Search results for: modular exponential

Authors: Sawsen Khlifa, Chiheb AMeur Abid, Belhassan Zouari

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Modular verification approaches have been widely attempted to cope with the well known state explosion problem. This paper deals with the modular verification of modular Petri nets. We propose a reduced version for the modular state space of a given modular Petri net. The new structure allows the creation of smaller modular graphs. Each one draws the behavior of the corresponding module and outlines some global information. Hence, this version helps to overcome the explosion problem and to use less memory space. In this condensed structure, the verification of some generic properties concerning one module is limited to the exploration of its associated graph.

Keywords: distributed systems, modular verification, petri nets, state space explosition

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Authors: Chanhyuck Jeon, Jongho Park, Jinwoong Choi, Sungnam Hong, Sun-Kyu Park

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Many industries put emphasis on environmentally-friendliness as environmental problems are on the rise all over the world. Among themselves, the Modular Bridge research is going on. Also performing cross-section optimization and duration reducing, this research aims at developing the modular bridge with Environment-Friendliness and economic feasibility. However, the difficulty lies in verifying environmental effectiveness because there are no field applications of the modular bridge until now. Therefore, this thesis is categorized according to the form of the modular bridge superstructure and assessed CO₂ emission quantification per work types and materials according to each form to verify the environmental effectiveness of the modular bridge.

Keywords: modular bridge, CO2 emission, environmentally friendly, quantification, carbon emission factor, LCA (Life Cycle Assessment)

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Authors: Rupali Verma, Maitreyee Dutta, Renu Vig

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Encryption and decryption in RSA are done by modular exponentiation which is achieved by repeated modular multiplication. Hence, efficiency of modular multiplication directly determines the efficiency of RSA cryptosystem. This paper designs a Modified Montgomery Modular multiplication in which addition of operands is computed by 4:2 compressor. The basic logic operations in addition are partitioned over two iterations such that parallel computations are performed. This reduces the critical path delay of proposed Montgomery design. The proposed design and RSA are implemented on Virtex 2 and Virtex 5 FPGAs. The two factors partitioning and parallelism have improved the frequency and throughput of proposed design.

Keywords: RSA, montgomery modular multiplication, 4:2 compressor, FPGA

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Authors: Sean Bryner S. Rey, Eric Tanjutco

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Modular execution strategies are performed to address the various challenges of any projects and are implemented on each project phase that covers Engineering, Procurement, Fabrication and Construction. It was until the recent years that the intent to surpass mechanical modularization approach were conceptualized to give solution to much greater demands of project components such as site location and adverse weather condition, material sourcing, construction schedule, safety risks and overall plot layout and allocation. The intent of this paper is to introduce the 3rd Generation Modular Execution with an overview of its advantages on project execution and will give emphasis on Engineering, Construction, Operation and Maintenance. Most importantly, the paper will present the key differentiator of 3rd Gen modular execution against other conventional project execution and the merits it bears for the industry.

Keywords: 3rd generation modular, process block, construction, operation & maintenance

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Authors: Khaled Shehata, Hanady Hussien, Sara Yehia

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Securing the data stored on E-passport is a very important issue. RSA encryption algorithm is suitable for such application with low data size. In this paper the design and implementation of 1024 bit-key RSA encryption and decryption module on an FPGA is presented. The module is verified through comparing the result with that obtained from MATLAB tools. The design runs at a frequency of 36.3 MHz on Virtex-5 Xilinx FPGA. The key size is designed to be 1024-bit to achieve high security for the passport information. The whole design is achieved through VHDL design entry which makes it a portable design and can be directed to any hardware platform.

Keywords: RSA, VHDL, FPGA, modular multiplication, modular exponential

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Authors: Berhane Tewelday Weldhiwot

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This research investigates the pivotal role of modular forms in modern cryptographic systems, particularly focusing on their applications in secure communications and data integrity. Modular forms, which are complex analytic functions with rich arithmetic properties, have gained prominence due to their connections to number theory and algebraic geometry. This study begins by outlining the fundamental concepts of modular forms and their historical development, followed by a detailed examination of their applications in cryptographic protocols such as elliptic curve cryptography and zero-knowledge proofs. By employing techniques from analytic number theory, the research delves into how modular forms can enhance the efficiency and security of cryptographic algorithms. The findings suggest that leveraging modular forms not only improves computational performance but also fortifies security measures against emerging threats in digital communication. This work aims to contribute to the ongoing discourse on integrating advanced mathematical theories into practical applications, ultimately fostering innovation in cryptographic methodologies.

Keywords: modular forms, cryptography, elliptic curves, applications, mathematical theory

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Authors: Jae Hee Chung, Tae Uk Kang, Byung Seo Kim

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This study aims to propose design technologies for the energy-saving modular housing units considering environmental and aesthetic aspects. Modular houses are environmentally friendly based on 3R (Reduce, Reuse, Recycle) because they can dramatically reduce carbon dioxide and construction wastes generated during the construction, use, and disposal process by the pre-fabrication at the factory and the recyclability of the unit, compared to the existing construction methods. The existing modular housing, however, tends to focus on quantitative aspects of energy reduction, such as windows, insulation, and introduction of renewable energy, and there is not much research on energy-saving type units considering the environmental aspects such as daylighting and ventilation, and the design that goes beyond the standardized appearance. Therefore, this study conducts theoretical investigation and analytical case studies on the energy-saving methods through various architectural planning elements as well as materials like insulation considering the environmental and aesthetic aspects in the modular housing. Then, comparative analysis on the energy efficiency through the energy simulation is conducted. As a conclusion, the energy-saving modular housing units considering environmental and aesthetics aspects are proposed. It is expected that this study will contribute to the supply and activation of modular housing through deriving design technologies for the energy-saving modular housing units that consider not only quantitative aspects but also qualitative aspects.

Keywords: aesthetic aspects, energy-saving, environmental, modular housing

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Authors: Achim Kampker, Peter Burggräf, Moritz Krunke, Hanno Voet

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As a reaction to current challenges in factory planning, many companies think about introducing factory standards to lower planning times and decrease planning costs. If these factory standards are set-up with a high level of modularity, they are defined as modular factory systems. This paper deals with the main current problems in the application of modular factory systems in practice and presents a solution approach with its basic models. The methodology is based on methods from factory planning but also uses the tools of other disciplines like product development or technology management to deal with the high complexity, which the development of modular factory systems implies. The four basic models that such a methodology has to contain are introduced and pointed out.

Keywords: factory planning, modular factory systems, factory standards, cost-benefit analysis

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Authors: Jae-Joon Song, Sang-Yoon Lee, Bong-Chul Joo

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The girder-type precast modular bridge has been developed as a simply supported bridge. The girder-type precast modular bridge could be applied to the multi-span bridges through the continuity method. The continuity of the girder-type precast modular bridge is achieved by using the link slab which is easy to construction and appropriate to the rapid construction. In this study, the link slab with transition zone was used for the continuity of the precast modular bridges, and the construction detail of link slab was modified. In addition, the modified iterative design method of link slab was proposed in this study. To verify the proposed design method, the fatigue test using the mock-up specimen was conducted with cycle loading condition up to two million cycles.

Keywords: precast, modular bridge, link slab

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Yu Zhao, Mengqin Sun, Yahui Zhang

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Apparel products (or apparel) with the sense of aesthetics, usability (ergonomics) and function are fundamental and varied in people’s daily life. The numerous apparel thus produced by apparel industry, have been triggered many issues, such as the waste of sources and the environmental pollutions. In this study, a hybrid architecture called modular architecture of apparel (MAA) has been proposed to deal with the variety of apparel, and thus to overcome the aforementioned issues. Generally, the establishment of MAA takes advantage of the modular design of a general product that a product is assembled with many modules through their modular interface connector. The development of MAA is to first analyze the structure of apparel in terms of the necessity to form an apparel and the aesthetics, ergonomics, and function of apparel; then to divide apparel into many segments (or module in product design) based on the structure of apparel; to develop modular interfaces and modular interface connectors in terms of the features of apparel’s modules. It is noted that in the general product design, modules of a product are only about the function and ergonomics, but in MAA, the module of aesthetics is developed. Further, an apparel design with employing the MAA is carried out to validate its usefulness and efficiency. There are three contributions out of this study, the first is to overcome the aforementioned issues (i.e. waste of source and environmental pollutions); the second is the improvement of the modular design for product by considering aesthetics; the third is to add the value in realizing the personalized mass production of apparel in the near future.

Keywords: apparel, architecture, modular design, segment

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Authors: Jongho Park, Ui-Cheol Shin, Jinwoong Choi, Sungnam Hong, Sun-Kyu Park

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While the numerous structures built the industrialization are aging, the effort for the maintenance is concentrated in many countries. However, the traffic jam, environmental damage, and enormous maintenance cost, and etc become a problem. So, in order to solve this, the modular bridge has been studied. This bridge is the structure which utilizes and assembles the standard precast member. Through this, the substitution of the existing bridge and advantage of the easy maintenance will be achieved. However, the reliability in the long-term behavior is insufficient due to the junction part between modular precast members. Therefore, in this research, the cyclic load loading experiment was performed on the junction and deflection was analyzed by long-term service in modular slab connection. The deflection of modular slab with junction was mostly generated when initial and final test.

Keywords: modular bridge, deflection, cyclic loading, junction

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Authors: Benjamin Goldsmith, Felix Heisel

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The building industry must reduce its emissions in order to meet 2030 neutrality targets, and modular and/or offsite construction is seen as an alternative to conventional construction methods which could help achieve this goal. Modular construction has previously been shown to be less wasteful and has a lower global warming potential (GWP). While many studies have been conducted investigating the life cycle impacts of modular and conventional construction, few studies have compared different types of modular assembly and construction in order to determine which offer the greatest environmental benefits over their whole life cycle. This study seeks to investigate three different modular construction types -infill frame, core, and podium- in order to determine environmental impacts such as GWP as well as circularity indicators. The study will focus on the emissions of the production, construction, and end-of-life phases. The circularity of the various approaches will be taken into consideration in order to acknowledge the potential benefits of the ability to reuse and/or reclaim materials, products, and assemblies. The study will conduct hypothetical case studies for the three different modular construction types, and in doing so, control the parameters of location, climate, program, and client. By looking in-depth at the GWP of the beginning and end phases of various simulated modular buildings, it will be possible to make suggestions on which type of construction has the lowest global warming potential.

Keywords: modular construction, offsite construction, life cycle analysis, global warming potential, environmental impact, circular economy

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Authors: Kyung-Suk Choi, Hyung-Joon Kim

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Modular structural systems are constructed using a method that they are assembled with prefabricated unit modular frames on-site. This provides a benefit that can significantly reduce building construction time. Their structural design is usually carried out under the assumption that the load-carrying mechanism is similar to that of a traditional steel moment-resisting system. However, both systems are different in terms of beam-column connection details which may strongly influence the lateral structural behavior. Specially, the presence of access holes in a beam-column joint of a unit modular frame could cause undesirable failure during strong earthquakes. Therefore, this study carried out finite element analyses (FEM) of unit modular frames to investigate the cyclic behavior of beam-column joints with the structural influence of access holes. Analysis results show that the unit modular frames present stable cyclic response with large deformation capacities, and their joints are classified into semi-rigid connections.

Keywords: unit modular frame, steel moment connection, nonlinear analytical model, moment-rotation relation

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Authors: Yulong Jia, Xiang Zhang, Ziyuan Wu, Shiji Hu

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The calculation of bilinear pairing is the core of the SM9 algorithm, which relies on the underlying prime domain algorithm and the quadratic extension domain algorithm. Among the field algorithms, modular multiplication operation is the most time-consuming part. Therefore, the underlying modular multiplication algorithm is optimized to maximize the operation speed of bilinear pairings. This paper uses a modular multiplication method based on non-least positive (NLP) combined with Karatsuba and schoolbook multiplication to improve the Montgomery algorithm. At the same time, according to the characteristics of multiplication operation in the quadratic extension domain, a quadratic extension domain FP2-NLP modular multiplication algorithm for bilinear pairings is proposed, which effectively reduces the operation time of modular multiplication in the quadratic extension domain. The sub-expanded domain Fp₂ -NLP modular multiplication algorithm effectively reduces the operation time of modular multiplication under the second-expanded domain. The multiplication unit in the quadratic extension domain is implemented using SMIC55nm process, and two different implementation architectures are designed to cope with different application scenarios. Compared with the existing related literature, The output latency of this design can reach a minimum of 15 cycles. The shortest time for calculating the (AB+CD)r⁻¹ mod form is 37.5ns, and the comprehensive area-time product (AT) is 11400. The final R-ate pairing algorithm hardware accelerator consumes 2670k equivalent logic gates and 1.8ms computing time in 55nm process.

Keywords: sm9, hardware, NLP, Montgomery

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Authors: Te-Jen Chang, Ping-Sheng Huang, Shan-Ten Cheng, Chih-Lin Lin, I-Hui Pan, Tsung- Hsien Lin

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RSA system is a great contribution for the encryption and the decryption. It is based on the modular exponentiation. We call this system as “a large of numbers for calculation”. The operation of a large of numbers is a very heavy burden for CPU. For increasing the computational speed, in addition to improve these algorithms, such as the binary method, the sliding window method, the addition chain method, and so on, the cluster computer can be used to advance computational speed. The cluster system is composed of the computers which are installed the MPICH2 in laboratory. The parallel procedures of the modular exponentiation can be processed by combining the sliding window method with the addition chain method. It will significantly reduce the computational time of the modular exponentiation whose digits are more than 512 bits and even more than 1024 bits.

Keywords: cluster system, modular exponentiation, sliding window, addition chain

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Authors: Jongho Park, Jinwoong Choi, Sungnam Hong, Seung-Kyung Kye, Sun-Kyu Park

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Recently, to cope with the rapidly changing construction trend because of aging infrastructures, modular bridge technology has been studied actively. Modular bridge is easily constructed by assembling standardized precast structure members in the field. It will be possible to construct rapidly and reduce construction cost efficiently. However, the shape examination of the transverse connection of T-type girder newly developed between the segmented modules is not performed. Therefore, the investigation of the connection shape is needed. In this study, shape of the modular T-girder bridge transverse connection was analyzed by finite element model that was verified in study which was verification of model for transverse connection using Abaqus. Connection angle was chosen as the parameter. The result of analyses showed that optimal value of angle is 130 degree.

Keywords: modular bridge, optimal transverse shape, parameter, FEM

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Authors: Khaled Elbehiery, Hussam Elbehiery

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Smart cities are a framework of technologies along with sustainable infrastructure to provide their citizens an improved quality of life, safer environment, affordability, and more, which in turn helps with the society's economic growth. The proposed research will focus on the primary building block of the smart city; the infrastructure of the house itself. The traditional method of building houses has been, for a long time, nothing but a costly manufacturing process, and consequently, buying a house becomes not an option for everyone anymore. The smart cities' Modular Houses are not using traditional building construction materials; the design reduces the common lengthy construction times and associated high costs. The Modular Houses are technological homes, low-cost and customizable based on a family's requirements. In addition, the Modular Houses are environmentally friendly and healthy enough to assist with the pandemic situation.

Keywords: smart cities, modular houses, single-unit property, multi-unit property, mobility features, chain-supply, livable environment, carbon footprint

Procedia PDF Downloads 126

Authors: Soonwon Kang, Jinwoong Choi, Sungnam Hong, Seung-Kyung Kye, Sun-Kyu Park

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The modular bridge is to be constructed by assembling standardized precast segments. This bridge is classified as a slab type and T-girder type. The T-girder bridge has transverse joint. However, it did not perform the verification on the transverse joint, but the slab type was done on the analytic study on the joint. Therefore, it is necessary for precast modular T-girder bridge that has a transverse joint to propose an appropriated model. In this study, specimens and analysis models compared integrated type with segmented type. Results of the integrated and segmented specimens, each of the deflection was 98.40mm and 74.66mm when the maximum load was 269.71kN and 248.29kN, in case of the modeling the specimens, each of the deflection was 84.04mm, 69.39mm when the maximum load was 269.71kN, 248.29kN, therefore, the precast T-girder modular bridges form the analytic model proposed appropriate.

Keywords: precast, T-girder modular bridge, finite element analysis, joint

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Authors: Grienggrai Rajchakit

Abstract:

This paper is concerned with the exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton's formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, time-varying delays, lyapunov-krasovskii functional, leibniz-newton's formula

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Authors: C. Copilusi, C. Ploscaru

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This paper addresses attention to a research regarding the design of a knee orthosis in a modular form used on children walking rehabilitation. This research is focused on the human lower limb kinematic analysis which will be used as input data on virtual simulations and prototype validation. From this analysis, important data will be obtained and used as input for virtual simulations of the knee modular orthosis. Thus, a knee orthosis concept was obtained and validated through virtual simulations by using MSC Adams software. Based on the obtained results, the modular orthosis prototype will be manufactured and presented in this article.

Keywords: human lower limb, children orthoses, kinematic analysis, knee orthosis

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Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

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Authors: Ayman Baklizi

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Based on type II censored data, we consider interval estimation of the quantiles of the two-parameter exponential distribution and the difference between the quantiles of two independent two-parameter exponential distributions. We derive asymptotic intervals, Bayesian, as well as intervals based on the generalized pivot variable. We also include some bootstrap intervals in our comparisons. The performance of these intervals is investigated in terms of their coverage probabilities and expected lengths.

Keywords: asymptotic intervals, Bayes intervals, bootstrap, generalized pivot variables, two-parameter exponential distribution, quantiles

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

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Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: covariation reasoning, exponential function, modeling, representations

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

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The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: exponential smoothing method, open data, operation estimation, train schedule

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Authors: Shubhakar Gupta, Dhruv Prakash, Apoorv Mehta

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In this project, we design a modular robot capable of using and switching between multiple methods of propulsion and classifying terrain, based on an Inertial Measurement Unit (IMU) input. We wanted to make a robot that is not only intelligent in its functioning but also versatile in its physical design. The advantage of a modular robot is that it can be designed to hold several movement-apparatuses, such as wheels, legs for a hexapod or a quadpod setup, propellers for underwater locomotion, and any other solution that may be needed. The robot takes roughness input from a gyroscope and an accelerometer in the IMU, and based on the terrain classification from an artificial neural network; it decides which method of propulsion would best optimize its movement. This provides the bot with adaptability over a set of terrains, which means it can optimize its locomotion on a terrain based on its roughness. A feature like this would be a great asset to have in autonomous exploration or research drones.

Keywords: modular robotics, terrain detection, terrain classification, neural network

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Annarita Zarrillo

Abstract:

This research is part of adaptive architecture, reflecting the evolution that the world of architectural design is going through. Today's architecture is no longer seen as a static system but, conversely, as a dynamic system that changes in response to the environment and the needs of users. One of the major forms of adaptivity is represented by kinetic structures. This study aims to underline the importance of experimentation on physical scale models for the study of dynamic structures and to present the case study of a modular kinetic structure designed through the use of parametric design software and created as a prototype in the laboratories of the Royal Danish Academy in Copenhagen.

Keywords: adaptive architecture, architectural application, kinetic structures, modular prototype

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Authors: Jude Inwumoh, Adam P. R. Taylor, Kosala Gunawardane

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Modular multilevel converters (MMC) exhibit a highly scalable and modular characteristic with good voltage/power expansion, fault tolerance capability, low output harmonic content, good redundancy, and a flexible front-end configuration. Fault detection, location, and isolation, as well as maintaining fault ride-through (FRT), are major challenges to MMC reliability and power supply sustainability. Different papers have been reviewed to seek the best MMC configuration with fault capability. DC faults are the most common fault, while the probability that AC fault occurs in a modular multilevel converter (MCC) is low; though, AC faults consequence are severe. This paper reviews several MMC topologies and modulation techniques in tackling faults. These fault control strategies are compared based on cost, complexity, controllability, and power loss. A meshed network of half-bridge (HB) MMC topology was optimal in rendering fault ride through than any other MMC topologies but only when combined with DC circuit breakers (CBS), AC CBS, and fault current limiters (FCL).

Keywords: MMC-HVDC, DC faults, fault current limiters, control scheme

Procedia PDF Downloads 139

Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, timevarying delays, Lyapunov-Krasovskii functional, Leibniz-Newton’s formula

Procedia PDF Downloads 458