Search results for: resource allocation without feedback

Authors: Kyaw Myo Lin, Pyone Lai Swe, Khine Zin Oo

Abstract:

In this paper, an approach combining analytical method for the distributed generator (DG) sizing and meta-heuristic search for the optimal location of DG has been presented. The optimal size of DG on each bus is estimated by the loss sensitivity factor method while the optimal sites are determined by Particle Swarm Optimization (PSO) based optimal reactive power dispatch for minimizing active power loss. To confirm the proposed approach, it has been tested on IEEE-30 bus test system. The adjustments of operating constraints and voltage profile improvements have also been observed. The obtained results show that the allocation of DGs results in a significant loss reduction with good voltage profiles and the combined approach is competent in keeping the system voltages within the acceptable limits.

Keywords: Analytical approach, distributed generations, optimal size, optimal location, optimal reactive power dispatch, particle swarm optimization algorithm.

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Authors: Naohiro Ban, Hiromitsu Ogawa, Manato Ono, Yoshihisa Ishida

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This paper describes an expanded system for a servo system design by using the Loop Shaping Design Procedure (LSDP). LSDP is one of the H∞ design procedure. By conducting Loop Shaping with a compensator and robust stabilization to satisfy the index function, we get the feedback controller that makes the control system stable. In this paper, we propose an expanded system for a servo system design and apply to the DC motor. The proposed method performs well in the DC motor positioning control. It has no steady-state error in the disturbance response and it has robust stability.

Keywords: Loop Shaping Design Procedure (LSDP), servosystem, DC motor.

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Authors: F. Urem, K. Fertalj, I. Livaja

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Constant upgrading of Enterprise Resource Planning (ERP) systems is necessary, but can cause new defects. This paper attempts to model the likelihood of defects after completed upgrades with Weibull defect probability density function (PDF). A case study is presented analyzing data of recorded defects obtained for one ERP subsystem. The trends are observed for the value of the parameters relevant to the proposed statistical Weibull distribution for a given one year period. As a result, the ability to predict the appearance of defects after the next upgrade is described.

Keywords: ERP, upgrade, reliability, Weibull model

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Authors: Apinan Aurasopon, Worawat Sa-ngiavibool

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This paper proposes a synchronized random switching frequency pulse width modulation (SRSFPWM). In this technique, the clock signal is used to control the random noise frequency which is produced by the feedback voltage of a hysteresis circuit. These make the triangular carrier frequency equaling to the random noise frequency in each switching period with the symmetrical positive and negative slopes of triangular carrier. Therefore, there is no error voltage in PWM signal. The PSpice simulated results shown the proposed technique improved the performance in case of low frequency harmonics of PWM signal comparing with conventional random switching frequency PWM.

Keywords: Random switching frequency pulse - width modulation.

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Authors: R. Oloomi, M. A. Sadrnia

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This paper proposes a new optimal feedback controller for voltage source converters VSC's, for current regulated voltage source converters, which allows compensate the harmonics of current produced by nonlinear loads and load reactive power. The aim of the present paper is to describe a novel switching signal generation technique called optimal controller which guarantees that the injected currents follow the reference currents determined by the compensation strategy, with the smallest possible tracking error and fixed switching frequency. It is compared with well-known hysteresis current controller HCC. The validity of presented method and its comparison with HCC is studied through simulation results.

Keywords: Hysteresis Current Controller, Optimal Controller, Switching pattern, Voltage Source Converter.

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Authors: Jamil Hijazi, Stirling Howieson

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Reducing energy consumption and CO₂ emissions are probably the greatest challenge now facing mankind. From considerations surrounding global warming and CO₂ production, it has to be recognized that oil is a finite resource and the KSA like many other oil-rich countries will have to start to consider a horizon where hydro-carbons are not the dominant energy resource. The employment of hybrid ground-cooling pipes in combination with the black body solar collection and radiant night cooling systems may have the potential to displace a significant proportion of oil currently used to run conventional air conditioning plant. This paper presents an investigation into the viability of such hybrid systems with the specific aim of reducing cooling load and carbon emissions while providing all year-round thermal comfort in a typical Saudi Arabian urban housing block. Soil temperatures were measured in the city of Jeddah. A parametric study then was carried out by computational simulation software (DesignBuilder) that utilized the field measurements and predicted the cooling energy consumption of both a base case and an ideal scenario (typical block retro-fitted with insulation, solar shading, ground pipes integrated with hypocaust floor slabs/stack ventilation and radiant cooling pipes embed in floor). Initial simulation results suggest that careful ‘ecological design’ combined with hybrid radiant and ground pipe cooling techniques can displace air conditioning systems, producing significant cost and carbon savings (both capital and running) without appreciable deprivation of amenity.

Keywords: Cooling load, energy efficiency, ground pipe cooling, hybrid cooling strategy, hydronic radiant systems, low carbon emission, passive designs, thermal comfort.

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Authors: Zarabizan Zakaria, Syuhaida Ismail, Aminah Md. Yusof

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Delay can be defined as time overrun or extension of time to complete the project. There are high possibilities that delay issues in final account closing cannot be avoided especially in construction project in Malaysia which is unique and dynamic in the terms of nature of design and technical skill. Delay in final account closing is a situation when the actual planning (time and budget allocation) of a construction project exceeds the planned schedule or on the other hand, final account closing exceeds the time and other provisions specified in the contract. The causes of delay discussed in this paper are appraised from the literature review. There are two main types of delay: excusable delay and non-excusable delay. The literature reviews on the delay in final account closing which is then translated into a theoretical framework are summarized in the context of construction players and academician perspective. It is anticipated that the finding reported in this paper could assist the planning of future strategies and guidelines of final account closing for the betterment of construction projects in Malaysia.

Keywords: Construction industry, construction contract, final account closing, delay.

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Authors: Karel Frajtak, Miroslav Bures, Ivan Jelinek

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Software testing is important stage of software development cycle. Current testing process involves tester and electronic documents with test case scenarios. In this paper we focus on new approach to testing process using automated test case generation and tester guidance through the system based on the model of the system. Test case generation and model-based testing is not possible without proper system model. We aim on providing better feedback from the testing process thus eliminating the unnecessary paper work.

Keywords: Model based testing, test automation, test generating, tester support.

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Authors: A. Castillo, A. Gutiérrez, J. M. Gutiérrez, J. M. Gómez, E. García-López

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Water has always been a very precious resource. However, many of us do not fully understand or appreciate water-s value until there will be a shortage. We intended to analyze the water consumption into the Spanish households to understand their behavior according to the habitants of the house. In this research was carried out a survey of users, asking for water consumption of their households. The aim of this paper is get a reference value of consumers in Spanish households to help to check their bill and realize if their consumption is excessive, including some tips to decrease it.

Keywords: Households, survey, water consumption.

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Authors: Oluwaseun K. Oyebode, Josiah A. Adeyemo

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Hydrological modelling plays a crucial role in the planning and management of water resources, most especially in water stressed regions where the need to effectively manage the available water resources is of critical importance. However, due to the complex, nonlinear and dynamic behaviour of hydro-climatic interactions, achieving reliable modelling of water resource systems and accurate projection of hydrological parameters are extremely challenging. Although a significant number of modelling techniques (process-based and data-driven) have been developed and adopted in that regard, the field of hydrological modelling is still considered as one that has sluggishly progressed over the past decades. This is majorly as a result of the identification of some degree of uncertainty in the methodologies and results of techniques adopted. In recent times, evolutionary computation (EC) techniques have been developed and introduced in response to the search for efficient and reliable means of providing accurate solutions to hydrological related problems. This paper presents a comprehensive review of the underlying principles, methodological needs and applications of a promising evolutionary computation modelling technique – genetic programming (GP). It examines the specific characteristics of the technique which makes it suitable to solving hydrological modelling problems. It discusses the opportunities inherent in the application of GP in water related-studies such as rainfall estimation, rainfall-runoff modelling, streamflow forecasting, sediment transport modelling, water quality modelling and groundwater modelling among others. Furthermore, the means by which such opportunities could be harnessed in the near future are discussed. In all, a case for total embracement of GP and its variants in hydrological modelling studies is made so as to put in place strategies that would translate into achieving meaningful progress as it relates to modelling of water resource systems, and also positively influence decision-making by relevant stakeholders.

Keywords: Computational modelling, evolutionary algorithms, genetic programming, hydrological modelling.

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Authors: N. Affi, A. El Fadl, M. El Otmani, M.C. Benismail, L.M. Idrissi

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The object of the present research was to assess the effects of partial rootzone drying (PRD) on tomato growth, productivity, biomass allocation and water use efficiency (WUE). Plants were grown under greenhouse, on a sand substrate. Three treatments were applied: a control that was fully and conventionally irrigated, PRD-70 and PRD-50 in which, respectively, 70% and 50% of water requirements were supplied using PRD. Alternation of irrigation between the two root halves took place each three days. The Control produces the highest total yield (252tons/ha). In terms of fruit number, PRD-50 showed 23% and 16% less fruits than PRD-70 and control, respectively. Fruit size was affected by treatment with PRD-50 treatment producing 66% and 53% more class 3 fruits than, control and PRD-70, respectively. For plant growth, the difference was not significant when comparing control to PRD-70 but was significant when comparing PRD-70 and control to PRD-50. No effect was on total biomass but root biomass was higher for stressed plants compared to control. WUE was 66% and 27% higher for PRD-50 and PRD-70 respectively compared to control.

Keywords: Biomass, growth, partial rootzone drying, water use efficiency yield.

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Authors: Shengqi Yu, Jinwei Zhao

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This paper presents a kind of analog circuit based temperature control system, which is mainly composed by threshold control signal circuit, synchronization signal circuit and trigger pulse circuit. Firstly, the temperature feedback signal function is realized by temperature sensor TS503F3950E. Secondly, the main control circuit forms the cycle controlled pulse signal to control the thyristor switching model. Finally two reverse paralleled thyristors regulate the output power by their switching state. In the consequence, this is a modernized and energy-saving domestic electric heating system.

Keywords: Time base circuit, automatic control, zero-crossing trigger, temperature control.

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Authors: A. Ribeiro, N. Valério, C. Vilarinho, J. Araujo, J. Carvalho

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Res2ValHUM project involves institutions from the Spanish Autonomous Region of Galicia and the north of Portugal (districts of Porto and Braga) and has as overall objectives of promotion of composting as an process for the correct managing of organic waste, valorization of compost in different fields or applications for the constitution of products with high added value, reducing of raw materials losses, and reduction of the amount of waste throw in landfills. Three main actions were designed to achieve the objectives: development of a management tool to improve collection and residue channeling for composting, sensibilization of the population for composting and characterization of the chemical and biological properties of compost and humic and fulvic substances to envisage high-value applications of compost. Here we present the cooperative activity of Galician and northern Portuguese institutions to valorize organic waste in both regions with common socio-economic characteristics and residue management problems. Results from the creation of the resource manage tool proved the existence of a large number of agricultural wastes that could be valorized. In the North of Portugal, the wastes from maize, oats, potato, apple, grape pomace, rye, and olive pomace can be highlighted. In the Autonomous Region of Galicia the wastes from maize, wheat, potato, apple, and chestnuts can be emphasized. Regarding the isolation and identification of microbial consortia from compost samples, results proved microorganisms belong mainly to the genus Bacillus spp. Among all the species identified in compost samples, Bacillus licheniformis can be highlighted in the production of humic and fulvic acids.

Keywords: Agricultural wastes, Bacillus licheniformis, Bacillus spp., Humic-acids, Fulvic-acids.

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Authors: Joe Imae, Kenjiro Shinagawa, Tomoaki Kobayashi, Guisheng Zhai

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We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of ‘virtual-time’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.

Keywords: Nonlinear Control, Optimal Control, Hamilton-Jacobi Equation, Virtual-Time

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Authors: M. Ravindra, R. Srinivasa Rao

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This paper presents a Generalized Binary Integer Linear Programming (GBILP) method for optimal allocation of Phasor Measurement Units (PMUs) and to generate Dynamic State Estimation (DSE) solution with complete observability. The GBILP method is formulated with Zero Injection Bus (ZIB) constraints to reduce the number of locations for placement of PMUs in the case of normal and single line contingency. The integration of PMU and conventional measurements is modeled in DSE process to estimate accurate states of the system. To estimate the dynamic behavior of the power system with proposed method, load change up to 40% considered at a bus in the power system network. The proposed DSE method is compared with traditional Weighted Least Squares (WLS) state estimation method in presence of load changes to show the impact of PMU measurements. MATLAB simulations are carried out on IEEE 14, 30, 57, and 118 bus systems to prove the validity of the proposed approach.

Keywords: Observability, phasor measurement units, PMU, state estimation, dynamic state estimation, SCADA measurements, zero injection bus.

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Authors: Trisha S. Malhotra

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While there exist frameworks to study the induction, manifestation, duration and general nature of emotions like shame, guilt, embarrassment and pride in humans, the same cannot be said for other species. This is because such 'complex' emotions have situational inductions and manifestations that supposedly vary due to differences between and within different species' ethology. This paper looks at the socio-adaptive functions of guilt to posit why this emotion might be observed across varying species. Primarily, the experimental paradigm of guilt-assessment in domesticated dogs is critiqued for lack of ethological consideration in its measurement and analysis. It is argued that a paradigm for guilt-assessment should measure the species-specific prosocial approach behavior instead of the immediate feedback of the 'guilty'. Finally, it is asserted that the origin of guilt is subjective and if it must be studied across a plethora of species, its definition must be tailored to fit accordingly.

Keywords: Guilt, assessment, dogs, prosocial approach behavior, empathy, species, ethology.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

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This paper examines the problem of designing a robust H8 state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H8 performance are derived. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear two-time scale systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: TS fuzzy, Markovian jumps, LMI, two-time scale systems.

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Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the automatic choosing functions of gradient optimization type for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by minimizing the Hamiltonian with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Jeffrey L. Duffany

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Graph coloring is an important problem in computer science and many algorithms are known for obtaining reasonably good solutions in polynomial time. One method of comparing different algorithms is to test them on a set of standard graphs where the optimal solution is already known. This investigation analyzes a set of 50 well known graph coloring instances according to a set of complexity measures. These instances come from a variety of sources some representing actual applications of graph coloring (register allocation) and others (mycieleski and leighton graphs) that are theoretically designed to be difficult to solve. The size of the graphs ranged from ranged from a low of 11 variables to a high of 864 variables. The method used to solve the coloring problem was the square of the adjacency (i.e., correlation) matrix. The results show that the most difficult graphs to solve were the leighton and the queen graphs. Complexity measures such as density, mobility, deviation from uniform color class size and number of block diagonal zeros are calculated for each graph. The results showed that the most difficult problems have low mobility (in the range of .2-.5) and relatively little deviation from uniform color class size.

Keywords: graph coloring, complexity, algorithm.

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Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

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This paper presents a new adaptive impedance control strategy, based on Function Approximation Technique (FAT) to compensate for unknown non-flat environment shape or time-varying environment location. The target impedance in the force controllable direction is modified by incorporating adaptive compensators and the uncertainties are represented by FAT, allowing the update law to be derived easily. The force error feedback is utilized in the estimation and the accurate knowledge of the environment parameters are not required by the algorithm. It is shown mathematically that the stability of the controller is guaranteed based on Lyapunov theory. Simulation results presented to demonstrate the validity of the proposed controller.

Keywords: Adaptive impedance control, Function Approximation Technique (FAT), impedance control, unknown environment position.

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Authors: Abbas Al-Refaie

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The research examines the factors that affect customer churn (CC) in the Jordanian telecom industry. A total of 700 surveys were distributed. Cluster analysis revealed three main clusters. Results showed that CC and customer satisfaction (CS) were the key determinants in forming the three clusters. In two clusters, the center values of CC were high, indicating that the customers were loyal and SC was expensive and time- and energy-consuming. Still, the mobile service provider (MSP) should enhance its communication (COM), and value added services (VASs), as well as customer complaint management systems (CCMS). Finally, for the third cluster the center of the CC indicates a poor level of loyalty, which facilitates customers churn to another MSP. The results of this study provide valuable feedback for MSP decision makers regarding approaches to improving their performance and reducing CC.

Keywords: Cluster analysis, telecom industry, switching cost, customer churn.

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Authors: Thi T. Nguyen, Lee N. Gordon-Brown

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A new deployment of the multiple criteria decision making (MCDM) techniques: the Simple Additive Weighting (SAW), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for portfolio allocation, is demonstrated in this paper. Rather than exclusive reference to mean and variance as in the traditional mean-variance method, the criteria used in this demonstration are the first four moments of the portfolio distribution. Each asset is evaluated based on its marginal impacts to portfolio higher moments that are characterized by trapezoidal fuzzy numbers. Then centroid-based defuzzification is applied to convert fuzzy numbers to the crisp numbers by which SAW and TOPSIS can be deployed. Experimental results suggest the similar efficiency of these MCDM approaches to selecting dominant assets for an optimal portfolio under higher moments. The proposed approaches allow investors flexibly adjust their risk preferences regarding higher moments via different schemes adapting to various (from conservative to risky) kinds of investors. The other significant advantage is that, compared to the mean-variance analysis, the portfolio weights obtained by SAW and TOPSIS are consistently well-diversified.

Keywords: Fuzzy numbers, SAW, TOPSIS, portfolio optimization, higher moments, risk management.

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Authors: Said C. Fares, Mary A. Fares

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It is well documented that introductory computer programming courses are difficult and that failure rates are high. The aim of this project was to reduce the high failure and withdrawal rates in learning to program. This paper presents a number of changes in module organization and instructional delivery system in teaching CS1. Daily out of class help sessions and tutoring services were applied, interactive lectures and laboratories, online resources, and timely feedback were introduced. Five years of data of 563 students in 21 sections was collected and analyzed. The primary results show that the failure and withdrawal rates were cut by more than half. Student surveys indicate a positive evaluation of the modified instructional approach, overall satisfaction with the course and consequently, higher success and retention rates.

Keywords: Failure Rate, Interactive Learning, Student engagement, CS1.

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Authors: Daniel Badulescu

Abstract:

Under the difficult access to finance of SMEs, they expect that its relationship with the banks shall constitute a real help to access appropriate financing, at reasonable costs and requirements, given the possibility of mutually beneficial and long lasting relation. The literature, but also the research we have carried on, is centered on such determinants as concentration and the length of the relationship, but at the same time, there is little certainty that banks are responding positively to them. Furthermore, although the trust is considered as being a fundamental element of bank relationship – see the case house bank – SMEs find that the banks finance them looking rather on collaterals and covenants than to trust. Moreover, a positive behavior, such as prompt or advance repayments of loans, doesn-t generate any positive feedback from the banks side. All these show a deep un-satisfaction of the SMEs concerning their relationship banking.

Keywords: Banks' behavior, relationship banking, SMEs.

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Authors: Sungsik Jo, Hyeonwoo Kim, Iksu Choi, Hunmo Kim

Abstract:

In the SHP, LVDT sensor is for detecting the length changes of the EHA output, and the thrust of the EHA is controlled by the pressure sensor. Sensor is possible to cause hardware fault by internal problem or external disturbance. The EHA of SHP is able to be uncontrollable due to control by feedback from uncertain information, on this paper; the sliding mode observer algorithm estimates the original sensor output information in permanent sensor fault. The proposed algorithm shows performance to recovery fault of disconnection and short circuit basically, also the algorithm detect various of sensor fault mode.

Keywords: Smart Hybrid Powerpack (SHP), Electro Hydraulic Actuator (EHA), Permanent Sensor fault tolerance, Sliding mode observer (SMO), Graphic User Interface (GUI).

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Authors: Petr Vcelak, Jana Kleckova

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Our Medicine-oriented research is based on a medical data set of real patients. It is a security problem to share patient private data with peoples other than clinician or hospital staff. We have to remove person identification information from medical data. The medical data without private data are available after a de-identification process for any research purposes. In this paper, we introduce an universal automatic rule-based de-identification application to do all this stuff on an heterogeneous medical data. A patient private identification is replaced by an unique identification number, even in burnedin annotation in pixel data. The identical identification is used for all patient medical data, so it keeps relationships in a data. Hospital can take an advantage of a research feedback based on results.

Keywords: DASTA, De-identification, DICOM, Health Level Seven, Medical data, OCR, Personal data

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Authors: M. Arja, G. Sauce, B. Souyri

Abstract:

Overall cost is a significant consideration in any decision-making process. Although many studies were carried out on overall cost in construction, little has treated the uncertainties of real life cycle development. On the basis of several case studies, a feedback process was performed on the historical data of studied buildings. This process enabled to identify some factors causing uncertainty during the operational period. As a result, the research proposes a new method for assessing the overall cost during a part of the building-s life cycle taking account of the building actual value, its end-of-life value and the influence of the identified life cycle uncertainty factors. The findings are a step towards a higher level of reliability in overall cost evaluation taking account of some usually unexpected uncertainty factors.

Keywords: Asset management, building life cycle uncertainty, building value, overall cost.

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Authors: Adeolu O. Dairo

Abstract:

Getting the consumer marketing strategy right is a crucial and complex task for firms with a large customer base such as mobile operators in a competitive mobile market. While empirical studies have made efforts to identify key constructs, no geospatial model has been developed to comprehensively assess the viability and interdependency of ground realities regarding the customer, competition, channel and the network quality of mobile operators. With this research, a geo-analytic framework is proposed for strategy formulation and allocation for mobile operators. Firstly, a fuzzy analytic network using a self-organizing feature map clustering technique based on inputs from managers and literature, which depicts the interrelationships amongst ground realities is developed. The model is tested with a mobile operator in the Nigeria mobile market. As a result, a customer-centric geospatial and visualization solution is developed. This provides a consolidated and integrated insight that serves as a transparent, logical and practical guide for strategic, tactical and operational decision making.

Keywords: Geospatial, geo-analytics, self-organizing map, customer-centric.

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Authors: Amirhossein Chambari, Seyed Habib Rahmaty, Vahid Hajipour, Aida Karimi

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This paper proposes a bi-objective model for the facility location problem under a congestion system. The idea of the model is motivated by applications of locating servers in bank automated teller machines (ATMS), communication networks, and so on. This model can be specifically considered for situations in which fixed service facilities are congested by stochastic demand within queueing framework. We formulate this model with two perspectives simultaneously: (i) customers and (ii) service provider. The objectives of the model are to minimize (i) the total expected travelling and waiting time and (ii) the average facility idle-time. This model represents a mixed-integer nonlinear programming problem which belongs to the class of NP-hard problems. In addition, to solve the model, two metaheuristic algorithms including nondominated sorting genetic algorithms (NSGA-II) and non-dominated ranking genetic algorithms (NRGA) are proposed. Besides, to evaluate the performance of the two algorithms some numerical examples are produced and analyzed with some metrics to determine which algorithm works better.

Keywords: Queuing, Location, Bi-objective, NSGA-II, NRGA

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Authors: Oscar Javier Herrera Ochoa, Ivan Dario Romero Fonseca

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This paper presents a design of a model for planning the distribution logistics operation. The significance of this work relies on the applicability of this fact to the analysis of small and medium enterprises (SMEs) of dry freight in Bogotá. Two stages constitute this implementation: the first one is the place where optimal planning is achieved through a hybrid model developed with mixed integer programming, which considers the transhipment operation based on a combined load allocation model as a classic transshipment model; the second one is the specific routing of that operation through the heuristics of Clark and Wright. As a result, an integral model is obtained to carry out the step by step planning of the distribution of dry freight for SMEs in Bogotá. In this manner, optimum assignments are established by utilizing transshipment centers with that purpose of determining the specific routing based on the shortest distance traveled.

Keywords: Transshipment model, mixed integer programming, saving algorithm, dry freight transportation.

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