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1

A quantitative study between HPGR and cone crusher aided ball mill grinding: mathematical modeling by evaluating the possible microfracture effect produced by HPGR technology and cone crusher

Rodríguez-Torres I., Tuzcu E.T., Reyes Iván A., Rosales-Marín G.

Physicochemical Problems of Mineral Processing

|

2024

|

Vol. 60, iss. 1

art. no. 177620

EN

High Pressure Grinding Rolls (HPGR) have been used in the mining industry for decades. However, there are limited quantifications of the particle properties after comminution. Furthermore, the influence of microcracks in grinding provided by this technology has not been extensively quantified. In the recent work, there were two comminution paths tested: 1 (Jaw crusher + cone crusher + ball mill) and 2 (Jaw crusher + HPGR + ball mill). The possible weakening effect aiding ball mill grinding due to microcracks of HPGR path was shown via specific energy, fines generation and breakage rate measurements. To achieve a quantification about the impact of microcracks and the high rate of reduction rate of HPGR technology, first the product was reconstructed using Rosin Rammler's Weibull double formula and the similar particle size distribution was obtained by a conventional cone crusher. By this way the feed size distribution to the grinding stage remained constant regardless of the type of crushing process (HPGR or cone crusher). The results showed that the microfractures generated by the HPGR technology influence the specific energy consumption, fines generation and breakage rates. Ball mill after HPGR consumed 12.46 kWh/t of specific energy, however ball mill after cone crusher consumed 14.36 kWh/t of specific energy. The experimental methodology proposed in this paper maintains a consistent feed size range (-1500 to +41.31 μm) to show that the size reduction observed in the sample undergoing HPGR grinding is not the primary factor contributing to reduced energy consumption and increased fines generation. Instead, it is predominantly associated with the microfractures generated through the compression in HPGR technology; the energy reduction (optimization) of a grinding path is shown in the study.

2

Thermal Operating Window in Selective Laser Melting Processes

Kozak Jerzy, Zakrzewski Tomasz, Witt Marta, Dębowska-Wąsak Martyna

Transactions on Aerospace Research

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2023

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Nr 4 (273)

18--32

EN

Selective laser melting (SLM) is one of the most effective methods of additive manufacturing (AM). It is used to manufacture products with very complex geometries using a wide range of materials. Practical process conditions are limited by the occurrence of undesirable melting instabilities that degrade the surface quality and lead to product defects. These disadvantages are related to the thermal limitations of the SLM process. The lower thermal limit is due to the need to completely melt the powder layer and partially remelt the underlying layer again to ensure proper bonding between the layers. Exceeding the upper thermal limit in the molten metal pool may cause extensive evaporation, boiling and ejection of molten metal droplets outside the melting area. The article presents an approach and methodology that enable the determination of thermal limits and the operating window of SLM/selective laser sintering (SLS) processes in a relatively simple way. The studies have been performed using various settings of SLM process parameters. The usefulness of the preliminary determination of thermal limitations and approximate prediction of operating window of SLM has been confirmed experimentally and by more accurate computer simulation.

3

Modelowanie matematyczne i badania symulacyjne bioreaktora z wymuszonym napowietrzaniem

Przysiężnik Michał, Bartecki Krzysztof

Pomiary Automatyka Robotyka

|

2023

|

R. 27, nr 2

77--88

PL

Proces kompostowania jest powszechnie stosowany w gospodarce odpadami jako metoda przekształcania lub stabilizacji odpadów organicznych. Ze względu na złożony, nieliniowy charakter zachodzących w nim zjawisk biologicznych oraz fizykochemicznych, jest on stosunkowo trudny z punktu widzenia predykcji oraz sterowania. Sterowanie procesem ma tu na celu uzyskiwanie w określonym horyzoncie czasowym produktu finalnego, czyli zwykle kompostu spełniającego określone wymagania jakościowe. W artykule zaprezentowano prosty model matematyczny procesu kompostowania z wymuszonym napowietrzaniem, potencjalnie umożliwiającym realizację wspomnianego celu sterowania. Opracowano model drugiego rzędu, z dwiema wielkościami wejściowymi reprezentującymi zewnętrzne oddziaływania na proces. Na podstawie modelu matematycznego przekształconego do postaci równań stanu, zbudowano w środowisku MATLAB/Simulink model komputerowy bioreaktora, który następnie wykorzystano do przeprowadzenia badań symulacyjnych. Pokazano, że możliwe jest oddziaływanie na proces za pomocą wymuszonego napowietrzania, bezpośrednio wpływającego na zmianę temperatury w bioreaktorze, a w konsekwencji również na czas otrzymania końcowego produktu reakcji. Wyniki analizy właściwości dynamicznych procesu, przeprowadzonej z wykorzystaniem modelu zlinearyzowanego wzdłuż wybranej, nominalnej trajektorii stanu, wskazują na zmienny charakter jego stabilności - począwszy od niestabilności w początkowych fazach reakcji, przez stabilizację w fazie pośredniej, aż do stabilności asymptotycznej, zakończonej osiągnięciem stanu równowagi.

EN

The composting process is commonly used in waste management as a method of converting or stabilizing organic waste. Due to the complex, non-linear nature of biological and physicochemical phenomena involved, this process is relatively difficult to predict and control. The control is usually aimed at obtaining the final product, that is, the compost that meets legal standards. The article presents a simple mathematical model of the composting process with forced aeration, which will potentially facilitate the control task. A second order model was developed, with two inputs signals. Based on the mathematical model in the form of the state equations, the computer model of the bioreactor was built in the MATLAB/Simulink environment, which was then used to conduct different simulation tests. It was shown that it is possible to control the process using forced aeration, directly influencing the temperature changes in the bioreactor, and consequently also the time of obtaining the final product of the reaction. The analysis of the dynamic properties of the process performed using its model linearized about some nominal state trajectory shows the changes in its internal stability - starting from the unstable character in the initial phases of the reaction, through stabilization in its intermediate phase, up to the asymptotic stability, ending in the stable equilibrium state.

4

Simultaneous pickup and delivery model suggestion for personnel transportation in COVID-19 pandemic conditions

Köse Erkan, Kokmazer Ahsen, Vural Danışment, Gökceoğlu Gökçe Gül, Şavlı Pınar

Operations Research and Decisions

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2023

|

Vol. 33, No. 4

119--131

EN

The impact of COVID-19 on the transportation costs of a large-scale company has been examined. Before the pandemic, shift personnel were transported to the factory by shuttles, and after a quick shift change, other shift personnel were transported back to their homes. However, with the implementation of laws mandating the reduction of shuttle seat capacities, transportation costs have risen significantly. To address this issue, a new simultaneous pickup and delivery model is proposed as an alternative to the separate transportation of shift workers. The results of this study indicate that the proposed model provides a substantial advantage in terms of both the number of vehicles used and the total distance traveled, leading to a significant reduction in costs. This research underscores the importance of effective operations research practices for the profitability of companies, particularly in extraordinary circumstances such as the COVID-19 pandemic.

5

Parameter identification of space manipulator’s flexible joint

Wojtunik Mateusz, Basmadji Fatina Liliana, Granosik Grzegorz, Seweryn Karol

Journal of Automation Mobile Robotics and Intelligent Systems

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2023

|

Vol. 17, No. 3

78--87

EN

A manipulator mounted on a satellite is often used to perform active debris removal missions. The space manipulator control system needs to take the dynamic model of the satellite‐manipulator system into account because of the influence of the manipulator motion on the position and attitude of the satellite. Therefore, precise modeling of the space manipulator dynamics as well as parameter identification are needed to improve the credibility of the simulation tools. In this paper, we presented the identification of the flexible‐joint space manipulator model based on dynamic equations of motion. Experiments were performed in an emulated microgravity environment using planar air bearings. The arbitrarily selected joint‐space trajectory was performed by the manipulator’s control system. The experiments were repeated multiple times in order to analyze the identification method sensitivity. The identification is based on the Simulink SimMechanics model. Thus, the procedure can be used for any space manipulator without the need to obtain analytical relations for dynamic equations each time. Including joint flexibility and spring viscous damping in the dynamic model allowed it to reflect the experimental measurements better than the reference model could. Identified parameters of the flexible joint have values of the same magnitude as corresponding real system parameters.

6

Partial mathematical modeling and analysis of the AES system

Stachowiak Sylwia, Kurkowski Mirosław

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 4

64-78

EN

Many types of decision problems can be solved using mathematical modeling and analysis. Such techniques are also developed on the border of mathematical logic and computer science. A good example is the translation of the issues examined into the Satisfiability Problem (SAT) of a logical propositional formula. Unfortunately, this method is not always practical, considering the high computational complexity of solving the SAT problem. It often happens that in the studied cases, the encoding formulas contain even hundreds of thousands of clauses and propositional variables. However, even in these cases, modern SAT solvers can sometimes successfully solve these problems. This approach can be used to cryptanalyze some symmetric ciphers or parts/modifications. In this case, the encryption algorithm is first translated into a boolean formula. Then additional formulas are created to encode randomly selected plaintext and the key bits. Using the SAT solver; we can count the values of the ciphertext bits. Then, using the SAT solver again, we proceed to the cryptanalysis of the cipher with the selected plaintext and proper ciphertext, looking for the bits of the encryption key. In this paper, we will present the new results of how SAT techniques behave against representative fragments of the AES cipher, the current standard for symmetric encryption. We also compare the results obtained in this case by several SAT solvers. In addition, we present the results of the SAT-solver CryptoMiniSat obtained during the attack on the 1st round of the AES-128 cipher.

7

Efektywne napowietrzanie w instalacji przetwarzania odpadów biodegradowalnych

Sidełko Robert, Grabek Piotr

Gaz, Woda i Technika Sanitarna

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2023

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Nr 11

39--42

PL

W artykule opisano metodę równoważenia hydraulicznego instalacji doprowadzającej powietrze do reaktora, wypełnionego kompostowanym materiałem. Algorytm obliczeniowy wykorzystuje zasady mechaniki płynów stosowane w układach otwartych, gdzie zmiany oporów przepływu, w zależności od wydatku powietrza, opisują doświadczalnie opracowane charakterystyki hydrauliczne. Wymiar praktyczny opisanego algorytmu polega na stworzeniu narzędzia umożliwiającego projektowanie systemu doprowadzającego powietrze do różnego rodzaju procesów, w których wymagane jest równomierne natlenienie złoża. Dotyczy to przede wszystkim kompostowania, jak również szeroko stosowanej biofiltracji w procesie oczyszczania np. powietrza poprocesowego.

EN

The article describes a method of hydraulic balancing of the installation supplying air to the reactor filled with composted material. The computational algorithm is based on the principles of fluid mechanics used in open systems in which changes in flow resistance depending on air efficiency are described by experimentally developed hydraulic characteristics. The practical dimension of the described algorithm consists in creating a tool enabling the design of a system supplying air to various types of processes where uniform oxygenation of the bed is required. This applies primarily to composting, as well as the widely used biofiltration in the purification process, e.g. of post-process air.

8

A comparative study of one-dimensional models for stratified thermal energy storage

Osiadacz Andrzej J., Kotyński Łukasz, Kwestarz Małgorzata

Gaz, Woda i Technika Sanitarna

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2023

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Nr 9

8--14

EN

In the article, a comparative analysis of one-dimensional dynamic models describing Thermal Energy Storages is carried out. A model based on energy balance was compared with a model of conductivity and convection and with a convection model. For each of them, the effect of time on the temperature distribution in the tank was examined and temperature distributions in the tank obtained for the analysed models were compared. Also, the effect of the number of nodes (discretization intervals) on the shape of the stratification curve was studied and the impact of the flow rate of the supplied hot water on the stratification curve was examined.

PL

W artykule dokonano analizy porównawczej jednowymiarowych dynamicznych modeli opisujących Thermal Energy Storages. Porównywano model oparty na bilansie energii z modelem przewodzenia i konwekcji oraz modelem konwekcyjnym. Dla każdego modelu badano wpływ czasu na rozkład temperatury w zasobniku, porównywano rozkłady temperatury w zasobniku otrzymane dla analizowanych modeli a także badano wpływ liczby węzłów (przedziałów dyskretyzacji) na kształt krzywej stratyfikacji. Badano także wpływ natężenia przepływu dostarczanej wody gorącej na krzywą stratyfikacji.

9

Preventing the development of emergency modes of interlocked electric drives of a rolling mill under the impact loads

Druzhinin Valeriy, Sivyakova Galina, Kalinin Alexey, Tytiuk Valerii, Nikolenko Anatolii, Kuznetsov Vitaliy Vadimovich, Kuzmenko Mykhailo

Diagnostyka

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2023

|

Vol. 24, No. 1

art. no. 2023105

EN

In recent years, due to the tightening of competition in the global market of steel producers, the requirements for the quality of hot-rolled steel have increased. The finishing group of the rolling mill is characterized by a complex structure of mechanical and electrical parts. The operation of electric drive systems of such units is characterized by the interrelation of electromagnetic processes, mechanical phenomena and technological factors. As experimental studies have shown, the quality of the supply voltage is inextricably linked with the impact nature of the loads in the rolling stands of the roughing and finishing groups of the hot rolling mill. A decrease in the supply voltage may be accompanied by the development of emergency modes of synchronous electric drives, leading to a decrease in the quality of the finished product.The paper developed a mathematical model of the power supply system of the rolling mill JSC "ArcelorMittal Temirtau". It is shown that this can lead to loss of synchronism of the synchronous motor. Such a voltage drop has a significant impact on the operation of DC electric drives of the finishing group. Various strategies are proposed to counter the development of emergency situations.

10

Investigation of local properties of the Fe-Si alloy subjected to mechanical and laser cutting

Gmyrek Zbigniew, Kucharska Barbara

Archives of Electrical Engineering

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2023

|

Vol. 72, nr 3

697--713

EN

The effective design of energy-saving electric motors with efficiency class IE4 and higher requires the use of material characteristics that take into account the core shaping process. Therefore, it becomes necessary to use analytical or numerical models that take into account the change of local properties of Fe-Si material. The aim of the work is to indicate a useful analytical model for estimating the local magnetic permeability of the material, as well as to understand the reasons for these changes. For this purpose, low-loss ferromagnetic materials cut with a guillotine and a laser were tested. Rectangular samples, cut at an angle of 0 degrees in relation to the rolling direction, were subjected to macroscopic and microscopic examinations. Finally, the main reasons for changes in material characteristics for both cutting technologies were indicated. Therefore, the proposed model takes into account not only the cutting technology used, but also the current width of the tested strip, for which the material characteristics are to be determined. The parameters of the analytical model are determined on the basis of a limited number of measurements carried out on samples of a simple geometric shape.

11

Wykorzystanie elementów uczenia maszynowego do modelowania stężenia zanieczyszczeń atmosferycznych: studium przypadku pyłu pm2.5 w Szczecinie

Bihałowicz Jan Stefan

Zeszyty Naukowe SGSP / Szkoła Główna Służby Pożarniczej

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2022

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Nr 81

7--28

PL

W pracy przedstawiono możliwość modelowania stężeń zanieczyszczeń w lokalizacji o określonym, stałym profilu emisji przy wykorzystaniu modeli uczenia maszynowego. Jako zanieczyszczenie wybrano pył PM2.5,a jako zmienne objaśniające przyjęto parametry metrologiczne mierzone na stacji synoptycznej. Przeprowadzono uczenie i walidację sześciu różnych modeli na podstawie obserwacji meteorologicznych zarejestrowanych w latach 2013–2018 na stacji IMGW-PIB w Szczecinie (Polska) oraz średniodobowych stężeń pyłu PM2.5 z tego samego okresu zmierzonych na stacji GIOŚ w Szczecinie przy ul. Andrzejewskiego, podzielonych na trzy równoliczne klasy stężeń. Dwa modele, które dawały najdokładniejsze wyniki, zostały szczegółowo przedstawione. Czułość tych modeli, w zależności od klasy stężenia pyłu, zawierała się pomiędzy 0,484 a 0,711. Te dwa modele zostały zastosowane do identyfikacji wzrostu średniodobowych stężeń w trakcie zdarzenia nietypowego – pożaru składowisk odpadów. Stężenia przewidziane w dniach, w których trwał pożar, były zaniżone względem faktycznych stężeń, co pozwala na zastosowanie modeli w identyfikacji zjawisk atypowych, które mają wpływ na stężenia zanieczyszczeń w danym miejscu.

EN

The work presents the possibilities of using machine learning in modeling pollutant concentra tions at locations with defined constant sources of emission. The PM2.5 was chosen as the pollutant to be studied with meteorological variables as exogenous variables measured at a weather station. Six different models were implemented and cross-validated on meteorological data recorded in 2013-2018 at the Institute of Meteorology and Water Management station in Szczecin, Poland, and PM2.5 concentrations from the same period divided into three classes, measured at the air quality station of the Chief Inspectorate of Environmental Protection (Poland) located at Andrzejewskiego Street in Szczecin. Two best-performing models were described in detail. The sensitivity of the models was found to vary from 0.484 to 0.711 depending on the class of PM2.5 concentration. Those two models were then applied to identify increases in PM concentrations that were caused by an extraordinary incident – landfill fire. It was proven that the predicted values of concentration that occur during the fire were underestimated as compared to actual concentration levels and hence such models can be applied in the identification of abnormal phenomena that may affect the concentrations of pollutants in a given location.

12

Mathematical modeling of the aeroion mode in a car

Biliaiev Mykola, Pshinko Oleksandr, Rusakova Tetiana, Biliaieva Viktoriia, Sładkowski Aleksander

Transport Problems

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2022

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T. 17, z. 2

19--32

EN

In this study, a mathematical method is proposed for calculating the concentration field of air ions of different polarities and dust levels in the passenger compartment, taking into account the geometry of the passenger compartment and seats, shelves, and other internal elements of the passenger compartment. The method also takes into account changes in the rate of the air flow ventilation, the location and number of ionizers, and sources of positive ions and dust, taking into account their different intensities and locations. On the basis of a numerical model for this method, software has been developed that allows users to carry out computational experiments without requiring much time for calculation. Based on the results, the optimal location of the ionizer in the passenger compartment of the car was determined to ensure comfortable conditions for the stay of passengers, which favorably affects their health. It has been found that the presence of two ionizers is optimal for creating comfort in the car with an ionization intensity of Qn= 0.47 ×1010 ions/s located at the top of the car. If there is one ionizer located on the dashboard or at the top of the car with a higher ionization rate than ions/s, it is not possible to simultaneously provide optimal ionization parameters for passengers in the front and rear seats of the car.

13

Innovative Method of Forecasting the Generator Gas Composition after the Process of Pyrolysis and Gasification

Slowak Anna Maria

Rocznik Ochrona Środowiska

|

2022

|

Tom 24

97--109

EN

The article presents a new approach to forecasting producer gas composition. Thermochemical treatment of biomass was presented as an effective method of producing flammable gas. The methods of predicting the gas composition of the generator are described, and then its efficiency depends on the device’s parameters. In order to create a method for forecasting gas composition, the authors’ works were used as the basis on which the energy characteristics of the gases obtained were assessed. It was assumed in this paper that it is essential to understand the influence of each parameter on the energy characteristics of the gas. It made it possible to optimize the composition and predict thermal characteristics. This article presents the results of experimental studies on biomass gasification and a mathematical model based on Gibbs free energy.

14

Wpływ jakości siatki numerycznej na wyniki symulacji rozprzestrzeniania się zanieczyszczeń w powietrzu

Lewak Michał, Tępiński Jarosław

Przemysł Chemiczny

|

2022

|

T. 101, nr 11

957--962

PL

Praca dotyczy matematycznego modelowania rozprzestrzeniania się zanieczyszczeń w powietrzu za pomocą obliczeniowej mechaniki płynów z wykorzystaniem modelu bilansowania pędu w fazie dyskretnej DPM (discrete phase model). Skupiono się na problemie zagęszczenia siatki numerycznej potrzebnej do tworzenia symulacji rozprzestrzeniania się zanieczyszczeń w powietrzu. Opierając się na parametrze określającym jakość numeryczną siatki, wykonano symulacje pracy pieca centralnego ogrzewania klasy I. Do określenia najlepszego stopnia zagęszczenia siatki wykorzystany został rozkład cząstek pyłu opuszczającego komin, z którego emitowane były zanieczyszczenia.

EN

A math. modeling of the operation of a class I central heating furnace was performed by computational fluid dynamics together with the DPM discrete-phase momentum balancing model. The problem of numerical mesh compaction needed to simulate the spread of pollutants in the air was focused on. Relying only on the qmesh parameter, which determines the quality of individual elements of the numerical mesh, was not sufficient. Therefore, the impact of the number of elements and the distribution of the qmesh parameter in the mesh on the obtained simulation results should be analyzed.

15

Mathematical modeling of processes and characteristics of wound-rotor induction motor

Malyar Vasyl, Hamola Orest, Maday Volodymyr, Vasylchyshyn Ivanna

Przegląd Elektrotechniczny

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2022

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R. 98, nr 4

90--93

EN

A mathematical model and algorithm to calculating electromechanical transients and starting static characteristics of wound-rotor induction motor have been developed. The calculation is based on a mathematical model of an induction motor, which considers the saturation of the magnetic circuit and the differential method of calculating the static characteristics. The electromagnetic processes in the motor are described by a system of nonlinear electric equilibrium equations written in transformed to orthogonal coordinate axes, which are solved by the parameter continuation differential method and Newton's iterative method. Calculation of loop fluxes and differential inductances is performed using the magnetization characteristic of the main magnetic flux and the stator and rotor leakage fluxes.

PL

Opracowano model matematyczny i algorytm do obliczania przebiegów elektromechanicznych i rozruchowych charakterystyk statycznych silnika indukcyjnego z wirnikiem uzwojonym. Obliczenia opierają się na modelu matematycznym silnika indukcyjnego, który uwzględnia nasycenie obwodu magnetycznego oraz różnicową metodę obliczania charakterystyk statycznych. Procesy elektromagnetyczne w silniku opisane są układem nieliniowych równań równowagi elektrycznej, zapisanych w postaci przekształconej na osie ortogonalne, które są rozwiązywane metodą różniczkową z kontynuacją parametrów oraz metodą iteracyjną Newtona. Obliczanie strumieni pętli i indukcyjności różnicowych odbywa się na podstawie charakterystyki magnetyzacji głównego strumienia magnetycznego oraz strumieni rozproszenia stojana i wirnika.

16

Mathematical modelling of marine power plants with thermochemical fuel treatment

Cherednichenko Oleksandr, Serbin Serhiy, Tkach Mykhaylo, Kowalski Jerzy, Chen Daifen

Polish Maritime Research

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2022

|

nr 3

99--108

EN

The article considers the methodological aspects of the theoretical investigation of marine power plants with thermochemical fuel treatment. The results of the study of the complex influence of temperature, pressure, and the ratio of steam / base fuel on the thermochemical treatment efficiency are presented. The adequacy of the obtained regression dependences was confirmed by the physical modelling of thermochemical fuel treatment processes. For a gas turbine power complex with a thermochemical fuel treatment system, the characteristics of the power equipment were determined separately with further merging of the obtained results and a combination of material and energy flow models. Algorithms, which provide settings for the mathematical models of structural and functional blocks, the optimisation of thermochemical energy transformations, and verification of developed models according to the indicators of existing gas turbine engines, were created. The influence of mechanical energy consumption during the organisation of thermochemical processing of fuel on the efficiency of thermochemical recuperation is analysed.

17

Facility location problem mathematical models - supply chain perspective

Redmer Adam

LogForum

|

2022

|

Vol. 18, no. 4

379--395

EN

Background: Supply chains are the networks linking sources of supply with demand points and composed of so-called actors, i.e., producers, distributors/wholesalers, retailers, and customers/consumers. As in every network, supply chains contain vertices and arcs, the former represented by factories and warehouses (including distribution centers). Such facilities cause long-term and expensive investments. As a result, decisions on location and number of them belong to the strategic level of management and require quantitative analysis. To do this, mathematical models of the Facility Location Problem (FLP) are constructed to allow an application of optimization methods. Methods: Mathematical optimization or programming is the selection of the best solution, with regard to some criterion, from a set of feasible alternatives. The fundamental of mathematical optimization is the formulation of mathematical models of analyzed problems. Mathematical models are composed of objective function, decision variables, constraints, and parameters. These components are presented and compared in the paper concerning FLP from a supply chain perspective. Results: The ten mathematical models of the FLP are presented, including the two original ones. The models are classified according to such features as facility type they concern, including the desirable, neutral, and undesirable ones. The models and their components are characterized. In addition, their applicability and elasticity are analyzed. Finally, the models are compared and discussed from the supply chain point of view. Conclusions: However, the FLP mathematical models are relatively similar; the most important element of them for supply chain appropriate representation is an objective function. It strongly influences the possible applicability of FLP models and their solutions, as well. The objective functions having broader applicability turned out to be the maximized number of supply/demand points covered by facilities and the minimized number of facilities necessary to cover supply/demand points. However, not to locate all allowed facilities (use all the location sites) or as many as supply/demand points, but an appropriate number of them, it is necessary to take into account facility fixed costs. Thus, when locating logistics facilities, the minimized total cost of serving supply/demand points is the most appropriate objective function.

18

Mathematical modeling and analysis of mycobacterium tuberculosis transmission in humans with hospitalization and reinfection

Mustapha Umar T., Idris Buhari, Musa Salihu S., Yusuf Abdullahi

Journal of Applied Mathematics and Computational Mechanics

|

2022

|

Vol. 21, nr 1

55--66

EN

Tuberculosis (TB), a serious public health infection that mainly affects the lungs, is caused by bacteria (Mycobacterium tuberculosis, TB). This research is designed and analyzed using a compartmental modelling approach to study the transmission dynamics of TB with different stages of infection. Qualitative analysis of the proposed model reveals that the model exhibits two equilibrium points: the disease-free equilibrium point (DFE) and the endemic equilibrium (EE). The basic reproduction number (R0 ) is determined using the next generation matrix technique, and stability analysis is carried out to show whether the disease can persist or die out in population. Further analysis of the model shows that the EE is globally asymptotically stable (GAS) when R0 > 1. With the aid of the forward sensitivity index method, we determine the most sensitive parameters of the model to control the spread of TB infection effectively. Our analysis shows that treatment (medication) and campaign awareness coupled with other key control measures, could help maintain the spread of MTB infection in human geographical boundaries.

19

ATiPreTA: An analytical model for time-dependent prediction of terrorist attacks

Kebir Oussama, Nouaouri Issam, Rejeb Lilia, Ben Said Lamjed

International Journal of Applied Mathematics and Computer Science

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2022

|

Vol. 32, no. 3

495--510

EN

In counter-terrorism actions, commanders are confronted with difficult and important challenges. Their decision-making processes follow military instructions and must consider the humanitarian aspect of the mission. In this paper, we aim to respond to the question: What would the casualties be if governmental forces reacted in a given way with given resources? Within a similar context, decision-support systems are required due to the variety and complexity of modern attacks as well as the enormous quantity of information that must be treated in real time. The majority of mathematical models are not suitable for real-time events. Therefore, we propose an analytical model for a time-dependent prediction of terrorist attacks (ATiPreTA). The output of our model is consistent with casualty data from two important terrorist events known in Tunisia: Bardo and Sousse attacks. The sensitivity and experimental analyses show that the results are significant. Some operational insights are also discussed.

20

Analiza wraz z oceną efektywności pracy elektrociepłowni zintegrowanej z układem akumulacji ciepła

Plutecki Zbigniew, Lichota Janusz, Kamiński Jacek, Saługa Piotr, Kaszyński Przemysław, Benalcazar Pablo, Sattler Paweł

Instal

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2022

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nr 9

16--25

PL

W pracy przedstawiono założenia i najważniejsze cechy modelu matematycznego wraz z przykładowymi wynikami badań symulacyjnych jakie wykonano w ramach analizy i oceny struktury techniczno-ekonomicznej, którą jest instalacja elektrociepłowni przed i po rozbudowie o instalację akumulacji ciepła. Opracowany model matematyczny pozwolił na odzwierciedlenie pracy rzeczywistego systemu oraz rozpatrywanych wariantów integracji z instalacją akumulacji ciepła w formie układu równań i nierówności z funkcją celu, którą jest maksymalizacja zysku ze sprzedaży energii elektrycznej i ciepła przy jednoczesnym minimalizowaniu zużycia węgla i energii elektrycznej potrzeb własnych wynikających z optymalizacji warunków pracy poszczególnych urządzeń i dynamicznego wykorzystania zjawiska akumulacji ciepła. Prezentowane wyniki pochodzą z zakończonych badań przemysłowych i prac rozwojowych związanych z realizacją projektu badawczego mającego na celu określenie technologii zapewniającej optymalną współpracę elektrociepłowni z układem wysokoefektywnej akumulacji ciepła.

EN

The paper presents the assumptions and most important features of the mathematical model, along with sample results of simulation studies that were carried out as part of the analysis and evaluation of the technical and economic structure, which is the installation of a combined heat and power plant before and after expansion with a heat accumulation installation. The developed mathematical model allowed to reflect the operation of the real system and the considered variants of integration with the heat accumulation installation in the form of a system of equations and inequalities with the objective function, which is to maximize the profit from the sale of electricity and heat while minimizing the consumption of coal and electricity own needs resulting from the optimization of the operating conditions of individual devices and the dynamic use of the heat accumulation phenomenon. The results presented here come from completed industrial research and development work related to the implementation of a research project aimed at determining the technology that ensures optimal cooperation of a thermal power plant with a highly efficient heat accumulation system.