Search results for: Numerical method

Authors: A. R. Bagirzade, A. Sh. Najafova, S. M. Yessirkepova, E. S. Albert

Abstract:

This article describes a text recognition method based on Optical Character Recognition (OCR). The features of the OCR method were examined using the ABBYY FineReader program. It describes automatic text recognition in images. OCR is necessary because optical input devices can only transmit raster graphics as a result. Text recognition describes the task of recognizing letters shown as such, to identify and assign them an assigned numerical value in accordance with the usual text encoding (ASCII, Unicode). The peculiarity of this study conducted by the authors using the example of the ABBYY FineReader, was confirmed and shown in practice, the improvement of digital text recognition platforms developed by Electronic Publication.

Keywords: ABBYY FineReader system, algorithm symbol recognition, OCR/ICR techniques, recognition technologies.

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Authors: C. Ardil

Abstract:

Using the aid of Hausdorff distance function and Minkowski distance function, this study proposes a novel method for selecting combat aircraft for Air Force. In order to do this, the proximity measure method was developed with determinate fuzzy degrees based on the relationship between attributes and combat aircraft alternatives. The combat aircraft selection attributes were identified as payloadability, maneuverability, speedability, stealthability, and survivability. Determinate fuzzy data from the combat aircraft attributes was then aggregated using the determinate fuzzy weighted arithmetic average operator. For the selection of combat aircraft, correlation analysis of the ranking order patterns of options was also examined. A numerical example from military aviation is used to demonstrate the applicability and effectiveness of the proposed method.

Keywords: Combat aircraft selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Hausdorff distance function, Minkowski distance function, PMM, MCDM

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Authors: Anant Lal, M. Elangovan

Abstract:

A general purpose viscous flow solver Ansys CFX was used to solve the unsteady three-dimensional (3D) Reynolds Averaged Navier-Stokes Equation (RANSE) for simulating a 3D numerical viscous wave tank. A flap-type wave generator was incorporated in the computational domain to generate the desired incident waves. Authors have made effort to study the physical behaviors of Flap type wave maker with governing parameters. Dependency of the water fill depth, Time period of oscillations and amplitude of oscillations of flap were studied. Effort has been made to establish relations between parameters. A validation study was also carried out against CFD methodology with wave maker theory. It has been observed that CFD results are in good agreement with theoretical results. Beaches of different slopes were introduced to damp the wave, so that it should not cause any reflection from boundary. As a conclusion this methodology can simulate the experimental wave-maker for regular wave generation for different wave length and amplitudes.

Keywords: CFD, RANSE, Flap type, wave-maker, VOF, seakeeping, numerical method.

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Authors: Shams-Ul-Islam, Waqas Sarwar Abbasi, Hamid Rahman

Abstract:

Numerical investigation of flow around a square cylinder are presented using the multi-relaxation-time lattice Boltzmann methods at different Reynolds numbers. A detail analysis are given in terms of time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficient, vorticity contours visualizations, streamlines and phase diagrams. A number of physical quantities mean drag coefficient, drag coefficient, Strouhal number and root-mean-square values of drag and lift coefficients are calculated and compared with the well resolved experimental data and numerical results available in open literature. The Reynolds numbers affected the physical quantities.

Keywords: Code validation, Force statistics, Multi-relaxation-time lattice Boltzmann method, Reynolds numbers, Square cylinder.

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Authors: M. Raciti Castelli, E. Benini

Abstract:

This paper presents a numerical investigation of the unsteady flow around an American 19th century vertical-axis windmill: the Stevens & Jolly rotor, patented on April 16, 1895. The computational approach used is based on solving the complete transient Reynolds-Averaged Navier-Stokes (t-RANS) equations: a full campaign of numerical simulation has been performed using the k-ω SST turbulence model. Flow field characteristics have been investigated for several values of tip speed ratio and for a constant unperturbed free-stream wind velocity of 6 m/s, enabling the study of some unsteady flow phenomena in the rotor wake. Finally, the global power generated from the windmill has been determined for each simulated angular velocity, allowing the calculation of the rotor power-curve.

Keywords: CFD, vertical-axis rotor, windmill.

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Authors: Y. Kurosawa, T. Yamaguchi

Abstract:

A numerical method is proposed to calculate damping properties for sound-proof structures involving elastic body, viscoelastic body, and porous media. For elastic and viscoelastic body displacement is modeled using conventional finite elements including complex modulus of elasticity. Both effective density and bulk modulus have complex quantities to represent damped sound fields in the porous media. Particle displacement in the porous media is discretised using finite element method. Displacement vectors as common unknown variables are solved under coupled condition between elastic body, viscoelastic body and porous media. Further, explicit expressions of modal loss factor for the mixed structures are derived using asymptotic method. Eigenvalue analysis and frequency responded were calculated for automotive test panel laminated viscoelastic and porous structures using this technique, the results almost agreed with the experimental results.

Keywords: Damping, Porous Media, Finite Element Method, Computer Aided Engineering.

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Authors: Davod Khojasteh Salkuyeh, Sayyed Hasan Azizi

Abstract:

We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess converge in one iteration. Some numerical results are given to illustrate the theoretical results.

Keywords: rank deficient least squares problems, AOR iterativemethod, Gauss-Seidel iterative method, semiconvergence.

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Authors: Seong Do Kim, Woo Young Jung

Abstract:

Recently, damages due to typhoons and strong wind are on the rise. Considering this issue, we evaluated the performance of soundproofing walls based on the strong wind fragility by means of numerical analysis. Among the components of the soundproof wall, aluminum frame was the most vulnerable member, thus we have considered different section of aluminum frame in the determination of wind fragility. Wind load was randomly generated using Monte Carlo Simulation method. Moreover, limit state was based on the test standard of road construction soundproofing wall. In this study, the strong wind fragility was determined by considering the influence factors of wind exposure category, soundproof wall’s installation position, and shape of aluminum frame section. Results of this study could be used to determine the section shape of the frame that has high resistance to the wind during construction of the soundproofing wall.

Keywords: Aluminum frame soundproofing wall, Monte Carlo Simulation, numerical simulation, wind fragility.

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Authors: Somayeh Alizadeh, Mehdi Ghazanfari, Mostafa Jafari, Salman Hooshmand

Abstract:

Fuzzy Cognitive Maps (FCMs) is a causal graph, which shows the relations between essential components in complex systems. Experts who are familiar with the system components and their relations can generate a related FCM. There is a big gap when human experts cannot produce FCM or even there is no expert to produce the related FCM. Therefore, a new mechanism must be used to bridge this gap. In this paper, a novel learning method is proposed to construct causal graph based on historical data and by using metaheuristic such Tabu Search (TS). The efficiency of the proposed method is shown via comparison of its results of some numerical examples with those of some other methods.

Keywords: Fuzzy Cognitive Map (FCM), Learning, Meta heuristic, Genetic Algorithm, Tabu search.

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Authors: M. Paroncini, F. Corvaro, G. Nardini, S. Pistolesi

Abstract:

A lightpipe is an about 99 percent specular reflective mirror pipe or duct that is used for the transmission of the daylight from the outside into a building. The lightpipes are usually used in the daylighting buildings, in the residential, industrial and commercial sectors. This paper is about the performances of a lightpipe installed in a laboratory (3 m x 2.6 m x 3 m) without windows. The aim is to analyse the luminous intensity distribution for several sky/sun conditions. The lightpipe was monitored during the year 2006. The lightpipe is 1 m long and the diameter of the top collector and of the internal diffuser device is 0.25 m. In the laboratory there are seven illuminance sensors: one external is located on the roof of the laboratory and six internal sensors are connected to a data acquisition system. The internal sensors are positioned under the internal diffusive device at an height of 0.85 m from the floor to simulate a working plane. The numerical data are obtained through a simulation software. This paper shows the comparison between the experimental and numerical results concerning the behavior of the lightpipe.

Keywords: Daylighting, Desktop Radiance, Lightpipe.

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Authors: Ryosuke Ito, Goro Obinata, Chikara Nagai, Youngwoo Kim

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This paper proposes a new parameter identification method based on Linear Fractional Transformation (LFT). It is assumed that the target linear system includes unknown parameters. The parameter deviations are separated from a nominal system via LFT, and identified by organizing I/O signals around the separated deviations of the real system. The purpose of this paper is to apply LFT to simultaneously identify the parameter deviations in systems with fewer outputs than unknown parameters. As a fundamental example, this method is implemented to one degree of freedom vibratory system. Via LFT, all physical parameters were simultaneously identified in this system. Then, numerical simulations were conducted for this system to verify the results. This study shows that all the physical parameters of a system with fewer outputs than unknown parameters can be effectively identified simultaneously using LFT.

Keywords: Identification, Linear Fractional Transformation, Right inverse system

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Authors: Ming-Hui Lee, Tsung-Chien Chen, Yuh-Shiou Tai

Abstract:

The intelligent fuzzy input estimator is used to estimate the input force of the rigid bar structural system in this study. The fuzzy Kalman filter without the input term and the fuzzy weighting recursive least square estimator are two main portions of this method. The practicability and accuracy of the proposed method were verified with numerical simulations from which the input forces of a rigid bar structural system were estimated from the output responses. In order to examine the accuracy of the proposed method, a rigid bar structural system is subjected to periodic sinusoidal dynamic loading. The excellent performance of this estimator is demonstrated by comparing it with the use of difference weighting function and improper the initial process noise covariance. The estimated results have a good agreement with the true values in all cases tested.

Keywords: Fuzzy Input Estimator, Kalman Filter, RecursiveLeast Square Estimator.

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Authors: T. H. Young, Y. J. Tsai

Abstract:

A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: Stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear.

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Authors: Karel Frana, Jianshun S. Zhang, Milos Muller

Abstract:

The indoor airflow with a mixed natural/forced convection was numerically calculated using the laminar and turbulent approach. The Boussinesq approximation was considered for a simplification of the mathematical model and calculations. The results obtained, such as mean velocity fields, were successfully compared with experimental PIV flow visualizations. The effect of the distance between the cooled wall and the heat exchanger on the temperature and velocity distributions was calculated. In a room with a simple shape, the computational code OpenFOAM demonstrated an ability to numerically predict flow patterns. Furthermore, numerical techniques, boundary type conditions and the computational grid quality were examined. Calculations using the turbulence model k-omega had a significant effect on the results influencing temperature and velocity distributions.

Keywords: natural and forced convections, numerical simulations, indoor airflows.

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Authors: Ahmed Mahmoudi, Imen Mejri, Mohamed A. Abbassi, Ahmed Omri

Abstract:

A numerical study based on the Lattice Boltzmann Method (LBM) is proposed to solve one, two and three dimensional heat and mass transfer for isothermal carbonization of thick wood particles. To check the validity of the proposed model, computational results have been compared with the published data and a good agreement is obtained. Then, the model is used to study the effect of reactor temperature and thermal boundary conditions, on the evolution of the local temperature and the mass distributions of the wood particle during carbonization

Keywords: Lattice Boltzmann Method, pyrolysis conduction, carbonization, Heat and mass transfer.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, C. Ardil

Abstract:

In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.

Keywords: Reduced Order Modeling, Stability, Mihailov Stability Criterion, Continued Fraction Expansions, Differential Evolution, Integral Squared Error.

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Authors: Yohannes Yirga, Daniel Tesfay

Abstract:

The convective heat and mass transfer in nanofluid flow through a porous media due to a permeable stretching sheet with magnetic field, viscous dissipation, chemical reaction and Soret effects are numerically investigated. Two types of nanofluids, namely Cu-water and Ag-water were studied. The governing boundary layer equations are formulated and reduced to a set of ordinary differential equations using similarity transformations and then solved numerically using the Keller box method. Numerical results are obtained for the skin friction coefficient, Nusselt number and Sherwood number as well as for the velocity, temperature and concentration profiles for selected values of the governing parameters. Excellent validation of the present numerical results has been achieved with the earlier linearly stretching sheet problems in the literature.

Keywords: Heat and mass transfer, magnetohydrodynamics, nanofluid.

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Authors: Akram G., Jasmy Y.

Abstract:

The finite-difference time-domain (FDTD) method is one of the most widely used computational methods in electromagnetic. This paper describes the design of two-dimensional (2D) FDTD simulation software for transverse magnetic (TM) polarization using Berenger's split-field perfectly matched layer (PML) formulation. The software is developed using Matlab programming language. Numerical examples validate the software.

Keywords: Finite difference time domain (FDTD) method, perfectly matched layer (PML), split-filed formulation, transverse magnetic (TM) polarization.

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Authors: Miroslav Byrtus

Abstract:

Large rotating systems, especially gear drives and gearboxes, occur as parts of many mechanical devices transmitting the torque with relatively small loss of power. With the increased demand for high speed machinery, mathematical modeling and dynamic analysis of gear drives gained importance. Mathematical description of such mechanical systems is a complex task evolving for several decades. In gear drive dynamic models, which include flexible shafts, bearings and gearing and use the finite elements, nonlinear effects due to gear mesh and bearings are usually ignored, for such models have large number of degrees of freedom (DOF) and it is computationally expensive to analyze nonlinear systems with large number of DOF. Therefore, these models are not suitable for simulation of nonlinear behavior with amplitude jumps in frequency response. The contribution uses a methodology of nonlinear large rotating system modeling which is based on degrees of freedom (DOF) number reduction using modal synthesis method (MSM). The MSM enables significant DOF number reduction while keeping the nonlinear behavior of the system in a specific frequency range. Further, the MSM with DOF number reduction is suitable for including detail models of nonlinear couplings (mainly gear and bearing couplings) into the complete gear drive models. Since each subsystem is modeled separately using different FEM systems, it is advantageous to parameterize models of subsystems and to use the parameterization for optimization of chosen design parameters. Final complex model of gear drive is assembled in MATLAB and MATLAB tools are used for dynamical analysis of the nonlinear system. The contribution is further focused on developing of a methodology for investigation of behavior of the system by Nonlinear Normal Modes with combination of the MSM using numerical continuation method. The proposed methodology will be tested using a two-stage gearbox including its housing.

Keywords: Vibro-impact system, rotating system, gear drive, modal synthesis method, numerical continuation method, periodic solution.

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Authors: Hossein Shokouhmand , Mohammad A. Esmaeili, Koohyar Vahidkhah

Abstract:

This paper presents a numerical study on surface heat transfer characteristics of laminar air flows in parallel-plate dimpled channels. The two-dimensional numerical model is provided by commercial code FLUENT and the results are obtained for channels with symmetrically opposing hemi-cylindrical cavities onto both walls for Reynolds number ranging from 1000 to 2500. The influence of variations in relative depth of dimples (the ratio of cavity depth to the cavity curvature diameter), the number of them and the thermophysical properties of channel walls on heat transfer enhancement is studied. The results are evident for existence of an optimum value for the relative depth of dimples in which the largest wall heat flux and average Nusselt number can be achieved. In addition, the results of conjugation simulation indicate that the overall influence of the ratio of wall thermal conductivity to the one of the fluid on heat transfer rate is not much significant and can be ignored.

Keywords: cavity, conjugation, heat transfer, laminar air flow, Numerical, parallel-plate channel.

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Authors: H. Nikzad, S. Yoshitomi

Abstract:

In this paper, an optimization procedure is applied for 3D Reinforced concrete building structure with shear wall.  In the optimization problem, cross sections of beams, columns and shear wall dimensions are considered as design variables and the optimal cross sections can be derived to minimize the total cost of the structure. As for final design application, the most suitable sections are selected to satisfy ACI 318-14 code provision based on static linear analysis. The validity of the method is examined through numerical example of 15 storied 3D RC building with shear wall.  This optimization method is expected to assist in providing a useful reference in design early stage, and to be an effective and powerful tool for structural design of RC shear wall structures.

Keywords: Structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures.

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Authors: K. Fraňa, S. Simon

Abstract:

The objective of the paper is a numerical study of heat transfer between perforated metal plates and the surrounding air flows. Different perforation structures can nowadays be found in various industrial products. Besides improving the mechanical properties, the perforations can intensify the heat transfer as well. The heat transfer coefficient depends on a wide range of parameters such as type of perforation, size, shape, flow properties of the surrounding air etc. The paper was focused on three different perforation structures which have been investigated from the point of the view of the production in the previous studies. To determine the heat coefficients and the Nusselt numbers, the numerical simulation approach was adopted. The calculations were performed using the OpenFOAM software. The three-dimensional, unstable, turbulent and incompressible air flow around the perforated surface metal plate was considered.

Keywords: Perforations, convective heat transfers, turbulent flows, numerical simulations.

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Authors: O. Solovyov, S. Eryomenko, V. Kobrin, V. Chmovzh

Abstract:

The methodology of numerical simulation and calculation of aerodynamic characteristics of aircraft taking into account impact of wake on it has been developed. The results of numerical experiment in comparison with the data obtained in the wind tunnel are presented. Efficiency of methodology of calculation and the reliability of the results is shown.

Keywords: Unmanned aircraft, vortex wake, aerodynamic characteristics.

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Authors: M. M. Shokrieh, A. Karamnejad

Abstract:

This paper deals with a numerical analysis of the transient response of composite beams with strain rate dependent mechanical properties by use of a finite difference method. The equations of motion based on Timoshenko beam theory are derived. The geometric nonlinearity effects are taken into account with von Kármán large deflection theory. The finite difference method in conjunction with Newmark average acceleration method is applied to solve the differential equations. A modified progressive damage model which accounts for strain rate effects is developed based on the material property degradation rules and modified Hashin-type failure criteria and added to the finite difference model. The components of the model are implemented into a computer code in Mathematica 6. Glass/epoxy laminated composite beams with constant and strain rate dependent mechanical properties under dynamic load are analyzed. Effects of strain rate on dynamic response of the beam for various stacking sequences, load and boundary conditions are investigated.

Keywords: Composite beam, Finite difference method, Progressive damage modeling, Strain rate.

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Authors: Dennis A. Apuan

Abstract:

Categorical data based on description of the agricultural landscape imposed some mathematical and analytical limitations. This problem however can be overcome by data transformation through coding scheme and the use of non-parametric multivariate approach. The present study describes data transformation from qualitative to numerical descriptors. In a collection of 103 random soil samples over a 60 hectare field, categorical data were obtained from the following variables: levels of nitrogen, phosphorus, potassium, pH, hue, chroma, value and data on topography, vegetation type, and the presence of rocks. Categorical data were coded, and Spearman-s rho correlation was then calculated using PAST software ver. 1.78 in which Principal Component Analysis was based. Results revealed successful data transformation, generating 1030 quantitative descriptors. Visualization based on the new set of descriptors showed clear differences among sites, and amount of variation was successfully measured. Possible applications of data transformation are discussed.

Keywords: data transformation, numerical descriptors, principalcomponent analysis

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Authors: Liu Xuedong, Liu Hanpeng, Zhou Ling

Abstract:

Study fluid flow and heat transfer characteristics of microchannel in a primary Cross-corrugated(CC) surface recuperators with corrugations and without corrugations, using CFD method. The pitch-over-height ratios P/H of Cross-corrugated (CC) surface is from 1.5 to 4.0, included angles β=75º. The study was performed using CFD software FLUENT to create unit model and simulate fluid temperature, velocity, heat transfer coefficient and other parameters. The results from these simulations were compared to experimental data. It is concluded that, when the Reynolds number is constant, if increase P/H, j/f will decrease, also the decreasing trend will become weak. Under the condition of P/H=2.2, if increase the inlet velocity j/f will decrease; in addition, the heat transfer performance in surface with corrugation will increase 10% compared to that without corrugation. The study results can provide the basis to optimize the design, select the type of heat transfer surface, the scale structure, and heat-transfer surface arrangement for recuperators.

Keywords: Cross-corrugated surface, Primary surface, Numerical simulation, Heat transfer.

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Authors: Worachat Wannawong, Usa W. Humphries, Prungchan Wongwises, Suphat Vongvisessomjai, Wiriya Lueangaram

Abstract:

A numerical analysis of wave and hydrodynamic models is used to investigate the influence of WAve and Storm Surge (WASS) in the regional and coastal zones. The numerical analyzed system consists of the WAve Model Cycle 4 (WAMC4) and the Princeton Ocean Model (POM) which used to solve the energy balance and primitive equations respectively. The results of both models presented the incorporated surface wave in the regional zone affected the coastal storm surge zone. Specifically, the results indicated that the WASS generally under the approximation is not only the peak surge but also the coastal water level drop which can also cause substantial impact on the coastal environment. The wave–induced surface stress affected the storm surge can significantly improve storm surge prediction. Finally, the calibration of wave module according to the minimum error of the significant wave height (Hs) is not necessarily result in the optimum wave module in the WASS analyzed system for the WASS prediction.

Keywords: energy balance equation, numerical analysis, primitiveequation, storm surge, wave.

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Authors: A. Rifa’i, Y. Takeshita, M. Komatsu

Abstract:

The post-rain puddles problem that occurs in the first yard of Prambanan Temple are often disturbing visitor activity. A poodle layer and a drainage system had ever built to avoid such a problem, but puddles still did not stop appearing after rain. Permeability parameter needs to be determined by using a simpler procedure to find exact method of solution. The instrument modelling was proposed according to the development of field permeability testing instrument. This experiment used a proposed Constant Discharge method. Constant Discharge method used a tube poured with constant water flow from unsaturated until saturated soil condition. Volumetric water content (θ) were monitored by soil moisture measurement device. The results were correlations between k and θ which were drawn by numerical approach from Van Genutchen model. Parameters θr optimum value obtained from the test was at very dry soil. Coefficient of permeability with a density of 19.8 kN/m3 for unsaturated conditions was in range of 3 x 10-6 cm/sec (Sr=68%) until 9.98 x 10-4 cm/sec (Sr=82%). The equipment and testing procedure developed in this research was quite effective, simple and easy to be implemented on determining field soil permeability coefficient value of sandy soil. Using constant discharge method in proposed permeability test, value of permeability coefficient under unsaturated condition can be obtained without establish soil water characteristic curve.

Keywords: Constant discharge method, in situ permeability test, sandy soil, unsaturated conditions.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, augmented linear system, nonlinear observer, formal linearization, electric power system.

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Authors: S. Panda, S. K. Tomar, R. Prasad, C. Ardil

Abstract:

Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.

Keywords: Model Order Reduction, Markov Parameters, Routh Approximation, Particle Swarm Optimization, Integral Squared Error, Steady State Stability.

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