Scipedia: Dejan Brkić's personal collection

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.

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.

Probability Analysis and Prevention of Offshore Oil and Gas Accidents: Fire as a Cause and a Consequence

Dejan Brkić — Thu, 28 Oct 2021 14:05:04 +0200

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.

Excel VBA-based user defined functions for highly precise Colebrook’s pipe flow friction approximations: A comparative overview

Dejan Brkić — Wed, 15 Sep 2021 14:42:03 +0200

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.

Offshore Oil and Gas Safety: Protection against Explosions

Dejan Brkić — Mon, 22 Mar 2021 13:55:03 +0100

Offshore oil and gas operations carry a high risk of explosions, which can be efficiently prevented in many cases. The two most used approaches for prevention are: (1) the “International Electrotechnical Commission System for Certification to Standards Relating to Equipment for Use in Explosive Atmospheres” (IECEx) and (2) European “Atmosphere Explosible” (ATEX) schemes. The main shortcoming for the IECEx scheme is in the fact that it does not cover nonelectrical equipment, while for the ATEX scheme, it is due to the allowed self-certification for a certain category of equipment in areas with a low probability of explosions, as well as the fact that it explicitly excludes mobile offshore drilling units from its scope. An advantage of the IECEx scheme is that it is prescribed by the US Coast Guard for protection against explosions on foreign mobile offshore drilling units, which intend to work on the US continental shelf but have never operated there before, with an additional requirement that the certificates should be obtained through a US-based Certified Body (ExCB). Therefore, to avoid bureaucratic obstacles and to be allowed to operate with minimized additional costs both in the US and the EU/EEA’s offshore jurisdictions (and very possibly worldwide), all mobile offshore drilling units should be certified preferably as required by the US Coast Guard.

Simplified Indirect Estimation of Pump Flow Discharge: An Example from Serbia

Dejan Brkić — Mon, 22 Mar 2021 13:41:02 +0100

In the absence of a flowmeter or due to its inaccuracy, the flow rate at the discharge section of the pipeline following the observed pump can be roughly estimated if the pressure can be measured instead. To use the proposed procedure two main conditions should be achieved: (1) a manometer should be installed at the discharge pipeline between the pump and the flow regulation valve, and (2) the actual curve that relates pressure and flow for the observed pump unit should be known in advance. The described example is from Serbia, but it is of interest for any water pumping station with a submersible pump (installed in wells or tanks) where a limited number of adequate places for the measuring of flow are available (if any are available at all), but where the pressure at the discharge pipe of the observed pump can be measured. This simplified method can find applicability in installations in remote rural regions where limited resources are available. The results show that the calculated values of the flow obtained by the presented method deviate greatly in relation to the measured values provided by the portable ultrasonic flowmeter, up to 60% at one of the measuring points. However, in relation to the measured values provided by the permanently installed flowmeter the discrepancy is significantly lower (0.6–6.8%).

Suitability for coding of the Colebrook’s flow friction relation expressed by symbolic regression approximations of the Wright-ω function

Dejan Brkić — Sun, 13 Dec 2020 23:18:02 +0100

This article analyses a form of the empirical Colebrook’s pipe flow friction equation given originally by the Lambert W-function and recently also by the Wright ω-function. These special functions are used to explicitly express the unknown flow friction factor of the Colebrook equation, which is in its classical formulation given implicitly. Explicit approximations of the Colebrook equation based on approximations of the Wright ω-function given by an asymptotic expansion and symbolic regression were analyzed in respect of speed and accuracy. Numerical experiments on 8 million Sobol’s quasi-Monte points clearly show that also both approaches lead to the approximately same complexity in terms of speed of execution in computers. However, the relative error of the developed symbolic regression-based approximations is reduced significantly, in comparison with the classical basic asymptotic expansion. These numerical results indicate promising results of artificial intelligence (symbolic regression) for developing fast and accurate explicit approximations.

List of Equations in https://doi.org/10.23967/j.rimni.2020.09.001

Dejan Brkić — Sat, 05 Sep 2020 14:50:02 +0200