Search results for: integral rotor/stator

Authors: Tina Ternes, Florian Kleinau

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The study investigates the content and triggers of mind wandering (MW) in readers of fictional texts. It asks whether readers’ MW is productive (text-related) or unproductive (text-unrelated). Methodologically, it bridges the gap between narratological and data-driven approaches by utilizing a sentence-by-sentence self-paced reading paradigm combined with thought probes in the reading of an excerpt of A. L. Kennedy’s “Baby Blue”. Results show that the contents of MW can be linked to text properties. We validated the role of self-reference in MW and found prediction errors to be triggers of MW. Results also indicate that the content of MW often travels along the lines of the text at hand and can thus be viewed as productive and integral to interpretation.

Keywords: narratology, mind wandering, reading fiction, meta cognition

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Authors: Abdul Wahed Al Zumor

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Saudi EFL Students majoring in English face difficulties in academic lectures listening comprehension in content courses like linguistics, applied linguistics or literature theories. To validate this assumption, a questionnaire assessing students' lecture comprehension experience was administered. The findings have shown that Saudi EFL learners face a great challenge in lecture comprehension at advanced levels. Literature has suggested a myriad of techniques which can enhance academic lecture comprehension. This study has used "reciprocal peer-questioning and responding technique" as an integral part of the academic lecture occupying the last ten minutes. Improvement in experimental students' scores in these courses has been noticed.

Keywords: EFL learners, lecture comprehension, content courses, peer questioning

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Authors: H. Abderrezek, M. N. Harmas

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DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so-called terminal scheme to achieve finite time convergence. Lyapunov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.

Keywords: DC-DC converter, PSO, finite time, terminal, synergetic control

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Authors: Shield B. Lin, Sameer Abdali

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Computer simulations were performed using MATLAB/Simulink for a vibration isolation system for astronaut’s exercise platform. Simulation parameters initially were based on an on-going experiment in a laboratory at NASA Johnson Space Center. The authors expanded later simulations to include other parameters. A discrete proportional-integral-derivative controller with a low-pass filter commanding a linear actuator served as the active control unit to push and pull a counterweight in balancing the disturbance forces. A spring-damper device is used as an optional passive control unit. Simulation results indicated such design could achieve near complete vibration isolation with small displacements of the exercise platform.

Keywords: control, counterweight, isolation, vibration

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Authors: Amir Jalalian-Khakshour, T. N. Croft

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Vertical Axis Wind Turbine (VAWT) systems are becoming increasingly popular as they have a number of advantages over traditional wind turbines. The advantages are reliability, ease of transportation and manufacturing. These attributes could make these technologies useful in developing economies. The performance characteristics of a VAWT are different from a horizontal axis wind turbine, which can be attributed to the low tip speed ratio operation. To unlock the potential of these VAWT systems, the operational behaviour in a number of system topologies and environmental conditions needs to be understood. In this study, a non-linear dynamic simulation method was developed in Matlab and validated against in field data of a large scale, 8-meter rotor diameter prototype. This simulation method has been utilised to determine the performance characteristics of a number of control methods and system topologies. The motivation for this research was to develop a simulation method which accurately captures the operating behaviour and is computationally inexpensive. The model was used to evaluate the performance through parametric studies and optimisation techniques. The study gave useful insights into the applications and energy generation potential of this technology.

Keywords: power generation, renewable energy, rotordynamics, wind energy

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Authors: Abolfazl Hosseinkhani, Sepehr Sanaye

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Different approaches have been used to predict the performance of the vertical axis wind turbines (VAWT), such as experimental, computational fluid dynamics (CFD), and analytical methods. Analytical methods, such as momentum models that use streamtubes, have low computational cost and sufficient accuracy. The double multiple streamtube (DMST) is one of the most commonly used of momentum models, which divide the rotor plane of VAWT into upwind and downwind. In fact, results from the DMST method have shown some discrepancy compared with experiment results; that is because the Darrieus turbine is a complex and aerodynamically unsteady configuration. In this study, analytical-experimental-based corrections, including dynamic stall, streamtube expansion, and finite blade length correction are used to improve the DMST method. Results indicated that using these corrections for a SANDIA 17-m VAWT will lead to improving the results of DMST.

Keywords: vertical axis wind turbine, analytical, double multiple streamtube, streamtube expansion model, dynamic stall model, finite blade length correction

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Authors: Amir Mohtarami, Hadi Kandjani

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The amount of business-critical information in enterprises is growing at an extraordinary rate, and the ability to catalog that information and properly protect it using traditional security mechanisms is not keeping pace. Alongside the Information Technology (IT), information security needs a holistic view in enterprise. In other words, a comprehensive architectural approach is required, focusing on the information itself, understanding what the data are, who owns it, and which business and regulatory policies should be applied to the information. Enterprise Architecture Frameworks provide useful tools to grasp different dimensions of IT in organizations. Usually this is done by the layered views on IT architecture, but not requisite security attention has been held in this frameworks. In this paper, after a brief look at the Enterprise Architecture (EA), we discuss the issue of security in the overall enterprise IT architecture. Due to the increasing importance of security, a rigorous EA program in an enterprise should be able to consider security architecture as an integral part of its processes and gives a visible roadmap and blueprint for this aim.

Keywords: enterprise architecture, architecture framework, security architecture, information systems

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Authors: Noxolo Mafu

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This study presents an overview of strategic planning in South African higher education institutions by tracing its trends and mystique in order to identify its impact. Over the democratic decades, strategic planning has become integral to institutional survival. It has been used as a potent tool by several institutions to catch up and surpass counterparts. While planning has always been part of higher education, strategic planning should be considered different. Strategic planning is primarily about development and maintenance of a strategic fitting between an institution and its dynamic opportunities. This presupposes existence of sets of stages that institutions pursue of which, can be regarded for assessment of the impact of strategic planning in an institution. The network theory serves guides the study in demystifying apparent organisational networks in strategic planning processes.

Keywords: network theory, strategy, planning, strategic planning, assessment, impact

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Authors: Belbahi Ahlam

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With the phenomenal growth in the Internet, network security has become an integral part of computer and information security. In order to come up with measures that make networks more secure, it is important to learn about the vulnerabilities that could exist in a computer network and then have an understanding of the typical attacks that have been carried out in such networks. The first half of this paper will expose the readers to the classical network attacks that have exploited the typical vulnerabilities of computer networks in the past and solutions that have been adopted since then to prevent or reduce the chances of some of these attacks. The second half of the paper will expose the readers to the different network security controls including the network architecture, protocols, standards and software/ hardware tools that have been adopted in modern day computer networks.

Keywords: network security, attacks and controls, computer and information, solutions

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Authors: Maha Hamoud Alatawi

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Drawing on the work of John McLeod and Ariel Watson, this paper explains the relationship between narrative and psychotherapy in two plays by the Irish playwright Conor McPherson. Dublin Carol presents John’s chequered past through his reminiscences of alcohol addiction and Shining City tells the story of John who is haunted by the ghost of his wife, recently died in a car accident, and who seeks the help of Ian, a therapist. At first, the significance of storytelling as an integral part of Irish culture is highlighted. Such a tradition features prominently in contemporary Irish drama. The paper concludes that it is the power of narrative and its therapeutic impact and not the act of psychotherapy and treatment which brings signs of change to characters’ lives.

Keywords: Conor McPherson, drama, psychotherapy, storytelling

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction

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Authors: Martin Alexander Eder, Sergei Semenov

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Many glass-epoxy composite structures, such as large utility wind turbine rotor blades (WTBs), comprise of adhesive joints with typically thick bond lines used to connect the different components during assembly. Performance optimization of rotor blades to increase power output by simultaneously maintaining high stiffness-to-low-mass ratios entails intricate geometries in conjunction with complex anisotropic material behavior. Consequently, adhesive joints in WTBs are subject to multiaxial stress states with significant stress gradients depending on the local joint geometry. Moreover, the dynamic aero-elastic interaction of the WTB with the airflow generates non-proportional, variable amplitude stress histories in the material. Empiricism shows that a prominent failure type in WTBs is high cycle fatigue failure of adhesive bond line interfaces, which in fact over time developed into a design driver as WTB sizes increase rapidly. Structural optimization employed at an early design stage, therefore, sets high demands on computationally efficient interface fatigue models capable of predicting the critical locations prone for interface failure. The numerical stress-based interface fatigue model presented in this work uses the Drucker-Prager criterion to compute three different damage indices corresponding to the two interface shear tractions and the outward normal traction. The two-parameter Drucker-Prager model was chosen because of its ability to consider shear strength enhancement under compression and shear strength reduction under tension. The governing interface damage index is taken as the maximum of the triple. The damage indices are computed through the well-known linear Palmgren-Miner rule after separate rain flow-counting of the equivalent shear stress history and the equivalent pure normal stress history. The equivalent stress signals are obtained by self-similar scaling of the Drucker-Prager surface whose shape is defined by the uniaxial tensile strength and the shear strength such that it intersects with the stress point at every time step. This approach implicitly assumes that the damage caused by the prevailing multiaxial stress state is the same as the damage caused by an amplified equivalent uniaxial stress state in the three interface directions. The model was implemented as Python plug-in for the commercially available finite element code Abaqus for its use with solid elements. The model was used to predict the interface damage of an adhesively bonded, tapered glass-epoxy composite cantilever I-beam tested by LM Wind Power under constant amplitude compression-compression tip load in the high cycle fatigue regime. Results show that the model was able to predict the location of debonding in the adhesive interface between the webfoot and the cap. Moreover, with a set of two different constant life diagrams namely in shear and tension, it was possible to predict both the fatigue lifetime and the failure mode of the sub-component with reasonable accuracy. It can be concluded that the fidelity, robustness and computational efficiency of the proposed model make it especially suitable for rapid fatigue damage screening of large 3D finite element models subject to complex dynamic load histories.

Keywords: adhesive, fatigue, interface, multiaxial stress

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Authors: Mrityunjay Kumar Sinha, Mayank Srivastava

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The position of interface and temperature variation of phase change thermal energy storage system under constant heat injection and radiative heat injection is analysed during charging/discharging process by Heat balance integral method. The charging/discharging process is solely governed by conduction. Phase change material is kept inside a rectangular cavity. Time-dependent fixed temperature and radiative boundary condition applied on one wall, all other walls are thermally insulated. Interface location and temperature variation are analysed by using MATLAB.

Keywords: conduction, melting/solidification, phase change materials, Stefan’s number

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Authors: G. Guramishvili, M. Moistsrapishvili, L. Andghuladze

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In the article are considered the problems arising at increasing of transferring from rolling stock axles on rail loading from 210 KN up to 270 KN and is offered for rail strength analysis definition of rail force loading complex integral characteristic with taking into account all affecting force factors that is characterizing specific operation condition of rail structure and defines the working capability of structure. As result of analysis due mentioned method is obtained that in the conditions of 270 KN loading the rail meets the working assessment criteria of rail and rail structures: Strength, rail track stability, rail links stability and its transverse stability, traffic safety condition that is rather important for post-Soviet countries railways.

Keywords: axial loading, rail force loading, rail structure, rail strength analysis, rail track stability

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Authors: G. Shabib, Esam H. Abd-Elhameed, G. Magdy

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In this paper, a comparison of discrete time PID, PSS controllers is presented through small signal stability of power system comprising of one machine connected to infinite bus system. This comparison achieved by using a new approach of discretization which converts the S-domain model of analog controllers to a Z-domain model to enhance the damping of a single machine power system. The new method utilizes the Plant Input Mapping (PIM) algorithm. The proposed algorithm is stable for any sampling rate, as well as it takes the closed loop characteristic into consideration. On the other hand, the traditional discretization methods such as Tustin’s method is produce satisfactory results only; when the sampling period is sufficiently low.

Keywords: PSS, power system stabilizer PID, proportional-integral-derivative PIM, plant input mapping

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Authors: Arthur D. Wiedemann, Christopher Fuller, Kyle A. Pascioni

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With the introduction of electric motors, small unmanned aerial vehicle designers have to consider trade-offs between acoustic noise and thrust generated. Currently, there are few low-computational tools available for predicting acoustic noise emitted by a propeller into the far-field. Artificial neural networks offer a highly non-linear and adaptive model for predicting isolated and interactive tonal noise. But neural networks require large data sets, exceeding practical considerations in modeling experimental results. A methodology known as physics guided machine learning has been applied in this study to reduce the required data set to train the network. After building and evaluating several neural networks, the best model is investigated to determine how the network successfully predicts the acoustic waveform. Lastly, a post-network transfer function is developed to remove discontinuity from the predicted waveform. Overall, methodologies from physics guided machine learning show a notable improvement in prediction performance, but additional loss functions are necessary for constructing predictive networks on small datasets.

Keywords: aeroacoustics, machine learning, propeller, rotor, neural network, physics guided machine learning

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Authors: Duy Nhat Tran, Van Tien Pham, Quang Trung Trinh, Tien Hai Tran, Van Cong Bui

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In recent years, artificial intelligence and the Internet of Things have experienced significant advancements. Collecting image data and real-time analysis and processing of tasks have become increasingly popular in various aspects of life. Optical scanning devices are widely used to observe and analyze different environments, whether fixed outdoors, mounted on mobile devices, or used in unmanned aerial vehicles. As a result, the interaction between the physical environment and these devices has become more critical in terms of safety. Two commonly used methods for addressing these challenges are active and passive approaches. Each method has its advantages and disadvantages, but combining both methods can lead to higher efficiency. One solution is to utilize direct-drive motors for position control and real-time feedback within the operational range to determine appropriate control parameters with high precision. If the maximum motor torque is smaller than the inertial torque and the rotor reaches the operational limit, the spring system absorbs the impact force. Numerous experiments have been conducted to demonstrate the effectiveness of device protection during operation.

Keywords: optical device, collision safety, collision absorption, precise mechanics

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Authors: Abdallah Benaissa

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In this paper, we consider the problem of asymptotics of double oscillatory integrals in the case of critical points of the second kind, the order of contact between the boundary and a level curve of the phase being even, the situation when the order of contact is odd will be studied in other occasions. Complete asymptotic expansions will be derived and the coefficient of the leading term will be computed in terms of the original data of the problem. A multitude of people have studied this problem using a variety of methods, but only in a special case when the order of contact is minimal: the more cited papers are a paper of Jones and Kline and an other one of Chako. These integrals are encountered in many areas of science, especially in problems of diffraction of optics.

Keywords: asymptotic expansion, double oscillatory integral, critical point of the second kind, optics diffraction

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Authors: Armin Amindari

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Hermetic compressors are used widely for refrigeration, heat pump, and air conditioning applications. With the improvement of energy conservation and environmental protection requirements, inverter compressors that operates at different speeds have become increasingly attractive in the industry. Although speed change capability is more efficient, passing through resonant frequencies may lead to excessive vibrations. In this work, an integrated vibration control approach based on flexible multi-body dynamics theory is used for optimizing the vibration amplitudes of the compressor at different operating speeds. To examine the compressor vibrations, all the forces and moments exerted on the cylinder block were clarified and minimized using balancers attached to the upper and lower ends of the motor rotor and crankshaft. The vibration response of the system was simulated using Motionview™ software. In addition, mass-spring optimization was adopted to shift the resonant frequencies out of the operating speeds. The modal shapes of the system were studied using Optistruct™ solver. Using this approach, the vibrations were reduced up to 56% through dynamic simulations. The results were in high agreement with various experimental test data. In addition, the vibration resonance problem observed at low speeds was solved by shifting the resonant frequencies through optimization studies.

Keywords: vibration, MBD, compressor, hermetic

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Authors: Chetna Jaswal, Nishi Srivastava, Ahammedul Kabeer AP, Puja Prasad

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We are a culture of mass media consumers and cinema as its integral part has high visibility and potential influence on public attitude towards disability which maintains no sociocultural boundaries but experiences substantial social marginalization. Given the lack of awareness and direct experience with disability, on-screen or film representations can give powerful and memorable definitions for the public that can contribute to framing the perception and attitude change. Social representation refers to common ways of thinking, conceiving about and evaluating social reality. It is a product of collective cognition, common sense and thought system. This study aims at analyzing the representations and narratives of disability in Indian cinema and Hollywood with the help of a conceptual understanding of social representation and its theoretical framework.

Keywords: disability, social representation, mainstream cinema, diversity

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Authors: Husam El-Asfour, Fateh Adhnouss, Kenneth McIsaac, Abdul Mutalib Wahaishi, Raafat Aburukba, Idris El-Feghia

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Although intelligence is commonly referred to as the observable behavior in various fields and domains, it must also be shown how it develops by exhibiting multiple forms and without observing the inherent behavior. There have been several official and informal definitions of intelligence in various areas; however, no scientific agreement on a definition has been agreed upon. There must be a single definition, structure, and precise modeling for articulating how intelligence is perceived by people and machines in order to comprehend intelligence. Another key challenge is defining the different environment types based on the integral elements (agents) and their possible interactions. On the basis of conceptualization, this paper proposes a formal model for defining and developing intelligence. Forms of intelligence are derived from an ontological view, and thus intelligence is defined, described, and modeled based on the various types of environments.

Keywords: intelligence, forms, transformation, conceptualization, ontological view

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Authors: Diego Mauricio Murillo Gomez, Enney Leon Gonzalez Ramirez, Hugo Piedrahita, Jairo Yate

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This paper proposes a methodology for the management of noise in open mining industries based on an integral concept, which takes into consideration occupational and environmental noise as a whole. The approach relies on the characterization of sources, the combination of several measurements’ techniques and the use of acoustic prediction software. A discussion about the difference between frequently used acoustic indicators such as Leq and LAV is carried out, aiming to establish common ground for homologation. The results show that the correct integration of this data not only allows for a more robust technical analysis but also for a more strategic route of intervention as several departments of the company are working together. Noise control measurements can be designed to provide a healthy acoustic surrounding in which the exposure workers but also the outdoor community is benefited.

Keywords: environmental noise, noise control, occupational noise, open mining

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Authors: Zuzana Komrsková

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This paper shows the connection between emoticons and politeness in written computer-mediated communication. It studies if there are some differences in the use of emoticon between Czech and English written tweets. My assumptions about the use of emoticons were based on the use of greetings and thanks in real, face to face situations. The first assumption, that welcome greeting phrase would be accompanied by positive emoticon was correct. But for the farewell greeting both positive and negative emoticons are possible. My results show lower frequency of negative emoticons in this context. I also found quite often both positive and negative emoticon in the same tweet. The expression of gratitude is associated with positive emotions. The results show that emoticons accompany polite phrases of greeting and thanks very often both in Czech and English. The use of emoticons with studied polite phrases shows that emoticons have become an integral part of these phrases.

Keywords: Czech, emoticon, english, politeness, twitter

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Authors: M. N. Tandjaoui, C. Banoudjafar, C. Benachaiba, O. Abdelkhalek, A. Kechich

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Advanced power electronic systems are deemed to be an integral part of renewable, green, and efficient energy systems. Wind energy is one of the renewable means of electricity generation that is now the world’s fastest growing energy source can bring new challenges when it is connected to the power grid due to the fluctuation nature of the wind and the comparatively new types of its generators. The wind energy is part of the worldwide discussion on the future of energy generation and use and consequent effects on the environment. However, this paper will introduce some of the requirements and aspects of the power electronic involved with modern wind generation systems, including modern power electronics and converters, and the issues of integrating wind turbines into power systems.

Keywords: power electronics, renewable energy, smart grid, green energy, power technology

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Authors: Reda Mankbadi

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In this paper we explore the use of a second-order unstructured-grid, finite-volume code for direct noise prediction. We consider a Mach 1.5 jet impinging on a perpendicular flat plate. Hybrid LES-RANS simulations are used to calculate directly both the flow field and the radiated sound. The ANSYS Fluent commercial code is utilized for the calculations. The acoustic field is obtained directly from the simulations and is compared with the integral approach of Ffowcs Williams-Hawkings (FWH). Results indicate the existence of a preferred radiation angle. The spectrum obtained is in good agreement with observations. This points out to the possibility of handling the effects of complicated geometries on noise radiation by using unstructured second-orders codes.

Keywords: CFD, Ffowcs Williams-Hawkings (FWH), imping jet, ANSYS fluent commercial code, hybrid LES-RANS simulations

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Authors: Elena Valionienė, Genutė Kalvaitienė

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The issue of resilience of an individual, an organisation, or an entire ecosystem of organisations has recently become an integral part of the education system, where the uncertainties that lead to societal development in the short term create economic, social, and psycho-emotional instability. The Maritime Transport Sector (MTS) is no exception, and the aim of the article is to model the possibilities of enhancing the professional, sociocultural, and psycho-emotional resilience of MTS specialists to proactively respond to crises caused by uncertainties. The research consists of theoretical model creation that helps to identify general maritime business resilience factors and critical success factors. This can develop high resilience and achieve business excellence in a highly volatile, uncertain, complex, and ambiguous (VUCA) environment.

Keywords: maritime transport sector, resilience, uncertainties, VUCA

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Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: Thiru Vandeyar

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The present study set out to determine how Q methodology may be used as an inclusive education policy development process. Utilising Q-methodology as a strategy of inquiry, this qualitative instrumental case study set out to explore how teachers, as a crucial but often neglected human resource, may be included in developing policy. A social constructivist lens and the theoretical moorings of Proudford’s emancipatory approach to educational change anchored in teachers’ ‘writerly’ interpretation of policy text was employed. Findings suggest that Q-method is a unique research approach to include teachers’ voices in policy development. Second, that beliefs, attitudes, and professionalism of teachers to improve teaching and learning using ICT are integral to policy formulation. The study indicates that teachers have unique beliefs about what statements should constitute a school’s information and communication (ICT) policy. Teachers’ experiences are an extremely valuable resource in and should not be ignored in the policy formulation process.

Keywords: teachers, q-methodology, education policy, ICT

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Authors: Yujiang Wu

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As electrical machine (e-machine) power density re-querulents become more stringent in vehicle electrification, mounting a temperature sensor for e-machine stator windings becomes increasingly difficult. This can lead to higher manufacturing costs, complicated harnesses, and reduced reliability. In this paper, we propose a deep-learning method for predicting electric machine winding temperature, which can either replace the sensor entirely or serve as a backup to the existing sensor. We compare the performance of our method, the stateful long short-term memory networks (LSTM) with truncated backpropagation through time (TBTT), with that of linear regression, as well as stateless LSTM with/without residual connection. Our results demonstrate the strength of combining stateful LSTM and TBTT in tackling nonlinear time series prediction problems with long sequence lengths. Additionally, in industrial applications, high-temperature region prediction accuracy is more important because winding temperature sensing is typically used for derating machine power when the temperature is high. To evaluate the performance of our algorithm, we developed a temperature-stratified MSE. We propose a simple but effective data preprocessing trick to improve the high-temperature region prediction accuracy. Our experimental results demonstrate the effectiveness of our proposed method in accurately predicting winding temperature, particularly in high-temperature regions, while also reducing manufacturing costs and improving reliability.

Keywords: deep learning, electrical machine, functional safety, long short-term memory networks (LSTM), thermal management, time series prediction

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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