Search results for: Multi Objective Optimization

Authors: Hamidreza Bagheri, Alireza Shariati

Abstract:

There are many difficulties in the purification of raw components and products. However, researchers are seeking better ways for purification. One of the recent methods is extraction using supercritical fluids. In this study, the phase equilibria of benzoic acid -supercritical carbon dioxide system were investigated. Regarding the phase equilibria of this system, the modeling of solid-supercritical fluid behavior was performed using the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) and Peng-Robinson equations of state (PR EoS). For this purpose, five PC-SAFT EoS parameters for pure benzoic acid were obtained using its experimental vapor pressure. Benzoic acid has association sites and the behavior of the benzoic acid-supercritical fluid system was well predicted using both equations of state, while the binary interaction parameter values for PR EoS were negative. Genetic algorithm, which is one of the most accurate global optimization algorithms, was also used to optimize the pure benzoic acid parameters and the binary interaction parameters. The AAD% value for the PC-SAFT EoS, were 0.22 for the carbon dioxide-benzoic acid system.

Keywords: Supercritical fluids, Solubility, Solid, PC-SAFT EoS, Genetic algorithm.

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Authors: Chul Kwak, Oh-Wook Kwon

Abstract:

In this paper, an extreme learning machine with an automatic segmentation algorithm is applied to heart disorder classification by heart sound signals. From continuous heart sound signals, the starting points of the first (S1) and the second heart pulses (S2) are extracted and corrected by utilizing an inter-pulse histogram. From the corrected pulse positions, a single period of heart sound signals is extracted and converted to a feature vector including the mel-scaled filter bank energy coefficients and the envelope coefficients of uniform-sized sub-segments. An extreme learning machine is used to classify the feature vector. In our cardiac disorder classification and detection experiments with 9 cardiac disorder categories, the proposed method shows significantly better performance than multi-layer perceptron, support vector machine, and hidden Markov model; it achieves the classification accuracy of 81.6% and the detection accuracy of 96.9%.

Keywords: Heart sound classification, extreme learning machine

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Authors: Yasser F. Hassan, Marwa Abdeen, Mustafa Fahmy

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In recent years multi-agent systems have emerged as one of the interesting architectures facilitating distributed collaboration and distributed problem solving. Each node (agent) of the network might pursue its own agenda, exploit its environment, develop its own problem solving strategy and establish required communication strategies. Within each node of the network, one could encounter a diversity of problem-solving approaches. Quite commonly the agents can realize their processing at the level of information granules that is the most suitable from their local points of view. Information granules can come at various levels of granularity. Each agent could exploit a certain formalism of information granulation engaging a machinery of fuzzy sets, interval analysis, rough sets, just to name a few dominant technologies of granular computing. Having this in mind, arises a fundamental issue of forming effective interaction linkages between the agents so that they fully broadcast their findings and benefit from interacting with others.

Keywords: Granular computing, rough sets, agents, traffic system.

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Authors: N.M Khairi, M.I. Naimah, M.S.B. Shah Rizam, M.T. Nooritawati, Z.A. Husna

Abstract:

Changes in stem diameter of orchid plants were investigated in a control growing climate. Previous studies have focused on stem diameter in relation to plant water on terrestrial plants in order to schedule the irrigation. The objective of this work was to evaluate the ability of the strain gauges to capture changes in the epiphytes plant stem. Experiments were carried out by using the sympodial orchid, Dendrobium Sonia in a stressed condition. From the findings, the sensor can detect changes in the plant stem and the result can easily be used as a reference for further studies for the development of a proper watering system.

Keywords: Strain gauge, stem diameter, Dendrobium Sonia, epiphyte, terrestrial

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Authors: D. Abdul Budan, T.S. Manjunatha

Abstract:

This paper demonstrates the feasibility of replacing the metal coil spring with the composite coil spring. Three different types of springs were made using glass fiber, carbon fiber and combination of glass fiber and carbon fiber. The objective of the study is to reduce the weight of the spring. According to the experimental results the spring rate of the carbon fiber spring is 34% more than the glass fiber spring and 45% more than the glass fiber/carbon fiber spring. The weight of the carbon fiber spring is 18% less than the glass fiber spring, 15% less than the Glass fiber/carbon fiber spring and 80% less than the steel spring.

Keywords: Carbon fiber, Glass fiber, Helical composite spring, spring rate.

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Authors: Driss Guerchi, Fatiha Djebbar

Abstract:

In this work we introduce an efficient method to limit the impact of the hiding process on the quality of the cover speech. Vector quantization of the speech spectral information reduces drastically the number of the secret speech parameters to be embedded in the cover signal. Compared to scalar hiding, vector quantization hiding technique provides a stego signal that is indistinguishable from the cover speech. The objective and subjective performance measures reveal that the current hiding technique attracts no suspicion about the presence of the secret message in the stego speech, while being able to recover an intelligible copy of the secret message at the receiver side.

Keywords: Speech steganography, LSF vector quantization, fast Fourier transform

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Authors: Vishnu Pratap Singh Kirar

Abstract:

Artificial Neural Network (ANN) can be trained using back propagation (BP). It is the most widely used algorithm for supervised learning with multi-layered feed-forward networks. Efficient learning by the BP algorithm is required for many practical applications. The BP algorithm calculates the weight changes of artificial neural networks, and a common approach is to use a twoterm algorithm consisting of a learning rate (LR) and a momentum factor (MF). The major drawbacks of the two-term BP learning algorithm are the problems of local minima and slow convergence speeds, which limit the scope for real-time applications. Recently the addition of an extra term, called a proportional factor (PF), to the two-term BP algorithm was proposed. The third increases the speed of the BP algorithm. However, the PF term also reduces the convergence of the BP algorithm, and criteria for evaluating convergence are required to facilitate the application of the three terms BP algorithm. Although these two seem to be closely related, as described later, we summarize various improvements to overcome the drawbacks. Here we compare the different methods of convergence of the new three-term BP algorithm.

Keywords: Neural Network, Backpropagation, Local Minima, Fast Convergence Rate.

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Authors: Lan Luo

Abstract:

In China’s construction industry, it is a normal practice to separately subcontract the decoration engineering part from construction engineering, and Building Information Modeling (BIM) is also done separately. Application of BIM in decoration engineering should be integrated with other disciplines, but Chinese current practice makes this very difficult and complicated. Currently, there are three barriers in the auditing of BIM application in decoration engineering in China: heavy workload; scarcity of qualified professionals; and lack of literature concerning audit contents, standards, and methods. Therefore, it is significant to perform research on what (contents) should be evaluated, in which phase, and by whom (professional qualifications) in BIM application in decoration construction so that the application of BIM can be promoted in a better manner. Based on this consideration, four principles of BIM auditing are proposed: Comprehensiveness of information, accuracy of data, aesthetic attractiveness of appearance, and scheme optimization. In the model audit, three methods should be used: Collision, observation, and contrast. In addition, BIM auditing at six stages is discussed and a checklist for work items and results to be submitted is proposed. This checklist can be used for reference by decoration project participants.

Keywords: Audit, evaluation, dimensions, methods, standards, building information modeling application, decoration engineering projects.

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Authors: K. Diwakar, N. Vasudevan, C. Senthilpari

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This paper presents MOSFET based analog to digital converter which is simple in design, has high resolution, and conversion rate better than dual slope ADC. It has no DAC which will limit the performance, no error in conversion, can operate for wide range of inputs and never become unstable. One of the industrial applications, where the proposed high resolution MOSFET ADC can be used is, for the positioning of control valves in a multi channel data acquisition and control system (DACS), using stepper motors as actuators of control valves. It is observed that in a DACS having ten control valves, 0.02% of positional accuracy of control valves can be achieved with the data update period of 250ms and with stepper motors of maximum pulse rate 20 Kpulses per sec. and minimum pulse width of 2.5 μsec. The reported accuracy so far by other authors is 0.2%, with update period of 255 ms and with 8 bit DAC. The accuracy in the proposed configuration is limited by the available precision stepper motor and not by the MOSFET based ADC.

Keywords: MOSFET based ADC, Actuators, Positional accuracy, Stepper Motors.

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Authors: Khairuddin Bin Osman, Ngo Boon Kiat, A. Hamid Bin hamidon, Khairul Azha Bin A. Aziz, Hazli Rafis Bin Abdul Rahman, Mazran Bin Esro

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Conventional industrial monitoring systems are tedious, inefficient and the at times integrity of the data is unreliable. The objective of this system is to monitor industrial processes specifically the fluid level which will measure the instantaneous fluid level parameter and respond by text messaging the exact value of the parameter to the user when being enquired by a privileged access user. The development of the embedded program code and the circuit for fluid level measuring are discussed as well. Suggestions for future implementations and efficient remote monitoring works are included.

Keywords: Industrial monitoring system, text messaging, embedded programming.

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Authors: L. Mirtskhulava, M. Khunjgurua, N. Lomineishvili, K. Bakuria

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Software reliability prediction gives a great opportunity to measure the software failure rate at any point throughout system test. A software reliability prediction model provides with the technique for improving reliability. Software reliability is very important factor for estimating overall system reliability, which depends on the individual component reliabilities. It differs from hardware reliability in that it reflects the design perfection. Main reason of software reliability problems is high complexity of software. Various approaches can be used to improve the reliability of software. We focus on software reliability model in this article, assuming that there is a time redundancy, the value of which (the number of repeated transmission of basic blocks) can be an optimization parameter. We consider given mathematical model in the assumption that in the system may occur not only irreversible failures, but also a failure that can be taken as self-repairing failures that significantly affect the reliability and accuracy of information transfer. Main task of the given paper is to find a time distribution function (DF) of instructions sequence transmission, which consists of random number of basic blocks. We consider the system software unreliable; the time between adjacent failures has exponential distribution.

Keywords: Exponential distribution, conditional mean time to failure, distribution function, mathematical model, software reliability.

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Authors: S. Sowmyayani, V. Murugan

Abstract:

With the advent of three-dimension (3D) technology, there are lots of research in converting 2D images to 3D images. The main difference between 2D and 3D is the visual illusion of depth in 3D images. In the recent era, there are more depth estimation techniques. The objective of this paper is to convert 2D images to 3D images with less computation time. For this, the input image is divided into blocks from which the depth information is obtained. Having the depth information, a depth map is generated. Then the 3D image is warped using the original image and the depth map. The proposed method is tested on Make3D dataset and NYU-V2 dataset. The experimental results are compared with other recent methods. The proposed method proved to work with less computation time and good accuracy.

Keywords: Depth map, 3D image warping, image rendering, bilateral filter, minimum spanning tree.

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Authors: Yunyoung Nam, Junghun Ryu, Yoo-Joo Choi, We-Duke Cho

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This paper presents a novel approach for representing the spatio-temporal topology of the camera network with overlapping and non-overlapping fields of view (FOVs). The topology is determined by tracking moving objects and establishing object correspondence across multiple cameras. To track people successfully in multiple camera views, we used the Merge-Split (MS) approach for object occlusion in a single camera and the grid-based approach for extracting the accurate object feature. In addition, we considered the appearance of people and the transition time between entry and exit zones for tracking objects across blind regions of multiple cameras with non-overlapping FOVs. The main contribution of this paper is to estimate transition times between various entry and exit zones, and to graphically represent the camera topology as an undirected weighted graph using the transition probabilities.

Keywords: Surveillance, multiple camera, people tracking, topology.

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Authors: B. G. Sheeparamatti, Prashant Hanasi, Vanita Abbigeri

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The objective of this work is to carryout critical comparison of different actuation mechanisms like electrostatic, thermal, piezoelectric, and magnetic with reference to a micro cantilever. The relevant parameters like force generated, displacement are compared in actuation methods. With these results, helps in choosing the best actuation method for a particular application. In this study, Comsol/Multiphysics software is used. Modeling and simulation is done by considering the micro cantilever of same dimensions as an actuator using all the above mentioned actuation techniques. In addition to their small size, micro actuators consume very little power and are capable of accurate results. In this work, a comparison of actuation mechanisms is done to decide the efficient system in micro domain.

Keywords: Actuation techniques, microswitch, micro actuator, microsystems.

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Authors: Akhilesh Khapre, Basudeb Munshi

Abstract:

A computational fluid dynamics simulation is done for non-Newtonian fluid in a baffled stirred tank. The CMC solution is taken as non-Newtonian shear thinning fluid for simulation. The Reynolds Average Navier Stocks equation with steady state multi reference frame approach is used to simulate flow in the stirred tank. The turbulent flow field is modelled using realizable k-ε turbulence model. The simulated velocity profiles of Rushton turbine is validated with literature data. Then, the simulated flow field of CD-6 impeller is compared with the Rushton turbine. The flow field generated by CD-6 impeller is less in magnitude than the Rushton turbine. The impeller global parameter, power number and flow number, and entropy generation due to viscous dissipation rate is also reported.

Keywords: Computational fluid dynamics, non-Newtonian, Rushton turbine, CD-6 impeller, power number, flow number, viscous dissipation rate.

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Authors: Santanu Ray, Alexander G. Shard

Abstract:

The adsorption of bovine serum albumin (BSA), immunoglobulin G (IgG) and fibrinogen (Fgn) on fluorinated selfassembled monolayers have been studied using time of flight secondary ion mass spectrometry (ToF-SIMS) and Spectroscopic Ellipsometry (SE). The objective of the work has to establish the utility of ToF-SIMS for the determination of the amount of protein adsorbed on the surface. Quantification of surface adsorbed proteins was carried out using SE and a good correlation between ToF-SIMS results and SE was achieved. The surface distribution of proteins were also analysed using Atomic Force Microscopy (AFM). We show that the surface distribution of proteins strongly affect the ToFSIMS results.

Keywords: ToF-SIMS, Spectroscopic Ellipsometry, Protein, Atomic Force Microscopy.

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Authors: Hazem M. El-Bakry, Qiangfu Zhao

Abstract:

Recently, fast neural networks for object/face detection were presented in [1-3]. The speed up factor of these networks relies on performing cross correlation in the frequency domain between the input image and the weights of the hidden layer. But, these equations given in [1-3] for conventional and fast neural networks are not valid for many reasons presented here. In this paper, correct equations for cross correlation in the spatial and frequency domains are presented. Furthermore, correct formulas for the number of computation steps required by conventional and fast neural networks given in [1-3] are introduced. A new formula for the speed up ratio is established. Also, corrections for the equations of fast multi scale object/face detection are given. Moreover, commutative cross correlation is achieved. Simulation results show that sub-image detection based on cross correlation in the frequency domain is faster than classical neural networks.

Keywords: Conventional Neural Networks, Fast Neural Networks, Cross Correlation in the Frequency Domain.

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Authors: Ninlawat Phuangchoke, Waraporn Viyanon, Setta Sasananan

Abstract:

The most important process of the water treatment plant process is coagulation, which uses alum and poly aluminum chloride (PACL). Therefore, determining the dosage of alum and PACL is the most important factor to be prescribed. This research applies an artificial neural network (ANN), which uses the Levenberg–Marquardt algorithm to create a mathematical model (Soft Jar Test) for chemical dose prediction, as used for coagulation, such as alum and PACL, with input data consisting of turbidity, pH, alkalinity, conductivity, and, oxygen consumption (OC) of the Bangkhen Water Treatment Plant (BKWTP), under the authority of the Metropolitan Waterworks Authority of Thailand. The data were collected from 1 January 2019 to 31 December 2019 in order to cover the changing seasons of Thailand. The input data of ANN are divided into three groups: training set, test set, and validation set. The coefficient of determination and the mean absolute errors of the alum model are 0.73, 3.18 and the PACL model are 0.59, 3.21, respectively.

Keywords: Soft jar test, jar test, water treatment plant process, artificial neural network.

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Authors: Ora Geiger

Abstract:

This paper discusses the question whether a person diagnosed with dyslexia will necessarily have difficulty in reading musical notes. The author specifies the characteristics of alphabet reading in comparison to musical notation reading, and concludes that there should be no contra-indication for teaching standard music reading to children with dyslexia if an appropriate process is offered. This conclusion is based on a long term case study and relies on two main characteristics of music reading: (1) musical notation system is a systematic, logical, relative set of symbols written on a staff; and (2) music reading learning connected with playing a musical instrument is a multi-sensory activity that combines sight, hearing, touch, and movement. The paper describes music reading teaching procedures, using soprano recorders, and provides unique teaching methods that have been found to be effective for students who were diagnosed with dyslexia. It provides theoretical explanations in addition to guidelines for music education practices.

Keywords: Alphabet reading, music reading, multisensory teaching method, dyslexia, recorder playing.

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Authors: Mohammad Jafarifar

Abstract:

Multiphase Induction Machine (IM) is normally controlled using rotor field oriented vector control. Under phase(s) loss, the machine currents can be optimally controlled to satisfy certain optimization criteria. In this paper we discuss the performance of double manifold sliding mode observer (DM-SMO) in Sensorless control of multiphase induction machine under unsymmetrical condition (one phase loss). This observer is developed using the IM model in the stationary reference frame. DM-SMO is constructed by adding extra feedback term to conventional single mode sliding mode observer (SM-SMO) which proposed in many literature. This leads to a fully convergent observer that also yields an accurate estimate of the speed and stator currents. It will be shown by the simulation results that the estimated speed and currents by the method are very well and error between real and estimated quantities is negligible. Also parameter sensitivity analysis shows that this method is rather robust against parameter variation.

Keywords: Multiphase induction machine, field oriented control, sliding mode, unsymmetrical condition, manifold.

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Authors: Anas M. Fares

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The lateral stiffness of buildings is one of the most important properties which define resistance to displacements under lateral loads. Moreover, it has a great impact on the natural period of the structures. Different stiffness’s values can ultimately affect the behavior of the structure under the seismic load and the lateral forces that will be applied to it. In this study the effect of cracking is studied on 2D shell thin cantilever shear wall by using ETABS. Multi linear elastic analysis is conducted with the ACI stiffness modifiers for each analysis step. The results showed that the cracks affect the value of the drift especially at the top of the high rise buildings and this will change the lateral stiffness and so change the fundamental period of the structures which lead to change in the applied shear force that comes from the earthquake. Finally, this study emphasizes that the finite element method can be considered as a good tool to predict the tensile stresses in the elements.

Keywords: Lateral loads, lateral displacement, reinforced concrete, shear wall, Cracks, ETABS, ACI code, stiffness.

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Authors: S. P. Jordan, G. Christian, S. P. Jeffs

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Modern composite materials are increasingly being chosen in replacement of heavier metallic material systems within many engineering fields including aerospace and automotive industries. The increasing push towards satisfying environmental targets are fuelling new material technologies and manufacturing processes. This paper will introduce materials and manufacturing processes using metal matrix composites along with manufacturing processes optimized at Alvant Ltd., based in Basingstoke in the UK which offers modern, cost effective, selectively reinforced composites for light-weighting applications within engineering. An overview and introduction into modern optimized manufacturing methods capable of producing viable replacements for heavier metallic and lower temperature capable polymer composites are offered. A review of the capabilities and future applications of this viable material is discussed to highlight the potential involved in further optimization of old manufacturing techniques, to fully realize the potential to lightweight material using cost-effective methods.

Keywords: Aluminum matrix composites, light-weighting, hybrid squeeze casting, strategically placed reinforcements.

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Authors: V. Goremikins, K. Rocens, D. Serdjuks

Abstract:

Suspended cable structures are most preferable for large spans covering due to rational use of structural materials, but the problem of suspended cable structures is initial shape change under the action of non-symmetrical load. The problem can be solved by increasing of relation of dead weight and imposed load, but this methods cause increasing of materials consumption.Prestressed cable truss usage is another way how the problem of shape change under the action of non-symmetrical load can be fixed. The better results can be achieved if we replace top chord with cable truss with cross web. Rational structure of the cable truss for prestressed cable truss top chord was developed using optimization realized in FEM program ANSYS 12 environment. Single cable and cable truss model work was discovered.Analytical and model testing results indicate, that usage of cable truss with the cross web as a top chord of prestressed cable truss instead of single cable allows to reduce total displacements by 13-16% in the case of non-symmetrical load. In case of uniformly distributed load single cable is preferable.

Keywords: Cable trusses, Non-symmetrical load, Cable truss models, Vertical displacements

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Authors: Ujjal K Ghosh, Ling Teen

Abstract:

Pervaporation has the potential to be an alternative to the other traditional separation processes such as distillation, adsorption, reverse osmosis and extraction. This study investigates the separation of phenol from water using a polyurethane membrane by pervaporation by applying the modified Maxwell-Stephen model. The modified Maxwell-Stefan model takes into account the non-ideal multi-component solubility effect, nonideal diffusivity of all permeating components, concentration dependent density of the membrane and diffusion coupling to predict various fluxes. Four cases has been developed to investigate the process parameters effects on the flux and weight fraction of phenol in the permeate values namely feed concentration, membrane thickness, operating temperature and operating downstream pressure. The model could describe semi-quantitatively the performance of the pervaporation membrane for the given system as a very good agreement between the observed and theoretical fluxes was observed.

Keywords: Pervaporation, Phenol, Polyurethane, Modified Maxwell-Stefan equation, Solution Diffusion

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Authors: S. Maheswari, P. Arockia Jansi Rani

Abstract:

Human action is recognized directly from the video sequences. The objective of this work is to recognize various human actions like run, jump, walk etc. Human action recognition requires some prior knowledge about actions namely, the motion estimation, foreground and background estimation. Region of interest (ROI) is extracted to identify the human in the frame. Then, optical flow technique is used to extract the motion vectors. Using the extracted features similarity measure based classification is done to recognize the action. From experimentations upon the Weizmann database, it is found that the proposed method offers a high accuracy.

Keywords: Background subtraction, human silhouette, optical flow, classification.

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Authors: Ahmad Yame, Ahad Ali, Badih Jawad, Daw Al-Werfalli Mohamed Nasser, Sabah Abro

Abstract:

Industries in general have a lot of waste. Wool textile company, Baniwalid, Libya has many complex problems that led to enormous waste generated due to the lack of lean strategies, expertise, technical support and commitment. To successfully address waste at wool textile company, this study will attempt to develop a methodical approach that integrates lean manufacturing tools to optimize performance characteristics such as lead time and delivery. This methodology will utilize Value Stream Mapping (VSM) techniques to identify the process variables that affect production. Once these variables are identified, Design of Experiments (DOE) Methodology will be used to determine the significantly influential process variables, these variables are then controlled and set at their optimal to achieve optimal levels of productivity, quality, agility, efficiency and delivery to analyze the outputs of the simulation model for different lean configurations. The goal of this research is to investigate how the tools of lean manufacturing can be adapted from the discrete to the continuous manufacturing environment and to evaluate their benefits at a specific industrial.

Keywords: Lean manufacturing, DOE, value stream mapping, textiles.

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Authors: Noppadon Sangwalpetch

Abstract:

The objective of this research is to use Rhizophora wood to design a walking stick for elderly. The research was conducted by studying the behavior and the type of walking sticks used by 70 elderly aged between 60-80 years in Pragnamdaeng Sub-District, Samudsongkram Province. Questionnaires were used to collect data which were calculated to find percentage, mean, and standard deviation. The results are as follows: 1) most elderly use walking sticks due to the Osteoarthritis of the knees. 2) Most elderly need to use walking sticks because the walking sticks help to balance their positioning and prevent from stumble. 3) Most elderly agree that Rhizophora wood is suitable to make a walking stick because of its strength and toughness. 4) The design of the walking stick should be fine and practical with comfortable handle and the tip of the stick must not be slippery.

Keywords: Elderly, Product design, Rhizophora wood, Walking Stick.

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Authors: Rafał Adamczak

Abstract:

State-of-the-art methods for secondary structure (Porter, Psi-PRED, SAM-T99sec, Sable) and solvent accessibility (Sable, ACCpro) predictions use evolutionary profiles represented by the position specific scoring matrix (PSSM). It has been demonstrated that evolutionary profiles are the most important features in the feature space for these predictions. Unfortunately applying PSSM matrix leads to high dimensional feature spaces that may create problems with parameter optimization and generalization. Several recently published suggested that applying feature extraction for the PSSM matrix may result in improvements in secondary structure predictions. However, none of the top performing methods considered here utilizes dimensionality reduction to improve generalization. In the present study, we used simple and fast methods for features selection (t-statistics, information gain) that allow us to decrease the dimensionality of PSSM matrix by 75% and improve generalization in the case of secondary structure prediction compared to the Sable server.

Keywords: Secondary structure prediction, feature selection, position specific scoring matrix.

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Authors: Amin Almasi

Abstract:

Composite laminates are relatively weak in out of plane loading, inter-laminar stress, stress concentration near the edge and stress singularities. This paper develops a new analytical formulation for laminated composite rotating disc fabricated from symmetric sequential quasi isotropic layers to predict three dimensional stress and deformation. This analysis is necessary to evaluate mechanical integrity of fiber reinforced multi-layer laminates used for high speed rotating applications such as high speed impellers. Three dimensional governing equations are written for rotating composite disc. Explicit solution is obtained with "Frobenius" expansion series. Based on analytical results, there are two separate zones of three dimensional stress fields in centre and edge of rotating disc. For thin discs, out of plane deformations and stresses are small in comparison with plane ones. For relatively thick discs deformation and stress fields are three dimensional.

Keywords: Composite Disc, Rotating Machine.

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Authors: Peter Benneth, Tsaroh N. Theophilus, Prince Benjamin

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This research work aims at studying the application of Legendre Transformation Method (LTM) to Hamilton Jacobi Bellman (HJB) equation which is an example of optimal control problem. We discuss the steps involved in modelling the HJB equation as it relates to mathematical finance by applying the Ito’s lemma and maximum principle theorem. By applying the LTM and dual theory, the resultant HJB equation is transformed to a linear Partial Differential Equation (PDE). Also, the Optimal Investment Strategy (OIS) and the optimal value function were obtained under the exponential utility function. Furthermore, some numerical results were also presented with observations that the OIS under exponential utility is directly proportional to the appreciation rate of the risky asset and inversely proportional to the instantaneous volatility, predetermined interest rate, risk averse coefficient. Finally, it was observed that the optimal fund size is an increasing function of the risk free interest rate. This result is consistent with some existing results.

Keywords: Legendre transformation method, Optimal investment strategy, Ito’s lemma, Hamilton Jacobi Bellman equation, Geometric Brownian motion, financial market.

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