Search results for: simplified method
19023 A Method for Measurement and Evaluation of Drape of Textiles
Authors: L. Fridrichova, R. Knížek, V. Bajzík
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Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.Keywords: drape, drape shape, automated drapemeter, fabric
Procedia PDF Downloads 65619022 Examining Cyber Crime and Its Impacts on E-Banking in Nigeria
Authors: Auwal Nata'ala
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The Information and Communication Technology (ICT) has had impacts in almost every area human endeavor. From business, industries, banks to none profit organizations. ICT has simplified business process such as sorting, summarizing, coding, updating and generating a report in a real-time processing mode. However, the use of these ICT facilities such as computer and internet has also brought unintended consequences of criminal activities such as spamming, credit card frauds, ATM frauds, phishing, identity theft, denial of services and other related cyber crimes. This study sought to examined cyber-crime and its impact on the banking institution in Nigeria. It also examined the existing policy framework and assessed the success of the institutional countermeasures in combating cyber crime in the banking industry. This paper X-ray’s cyber crimes, policies issues and provides insight from a Nigeria perspective.Keywords: cyber crimes, e-banking, policies, ICT
Procedia PDF Downloads 40719021 Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems
Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok
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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods
Procedia PDF Downloads 41119020 Reflection on Using Bar Model Method in Learning and Teaching Primary Mathematics: A Hong Kong Case Study
Authors: Chui Ka Shing
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This case study research attempts to examine the use of the Bar Model Method approach in learning and teaching mathematics in a primary school in Hong Kong. The objectives of the study are to find out to what extent (a) the Bar Model Method approach enhances the construction of students’ mathematics concepts, and (b) the school-based mathematics curriculum development with adopting the Bar Model Method approach. This case study illuminates the effectiveness of using the Bar Model Method to solve mathematics problems from Primary 1 to Primary 6. Some effective pedagogies and assessments were developed to strengthen the use of the Bar Model Method across year levels. Suggestions including school-based curriculum development for using Bar Model Method and further study were discussed.Keywords: bar model method, curriculum development, mathematics education, problem solving
Procedia PDF Downloads 22119019 An Analytical Method for Bending Rectangular Plates with All Edges Clamped Supported
Authors: Yang Zhong, Heng Liu
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The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates
Procedia PDF Downloads 60019018 Modern Methods of Technology and Organization of Production of Construction Works during the Implementation of Construction 3D Printers
Authors: Azizakhanim Maharramli
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The gradual transition from entrenched traditional technology and organization of construction production to innovative additive construction technology inevitably meets technological, technical, organizational, labour, and, finally, social difficulties. Therefore, the chosen nodal method will lead to the elimination of the above difficulties, combining some of the usual methods of construction and the myth in world practice that the labour force is subjected to a strong stream of reduction. The nodal method of additive technology will create favourable conditions for the optimal degree of distribution of labour across facilities due to the consistent performance of homogeneous work and the introduction of additive technology and traditional technology into construction production.Keywords: parallel method, sequential method, stream method, combined method, nodal method
Procedia PDF Downloads 9519017 About Some Results of the Determination of Alcohol in Moroccan Gasoline-Alcohol Mixtures
Authors: Mahacine Amrani
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A simple and rapid method for the determination of alcohol in gasoline-alcohol mixtures using density measurements is described. The method can determine a minimum of 1% of alcohol by volume. The precision of the method is ± 3%.The method is more useful for field test in the quality assessment of alcohol blended fuels.Keywords: gasoline-alcohol, mixture, alcohol determination, density, measurement, Morocco
Procedia PDF Downloads 32219016 The Finite Element Method for Nonlinear Fredholm Integral Equation of the Second Kind
Authors: Melusi Khumalo, Anastacia Dlamini
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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations
Procedia PDF Downloads 37719015 An Online 3D Modeling Method Based on a Lossless Compression Algorithm
Authors: Jiankang Wang, Hongyang Yu
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This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image
Procedia PDF Downloads 8219014 A Method for Modeling Flexible Manipulators: Transfer Matrix Method with Finite Segments
Authors: Haijie Li, Xuping Zhang
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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method
Procedia PDF Downloads 43019013 Dynamic Response Analysis of Structure with Random Parameters
Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire
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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters
Procedia PDF Downloads 19119012 A New Approach to Image Stitching of Radiographic Images
Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof
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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.Keywords: image stitching, direct based method, panoramic image, X-ray
Procedia PDF Downloads 54219011 Network Based Speed Synchronization Control for Multi-Motor via Consensus Theory
Authors: Liqin Zhang, Liang Yan
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This paper addresses the speed synchronization control problem for a network-based multi-motor system from the perspective of cluster consensus theory. Each motor is considered as a single agent connected through fixed and undirected network. This paper presents an improved control protocol from three aspects. First, for the purpose of improving both tracking and synchronization performance, this paper presents a distributed leader-following method. The improved control protocol takes the importance of each motor’s speed into consideration, and all motors are divided into different groups according to speed weights. Specifically, by using control parameters optimization, the synchronization error and tracking error can be regulated and decoupled to some extent. The simulation results demonstrate the effectiveness and superiority of the proposed strategy. In practical engineering, the simplified models are unrealistic, such as single-integrator and double-integrator. And previous algorithms require the acceleration information of the leader available to all followers if the leader has a varying velocity, which is also difficult to realize. Therefore, the method focuses on an observer-based variable structure algorithm for consensus tracking, which gets rid of the leader acceleration. The presented scheme optimizes synchronization performance, as well as provides satisfactory robustness. What’s more, the existing algorithms can obtain a stable synchronous system; however, the obtained stable system may encounter some disturbances that may destroy the synchronization. Focus on this challenging technological problem, a state-dependent-switching approach is introduced. In the presence of unmeasured angular speed and unknown failures, this paper investigates a distributed fault-tolerant consensus tracking algorithm for a group non-identical motors. The failures are modeled by nonlinear functions, and the sliding mode observer is designed to estimate the angular speed and nonlinear failures. The convergence and stability of the given multi-motor system are proved. Simulation results have shown that all followers asymptotically converge to a consistent state when one follower fails to follow the virtual leader during a large enough disturbance, which illustrates the good performance of synchronization control accuracy.Keywords: consensus control, distributed follow, fault-tolerant control, multi-motor system, speed synchronization
Procedia PDF Downloads 12519010 The Optimization of Copper Sulfate and Tincalconite Molar Ratios on the Hydrothermal Synthesis of Copper Borates
Authors: E. Moroydor Derun, N. Tugrul, F. T. Senberber, A. S. Kipcak, S. Piskin
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In this research, copper borates are synthesized by the reaction of copper sulfate pentahydrate (CuSO4.5H2O) and tincalconite (Na2O4B7.10H2O). The experimental parameters are selected as 80°C reaction temperature and 60 of reaction time. The effect of mole ratio of CuSO4.5H2O to Na2O4B7.5H2O is studied. For the identification analyses X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR) techniques are used. At the end of the experiments, synthesized copper borate is matched with the powder diffraction file of “00-001-0472” [Cu(BO2)2] and characteristic vibrations between B and O atoms are seen. The proper crystals are obtained at the mole ratio of 3:1. This study showed that simplified synthesis process is suitable for the production of copper borate minerals.Keywords: hydrothermal synthesis, copper borates, copper sulfate, tincalconite
Procedia PDF Downloads 38119009 Numerical Solutions of Generalized Burger-Fisher Equation by Modified Variational Iteration Method
Authors: M. O. Olayiwola
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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation
Procedia PDF Downloads 43019008 Stochastic Age-Structured Population Models
Authors: Arcady Ponosov
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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation
Procedia PDF Downloads 25419007 Spectral Domain Fast Multipole Method for Solving Integral Equations of One and Two Dimensional Wave Scattering
Authors: Mohammad Ahmad, Dayalan Kasilingam
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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain
Procedia PDF Downloads 40619006 Analytical Method Development and Validation of Stability Indicating Rp - Hplc Method for Detrmination of Atorvastatin and Methylcobalamine
Authors: Alkaben Patel
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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation
Procedia PDF Downloads 33619005 Application of Fourier Series Based Learning Control on Mechatronic Systems
Authors: Sandra Baßler, Peter Dünow, Mathias Marquardt
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A Fourier series based learning control (FSBLC) algorithm for tracking trajectories of mechanical systems with unknown nonlinearities is presented. Two processes are introduced to which the FSBLC with PD controller is applied. One is a simplified service robot capable of climbing stairs due to special wheels and the other is a propeller driven pendulum with nearly the same requirements on control. Additionally to the investigation of learning the feed forward for the desired trajectories some considerations on the implementation of such an algorithm on low cost microcontroller hardware are made. Simulations of the service robot as well as practical experiments on the pendulum show the capability of the used FSBLC algorithm to perform the task of improving control behavior for repetitive task of such mechanical systems.Keywords: climbing stairs, FSBLC, ILC, service robot
Procedia PDF Downloads 31419004 ANN Modeling for Cadmium Biosorption from Potable Water Using a Packed-Bed Column Process
Authors: Dariush Jafari, Seyed Ali Jafari
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The recommended limit for cadmium concentration in potable water is less than 0.005 mg/L. A continuous biosorption process using indigenous red seaweed, Gracilaria corticata, was performed to remove cadmium from the potable water. The process was conducted under fixed conditions and the breakthrough curves were achieved for three consecutive sorption-desorption cycles. A modeling based on Artificial Neural Network (ANN) was employed to fit the experimental breakthrough data. In addition, a simplified semi empirical model, Thomas, was employed for this purpose. It was found that ANN well described the experimental data (R2>0.99) while the Thomas prediction were a bit less successful with R2>0.97. The adjusted design parameters using the nonlinear form of Thomas model was in a good agreement with the experimentally obtained ones. The results approve the capability of ANN to predict the cadmium concentration in potable water.Keywords: ANN, biosorption, cadmium, packed-bed, potable water
Procedia PDF Downloads 43119003 A Comparison of Bias Among Relaxed Divisor Methods Using 3 Bias Measurements
Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori
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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.Keywords: apportionment, bias, divisor, fair, measurement
Procedia PDF Downloads 36619002 Nondestructive Electrochemical Testing Method for Prestressed Concrete Structures
Authors: Tomoko Fukuyama, Osamu Senbu
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Prestressed concrete is used a lot in infrastructures such as roads or bridges. However, poor grout filling and PC steel corrosion are currently major issues of prestressed concrete structures. One of the problems with nondestructive corrosion detection of PC steel is a plastic pipe which covers PC steel. The insulative property of pipe makes a nondestructive diagnosis difficult; therefore a practical technology to detect these defects is necessary for the maintenance of infrastructures. The goal of the research is a development of an electrochemical technique which enables to detect internal defects from the surface of prestressed concrete nondestructively. Ideally, the measurements should be conducted from the surface of structural members to diagnose non-destructively. In the present experiment, a prestressed concrete member is simplified as a layered specimen to simulate a current path between an input and an output electrode on a member surface. The specimens which are layered by mortar and the prestressed concrete constitution materials (steel, polyethylene, stainless steel, or galvanized steel plates) were provided to the alternating current impedance measurement. The magnitude of an applied electric field was 0.01-volt or 1-volt, and the frequency range was from 106 Hz to 10-2 Hz. The frequency spectrums of impedance, which relate to charge reactions activated by an electric field, were measured to clarify the effects of the material configurations or the properties. In the civil engineering field, the Nyquist diagram is popular to analyze impedance and it is a good way to grasp electric relaxation using a shape of the plot. However, it is slightly not suitable to figure out an influence of a measurement frequency which is reciprocal of reaction time. Hence, Bode diagram is also applied to describe charge reactions in the present paper. From the experiment results, the alternating current impedance method looks to be applicable to the insulative material measurement and eventually prestressed concrete diagnosis. At the same time, the frequency spectrums of impedance show the difference of the material configuration. This is because the charge mobility reflects the variety of substances and also the measuring frequency of the electric field determines migration length of charges which are under the influence of the electric field. However, it could not distinguish the differences of the material thickness and is inferred the difficulties of prestressed concrete diagnosis to identify the amount of an air void or a layer of corrosion product by the technique.Keywords: capacitance, conductance, prestressed concrete, susceptance
Procedia PDF Downloads 41319001 Solution for Thick Plate Resting on Winkler Foundation by Symplectic Geometry Method
Authors: Mei-Jie Xu, Yang Zhong
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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system
Procedia PDF Downloads 30519000 Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease
Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly
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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.Keywords: Parkinson's disease, step method, delay differential equation, two delays
Procedia PDF Downloads 20518999 Naphtha Catalytic Reform: Modeling and Simulation of Unity
Authors: Leal Leonardo, Pires Carlos Augusto de Moraes, Casiraghi Magela
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In this work were realized the modeling and simulation of the catalytic reformer process, of ample form, considering all the equipment that influence the operation performance. Considered it a semi-regenerative reformer, with four reactors in series intercalated with four furnaces, two heat exchanges, one product separator and one recycle compressor. A simplified reactional system was considered, involving only ten chemical compounds related through five reactions. The considered process was the applied to aromatics production (benzene, toluene, and xylene). The models developed to diverse equipment were interconnecting in a simulator that consists of a computer program elaborate in FORTRAN 77. The simulation of the global model representative of reformer unity achieved results that are compatibles with the literature ones. It was then possible to study the effects of operational variables in the products concentration and in the performance of the unity equipment.Keywords: catalytic reforming, modeling, simulation, petrochemical engineering
Procedia PDF Downloads 51618998 1G2A IMU\GPS Integration Algorithm for Land Vehicle Navigation
Authors: O. Maklouf, Ahmed Abdulla
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A general decline in the cost, size, and power requirements of electronics is accelerating the adoption of integrated GPS/INS technologies in consumer applications such Land Vehicle Navigation. Researchers are looking for ways to eliminate additional components from product designs. One possibility is to drop one or more of the relatively expensive gyroscopes from microelectromechanical system (MEMS) versions of inertial measurement units (IMUs). For land vehicular use, the most important gyroscope is the vertical gyro that senses the heading of the vehicle and two horizontal accelerometers for determining the velocity of the vehicle. This paper presents a simplified integration algorithm for strap down (ParIMU)\GPS combination, with data post processing for the determination of 2-D components of position (trajectory), velocity and heading. In the present approach we have neglected earth rotation and gravity variations, because of the poor gyroscope sensitivities of the low-cost IMU and because of the relatively small area of the trajectory.Keywords: GPS, ParIMU, INS, Kalman filter
Procedia PDF Downloads 51618997 A Superposition Method in Analyses of Clamped Thick Plates
Authors: Alexander Matrosov, Guriy Shirunov
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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.Keywords: general solution, method of initial functions, superposition method, thick isotropic plates
Procedia PDF Downloads 59818996 Solution of Hybrid Fuzzy Differential Equations
Authors: Mahmood Otadi, Maryam Mosleh
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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.Keywords: fuzzy number, fuzzy ODE, HAM, approximate method
Procedia PDF Downloads 51118995 Optimal Control of Volterra Integro-Differential Systems Based on Legendre Wavelets and Collocation Method
Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh
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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation
Procedia PDF Downloads 38818994 A Class of Third Derivative Four-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations
Authors: Cletus Abhulimen, L. A. Ukpebor
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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations
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