandable waste-to-energy concept that integrates gasiﬁcation and pyrolysis processes production of combustible gases and liquid fuels. Particular emphasis is placed on the use of transparent and interpretable modelling approaches to support system optimization and future scalability. The proposed methodology is demonstrated on two experimental systems currently operated at CEET Explorer, VSB– Technical University of Ostrava, Czech Republic: (i) A primary gasiﬁcation facility equipped with a plasma torch, reactor, hydrogen separator and tank, fuel cells, and renewable grid connections; and (ii) a secondary pyrolysis unit designed to maximize pyrolysis oil production. Both systems are modelled and simulated using in-house software developed in Python, employing

Evaluating the unavailability of interconnected power and communication networks with open-source tools on a petascale cluster

Dejan Brkić — Tue, 09 Dec 2025 16:40:24 +0100

In reliability engineering, unavailability is deﬁned as the probability that a system is not operational at a given point in time, typically due to failure or maintenance. A critical gap in reliability analysis by systematically evaluating the time-dependent unavailability of real interconnected power and communication networks in the Czech Republic is addressed in this work. These networks are modelled as acyclic graphs using open-source R packages. Unlike previous studies relying on commercial tools, the research presented here offers a novel, reproducible, and scalable framework. The main contribution lies in the innovative application and benchmarking of ftaproxim, an R package based on proxel simulation, which models ageing components during their entire life using various probabilistic distributions. This approach contrasts with traditional tools such as the FaultTree package, which are limited to asymptotic unavailability analysis. Here presented work evaluates both R packages on a real infrastructure model and compares their performance and computational efﬁciency on the Barbora supercomputer cluster against commercial software (Matlab). It is demonstrated how ftaproxim’s tolerance and time-step parameters can be tuned for robust computational efﬁciency and accuracy, an aspect previously unexplored. The results of the presented study show that unavailability computations can be completed in approximately 5 h under optimal settings, with absolute errors ranging from 1.0× 10−4to 9.6× 10−4when compared to commercial solutions. This integrated approach, combining open-source tools, high-

Sampling the Darcy friction factor using Halton, Hammersley, Sobol, and Korobov sequences: Data points from the Colebrook relation

Dejan Brkić — Thu, 20 Nov 2025 13:39:42 +0100

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

Reducing the number of input variables through symbolic regression

Dejan Brkić — Tue, 02 Sep 2025 17:37:33 +0200

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.

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

Dejan Brkić — Wed, 13 Aug 2025 19:47:13 +0200

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.

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

Dejan Brkić — Thu, 24 Jul 2025 13:30:44 +0200

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.

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

Dejan Brkić — Fri, 11 Jul 2025 14:21:43 +0200

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.

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

Dejan Brkić — Mon, 19 May 2025 15:11:23 +0200

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.

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

Dejan Brkić — Thu, 16 Jan 2025 14:54:03 +0100

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.

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

Dejan Brkić — Thu, 16 Jan 2025 14:35:03 +0100

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.

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

Dejan Brkić — Thu, 01 Feb 2024 13:37:03 +0100

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.

Serbian Energy Sector in a Gap Between East and West

Dejan Brkić — Thu, 18 Jan 2024 11:57:05 +0100

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.

Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter

Dejan Brkić — Thu, 14 Sep 2023 21:23:03 +0200

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.

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

Dejan Brkić — Tue, 04 Jul 2023 20:56:03 +0200

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.

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

Dejan Brkić — Wed, 31 May 2023 17:14:03 +0200

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

Dejan Brkić — Sun, 25 Sep 2022 19:36:02 +0200

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.

Reliability-Based Criterion for Evaluating Explicit Approximations of Colebrook Equation

Dejan Brkić — Fri, 24 Jun 2022 02:58:02 +0200

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.

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

Dejan Brkić — Thu, 19 May 2022 16:55:02 +0200

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.

Steady-State Analysis of Electrical Networks in Pandapower Software: Computational Performances of Newton–Raphson, Newton–Raphson with Iwamoto Multiplier, and Gauss– Seidel Methods

Dejan Brkić — Sun, 06 Mar 2022 14:34:02 +0100

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.

Approximate flow friction factor: Estimation of the accuracy using Sobol’s Quasi-Random sampling

Dejan Brkić — Sun, 06 Mar 2022 14:26:03 +0100

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.