Search results for: travel time model

Authors: Kejun Zhuang, Hailong Zhu

Abstract:

The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem.

Keywords: Hes1, Hopf bifurcation, time delay, transcriptional repression loop

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Authors: Ryad Zemouri, Paul Ciprian Patic

Abstract:

An adaptive software reliability prediction model using evolutionary connectionist approach based on Recurrent Radial Basis Function architecture is proposed. Based on the currently available software failure time data, Fuzzy Min-Max algorithm is used to globally optimize the number of the k Gaussian nodes. The corresponding optimized neural network architecture is iteratively and dynamically reconfigured in real-time as new actual failure time data arrives. The performance of our proposed approach has been tested using sixteen real-time software failure data. Numerical results show that our proposed approach is robust across different software projects, and has a better performance with respect to next-steppredictability compared to existing neural network model for failure time prediction.

Keywords: Neural network, Prediction error, Recurrent RadialBasis Function Network, Reliability prediction.

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Authors: Hamed Sabahno

Abstract:

In this paper, an inventory model with finite and constant replenishment rate, price dependant demand rate, time value of money and inflation, finite time horizon, lead time and exponential deterioration rate and with the objective of maximizing the present worth of the total system profit is developed. Using a dynamic programming based solution algorithm, the optimal sequence of the cycles can be found and also different optimal selling prices, optimal order quantities and optimal maximum inventories can be obtained for the cycles with unequal lengths, which have never been done before for this model. Also, a numerical example is used to show accuracy of the solution procedure.

Keywords: Deteriorating items, Dynamic programming, Finitereplenishment rate, Inventory control, Operation Research.

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Authors: Giuliano Raimondo, Jörg Wangemann, Peer Drechsel

Abstract:

In systems development involving Fuel Cells generators, it is important to have from an early stage of the project a dynamic model for the electrical behavior of the stack to be shared between involved development parties. It allows independent and early design and tests of fuel cell related power electronic. This paper presents an empirical Fuel Cell system model derived from characterization tests on a real system. Moreover, it is illustrated how the obtained model is used to build and validate a real-time Fuel Cell system emulator which is used for aerospace electrical integration testing activities.

Keywords: Fuel cell dynamics, real time simulation, fuel cell, modelling, testing.

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Authors: Krzysztof Fujarewicz

Abstract:

This paper presents a predictive model of sensor readings for mobile robot. The model predicts sensor readings for given time horizon based on current sensor readings and velocities of wheels assumed for this horizon. Similar models for such anticipation have been proposed in the literature. The novelty of the model presented in the paper comes from the fact that its structure takes into account physical phenomena and is not just a black box, for example a neural network. From this point of view it may be regarded as a semi-phenomenological model. The model is developed for the Khepera robot, but after certain modifications, it may be applied for any robot with distance sensors such as infrared or ultrasonic sensors.

Keywords: Mobile robot, sensors, prediction, anticipation.

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Authors: Waralak Vongdoiwang Siricharoen

Abstract:

One of object oriented software developing problem is the difficulty of searching the appropriate and suitable objects for starting the system. In this work, ontologies appear in the part of supporting the object discovering in the initial of object oriented software developing. There are many researches try to demonstrate that there is a great potential between object model and ontologies. Constructing ontology from object model is called ontology engineering can be done; On the other hand, this research is aiming to support the idea of building object model from ontology is also promising and practical. Ontology classes are available online in any specific areas, which can be searched by semantic search engine. There are also many helping tools to do so; one of them which are used in this research is Protégé ontology editor and Visual Paradigm. To put them together give a great outcome. This research will be shown how it works efficiently with the real case study by using ontology classes in travel/tourism domain area. It needs to combine classes, properties, and relationships from more than two ontologies in order to generate the object model. In this paper presents a simple methodology framework which explains the process of discovering objects. The results show that this framework has great value while there is possible for expansion. Reusing of existing ontologies offers a much cheaper alternative than building new ones from scratch. More ontologies are becoming available on the web, and online ontologies libraries for storing and indexing ontologies are increasing in number and demand. Semantic and Ontologies search engines have also started to appear, to facilitate search and retrieval of online ontologies.

Keywords: Software Developing, Ontology, Ontology Library, Artificial Intelligent, Protégé, Object Model.

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Authors: Martin Kendra, Jaroslav Mašek, Juraj Čamaj, Matej Babin

Abstract:

The railway transport is considered as a one of the most environmentally friendly mode of transport. With future prediction of increasing of freight transport there are lines facing problems with demanded capacity. Increase of the track capacity could be achieved by infrastructure constructive adjustments. The contribution shows how the travel time can be minimized and the track capacity increased by changing some of the basic infrastructure and operation parameters, for example, the minimal curve radius of the track, the number of tracks, or the usable track length at stations. Calculation of the necessary parameter changes is based on the fundamental physical laws applied to the train movement, and calculation of the occupation time is dependent on the changes of controlling the traffic between the stations.

Keywords: Curve radius, maximum curve speed, track mass capacity, reconstruction.

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Authors: C. Umpuch, N. Bunmanan, U. Kueasing, P. Kaewsan

Abstract:

This work was to study batch biosorption of Pb(II) ions from aqueous solution by Luffa charcoal. The effect of operating parameters such as adsorption contact time, initial pH solution and different initial Pb(II) concentration on the sorption of Pb(II) were investigated. The results showed that the adsorption of Pb(II) ions was initially rapid and the equilibrium time was 10 h. Adsorption kinetics of Pb(II) ions onto Luffa charcoal could be best described by the pseudo-second order model. At pH 5.0 was favorable for the adsorption and removal of Pb(II) ions. Freundlich adsorption isotherm model was better fitted for the adsorption of Pb(II) ions than Langmuir and Timkin isotherms, respectively. The highest monolayer adsorption capacity obtained from Langmuir isotherm model was 51.02 mg/g. This study demonstrated that Luffa charcoal could be used for the removal of Pb(II) ions in water treatment.

Keywords: Lead (II), Luffa charcoal, Biosorption, initial pHsolution, contact time, adsorption isotherm.

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Authors: Ching-I Chen

Abstract:

The continued rise of e-commerce is the main driver of the rapid growth of global online purchase. Consumers can nearly buy everything they want at one occasion through online shopping. The purchase behavior models which focus on single product category are insufficient to describe online shopping behavior. Therefore, analysis of multi-category purchase gets more and more popular. For example, market basket analysis explores customers’ buying tendency of the association between product categories. The information derived from market basket analysis facilitates to make cross-selling strategies and product recommendation system.

To detect the association between different product categories, we use the market basket analysis with the multidimensional scaling technique to build an associated map which describes how likely multiple product categories are bought at the same time. Besides, we also build an inter-purchase time model for associated products to describe how likely a product will be bought after its associated product is bought. We classify inter-purchase time behaviors of multi-category products into nine types, and use a mixture regression model to integrate those behaviors under our assumptions of purchase sequences. Our sample data is from comScore which provides a panelist-label database that captures detailed browsing and buying behavior of internet users across the United States. Finding the inter-purchase time from books to movie is shorter than the inter-purchase time from movies to books. According to the model analysis and empirical results, this research finally proposes the applications and recommendations in the management.

Keywords: Multiple-category purchase behavior, inter-purchase time, market basket analysis.

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Authors: Nabilah Filzah Mohd Radzuan, Zalinda Othman, Azuraliza Abu Bakar, Abdul Razak Hamdan

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Uncertain data is believed to be an important issue in building up a prediction model. The main objective in the time series uncertainty analysis is to formulate uncertain data in order to gain knowledge and fit low dimensional model prior to a prediction task. This paper discusses the performance of a number of techniques in dealing with uncertain data specifically those which solve uncertain data condition by minimizing the loss of compression properties.

Keywords: Compression properties, uncertainty, uncertain time series, mining technique, weather prediction.

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Authors: Xiaoshu Lu, Martti Viljanen

Abstract:

A new analytical model is developed which provides close-formed solutions for both transient indoor and envelope temperature changes in buildings. Time-dependent boundary temperature is presented as Fourier series which can approximate real weather conditions. The final close-formed solutions are simple, concise, and comprehensive. The model was compared with numerical results and good accuracy was obtained. The model can be used as design and control guidelines in engineering applications for analysing mechanical heat transfer properties for buildings.

Keywords: Analytical model, heat transfer, whole building.

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Authors: Abdoullah Fath-Allah, Laila Cheikhi, Rafa E. Al-Qutaish, Ali Idri

Abstract:

The e-government emerging concept transforms the way in which the citizens are dealing with their governments. Thus, the citizens can execute the intended services online anytime and anywhere. This results in great benefits for both the governments (reduces the number of officers) and the citizens (more flexibility and time saving). Therefore, building a maturity model to assess the egovernment portals becomes desired to help in the improvement process of such portals. This paper aims at proposing an egovernment maturity model based on the measurement of the best practices’ presence. The main benefit of such maturity model is to provide a way to rank an e-government portal based on the used best practices, and also giving a set of recommendations to go to the higher stage in the maturity model.

Keywords: Best practices, e-government portal, maturity model, quality model.

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Authors: Hui Hsin Huang

Abstract:

The downstream manufactures will order their materials from different upstream suppliers to maintain a certain level of the demand. This paper proposes a bivariate model to portray this phenomenon of material demand. We use empirical data to estimate the parameters of model and evaluate the RMSD of model calibration. The results show that the model has better fitness.

Keywords: Farlie-Gumbel-Morgenstern family of bivariate distributions, multi-source ordering, materials demand quantity, recency, ordering time.

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Authors: Amir Azizi, Amir Yazid b. Ali, Loh Wei Ping, Mohsen Mohammadzadeh

Abstract:

Uncertainties of a serial production line affect on the production throughput. The uncertainties cannot be prevented in a real production line. However the uncertain conditions can be controlled by a robust prediction model. Thus, a hybrid model including autoregressive integrated moving average (ARIMA) and multiple polynomial regression, is proposed to model the nonlinear relationship of production uncertainties with throughput. The uncertainties under consideration of this study are demand, breaktime, scrap, and lead-time. The nonlinear relationship of production uncertainties with throughput are examined in the form of quadratic and cubic regression models, where the adjusted R-squared for quadratic and cubic regressions was 98.3% and 98.2%. We optimized the multiple quadratic regression (MQR) by considering the time series trend of the uncertainties using ARIMA model. Finally the hybrid model of ARIMA and MQR is formulated by better adjusted R-squared, which is 98.9%.

Keywords: ARIMA, multiple polynomial regression, production throughput, uncertainties

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Authors: Taiki Baba, Tomoaki Hashimoto

Abstract:

The random dither quantization method enables us to achieve much better performance than the simple uniform quantization method for the design of quantized control systems. Motivated by this fact, the stochastic model predictive control method in which a performance index is minimized subject to probabilistic constraints imposed on the state variables of systems has been proposed for linear feedback control systems with random dither quantization. In other words, a method for solving optimal control problems subject to probabilistic state constraints for linear discrete-time control systems with random dither quantization has been already established. To our best knowledge, however, the feasibility of such a kind of optimal control problems has not yet been studied. Our objective in this paper is to investigate the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization. To this end, we provide the results of numerical simulations that verify the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization.

Keywords: Model predictive control, stochastic systems, probabilistic constraints, random dither quantization.

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Authors: Amjaad Alsalamah, Liyakathunsia Syed

Abstract:

Transportation is an essential need for many people to go to their work, school, and home. In particular, the main common method inside many cities is to drive the car. Driving a car can be an easy job to reach the destination and load all stuff in a reasonable time. However, deciding to find a parking lot for a car can take a long time using the traditional system that can issue a paper ticket for each customer. The old system cannot guarantee a parking lot for all customers. Also, payment methods are not always available, and many customers struggled to find their car among a numerous number of cars. As a result, this research focuses on providing an online smart parking system in order to save time and budget. This system provides a flexible management system for both parking owner and customers by receiving all request via the online system and it gets an accurate result for all available parking and its location.

Keywords: Smart parking system, IoT, tracking system, process model, cost, time.

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Authors: Mustafa S. Fawad, Wang Wencheng, Wu Enhua

Abstract:

Shadows add great amount of realism to a scene and many algorithms exists to generate shadows. Recently, Shadow volumes (SVs) have made great achievements to place a valuable position in the gaming industries. Looking at this, we concentrate on simple but valuable initial partial steps for further optimization in SV generation, i.e.; model simplification and silhouette edge detection and tracking. Shadow volumes (SVs) usually takes time in generating boundary silhouettes of the object and if the object is complex then the generation of edges become much harder and slower in process. The challenge gets stiffer when real time shadow generation and rendering is demanded. We investigated a way to use the real time silhouette edge detection method, which takes the advantage of spatial and temporal coherence, and exploit the level-of-details (LOD) technique for reducing silhouette edges of the model to use the simplified version of the model for shadow generation speeding up the running time. These steps highly reduce the execution time of shadow volume generations in real-time and are easily flexible to any of the recently proposed SV techniques. Our main focus is to exploit the LOD and silhouette edge detection technique, adopting them to further enhance the shadow volume generations for real time rendering.

Keywords: LOD, perception, Shadow Volumes, SilhouetteEdge, Spatial and Temporal coherence.

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Authors: A. O. Ogunlela, B. Adelodun

Abstract:

Flood routing is used in estimating the travel time and attenuation of flood waves as they move downstream a river or channel. The routing procedure is usually classified as hydrologic or hydraulic. Hydraulic methods utilize the equations of continuity and motion. Kinematic routing, a hydraulic technique was used in routing Asa River at Ilorin. The river is of agricultural and industrial importance to Ilorin, the capital of Kwara State, Nigeria. This paper determines the kinematic parameters of kinematic wave velocity, time step, time required to traverse, weighting factor and change in length. Values obtained were 4.67 m/s, 19 secs, 21 secs, 0.75 and 100 m, respectively. These parameters adequately reflect the watershed and flow characteristics essential for the routing. The synthetic unit hydrograph was developed using the Natural Resources Conservation Service (NRCS) method. 24-hr 10yr, 25yr, 50yr and 100yr storm hydrographs were developed from the unit hydrograph using convolution procedures and the outflow hydrographs were obtained for each of 24-hr 10yr, 25yr, 50yr and 100yr indicating 0.11 m³/s, 0.10 m³/s, 0.10 m³/s and 0.10 m³/s attenuations respectively.

Keywords: Asa River, Kinematic parameters, Routing

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Authors: Wei Lo, Ming-En Kuo

Abstract:

While to minimize the overall project cost is always one of the objectives of construction managers, to obtain the maximum economic return is definitely one the ultimate goals of the project investors. As there is a trade-off relationship between the project time and cost, and the project delivery time directly affects the timing of economic recovery of an investment project, to provide a method that can quantify the relationship between the project delivery time and cost, and identify the optimal delivery time to maximize economic return has always been the focus of researchers and industrial practitioners. Using genetic algorithms, this study introduces an optimization model that can quantify the relationship between the project delivery time and cost and furthermore, determine the optimal delivery time to maximize the economic return of the project. The results provide objective quantification for accurately evaluating the project delivery time and cost, and facilitate the analysis of the economic return of a project.

Keywords: Time-Cost Trade-Off, Genetic Algorithms, Resource Integration, Economic return.

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Authors: A. Nourmohammadzadeh, R. Tavakkoli- Moghaddam

Abstract:

As the air traffic increases at a hub airport, some flights cannot land or depart at their preferred target time. This event happens because the airport runways become occupied to near their capacity. It results in extra costs for both passengers and airlines because of the loss of connecting flights or more waiting, more fuel consumption, rescheduling crew members, etc. Hence, devising an appropriate scheduling method that determines a suitable runway and time for each flight in order to efficiently use the hub capacity and minimize the related costs is of great importance. In this paper, we present a mixed-integer zero-one model for scheduling a set of mixed landing and departing flights (despite of most previous studies considered only landings). According to the fact that the flight cost is strongly affected by the level of airline, we consider different airline categories in our model. This model presents a single objective minimizing the total sum of three terms, namely 1) the weighted deviation from targets, 2) the scheduled time of the last flight (i.e., makespan), and 3) the unbalancing the workload on runways. We solve 10 simulated instances of different sizes up to 30 flights and 4 runways. Optimal solutions are obtained in a reasonable time, which are satisfactory in comparison with the traditional rule, namely First- Come-First-Serve (FCFS) that is far apart from optimality in most cases.

Keywords: Arrival and departure scheduling, Airline level, Mixed-integer model

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Authors: Shamsuddin Ahmed, M. G. M. Khan, Biman Prasad, Avlin Prasad

Abstract:

The focus of this paper is to construct daily time series exchange rate forecast models of Samoan Tala/USD and Tala/AUD during the year 2008 to 2012 with neural network The performance of the models was measured by using varies error functions such as Root Square mean error (RSME), Mean absolute error (MAE), and Mean absolute percentage error (MAPE). Our empirical findings suggest that AR (1) model is an effective tool to forecast the Tala/USD and Tala/AUD.

Keywords: Neural Network Forecasting Model, Autoregressive time series, Exchange rate, Tala/AUD, winters model.

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Authors: Eva Nedeliakova, Juraj Camaj, Jaroslav Masek

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This contribution is focused on the methodology for identifying levels of quality and improving quality through new logistics model in railway transport. It is oriented on the application of dynamic quality models, which represent an innovative method of evaluation quality services. Through this conception, time factor, expected, and perceived quality in each moment of the transportation process within logistics chain can be taken into account. Various models describe the improvement of the quality which emphases the time factor throughout the whole transportation logistics chain. Quality of services in railway transport can be determined by the existing level of service quality, by detecting the causes of dissatisfaction employees but also customers, to uncover strengths and weaknesses. This new logistics model is able to recognize critical processes in logistic chain. It includes service quality rating that must respect its specific properties, which are unrepeatability, impalpability, their use right at the time they are provided and particularly changeability, which is significant factor in the conditions of rail transport as well. These peculiarities influence the quality of service regarding the constantly increasing requirements and that result in new ways of finding progressive attitudes towards the service quality rating.

Keywords: Logistics model, quality, railway transport.

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Authors: Ahmed H. Abdullah, Pavel Kroupa

Abstract:

Globular clusters (GC) are important objects for tracing the early evolution of a galaxy. We study the correlation between the cluster population and the global properties of the host galaxy. We found that the correlation between cluster population (NGC) and the baryonic mass (Mb) of the host galaxy are best described as 10 −5.6038Mb. In order to understand the origin of the U -shape relation between the GC specific frequency (SN) and Mb (caused by the high value of SN for dwarfs galaxies and giant ellipticals and a minimum SN for intermediate mass galaxies≈ 1010M), we derive a theoretical model for the specific frequency (SNth). The theoretical model for SNth is based on the slope of the power-law embedded cluster mass function (β) and different time scale (Δt) of the forming galaxy. Our results show a good agreement between the observation and the model at a certain β and Δt. The model seems able to reproduce higher value of SNth of β = 1.5 at the midst formation time scale.

Keywords: Galaxies, dwarf, globular cluster, specific frequency, formation time scale.

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Authors: T. Sakamoto, N. Hori

Abstract:

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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Authors: Mahmoud Zarrini, R. N. Pralhad

Abstract:

In this paper, mathematical modeling of detonation in the ground is studied. Estimation of flow parameters such as velocity, maximum velocity, acceleration, maximum acceleration, shock pressure as a result of an explosion in the ground have been computed in an appropriate dynamic model approach. The variation of these parameters with the diameter of detonation place (L), density of earth or stone (¤ü), time decay of detonation (T), peak pressure (Pm), and time (t) have been analyzed. The model has been developed from the concept of underwater explosions [Refs. [1]-[3]] with appropriate changes to the present model requirements.

Keywords: Shock velocity, detonation, shock acceleration, shock pressure.

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Authors: E. V. Larkin, T. A. Akimenko, A. V. Bogomolov, A. N. Privalov

Abstract:

The digital control system of mobile robots (MR) control is considered. It is shown that sequential interpretation of control algorithm operators, unfolding in physical time, suggests the occurrence of time delays between inputting data from sensors and outputting data to actuators. Another destabilizing control factor is presence of backlash in the joints of an actuator with an executive unit. Complex model of control system, which takes into account the dynamics of the MR, the dynamics of the digital controller and backlash in actuators, is worked out. The digital controller model is divided into two parts: the first part describes the control law embedded in the controller in the form of a control program that realizes a polling procedure when organizing transactions to sensors and actuators. The second part of the model describes the time delays that occur in the Von Neumann-type controller when processing data. To estimate time intervals, the algorithm is represented in the form of an ergodic semi-Markov process. For an ergodic semi-Markov process of common form, a method is proposed for estimation a wandering time from one arbitrary state to another arbitrary state. Example shows how the backlash and time delays affect the quality characteristics of the MR control system functioning.

Keywords: Mobile robot, backlash, control algorithm, Von Neumann controller, semi-Markov process, time delay.

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Authors: Jia-Jang Wu

Abstract:

The objective of this research is to develop a general technique so that one may predict the dynamic behaviour of a three-dimensional scale crane model subjected to time-dependent moving point forces by means of conventional finite element computer packages. To this end, the whole scale crane model is divided into two parts: the stationary framework and the moving substructure. In such a case, the dynamic responses of a scale crane model can be predicted from the forced vibration responses of the stationary framework due to actions of the four time-dependent moving point forces induced by the moving substructure. Since the magnitudes and positions of the moving point forces are dependent on the relative positions between the trolley, moving substructure and the stationary framework, it can be found from the numerical results that the time histories for the moving speeds of the moving substructure and the trolley are the key factors affecting the dynamic responses of the scale crane model.

Keywords: Moving load, moving substructure, dynamic responses, forced vibration responses.

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Authors: Sourabh Jain, Sukhvir Singh Jain, Gaurav V. Jain

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Intelligent Transportation System is an integrated application of communication, control and monitoring and display process technologies for developing a user–friendly transportation system for urban areas in developing countries. In fact, the development of a country and the progress of its transportation system are complementary to each other. Urban traffic has been growing vigorously due to population growth as well as escalation of vehicle ownership causing congestion, delays, pollution, accidents, high-energy consumption and low productivity of resources. The development and management of urban transport in developing countries like India however, is at tryout stage with very few accumulations. Under the umbrella of ITS, urban corridor management strategy have proven to be one of the most successful system in accomplishing these objectives. The present study interprets and figures out the performance of the 27.4 km long Urban Bus route having six intersections, five flyovers and 29 bus stops that covers significant area of the city by causality analysis. Performance interpretations incorporate Passenger Boarding and Alighting, Dwell time, Distance between Bus Stops and Total trip time taken by bus on selected urban route.

Keywords: Congestion, Dwell time, delay, passengers boarding alighting, travel time.

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Authors: A. B. Dariane, A. M. Moradi

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A direct search approach to determine optimal reservoir operating is proposed with ant colony optimization for continuous domains (ACOR). The model is applied to a system of single reservoir to determine the optimum releases during 42 years of monthly steps. A disadvantage of ant colony based methods and the ACOR in particular, refers to great amount of computer run time consumption. In this study a highly effective procedure for decreasing run time has been developed. The results are compared to those of a GA based model.

Keywords: Ant colony optimization, continuous, metaheuristics, reservoir, decreasing run time, genetic algorithm.

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Authors: Bubaker M. F. Bushofa, Abdel Hafez A. Azab

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This article is based on the technique which is called Discrete Parameter Tracking (DPT). First introduced by A. A. Azab [8] which is applicable for less order reference model. The order of the reference model is (n-l) and n is the number of the adjustable parameters in the physical plant. The technique utilizes a modified gradient method [9] where the knowledge of the exact order of the nonadaptive system is not required, so, as to eliminate the identification problem. The applicability of the mentioned technique (DPT) was examined through the solution of several problems. This article introduces the solution of a third order system with three adjustable parameters, controlled according to second order reference model. The adjustable parameters have great initial error which represent condition. Computer simulations for the solution and analysis are provided to demonstrate the simplicity and feasibility of the technique.

Keywords: Adaptive Control System, Discrete Parameter Tracking, Discrete Time Model.

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