Search results for: Optimal Termination Model

Authors: Jianqiao. Yu, Jianbo. Wang, Xinzhen. He

Abstract:

This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.

Keywords: quasi-linear model, simulation, state transformation approach, the ADMIRE model.

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Authors: Eatedal A. Alabdulkreem, Hamed S. Al-Raweshidy, Maysam F. Abbod

Abstract:

Border Gateway Protocol (BGP) is the standard routing protocol between various autonomous systems (AS) in the internet. In the event of failure, a considerable delay in the BGP convergence has been shown by empirical measurements. During the convergence time the BGP will repeatedly advertise new routes to some destination and withdraw old ones until it reach a stable state. It has been found that the KEEPALIVE message timer and the HOLD time are tow parameters affecting the convergence speed. This paper aims to find the optimum value for the KEEPALIVE timer and the HOLD time that maximally reduces the convergence time without increasing the traffic. The KEEPALIVE message timer optimal value founded by this paper is 30 second instead of 60 seconds, and the optimal value for the HOLD time is 90 seconds instead of 180 seconds.

Keywords: BGP, Convergence Time, HOLD time, Keep alive.

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Authors: N. Rugthaicharoencheep, T. Langtharthong

Abstract:

This paper presents the optimal placement and sizing of distributed generation (DG) in a distribution system. The problem is to reliability improvement of distribution system with distributed generations. The technique employed to solve the minimization problem is based on a developed Tabu search algorithm and reliability worth analysis. The developed methodology is tested with a distribution system of Roy Billinton Test System (RBTS) bus 2. It can be seen from the case study that distributed generation can reduce the customer interruption cost and therefore improve the reliability of the system. It is expected that our proposed method will be utilized effectively for distribution system operator.

Keywords: Distributed generation Optimization technique Reliability improvement, Distribution system.

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Authors: M. Javanmard

Abstract:

This study was aimed at analyzing the effects of packaging (MAP) and preservation conditions on the packaged fresh walnut kernel quality. The central composite plan was used for evaluating the effect of oxygen (0–10%), carbon dioxide (0-10%), and temperature (4-26 °C) on qualitative characteristics of walnut kernels. Also, the response level technique was used to find the optimal conditions for interactive effects of factors, as well as estimating the best conditions of process using least amount of testing. Measured qualitative parameters were: peroxide index, color, decreased weight, mould and yeast counting test, and sensory evaluation. The results showed that the defined model for peroxide index, color, weight loss, and sensory evaluation is significant (p < 0.001), so that increase of temperature causes the peroxide value, color variation, and weight loss to increase and it reduces the overall acceptability of walnut kernels. An increase in oxygen percentage caused the color variation level and peroxide value to increase and resulted in lower overall acceptability of the walnuts. An increase in CO₂ percentage caused the peroxide value to decrease, but did not significantly affect other indices (p ≥ 0.05). Mould and yeast were not found in any samples. Optimal packaging conditions to achieve maximum quality of walnuts include: 1.46% oxygen, 10% carbon dioxide, and temperature of 4 °C.

Keywords: Shelled walnut, MAP, quality, storage temperature.

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Authors: Mohammed S. Al-Ansari

Abstract:

This paper presents an analytical model to estimate the cost of an optimized design of reinforced concrete isolated footing base on structural safety. Flexural and optimized formulas for square and rectangular footingare derived base on ACI building code of design, material cost and optimization. The optimization constraints consist of upper and lower limits of depth and area of steel. Footing depth and area of reinforcing steel are to be minimized to yield the optimal footing dimensions. Optimized footing materials cost of concrete, reinforcing steel and formwork of the designed sections are computed. Total cost factor TCF and other cost factors are developed to generalize and simplify the calculations of footing material cost. Numerical examples are presented to illustrate the model capability of estimating the material cost of the footing for a desired axial load.

Keywords: Footing, Depth, Concrete, Steel, Formwork, Optimization, Material cost, Cost Factors.

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Authors: Zahra Hatami, Hesham Ali, David Volkman

Abstract:

Selecting a portfolio for investing is a crucial decision for individuals and legal entities. In the last two decades, with economic globalization, a stream of financial innovations has rushed to the aid of financial institutions. The importance of selecting stocks for the portfolio is always a challenging task for investors. This study aims to create a financial network to identify optimal portfolios using network centralities metrics. This research presents a community detection technique of superior stocks that can be described as an optimal stock portfolio to be used by investors. By using the advantages of a network and its property in extracted communities, a group of stocks was selected for each of the various time periods. The performance of the optimal portfolios was compared to the famous index. Their Sharpe ratio was calculated in a timely manner to evaluate their profit for making decisions. The analysis shows that the selected potential portfolio from stocks with low centrality measurement can outperform the market; however, they have a lower Sharpe ratio than stocks with high centrality scores. In other words, stocks with low centralities could outperform the S&P500 yet have a lower Sharpe ratio than high central stocks.

Keywords: Portfolio management performance, network analysis, centrality measurements, Sharpe ratio.

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Authors: Alawode Kehinde O., Jubril Abimbola M. Komolafe Olusola A.

Abstract:

This paper solves the environmental/ economic dispatch power system problem using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and its hybrid with a Convergence Accelerator Operator (CAO), called the NSGA-II/CAO. These multiobjective evolutionary algorithms were applied to the standard IEEE 30-bus six-generator test system. Several optimization runs were carried out on different cases of problem complexity. Different quality measure which compare the performance of the two solution techniques were considered. The results demonstrated that the inclusion of the CAO in the original NSGA-II improves its convergence while preserving the diversity properties of the solution set.

Keywords: optimal power flow, multiobjective power dispatch, evolutionary algorithm

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Authors: Z. Hormozi Moghaddam, M. Mokhtari-Dizaji, M. Movahedin, M. E. Ravari

Abstract:

Mechanical index (MI) is used for quantifying acoustic cavitation and the relationship between acoustic pressure and the frequency. In this study, modeling of the MI was applied to provide treatment protocol and to understand the effective physical processes on reproducibility of stem cells. The acoustic pressure and MI equations are modeled and solved to estimate optimal MI for 28, 40, 150 kHz and 1 MHz frequencies. Radial and axial acoustic pressure distribution was extracted. To validate the results of the modeling, the acoustic pressure in the water and near field depth was measured by a piston hydrophone. Results of modeling and experiments show that the model is consistent well to experimental results with 0.91 and 0.90 correlation of coefficient (p<0.05) for 1 MHz and 40 kHz. Low intensity ultrasound with 0.40 MI is more effective on the proliferation rate of the spermatogonial stem cells during the seven days of culture, in contrast, high MI has a harmful effect on the spermatogonial stem cells. This model provides proper treatment planning in vitro and in vivo by estimating the cavitation phenomenon.

Keywords: Ultrasound, mechanical index, modeling, stem cell.

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Authors: Allan Tubaileh, Ibrahim Hammad, Loay Al Kafafi

Abstract:

A new approach to determine the machine layout in flexible manufacturing cell, and to find the feasible robot configuration of the robot to achieve minimum cycle time is presented in this paper. The location of the input/output location and the optimal robot configuration is obtained for all sequences of work tasks of the robot within a specified period of time. A more realistic approach has been presented to model the problem using the robot joint space. The problem is formulated as a nonlinear optimization problem and solved using Sequential Quadratic Programming algorithm.

Keywords: Robotics, Layout.

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Authors: Ljerka Hrženjak-Šego, Željko Polić, Zdravka Aljinović

Abstract:

In general, reports are a form of representing data in such way that user gets the information he needs. They can be built in various ways, from the simplest (“select from") to the most complex ones (results derived from different sources/tables with complex formulas applied). Furthermore, rules of calculations could be written as a program hard code or built in the database to be used by dynamic code. This paper will introduce two types of reports, defined in the DB structure. The main goal is to manage calculations in optimal way, keeping maintenance of reports as simple and smooth as possible.

Keywords: Data Definition diagram, Server Model Diagram, system modelling, reports.

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Authors: Kiyoshi Sawada, Takashi Mitsuishi

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This paper proposes a model of adding relations between members of the same level in a pyramid organization structure which is a complete K-ary tree such that the communication of information between every member in the organization becomes the most efficient. When edges between one node and every other node with the same depth N in a complete K-ary tree of height H are added, an optimal depth N* = H is obtained by minimizing the total path length which is the sum of lengths of shortest paths between every pair of all nodes.

Keywords: complete K-ary tree, organization structure, shortest path

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Authors: Lenka Ševelová, Aleš Florian

Abstract:

Appropriate and progressive tool for analyzing behavior of low volume roads are probabilistic models used in reliability analyses. The necessary part of the probabilistic model is the deterministic model of structural behavior. The FE model of low volume roads is created in the ANSYS software. It is able to determine the state of stress and deformation in any point of the structure and thus generate data required for the reliability analysis. The paper compares two material constitutive models used for modeling of unbound non-homogenous materials used in low volume roads. The first model is linear elastic model according to Hook theory (H model), the second one is nonlinear elastic-plastic Drucker-Prager model (D-P model).

Keywords: FEA, FEM, geotechnical materials, low volume roads, material constitutive models, pavement.

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Authors: R. Oonsivilai, A. Oonsivilai

Abstract:

Realistic systems generally are systems with various inputs and outputs also known as Multiple Input Multiple Output (MIMO). Such systems usually prove to be complex and difficult to model and control purposes. Therefore, decomposition was used to separate individual inputs and outputs. A PID is assigned to each individual pair to regulate desired settling time. Suitable parameters of PIDs obtained from Genetic Algorithm (GA), using Mean of Squared Error (MSE) objective function.

Keywords: Gas Turbine, PID, Genetic Algorithm, Transfer function.Mean of Squared Error

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Authors: Promise A. Azor, Avievie Igodo, Esabai M. Ase

Abstract:

The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.

Keywords: Legendre transform, logarithm utility, optimal distribution plan, return clause of premium, charge on balance, Weibull mortality function.

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Authors: Parvinder S. Sandhu, Iqbaldeep Kaur, Amit Verma, Inderpreet Kaur, Birinderjit S. Kalyan

Abstract:

This work is a proposed model of CMOS for which the algorithm has been created and then the performance evaluation of this proposition has been done. In this context, another commonly used model called ZSTT (Zero Switching Time Transient) model is chosen to compare all the vital features and the results for the Proposed Equivalent CMOS are promising. In the end, the excerpts of the created algorithm are also included

Keywords: Dual Capacitor Model, ZSTT, CMOS, SPICEMacro-Model.

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Authors: Sungin Jeong

Abstract:

This paper presents a linear oscillating generator of cylindrical type for hybrid electric vehicle application. The focus of the study is the suggestion of the optimal model and the design rule of the cylindrical linear oscillating generator with permanent magnet in the back-iron translator. The cylindrical topology is achieved using equivalent magnetic circuit considering leakage elements as initial modeling. This topology with permanent magnet in the back-iron translator is described by number of phases and displacement of stroke. For more accurate analysis of an oscillating machine, it will be compared by moving just one-pole pitch forward and backward the thrust of single-phase system and three-phase system. Through the analysis and comparison, a single-phase system of cylindrical topology as the optimal topology is selected. Finally, the detailed design of the optimal topology takes the magnetic saturation effects into account by finite element analysis. Besides, the losses are examined to obtain more accurate results; copper loss in the conductors of machine windings, eddy-current loss of permanent magnet, and iron-loss of specific material of electrical steel. The considerations of thermal performances and mechanical robustness are essential, because they have an effect on the entire efficiency and the insulations of the machine due to the losses of the high temperature generated in each region of the generator. Besides electric machine with linear oscillating movement requires a support system that can resist dynamic forces and mechanical masses. As a result, the fatigue analysis of shaft is achieved by the kinetic equations. Also, the thermal characteristics are analyzed by the operating frequency in each region. The results of this study will give a very important design rule in the design of linear oscillating machines. It enables us to more accurate machine design and more accurate prediction of machine performances.

Keywords: Equivalent magnetic circuit, finite element analysis, hybrid electric vehicle, free piston engine, cylindrical linear oscillating generator

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Authors: Maricar G. Misola, Bryan B. Navarro

Abstract:

Facility Layout Problem (FLP) is one of the essential problems of several types of manufacturing and service sector. It is an optimization problem on which the main objective is to obtain the efficient locations, arrangement and order of the facilities. In the literature, there are numerous facility layout problem research presented and have used meta-heuristic approaches to achieve optimal facility layout design. This paper presented genetic algorithm to solve facility layout problem; to minimize total cost function. The performance of the proposed approach was verified and compared using problems in the literature.

Keywords: Facility Layout Problem, Genetic Algorithm, Material Handling Cost, Meta-heuristic Approach.

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Authors: S. Khoshemehry, M. J. Pourvaghar

Abstract:

Inflammatory markers are known as the main predictors of cardiovascular diseases. This study aimed at determining the effect of 8 weeks of interval endurance training on hs-CRP level and some anthropometric parameters in overweight men. Following the call for participation in research project in Kashan, 73 volunteers participated in it and constituted the statistical population of the study. Then, 28 overweight young men from the age of 22 to 25 years old were randomly assigned into two groups of experimental and control group (n=14). Anthropometric and the blood sample was collected before and after the termination of the program for measuring hs-CRP. The interval endurance program was performed at 60 to 75% of maximum heart rate in 2 sessions per week for 8 weeks. Kolmogorov-Smirnov test was used to test whether two samples come from the same distribution and T-test was used to assess the difference of two groups which were statistically significant at the level of 0.05. The result indicated that there was a significant difference between the hs-RP, weight, BMI and W/H ratio of overweight men in posttest in the exercise group (P≤0.05) but not in the control group. Interval endurance training program causes decrease in hs-CRP level and anthropometric parameters.

Keywords: Interval endurance training program, hs-CRP, overweight, anthropometric.

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Authors: S. Hamid Mirmohammadi, Shahrazad Tamjidzad

Abstract:

This paper is concerned with the single-item continuous review inventory system in which demand is stochastic and discrete. The budget consumed for purchasing the ordered items is not restricted but it incurs extra cost when exceeding specific value. The unit purchasing price depends on the quantity ordered under the all-units discounts cost structure. In many actual systems, the budget as a resource which is occupied by the purchased items is limited and the system is able to confront the resource shortage by charging more costs. Thus, considering the resource shortage costs as a part of system costs, especially when the amount of resource occupied by the purchased item is influenced by quantity discounts, is well motivated by practical concerns. In this paper, an optimization problem is formulated for finding the optimal (r, Q) policy, when the system is influenced by the budget limitation and a discount pricing simultaneously. Properties of the cost function are investigated and then an algorithm based on a one-dimensional search procedure is proposed for finding an optimal (r, Q) policy which minimizes the expected system costs.

Keywords: (r, Q) policy, Stochastic demand, backorders, limited resource, quantity discounts.

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Authors: Hossein Abbasi

Abstract:

The stability is an important topic to plan and manage the energy in the microgrids as the same as the conventional power systems. The voltage and frequency stability is one of the most important issues recently studied in microgrids. The objectives of this paper are the modelling and designing of the components and optimal controllers for the voltage and frequency control of the AC/DC hybrid microgrid under the different disturbances. Since the PI controllers have the advantages of simple structure and easy implementation, so they are designed and modeled in this paper. The harmony search (HS) algorithm is used to optimize the controllers’ parameters. According to the achieved results, the PI controllers have a good performance in voltage and frequency control of the microgrid.

Keywords: Frequency control, HS algorithm, microgrid, PI controller, voltage control.

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Authors: Mohammad Fuad Mohammad Naser, Faycal Ikhouane

Abstract:

LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.

Keywords: Hysteresis, LuGre model, operator, (strong) consistency.

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Authors: Bogdan Walek, Jiri Bartos, Cyril Klimes

Abstract:

This article deals with the conceptual modeling under uncertainty. First, the division of information systems with their definition will be described, focusing on those where the construction of a conceptual model is suitable for the design of future information system database. Furthermore, the disadvantages of the traditional approach in creating a conceptual model and database design will be analyzed. A comprehensive methodology for the creation of a conceptual model based on analysis of client requirements and the selection of a suitable domain model is proposed here. This article presents the expert system used for the construction of a conceptual model and is a suitable tool for database designers to create a conceptual model.

Keywords: Conceptual model, conceptual modeling, database, methodology, uncertainty, information system, entity, attribute, relationship, conceptual domain model, fuzzy.

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Authors: Ju-Hong Lee, Yi-Lin Shieh

Abstract:

This paper deals with the optimal design of two-channel recursive parallelogram quadrature mirror filter (PQMF) banks. The analysis and synthesis filters of the PQMF bank are composed of two-dimensional (2-D) recursive digital all-pass filters (DAFs) with nonsymmetric half-plane (NSHP) support region. The design problem can be facilitated by using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters. For finding the coefficients of the 2-D recursive NSHP DAFs, we appropriately formulate the design problem to result in an optimization problem that can be solved by using a weighted least-squares (WLS) algorithm in the minimax (L_∞) optimal sense. The designed 2-D recursive PQMF bank achieves perfect magnitude response and possesses satisfactory phase response without requiring extra phase equalizer. Simulation results are also provided for illustration and comparison.

Keywords: Parallelogram Quadrature Mirror Filter Bank, Doubly Complementary Filter, Nonsymmetric Half-Plane Filter, Weighted Least Squares Algorithm, Digital All-Pass Filter.

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Authors: Nelson K. Lujara

Abstract:

The performance characteristics of a photovoltaic induction motor drive water pumping system with and without maximum power tracker is analyzed and presented. The analysis is done through determination and assessment of critical loss components in the system using computer aided design (CAD) tools for optimal operation of the system. The results can be used to formulate a well-calibrated computer aided design package of photovoltaic water pumping systems based on the induction motor drive. The results allow the design engineer to pre-determine the flow rate and efficiency of the system to suit particular application.

Keywords: Photovoltaic, water pumping, losses, induction motor.

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Authors: J. Levendovszky, I. Koncz, P. Boros

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The paper is concerned with developing stochastic delay mechanisms for efficient multicast protocols and for smooth mobile handover processes which are capable of preserving a given Quality of Service (QoS). In both applications the participating entities (receiver nodes or subscribers) sample a stochastic timer and generate load after a random delay. In this way, the load on the networking resources is evenly distributed which helps to maintain QoS communication. The optimal timer distributions have been sought in different p.d.f. families (e.g. exponential, power law and radial basis function) and the optimal parameter have been found in a recursive manner. Detailed simulations have demonstrated the improvement in performance both in the case of multicast and mobile handover applications.

Keywords: Multicast communication, stochactic delay mechanisms.

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Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger

Abstract:

Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model.

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Authors: Muhammad Marsudi, Dzuraidah Abdul Wahab, Che Hassan Che Haron

Abstract:

Modeling of a manufacturing system enables one to identify the effects of key design parameters on the system performance and as a result to make correct decision. This paper proposes a manufacturing system modeling approach using a spreadsheet model based on queuing network theory, in which a static capacity planning model and stochastic queuing model are integrated. The model was used to improve the existing system utilization in relation to product design. The model incorporates few parameters such as utilization, cycle time, throughput, and batch size. The study also showed that the validity of developed model is good enough to apply and the maximum value of relative error is 10%, far below the limit value 32%. Therefore, the model developed in this study is a valuable alternative model in evaluating a manufacturing system

Keywords: Manufacturing system, product design, spreadsheet model, utilization.

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Authors: Hwan Su Jung, Ahn Jun Gil, Jong Tae Kim

Abstract:

Power management techniques are necessary to save power in the microprocessor. By changing the frequency and/or operating voltage of processor, DVFS can control power consumption. In this paper, we perform a case study to find optimal power state transition for DVFS. We propose the equation to find the optimal ratio between executions of states while taking into account the deadline of processing time and the power state transition delay overhead. The experiment is performed on the Cortex-M4 processor, and average 6.5% power saving is observed when DVFS is applied under the deadline condition.

Keywords: Deadline, Dynamic Voltage Frequency Scaling, Power State Transition.

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Authors: Salem Alsanusi, Loubna Bentaher

Abstract:

Response Surface Methods (RSM) provide statistically validated predictive models that can then be manipulated for finding optimal process configurations. Variation transmitted to responses from poorly controlled process factors can be accounted for by the mathematical technique of propagation of error (POE), which facilitates ‘finding the flats’ on the surfaces generated by RSM. The dual response approach to RSM captures the standard deviation of the output as well as the average. It accounts for unknown sources of variation. Dual response plus propagation of error (POE) provides a more useful model of overall response variation. In our case, we implemented this technique in predicting compressive strength of concrete of 28 days in age. Since 28 days is quite time consuming, while it is important to ensure the quality control process. This paper investigates the potential of using design of experiments (DOE-RSM) to predict the compressive strength of concrete at 28th day. Data used for this study was carried out from experiment schemes at university of Benghazi, civil engineering department. A total of 114 sets of data were implemented. ACI mix design method was utilized for the mix design. No admixtures were used, only the main concrete mix constituents such as cement, coarseaggregate, fine aggregate and water were utilized in all mixes. Different mix proportions of the ingredients and different water cement ratio were used. The proposed mathematical models are capable of predicting the required concrete compressive strength of concrete from early ages.

Keywords: Mix proportioning, response surface methodology, compressive strength, optimal design.

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Authors: S. A. Faizi, S. Yoshitomi

Abstract:

The optimal design procedure of buckling restrained braces (BRBs) in reinforced concrete (RC) building structures can provide the distribution of horizontal stiffness of BRBs at each story, which minimizes story drift response of the structure under the constraint of specified total stiffness of BRBs. In this paper, a simple rule is proposed to convert continuous horizontal stiffness of BRBs into sectional sizes of BRB which are available from standardized section list assuming realistic structural design stage.

Keywords: Buckling restrained brace, building engineering, optimal damper placement, structural engineering.

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