Search results for: optimal replacement

Authors: Limouzade E., Joorabian M.

Abstract:

Most of the losses in a power system relate to the distribution sector which always has been considered. From the important factors which contribute to increase losses in the distribution system is the existence of radioactive flows. The most common way to compensate the radioactive power in the system is the power to use parallel capacitors. In addition to reducing the losses, the advantages of capacitor placement are the reduction of the losses in the release peak of network capacity and improving the voltage profile. The point which should be considered in capacitor placement is the optimal placement and specification of the amount of the capacitor in order to maximize the advantages of capacitor placement. In this paper, a new technique has been offered for the placement and the specification of the amount of the constant capacitors in the radius distribution network on the basis of Genetic Algorithm (GA). The existing optimal methods for capacitor placement are mostly including those which reduce the losses and voltage profile simultaneously. But the retaliation cost and load changes have not been considered as influential UN the target function .In this article, a holistic approach has been considered for the optimal response to this problem which includes all the parameters in the distribution network: The price of the phase voltage and load changes. So, a vast inquiry is required for all the possible responses. So, in this article, we use Genetic Algorithm (GA) as the most powerful method for optimal inquiry.

Keywords: Genetic Algorithm (GA), capacitor placement, voltage profile, network losses, Simulating Annealing (SA), distribution network.

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Authors: Benmalek M. Larbi, R. Harbi, S. Boukor

Abstract:

This paper reports an experimental work that aimed to investigate the effects of clay brick waste, as part of fine aggregate, on rendering mortar performance. The brick, in crushed form, was from a local brick manufacturer that was rejected due to being of-standard. It was used to replace 33.33 %, 50 %, 66.66 % and 100 % by weight of the quarry sand in mortar. Effects of the brick replacement on the mortar key properties intended for wall plastering were investigated; these are workability, compressive strength, flexural strength, linear shrinkage, water absorption by total immersion and by capillary suction. The results showed that as the brick replacement level increased, the mortar workability reduced. The linear shrinkage increases over time and decreases with the introduction of brick waste. The compressive and flexural strengths decrease with the increase of brick waste because of their great water absorption.

Keywords: Clay brick waste, mortar, properties, quarry sand.

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Authors: Yin-Yann Chen, Tzu-Ling Chen

Abstract:

This study presents the case of an actual Taiwanese semiconductor assembly and testing manufacturer. Three major bottleneck manufacturing processes, namely, die bond, wire bond, and molding, are analyzed to determine how to use finite resources to achieve the optimal capacity allocation. A medium-term capacity allocation planning model is developed by considering the optimal total profit to satisfy the promised volume demanded by customers and to obtain the best migration decision among production lines for machines and tools. Finally, sensitivity analysis based on the actual case is provided to explore the effect of various parameter levels.

Keywords: Capacity planning, capacity allocation, machine migration, resource configuration.

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Authors: Akbar Banitalebi, Mohd Ismail Abd Aziz, Rohanin Ahmad

Abstract:

A new stochastic algorithm called Probabilistic Global Search Johor (PGSJ) has recently been established for global optimization of nonconvex real valued problems on finite dimensional Euclidean space. In this paper we present convergence guarantee for this algorithm in probabilistic sense without imposing any more condition. Then, we jointly utilize this algorithm along with control parameterization technique for the solution of constrained optimal control problem. The numerical simulations are also included to illustrate the efficiency and effectiveness of the PGSJ algorithm in the solution of control problems.

Keywords: Optimal Control Problem, Constraints, Direct Methods, Stochastic Algorithm

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Authors: R. Dariani, S. Schmidt, R. Kasper

Abstract:

Based on a non-linear single track model which describes the dynamics of vehicle, an optimal path planning strategy is developed. Real time optimization is used to generate reference control values to allow leading the vehicle alongside a calculated lane which is optimal for different objectives such as energy consumption, run time, safety or comfort characteristics. Strict mathematic formulation of the autonomous driving allows taking decision on undefined situation such as lane change or obstacle avoidance. Based on position of the vehicle, lane situation and obstacle position, the optimization problem is reformulated in real-time to avoid the obstacle and any car crash.

Keywords: Autonomous driving, Obstacle avoidance, Optimal control, Path planning.

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Authors: I. A. Farhat

Abstract:

The problem of optimal planning of multiple sources of distributed generation (DG) in distribution networks is treated in this paper using an improved Ant Colony Optimization algorithm (ACO). This objective of this problem is to determine the DG optimal size and location that in order to minimize the network real power losses. Considering the multiple sources of DG, both size and location are simultaneously optimized in a single run of the proposed ACO algorithm. The various practical constraints of the problem are taken into consideration by the problem formulation and the algorithm implementation. A radial power flow algorithm for distribution networks is adopted and applied to satisfy these constraints. To validate the proposed technique and demonstrate its effectiveness, the well-know 69-bus feeder standard test system is employed.cm.

Keywords: About Ant Colony Optimization (ACO), Distributed Generation (DG).

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Authors: S. T. Tan, H. Hashim, W. S. Ho, C. T. Lee

Abstract:

Rapid economic development and population growth in Malaysia had accelerated the generation of solid waste. This issue gives pressure for effective management of municipal solid waste (MSW) to take place in Malaysia due to the increased cost of landfill. This paper discusses optimal planning of waste-to-energy (WTE) using a combinatorial simulation and optimization model through mixed integer linear programming (MILP) approach. The proposed multi-period model is tested in Iskandar Malaysia (IM) as case study for a period of 12 years (2011 -2025) to illustrate the economic potential and tradeoffs involved in this study. In this paper, 3 scenarios have been used to demonstrate the applicability of the model: (1) Incineration scenario (2) Landfill scenario (3) Optimal scenario. The model revealed that the minimum cost of electricity generation from 9,995,855 tonnes of MSW is estimated as USD 387million with a total electricity generation of 50MW /yr in the optimal scenario.

Keywords: Mixed Integer Linear Programming (MILP), optimization, solid waste management (SWM), Waste-to-energy (WTE).

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Authors: Mehdi Karbalaye Zadeh, Ehsan M. Siavashi

Abstract:

The controllable electrical loss which consists of the copper loss and iron loss can be minimized by the optimal control of the armature current vector. The control algorithm of current vector minimizing the electrical loss is proposed and the optimal current vector can be decided according to the operating speed and the load conditions. The proposed control algorithm is applied to the experimental PM motor drive system and this paper presents a modern approach of speed control for permanent magnet synchronous motor (PMSM) applied for Electric Vehicle using a nonlinear control. The regulation algorithms are based on the feedback linearization technique. The direct component of the current is controlled to be zero which insures the maximum torque operation. The near unity power factor operation is also achieved. More over, among EV-s motor electric propulsion features, the energy efficiency is a basic characteristic that is influenced by vehicle dynamics and system architecture. For this reason, the EV dynamics are taken into account.

Keywords: PMSM, Electric Vehicle, Optimal control, Traction.

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Authors: Neha Khanduja

Abstract:

This paper presents a comparative analysis of continuously stirred tank reactor (CSTR) control based on adaptive control and optimal tuning of PID control based on particle swarm optimization. In the design of adaptive control, Model reference adaptive control (MRAC) scheme is used, in which the adaptation law have been developed by MIT rule & Lyapunov’s rule. In PSO control parameters of PID controller is tuned by using the concept of particle swarm optimization to get optimized operating point for minimum integral square error (ISE) condition. The results show the adjustment of PID parameters converting into the optimal operating point and the good control response can be obtained by the PSO technique.

Keywords: Model reference adaptive control (MRAC), optimal control, particle swarm optimization (PSO).

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Authors: Jeffrey L. Duffany

Abstract:

The equivalence class subset algorithm is a powerful tool for solving a wide variety of constraint satisfaction problems and is based on the use of a decision function which has a very high but not perfect accuracy. Perfect accuracy is not required in the decision function as even a suboptimal solution contains valuable information that can be used to help find an optimal solution. In the hardest problems, the decision function can break down leading to a suboptimal solution where there are more equivalence classes than are necessary and which can be viewed as a mixture of good decision and bad decisions. By choosing a subset of the decisions made in reaching a suboptimal solution an iterative technique can lead to an optimal solution, using series of steadily improved suboptimal solutions. The goal is to reach an optimal solution as quickly as possible. Various techniques for choosing the decision subset are evaluated.

Keywords: np-complete, complexity, algorithm.

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

Abstract:

Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: M. Ravindra, R. Srinivasa Rao, V. Shanmukha Naga Raju

Abstract:

This paper presents state estimation with Phasor Measurement Unit (PMU) allocation to obtain complete observability of network. A matrix is designed with modeling of zero injection constraints to minimize PMU allocations. State estimation algorithm is developed with optimal allocation of PMUs to find accurate states of network. The incorporation of PMU into traditional state estimation process improves accuracy and computational performance for large power systems. The nonlinearity integrated with zero injection (ZI) constraints is remodeled to linear frame to optimize number of PMUs. The problem of optimal PMU allocation is regarded with modeling of ZI constraints, PMU loss or line outage, cost factor and redundant measurements. The proposed state estimation with optimal PMU allocation has been compared with traditional state estimation process to show its importance. MATLAB programming on IEEE 14, 30, 57, and 118 bus networks is implemented out by Binary Integer Programming (BIP) method and compared with other methods to show its effectiveness.

Keywords: Observability, phasor measurement units, synchrophasors, SCADA measurements, zero injection bus.

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Authors: Chang Su Woo, Hyun Sung Park

Abstract:

Useful lifetime evaluation of railpads were very important in design procedure to assure the safety and reliability. It is, therefore, necessary to establish a suitable criterion for the replacement period of rail pads. In this study, we performed properties and accelerated heat aging tests of rail pads considering degradation factors and all environmental conditions including operation, and then derived a lifetime prediction equation according to changes in hardness, thickness, and static spring constants in the Arrhenius plot to establish how to estimate the aging of rail pads. With the useful lifetime prediction equation, the lifetime of e-clip pads was 2.5 years when the change in hardness was 10% at 25°C; and that of f-clip pads was 1.7 years. When the change in thickness was 10%, the lifetime of e-clip pads and f-clip pads is 2.6 years respectively. The results obtained in this study to estimate the useful lifetime of rail pads for high speed trains can be used for determining the maintenance and replacement schedule for rail pads.

Keywords: Rail pads, accelerated test, Arrhenius plot, useful lifetime prediction.

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Authors: K. Varesi

Abstract:

This paper proposes a Particle Swarm Optimization (PSO) based technique for the optimal allocation of Distributed Generation (DG) units in the power systems. In this paper our aim is to decide optimal number, type, size and location of DG units for voltage profile improvement and power loss reduction in distribution network. Two types of DGs are considered and the distribution load flow is used to calculate exact loss. Load flow algorithm is combined appropriately with PSO till access to acceptable results of this operation. The suggested method is programmed under MATLAB software. Test results indicate that PSO method can obtain better results than the simple heuristic search method on the 30-bus and 33- bus radial distribution systems. It can obtain maximum loss reduction for each of two types of optimally placed multi-DGs. Moreover, voltage profile improvement is achieved.

Keywords: Distributed Generation (DG), Optimal Allocation, Particle Swarm Optimization (PSO), Power Loss Minimization, Voltage Profile Improvement.

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Authors: Narottam Chand

Abstract:

Wireless sensor networks (WSNs) consist of number of tiny, low cost and low power sensor nodes to monitor some physical phenomenon. The major limitation in these networks is the use of non-rechargeable battery having limited power supply. The main cause of energy consumption in such networks is communication subsystem. This paper presents an energy efficient Cluster Cooperative Caching at Sensor (C3S) based upon grid type clustering. Sensor nodes belonging to the same cluster/grid form a cooperative cache system for the node since the cost for communication with them is low both in terms of energy consumption and message exchanges. The proposed scheme uses cache admission control and utility based data replacement policy to ensure that more useful data is retained in the local cache of a node. Simulation results demonstrate that C3S scheme performs better in various performance metrics than NICoCa which is existing cooperative caching protocol for WSNs.

Keywords: Cooperative caching, cache replacement, admission control, WSN, clustering.

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Authors: Muhammad Nouman Haral, Abdulaziz I. Al-Negheimesh, Galal Fares, Mohammad Iqbal Khan, Abdulrahman M. Alhozaimy

Abstract:

Natural pozzolan (NP) is one of the potential prehistoric alternative binders in the construction industry. It has been investigated as cement replacement in ordinary concrete by several researchers for many purposes. Various supplementary cementitious materials (SCMs) such as fly ash, limestone dust and silica fume are widely used in the production of SCC; however, limited studies to address the effect of NP on the properties of SCC are documented. The current research is composed of different SCC paste and concrete mixtures containing different replacement levels of local NP as an alternative SCM. The effect of volume of paste containing different amounts of local NP related to W/B ratio and cement content on SCC fresh properties was assessed. The variations in the fresh properties of SCC paste and concrete represented by slump flow (flowability) and the flow rate were determined and discussed. The results indicated that the flow properties of SCC paste and concrete mixtures, at their optimized superplasticizer dosages, were affected by the binder content of local NP and the total volume fraction of SCC paste.

Keywords: Binder, fresh properties, natural pozzolan, paste, SCC.

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Authors: Hai Quang Hong Dam, Hai Ho, Minh Hoang Le Ngo

Abstract:

This paper investigates the problem of blind speech separation from the speech mixture of two speakers. A voice activity detector employing the Steered Response Power - Phase Transform (SRP-PHAT) is presented for detecting the activity information of speech sources and then the desired speech signals are extracted from the speech mixture by using an optimal beamformer. For evaluation, the algorithm effectiveness, a simulation using real speech recordings had been performed in a double-talk situation where two speakers are active all the time. Evaluations show that the proposed blind speech separation algorithm offers a good interference suppression level whilst maintaining a low distortion level of the desired signal.

Keywords: Blind speech separation, voice activity detector, SRP-PHAT, optimal beamformer.

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Authors: Minjeong Kim, Seungchul Lee, Iman Janghorban Esfahani, Jeong Tai Kim, Chang Kyoo Yoo

Abstract:

This study was carried out for an underground subway station at Seoul Metro, Korea. The optimal set-points of the ventilation control system are determined every 3 hours, then, the ventilation controller adjusts the ventilation fan speed according to the optimal set-point changes. Compared to manual ventilation system which is operated irrespective of the OAQ, the IDP-based ventilation control system saves 3.7% of the energy consumption. Compared to the fixed set-point controller which is operated irrespective of the IAQ diurnal variation, the IDP-based controller shows better performance with a 2% decrease in energy consumption, maintaining the comfortable IAQ range inside the station.

Keywords: Indoor air quality, iterative dynamic algorithm, outdoor air information, ventilation control system.

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Authors: Khalil Banan, Mohammad B.B. Sharifian, Jafar Mohammadi

Abstract:

Due to the high percentage of induction motors in industrial market, there exist a large opportunity for energy savings. Replacement of working induction motors with more efficient ones can be an important resource for energy savings. A calculation of energy savings and payback periods, as a result of such a replacement, based on nameplate motor efficiency or manufacture-s data can lead to large errors [1]. Efficiency of induction motors (IMs) can be extracted using some procedures that use the no-load test results. In the cases that we must estimate the efficiency on-line, some of these procedures can-t be efficient. In some cases the efficiency estimates using the rating values of the motor, but these procedures can have errors due to the different working condition of the motor. In this paper the efficiency of an IM estimated by using the genetic algorithm. The results are compared with the measured values of the torque and power. The results show smaller errors for this procedure compared with the conventional classical procedures, hence the cost of the equipments is reduced and on-line estimation of the efficiency can be made.

Keywords: Genetic algorithm, induction motor, efficiency.

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Authors: Tawiwat V., Phermsak S., Noppasit C.

Abstract:

This paper deals with under actuator dynamic systems such as spring-mass-damper system when the number of control variable is less than the number of state variable. In order to apply optimal control, the controllability must be checked. There are many objective functions to be selected as the goal of the optimal control such as minimum energy, maximum energy and minimum jerk. As the objective function is the first priority, if one like to have the second goal to be applied; however, it could not fit in the objective function format and also avoiding the vector cost for the objective, this paper will illustrate the problem of under actuator dynamic systems with the easiest to deal with comparing between minimum energy and minimum jerk.

Keywords: Under actuator, Dynamic optimal control, Minimumjerk, Minimum energy.

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Authors: M. Wendeker, K. Siadkowska, P. Magryta, Z. Czyz, K. Skiba

Abstract:

In the paper environmental impact analysis the optimal Diesel engine for a light helicopter was performed. The paper consist an answer to the question of what the optimal Diesel engine for a light helicopter is, taking into consideration its expected performance and design capacity. The use of turbocharged engine with self-ignition and an electronic control system can substantially reduce the negative impact on the environment by decreasing toxic substance emission, fuel consumption and therefore carbon dioxide emission. In order to establish the environmental benefits of the diesel engine technologies, mathematical models were created, providing additional insight on the environmental impact and performance of a classic turboshaft and an advanced diesel engine light helicopter, incorporating technology developments.

Keywords: Diesel engine, helicopter, simulation, environmental impact.

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Authors: C. Bruni, F. Delli Priscoli, G. Koch, I. Marchetti

Abstract:

The Connection Admission Control (CAC) problem is formulated in this paper as a discrete time optimal control problem. The control variables account for the acceptance/ rejection of new connections and forced dropping of in-progress connections. These variables are constrained to meet suitable conditions which account for the QoS requirements (Link Availability, Blocking Probability, Dropping Probability). The performance index evaluates the total throughput. At each discrete time, the problem is solved as an integer-valued linear programming one. The proposed procedure was successfully tested against suitably simulated data.

Keywords: Connection Admission Control, Optimal Control, Integer valued Linear Programming, Quality of Service Requirements, Robust Control.

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Authors: H. Kazemi Karegar, S. Jalilzadeh, V. Nabaei, A. Shabani

Abstract:

In this paper, the problem of finding the optimal topological configuration of a deregulated distribution network is considered. The new features of this paper are proposing a multiobjective function and its application on deregulated distribution networks for finding the optimal configuration. The multi-objective function will be defined for minimizing total Energy Supply Costs (ESC) and energy losses subject to load flow constraints. The optimal configuration will be obtained by using Binary Genetic Algorithm (BGA).The proposed method has been tested to analyze a sample and a practical distribution networks.

Keywords: Binary Genetic Algorithm, Deregulated Distribution Network, Minimizing Cost, Reconfiguration.

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Authors: Imen Dhaou

Abstract:

This study examines conditional Value at Risk by applying the GJR-EVT-Copula model, and finds the optimal portfolio for eight Dow Jones Islamic-conventional pairs. Our methodology consists of modeling the data by a bivariate GJR-GARCH model in which we extract the filtered residuals and then apply the Peak over threshold model (POT) to fit the residual tails in order to model marginal distributions. After that, we use pair-copula to find the optimal portfolio risk dependence structure. Finally, with Monte Carlo simulations, we estimate the Value at Risk (VaR) and the conditional Value at Risk (CVaR). The empirical results show the VaR and CVaR values for an equally weighted portfolio of Dow Jones Islamic-conventional pairs. In sum, we found that the optimal investment focuses on Islamic-conventional US Market index pairs because of high investment proportion; however, all other index pairs have low investment proportion. These results deliver some real repercussions for portfolio managers and policymakers concerning to optimal asset allocations, portfolio risk management and the diversification advantages of these markets.

Keywords: CVaR, Dow Jones Islamic index, GJR-GARCH-EVT-pair copula, portfolio optimization.

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Authors: Vitoldas Vaitkevičius, Evaldas Šerelis

Abstract:

Silica fume, also known as microsilica (MS) or  condensed silica fume is a by-product of the production of silicon  metal or ferrosilicon alloys. Silica fume is one of the most effective  pozzolanic additives which could be used for ultrahigh performance  and other types of concrete. Despite the fact, however is not entirely  clear, which amount of silica fume is most optimal for UHPC. Main  objective of this experiment was to find optimal amount of silica  fume for UHPC with and without thermal treatment, when different  amount of quartz powder is substituted by silica fume. In this work  were investigated four different composition of UHPC with different  amount of silica fume. Silica fume were added 0, 10, 15 and 20% of  cement (by weight) to UHPC mixture. Optimal amount of silica fume  was determined by slump, viscosity, qualitative and quantitative  XRD analysis and compression strength tests methods.

Keywords: Compressive strength, silica fume, ultrahigh performance concrete, XRD.

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Authors: Sangeeta Mandal, Rajib Kar, Durbadal Mandal, Sakti Prasad Ghoshal

Abstract:

In this paper, an optimal design of linear phase digital high pass finite impulse response (FIR) filter using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSO-CFIWA) has been presented. In the design process, the filter length, pass band and stop band frequencies, feasible pass band and stop band ripple sizes are specified. FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital filter design. Given the filter specifications to be realized, the PSO-CFIWA algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency response characteristic. In this paper, for the given problem, the designs of the optimal FIR high pass filters of different orders have been performed. The simulation results have been compared to those obtained by the well accepted algorithms such as Parks and McClellan algorithm (PM), genetic algorithm (GA). The results justify that the proposed optimal filter design approach using PSOCFIWA outperforms PM and GA, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

Keywords: FIR Filter; PSO-CFIWA; PSO; Parks and McClellanAlgorithm, Evolutionary Optimization Technique; MagnitudeResponse; Convergence; High Pass Filter

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Authors: Vu Ngoc Pi

Abstract:

This paper presents a new study on the applications of optimization and regression analysis techniques for optimal calculation of partial ratios of four-step helical gearboxes for getting minimal gearbox length. In the paper, basing on the moment equilibrium condition of a mechanic system including four gear units and their regular resistance condition, models for determination of the partial ratios of the gearboxes are proposed. In particular, explicit models for calculation of the partial ratios are proposed by using regression analysis. Using these models, the determination of the partial ratios is accurate and simple.

Keywords: Gearbox design; optimal design; helical gearbox, transmission ratio.

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Authors: Maria Kalinina, Aron Larsson, Leif Olsson

Abstract:

In the multi objective optimization, in the case when generated set of Pareto optimal solutions is large, occurs the problem to select of the best solution from this set. In this paper, is suggested a method to order of Pareto set. Ordering the Pareto optimal set carried out in conformity with the introduced distance function between each solution and selected reference point, where the reference point may be adjusted to represent the preferences of a decision making agent. Preference information about objective weights from a decision maker may be expressed imprecisely. The developed elicitation procedure provides an opportunity to obtain surrogate numerical weights for the objectives, and thus, to manage impreciseness of preference. The proposed method is a scalable to many objectives and can be used independently or as complementary to the various visualization techniques in the multidimensional case.

Keywords: Imprecise weights, Multiple objectives, Pareto optimality, Visualization.

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Authors: R. Srinivasa Rao

Abstract:

This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 9 and 34 bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.

Keywords: Distribution systems, Capacitor allocation, Loss reduction, Fuzzy, PGSA.

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Authors: Leila Jafari, Viliam Makis

Abstract:

In this paper, the joint optimization of the economic manufacturing quantity (EMQ), safety stock level, and condition-based maintenance (CBM) is presented for a partially observable, deteriorating system subject to random failure. The demand is stochastic and it is described by a Poisson process. The stochastic model is developed and the optimization problem is formulated in the semi-Markov decision process framework. A modification of the policy iteration algorithm is developed to find the optimal policy. A numerical example is presented to compare the optimal policy with the policy considering zero safety stock.

Keywords: Condition-based maintenance, economic manufacturing quantity, safety stock, stochastic demand.

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