Search results for: Energy Optimization

Authors: Mhand Hifi, Hedi Mhalla, Mustapha Michaphy

Abstract:

In this paper, we study the multi-scenario knapsack problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of an adaptive algorithm for solving heuristically the problem. The used method combines two complementary phases: a size reduction phase and a dynamic 2- opt procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for reducing the size problem. Second, the adaptive search procedure is applied in order to attain a feasible solution Finally, the performances of two versions of the proposed algorithm are evaluated on a set of randomly generated instances.

Keywords: combinatorial optimization, max-min optimization, knapsack, heuristics, problem reduction

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Authors: B.Bahmani Firouzi, T. Niknam, M. Nayeripour

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Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the kmeans algorithm. Solutions obtained from this technique depend on the initialization of cluster centers and the final solution converges to local minima. In order to overcome K-means algorithm shortcomings, this paper proposes a hybrid evolutionary algorithm based on the combination of PSO, SA and K-means algorithms, called PSO-SA-K, which can find better cluster partition. The performance is evaluated through several benchmark data sets. The simulation results show that the proposed algorithm outperforms previous approaches, such as PSO, SA and K-means for partitional clustering problem.

Keywords: Data clustering, Hybrid evolutionary optimization algorithm, K-means algorithm, Simulated Annealing (SA), Particle Swarm Optimization (PSO).

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Authors: Li Shoutao, Gordon Lee

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Evolutionary robotics is concerned with the design of intelligent systems with life-like properties by means of simulated evolution. Approaches in evolutionary robotics can be categorized according to the control structures that represent the behavior and the parameters of the controller that undergo adaptation. The basic idea is to automatically synthesize behaviors that enable the robot to perform useful tasks in complex environments. The evolutionary algorithm searches through the space of parameterized controllers that map sensory perceptions to control actions, thus realizing a specific robotic behavior. Further, the evolutionary algorithm maintains and improves a population of candidate behaviors by means of selection, recombination and mutation. A fitness function evaluates the performance of the resulting behavior according to the robot-s task or mission. In this paper, the focus is in the use of genetic algorithms to solve a multi-objective optimization problem representing robot behaviors; in particular, the A-Compander Law is employed in selecting the weight of each objective during the optimization process. Results using an adaptive fitness function show that this approach can efficiently react to complex tasks under variable environments.

Keywords: adaptive fuzzy neural inference, evolutionary tuning

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Authors: Mahdi Pirmoradian, Olayinka Adigun, Christos Politis

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Cooperative spectrum sensing is a crucial challenge in cognitive radio networks. Cooperative sensing can increase the reliability of spectrum hole detection, optimize sensing time and reduce delay in cooperative networks. In this paper, an efficient central capacity optimization algorithm is proposed to minimize cooperative sensing time in a homogenous sensor network using OR decision rule subject to the detection and false alarm probabilities constraints. The evaluation results reveal significant improvement in the sensing time and normalized capacity of the cognitive sensors.

Keywords: Cooperative networks, normalized capacity, sensing time.

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Authors: Konstantinos Metaxiotis, Konstantinos Liagkouras

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The objective of this study is to examine the performance of three well-known multiobjective evolutionary algorithms for solving optimization problems. The first algorithm is the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), the second one is the Strength Pareto Evolutionary Algorithm 2 (SPEA-2), and the third one is the Multiobjective Evolutionary Algorithms based on decomposition (MOEA/D). The examined multiobjective algorithms are analyzed and tested on the ZDT set of test functions by three performance metrics. The results indicate that the NSGA-II performs better than the other two algorithms based on three performance metrics.

Keywords: MOEAs, Multiobjective optimization, ZDT test functions, performance metrics.

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Authors: M. R. Aghaebrahimi, S. H. Zahiri, M. Amiri

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In this paper a data miner based on the learning automata is proposed and is called LA-miner. The LA-miner extracts classification rules from data sets automatically. The proposed algorithm is established based on the function optimization using learning automata. The experimental results on three benchmarks indicate that the performance of the proposed LA-miner is comparable with (sometimes better than) the Ant-miner (a data miner algorithm based on the Ant Colony optimization algorithm) and CNZ (a well-known data mining algorithm for classification).

Keywords: Data mining, Learning automata, Classification rules, Knowledge discovery.

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Authors: Ali Dinarveis

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This paper compares the energy and exergy efficiency of a vapour compression refrigeration system using refrigerants of different groups. In this study, five different refrigerants including R507A, R134a, R114, R22 and R717 have been studied. EES Program is used to solve the thermodynamic equations. The results of this analysis are shown graphically. Based on the results, energy and exergy efficiencies for R717 are higher than the other refrigerants. Also, the energy and exergy efficiencies will be decreased with increasing the condensing temperature and decreasing the evaporating temperature.

Keywords: Energy, exergy, refrigeration, temperature, thermodynamic.

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Authors: Okezie A. Ihugba

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The bounds testing ARDL (2, 2, 2, 2, 0) technique to cointegration was used in this study to investigate the effect of energy consumption and energy loss on Nigeria's manufacturing sector from 1981 to 2020. The model was created to determine the relationship between these three variables while also accounting for interactions with control variables such as inflation and commercial bank loans to the manufacturing sector. When the dependent variables are energy consumption and energy loss, the bound tests show that the variables of interest are bound together in the long run. Because electricity consumption is a critical factor in determining manufacturing value-added in Nigeria, some intriguing observations were made. According to the findings, the relationship between log of electricity consumption (LELC) and log of manufacturing value added (LMVA) is statistically significant. According to the findings, electricity consumption reduces manufacturing value-added. The target variable (energy loss) is statistically significant and has a positive sign. In Nigeria, a 1% reduction in energy loss increases manufacturing value-added by 36% in the first lag and 35% in the second. According to the study, the government should speed up the ongoing renovation of existing power plants across the country, as well as the construction of new gas-fired power plants. This will address a number of issues, including overpricing of electricity as a result of grid failure.

Keywords: ARDL, cointegration, Nigeria's manufacturing, electricity.

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Authors: Meng Hu, Lili Wang

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In this paper, applying He-s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy.

Keywords: He's energy balance method, periodic solution, nonlinear oscillator, discontinuous, fractional potential.

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Authors: Lekbir Adel, Alloui-Lombarkia Ourida, Mekentichi Sihem, Noui Yassine, Baississe Salima

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The objective of this study was to optimize the extraction conditions for phenolic compounds, total flavonoids, and antioxidant activity from Deglet-Nour variety. The extraction of active components from natural sources depends on different factors. The knowledge of the effects of different extraction parameters is useful for the optimization of the process, as well for the ability to predict the extraction yield. The effects of extraction variables, namely types of solvent (methanol, ethanol and acetone) and extraction time (1h, 6h, 12h and 24h) on phenolics extraction yield were evaluated. It has been shown that the time of extraction and types of solvent have a statistically significant influence on the extraction of phenolic compounds from Deglet-Nour variety. The optimised conditions yielded values of 80.19 ± 6.37 mg GAE/100 g FW for TPC, 2.34 ± 0.27 mg QE/100 g FW for TFC and 90.20 ± 1.29% for antioxidant activity were methanol solvent and 6 hours of time. According to the results obtained in this study, Deglet-Nour variety can be considered as a natural source of phenolic compounds with good antioxidant capacity.

Keywords: Deglet-Nour variety, Date palm Fruit, Phenolic compounds, Total flavonoids, Antioxidant activity, Extraction, Optimization.

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Authors: Shinya Yokoyama, Katsunari Jonouchi, Kenji Imou

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This paper discusses the utilization of marine biomass as an energy resource in Japan. A marine biomass energy system in Japan was proposed consisting of seaweed cultivation (Laminaria japonica) at offshore marine farms, biogas production via methane fermentation of the seaweeds, and fuel cell power generation driven by the generated biogas. We estimated energy output, energy supply potential, and CO2 mitigation in Japan on the basis of the proposed system. As a result, annual energy production was estimated to be 1.02-109 kWh/yr at nine available sites. Total CO2 mitigation was estimated to be 1.04-106 tonnes per annum at the nine sites. However, the CO2 emission for the construction of relevant facilities is not taken into account in this paper. The estimated CO2 mitigation is equivalent to about 0.9% of the required CO2 mitigation for Japan per annum under the Kyoto Protocol framework.

Keywords: CO2 mitigation, Fuel cell power generation, Laminaria japonica, Marine biomass, Seaweed.

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Authors: Rizwan Moeen, Riaz Ahmad, Tanweer Ul Islam, Shahid Ikramullah, Muhammad Umer

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Supplier appraisal fosters energy in Supply Chain Management and helps in best optimization of viable business partners for a company. Many Decision Making techniques have already been proposed by researchers for supplier-s appraisal. However, Analytic Hierarchy Process (AHP) is assumed to be the most structured technique to attain near-best solution of the problem. This paper focuses at implementation of AHP in the procurement processes. It also suggests that on what factors a Public Sector Enterprises must focus while dealing with their suppliers and what should the suppliers do to synchronize their activities with the strategic objectives of Organization. It also highlights the weak areas in supplier appraisal process with a view to suggest viable recommendations.

Keywords: AHP, MCDM techniques, Supply Chain Management (SCM), Supplier appraisal.

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Authors: M. Miladi, T. Ezzedine, R. Bouallegue

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In the current decade, wireless sensor networks are emerging as a peculiar multi-disciplinary research area. By this way, energy efficiency is one of the fundamental research themes in the design of Medium Access Control (MAC) protocols for wireless sensor networks. Thus, in order to optimize the energy consumption in these networks, a variety of MAC protocols are available in the literature. These schemes were commonly evaluated under simple network density and a few results are published on their robustness in realistic network-s size. We, in this paper, provide an analytical study aiming to highlight the energy waste sources in wireless sensor networks. Then, we experiment three energy efficient hybrid CSMA/CA based MAC protocols optimized for wireless sensor networks: Sensor-MAC (SMAC), Time-out MAC (TMAC) and Traffic aware Energy Efficient MAC (TEEM). We investigate these protocols with different network densities in order to discuss the end-to-end performances of these schemes (i.e. in terms of energy efficiency, delay and throughput). Through Network Simulator (NS- 2) implementations, we explore the behaviors of these protocols with respect to the network density. In fact, this study may help the multihops sensor networks designers to design or select the MAC layer which matches better their applications aims.

Keywords: Energy efficiency, medium access control, network density, wireless sensor networks.

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Authors: E. Sok, Y. Zhuo, S. Wang

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A hybrid Photovoltaic/Thermal (PV/T) solar system integrates photovoltaic and solar thermal technologies into one single solar energy device, with dual generation of electricity and heat energy. The aim of the present study is to evaluate the potential for introduction of the PV/T technology into Northern China. For this purpose, outdoor experiments were conducted on a prototype of a PV/T water-heating system. The annual thermal and electrical performances were investigated under the climatic conditions of Beijing. An economic analysis of the system was then carried out, followed by a sensitivity study. The analysis revealed that the hybrid system is not economically attractive with the current market and energy prices. However, considering the continuous commitment of the Chinese government towards policy development in the renewable energy sector, and technological improvements like the increasing cost-effectiveness of PV cells, PV/Thermal technology may become economically viable in the near future.

Keywords: Hybrid Photovoltaic/Thermal (PV/T), Solar energy, Economic analysis

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Authors: Amir Sepasi Zahmati, Bahman Abolhassani, Ali Asghar Beheshti Shirazi, Ali Shojaee Bakhtiari

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A wireless sensor network with a large number of tiny sensor nodes can be used as an effective tool for gathering data in various situations. One of the major issues in wireless sensor networks is developing an energy-efficient routing protocol which has a significant impact on the overall lifetime of the sensor network. In this paper, we propose a novel hierarchical with static clustering routing protocol called Energy-Efficient Protocol with Static Clustering (EEPSC). EEPSC, partitions the network into static clusters, eliminates the overhead of dynamic clustering and utilizes temporary-cluster-heads to distribute the energy load among high-power sensor nodes; thus extends network lifetime. We have conducted simulation-based evaluations to compare the performance of EEPSC against Low-Energy Adaptive Clustering Hierarchy (LEACH). Our experiment results show that EEPSC outperforms LEACH in terms of network lifetime and power consumption minimization.

Keywords: Clustering methods, energy efficiency, routingprotocol, wireless sensor networks.

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Authors: Awni H. Alkhazaleh, Baljinder K. Kandola

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In this study, a form-stable composite Paraffin/Nanoclay (PA-NC) has been prepared by absorbing PA into porous particles of NC to be used for low-temperature latent heat thermal energy storage. The leakage test shows that the maximum mass fraction of PA that can be incorporated in NC without leakage is 60 wt.%. Differential scanning calorimetry (DSC) has been used to measure the thermal properties of the PA and PA-NC both before and after incorporation in plasterboard (PL). The mechanical performance of the samples has been evaluated in flexural mode. The thermal energy storage performance has been studied using a small test chamber (100 mm × 100 mm × 100 mm) made from 10 mm thick PL and measuring the temperatures using thermocouples. The flammability of the PL+PL-NC has been discussed using a cone calorimeter. The results indicate that the form composite PA has good potential for use as thermal energy storage materials in building applications.

Keywords: Flammability, paraffin, plasterboard, thermal energy storage.

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Authors: Donglan Zha, Jiansong Si

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Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions.

Keywords: Bias of technical change, CES production function, elasticity of substitution, energy input.

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Authors: Maziar Noei

Abstract:

Adsorption of a boron nitride nanotube (BNNT) was examined toward ethylacetylene (C4H6) molecule by using density functional theory (DFT) calculations at the B3LYP/6-31G (d) level, and it was found that the adsorption energy (Ead) of ethylacetylene the pristine nanotubes is about -1.60kcal/mol. But when nanotube has been doped with Si and Al atoms, the adsorption energy of ethylacetylene molecule was increased. Calculation showed that when the nanotube is doping by Al, the adsorption energy is about - 24.19kcal/mol and also the amount of HOMO/LUMO energy gap (Eg) will reduce significantly. Boron nitride nanotube is a suitable adsorbent for ethylacetylene and can be used in separation processes ethylacetylene. It is seem that nanotube (BNNT) is a suitable semiconductor after doping, and the doped BNNT in the presence of ethylacetylene an electrical signal is generating directly and therefore can potentially be used for ethylacetylene sensors.

Keywords: Sensor, Nanotube, DFT, Ethylacetylene.

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Authors: Farhad Kolahan, Mehdi Heidari

Abstract:

Gas Metal Arc Welding (GMAW) processes is an important joining process widely used in metal fabrication industries. This paper addresses modeling and optimization of this technique using a set of experimental data and regression analysis. The set of experimental data has been used to assess the influence of GMAW process parameters in weld bead geometry. The process variables considered here include voltage (V); wire feed rate (F); torch Angle (A); welding speed (S) and nozzle-to-plate distance (D). The process output characteristics include weld bead height, width and penetration. The Taguchi method and regression modeling are used in order to establish the relationships between input and output parameters. The adequacy of the model is evaluated using analysis of variance (ANOVA) technique. In the next stage, the proposed model is embedded into a Simulated Annealing (SA) algorithm to optimize the GMAW process parameters. The objective is to determine a suitable set of process parameters that can produce desired bead geometry, considering the ranges of the process parameters. Computational results prove the effectiveness of the proposed model and optimization procedure.

Keywords: Weld Bead Geometry, GMAW welding, Processparameters Optimization, Modeling, SA algorithm

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Authors: Suhas K, Sripadaraja K

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This paper details few mechanical modeling and design issues of RF MEMS switches. We concentrate on an electrostatically actuated broad side series switch; surface micromachined with a crab leg membrane. The same results are extended to any complex structure. With available experimental data and fabrication results, we present the variation in dynamic performance and compliance of the switch with reference to few design issues, which we find are critical in deciding the dynamic behavior of the switch, without compromise on the RF characteristics. The optimization of pull in voltage, transient time and resonant frequency with regard to these critical design parameters are also presented.

Keywords: Microelectromechanical Systems (MEMS), RadioFrequency MEMS, Modeling, Actuators

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Authors: I. Herraiz-Cardona, C. González-Buch, E. Ortega, V. Pérez-Herranz, J. García-Antón

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Hydrogen is considered to be the most promising candidate as a future energy carrier. One of the most used technologies for the electrolytic hydrogen production is alkaline water electrolysis. However, due to the high energy requirements, the cost of hydrogen produced in such a way is high. In continuous search to improve this process using advanced electrocatalytic materials for the hydrogen evolution reaction (HER), Ni type Raney and macro-porous Ni-Co electrodes were prepared on AISI 304 stainless steel substrates by electrodeposition. The developed electrodes were characterized by SEM and confocal laser scanning microscopy. HER on these electrodes was evaluated in 30 wt.% KOH solution by means of hydrogen discharge curves and galvanostatic tests. Results show that the developed electrodes present a most efficient behaviour for HER when comparing with the smooth Ni cathode. It has been reported a reduction in the energy consumption of the electrolysis cell of about 25% by using the developed coatings as cathodes.

Keywords: Alkaline water electrolysis, energy efficiency, porous nickel electrodes

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Authors: Masoud Mohammadpour, Blair Carlson, Radovan Kovacevic

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The quality of laser welded-brazed (LWB) joints were strongly dependent on the main process parameters, therefore the effect of laser power (3.2–4 kW), welding speed (60–80 mm/s) and wire feed rate (70–90 mm/s) on mechanical strength and surface roughness were investigated in this study. The comprehensive optimization process by means of response surface methodology (RSM) and desirability function was used for multi-criteria optimization. The experiments were planned based on Box– Behnken design implementing linear and quadratic polynomial equations for predicting the desired output properties. Finally, validation experiments were conducted on an optimized process condition which exhibited good agreement between the predicted and experimental results. AlSi3Mn1 was selected as the filler material for joining aluminum alloy 6022 and hot-dip galvanized steel in coach peel configuration. The high scanning speed could control the thickness of IMC as thin as 5 µm. The thermal simulations of joining process were conducted by the Finite Element Method (FEM), and results were validated through experimental data. The Fe/Al interfacial thermal history evidenced that the duration of critical temperature range (700–900 °C) in this high scanning speed process was less than 1 s. This short interaction time leads to the formation of reaction-control IMC layer instead of diffusion-control mechanisms.

Keywords: Laser welding-brazing, finite element, response surface methodology, multi-response optimization, cross-beam laser.

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Authors: Henrik Prinzhorn, Peter Nyhuis, Johannes Wagner, Peter Burggräf, Torben Schmitz, Christina Reuter

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Assembling large-scale products, such as airplanes, locomotives, or wind turbines, involves frequent process interruptions induced by e.g. delayed material deliveries or missing availability of resources. This leads to a negative impact on the logistical performance of a producer of xxl-products. In industrial practice, in case of interruptions, the identification, evaluation and eventually the selection of an alternative order of assembly activities (‘assembly alternative’) leads to an enormous challenge, especially if an optimized logistical decision should be reached. Therefore, in this paper, an innovative, optimization model for the identification of assembly alternatives that addresses the given problem is presented. It describes make-to-order, large-scale product assembly processes as a resource constrained project scheduling (RCPS) problem which follows given restrictions in practice. For the evaluation of the assembly alternative, a cost-based definition of the logistical objectives (delivery reliability, inventory, make-span and workload) is presented.

Keywords: Assembly scheduling, large-scale products, make-to-order, rescheduling, optimization.

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Authors: Saeed Vahidifar, Mohammad Nakhaee Sharif, Mohammad Ghaffari

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Few people would dispute the fact that one of the most common applications of energy is creating comfort in buildings, so it is probably true to say that management of energy consumption is required due to the environmental issues and increasing the efficiency of mechanical systems. From the geographical point of view, Iran is located in a warm and semi-arid region; therefore, air-cooled chillers are usually used for cooling residential buildings, commercial buildings, medical buildings, etc. In this study, a heat exchanger was designed for providing laundry hot water by utilizing condenser heat lost base on analytical results of a 540-bed hospital in the city of Mashhad in Iran. In this paper, by using the analytical method, energy consumption reduces about 13%, and coefficient of performance increases a bit. Results show that this method can help in the management of energy consumption a lot.

Keywords: Energy management, air-cooled chiller, heat exchanger, hospital laundry system.

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Authors: Hebberly Ahatlan

Abstract:

The process of digitizing energy systems involves transforming traditional energy infrastructure into interconnected, data-driven systems that enhance efficiency, sustainability, and responsiveness. As smart grids become increasingly integral to the efficient distribution and management of electricity from both fossil and renewable energy sources, the energy industry faces strategic challenges associated with digitalization and interoperability — particularly in the context of modern energy business models, such as virtual power plants (VPPs). The critical challenge in modern smart grids is to seamlessly integrate diverse technologies and systems, including virtualization, grid computing and service-oriented architecture (SOA), across the entire energy ecosystem. Achieving this requires addressing issues like semantic interoperability, Information Technology (IT) and Operational Technology (OT) convergence, and digital asset scalability, all while ensuring security and risk management. This paper proposes a four-layer digitalization framework to tackle these challenges, encompassing persistent data protection, trusted key management, secure messaging, and authentication of IoT resources. Data assets generated through this framework enable AI systems to derive insights for improving smart grid operations, security, and revenue generation. Furthermore, this paper also proposes a Trusted Energy Interoperability Alliance as a universal guiding standard in the development of this digitalization framework to support more dynamic and interoperable energy markets.

Keywords: Digitalization, IT/OT convergence, semantic interoperability, TEIA alliance, VPP.

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Authors: A. Maitarad, P. Maitarad

Abstract:

In order to find the particular interaction energy between cylcloguanil and the amino acids surrounding the pocket of wild type and quadruple mutant type PfDHFR enzymes, the MP2 method with basis set 6-31G(d,p) level of calculations was performed. The obtained interaction energies found that Asp54 has the strongest interaction energy to both wild type and mutant type of - 12.439 and -11.250 kcal/mol, respectively and three amino acids; Asp54, Ile164 and Ile14 formed the H-bonding with cycloguanil drug. Importantly, the mutation at Ser108Asn was the key important of cycloguanil resistant with showing repulsive interaction energy.

Keywords: Cycloguanil, DHFR, malaria disease, interactionenergy, quantum calculations

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Authors: M. M. Sadeghi, S. Vahdani

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Masonry dome structures had been widely used for covering large spans in the past. The seismic assessment of these historical structures is very complicated due to the nonlinear behavior of the material, their rigidness, and special stability configuration. The assessment method based on energy balance concept, as well as the standard pushover analysis, is used to evaluate the effectiveness of these methods in the case of masonry dome structures. The Soltanieh dome building is used as an example to which two methods are applied. The performance points are given from superimposing the capacity, and demand curves in Acceleration Displacement Response Spectra (ADRS) and energy coordination are compared with the nonlinear time history analysis as the exact result. The results show a good agreement between the dynamic analysis and the energy balance method, but standard pushover method does not provide an acceptable estimation.

Keywords: Energy balance method, pushover analysis, time history analysis, masonry dome.

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Authors: B. Rezaei, G. R. Boroun, M. Abdolmaleki

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The bound state energy of three quark systems is studied in the framework of a non- relativistic spin independent phenomenological model. The hyper- spherical coordinates are considered for the solution this system. According to Jacobi coordinate, we determined the bound state energy for (uud) and (ddu) quark systems, as quarks are flavorless mass, and it is restrict that choice potential at low and high range in nucleon bag for a bound state.

Keywords: Adiabatic expansion, grand angular momentum, binding energy, perturbation, baryons.

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Authors: N. Arulanand, P. Dhara

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Optimizing the parameters in the controller plays a vital role in the control theory and its applications. Optimizing the PID parameters is finding out the best value from the feasible solutions. Finding the optimal value is an optimization problem. Inverted Pendulum is a very good platform for control engineers to verify and apply different logics in the field of control theory. It is necessary to find an optimization technique for the controller to tune the values automatically in order to minimize the error within the given bounds. In this paper, the algorithmic concepts of Harmony search (HS) and Genetic Algorithm (GA) have been analyzed for the given range of values. The experimental results show that HS performs well than GA.

Keywords: Genetic Algorithm, Harmony Search Algorithm, Inverted Pendulum, PID Controller.

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Authors: Shi Chen, Zi Y. Chen, Jian K. Dan, Jian F. Li

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Evolution of one-dimensional electron system under high-energy-density (HED) conditions is investigated, using the principle of least-action and variational method. In a single-mode modulation model, the amplitude and spatial wavelength of the modulation are chosen to be general coordinates. Equations of motion are derived by considering energy conservation and force balance. Numerical results show that under HED conditions, electron density modulation could exist. Time dependences of amplitude and wavelength are both positively related to the rate of energy input. Besides, initial loading speed has a significant effect on modulation amplitude, while wavelength relies more on loading duration.

Keywords: Electron density modulation, HED, nonlinearevolution, plasmas.

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